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The Epidemiology ofDiabetes and Cancer
Detailed report
SDCMay 2014
http://BendixCarstensen.com/DMCa/EpiDMCa
Version 1.3
Compiled Thursday 31st July, 2014, 15:10from:
C:/Bendix/Steno/DM-register/NDR/projects/Cancer/papers/EpiDMCa/Report.tex
Bendix Carstensen Steno Diabetes Center, Gentofte, Denmark&
Department of Biostatistics, University of Copenhagen
[email protected]
http://BendixCarstensen.com
Marit Eika Jørgensen Steno Diabetes Center, Gentofte,
[email protected]
Søren Friis Danish Cancer Society, Copenhagen,
[email protected]
http://BendixCarstensen.com/DMCa/EpiDMCahttp://BendixCarstensen.com
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Contents
1 Article 11.1 Introduction . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 2
1.1.1 Incidence of cancer . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 21.1.2 Mortality after cancer diagnosis . . . . .
. . . . . . . . . . . . . . . . 31.1.3 The broader picture . . . .
. . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 41.3 Results . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 51.4 Discussion . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 5
1.4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 6References . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 14
2 Background calculations 152.1 Comparing cancer RRs from
published studies . . . . . . . . . . . . . . . . . 152.2 Overview
of rate computation . . . . . . . . . . . . . . . . . . . . . . . .
. . 25
2.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 252.2.2 Total population follow-up . . . . . . .
. . . . . . . . . . . . . . . . . 252.2.3 The follow-up after DM
and Ca . . . . . . . . . . . . . . . . . . . . . 272.2.4 Setting up
the analysis data frame . . . . . . . . . . . . . . . . . . .
32
2.3 Modelling of rates . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 362.3.1 Prerequisites for the natural
splines . . . . . . . . . . . . . . . . . . . 362.3.2 Computing the
state probabilities . . . . . . . . . . . . . . . . . . . . 382.3.3
Average change in cancer incidence rates . . . . . . . . . . . . .
. . . 392.3.4 Secular trends . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 402.3.5 Transition rates . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 402.3.6 Transition
probabilities . . . . . . . . . . . . . . . . . . . . . . . . . .
42
ii
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Chapter 1
Article
1
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Abstract
The literature on cancer occurrence in persons with diabetes has
almost invariably beenconcerned with relative measures. In this
paper we briefly review this, but the aim is toquantify the
absolute occurrence of diabetes and cancer in the population in
order to give afuller picture, which also includes the competing
mortality risk. Overall we find that some35% of the population will
have a diagnosis of diabetes in their lifetime, 40% a diagnosis
ofcancer, and about 15% will have both diagnoses. The impact of
differing mortality betweenpersons with and without diabetes is
illustrated by the fact that a person without diabetesat age 50
have a smaller lifetime risk of cancer than a person aged 50 with
diabetes. Thus,the differences in cancer occurrence between persons
with and without diabetes are ofquantitatively smaller importance
than the differences in mortality.
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2 Article Diabetes & Cancer
Keywords: Diabetes and cancer, epidemiology, demography,
lifetime risk of diabetes andcancer, absolute risk of diabetes.
1.1 Introduction
The link between diabetes and cancer occurrence is well
established, and comprehensivepopulation-based studies have
demonstrated that the association relates to both cancerincidence
and mortality [1, 2, 3].
Recently, an increasing number of studies have examined cancer
incidence amongpatients with diabetes, particularly following the
report in 2009 of a potential associationbetween the insulin analog
glargine and cancer risk [4, 5, 6, 7]. The majority of the
studieshave focused on comparisons of cancer incidence among
diabetes patients using differentantidiabetic regimes. However,
these studies are prone to bias due to confounding byindication, as
illustrated convincingly Andersson et al. [8] who reported that the
use of anytype of antidiabetic drug, whether insulins or various
forms of oral antidiabetics (OADs),was associated with a markedly
elevated rate ratio (RR) for cancer shortly after initiationof the
drug, which subsequently declined to a value close to 1.
To our knowledge, the study by Andersson et al. is the only
study published so far thatfollowed the entire population of
diabetes patients, avoiding selection of subgroups ofpatients, and
thus appear to be the most credible study because of minimized
selectionbias. We have previously reported that newly diagnosed
diabetes patients experience astrongly elevated excess cancer
incidence shortly after the diagnosis which levels off 2–3years
following the diagnosis [9], and a similar pattern has also been
observed in otherstudies [1, 10, 8]. Hence, based on the the
available studies, any potential long-term effectsof antidiabetic
drugs are likely to be small and difficult to ascribe to a
particularcause-effect relationship, if any.
As any potential long-term effects of diabetes drugs are likely
to be small in terms ofmodification of cancer occurrence, we have
chosen to ignore these in the present broaderdiscussion of the
relationship between diabetes and cancer occurrence.
In this paper we have chosen to focus on the general population
impact of diabetes andcancer rather than any comprehensive
discussion of the potential relationship betweendiabetes and cancer
occurrence. Specifically, we will evaluate the high mortality
amongcancer patients with pre-existing diabetes, as demonstrated in
a few previous studies[11, 12], and quantify the effects of this at
the population level.
1.1.1 Incidence of cancer
Cancer incidence studies have shown cancer incidence rate ratios
of similar magnitude incomparisons of diabetes patients and persons
without diabetes; Figure 1.1 compares theRR of different types of
cancer between people with and without diabetes from the
majorpopulation based studies of diabetes occurrence, that is
studies with more than 1000 cancercases among persons with
diabetes. Key characteristics of these studies are presented
inTable 1.1.
The general picture from the major cancer incidence studies are
strongly elevatedincidence rates of liver and pancreatic cancer,
and somewhat elevated rates of cancer of theendometrium, kidney and
to a smaller extent of cancers of the digestive system (Figure
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Article 1.1 Introduction 3
Table 1.1: Population based studies of incidence of several
major cancer sites in diabetespatients compared to non-diabetics,
with more than 1000 cancers among DM patients.
No. cancersStudy Country No. sites in DM ptt.
Adami et al. [1] Sweden 21 2,417Wideroffa et al. [2] Denmark 29
8,831Coughlinb et al. [3] USA 16 2,183Johnson et al. [10] Canada 10
12,438Carstensena et al. [9] Denmark 24 22,826Sasazuki et al. [13]
Japan 16 2,388Kajüter et al. [14] Germany 8 3,664
aThese two Danish studies are non-overlapping.bCancer mortality
study.
1.1). Single-site studies have generally reported colon cancer
as a cancer type occurring inclear excess among people with
diabetes. However, this is likely because colon cancer is afairly
frequent disease and hence exhibits clearly detectable rate
elevations as opposed torarer cancers which could have similarly
elevated rates without formally significantelevation due to limited
number of events in the study populations.
However, little attention has been paid to differences between
people with and withoutdiabetes in relation to the actual size and
shape of age-specific cancer incidence rates.Using Danish data we
found that the average increase in cancer incidence rates from age
40to age 70 years was 10.6% per year for men and 7.2% per year for
women, corresponding toincreases of 35% and 23%, respectively, over
3 years of age. This means that the observedelevation of cancer
risk in persons with diabetes by a factor of 1.1–1.2 is of a
magnitudethat is smaller than that conveyed by an aging of 3
years.
1.1.2 Mortality after cancer diagnosis
It is also well known that cancer patients with pre-existing
diabetes have a higher mortalitythan cancer patients without
diabetes at diagnosis, however, it is difficult to discernwhether
this is due solely to the impaired survival associated with the two
diseases or ifthere is interaction between diabetes and cancer
which worsen the cancer prognosis. In asystematic review, Barone et
al. [15] estimated that the overall mortality rate-ratiobetween
cancer patients with and without cancer was 1.41. In a recent
nationwide study inDenmark [11], we observed a similar excess
mortality among cancer patients with diabetesat diagnosis, and with
increasing mortality rates by increasing severity of diabetes.
1.1.3 The broader picture
The above mentioned studies are all aimed at describing
differences in patterns of cancerincidence rates or mortality rates
of cancer patients between persons with and withoutdiabetes.
These types of comparisons are illustrated in context in Figure
1.2 in which cancerincidence rates are shown in red and mortality
rates among cancer patients in black.
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4 Article Diabetes & Cancer
Studies of diabetes and cancer incidence and mortality have
traditionally focused only onpairwise comparison of the thick and
thin transition rates in Figure 1.2. It is commendableto describe
variations between these rates that may give clues to mechanisms
underlyingthe different (typically higher) rates among persons with
diabetes compared with thosewithout diabetes. For most of the rates
in Figure 1.2, however, the major determinant isage, so by only
comparing the rates (controlling for age), the impact of the aging
in thepopulation is lost.
As an example of how to incorporate the impact of the
age-dependence of the incidenceof cancer and mortality in the
general population, we will use nationwide Danish data toestimate
all 9 sets of rates shown in Figure 1.2 by sex, age and calendar
time. This willeventually enable us to illustrate what fraction of
persons in a given age who willeventually contract cancer,
depending on whether they suffer from diabetes at the giventime. It
will also provide the possibility to quantify the fraction of
persons in a birth cohortwho will end in each of the 5 “death”
states.
1.1.3.1 Duration dependence
While it is known that both mortality and cancer incidence
depends strongly on diabetesduration, in that it is elevated during
the initial period after diagnosis (surveillance bias),the period
is for most types of events quite short, so ignoring the duration
effects will haveonly minor influence on the summary measures.
1.2 Methods
We merged the Danish National Diabetes Register [16, 17] with
the Danish CancerRegister [18], and classified all follow up time
after 1995 and after any of the two diagnosesby sex, age, calendar
time and date of birth in 1-year classes (Lexis triangles). We
classifieddeaths and diagnoses of diabetes and cancer similarly. We
also extracted the totalpopulation size and number of deaths from
the Human Mortality Data Base [19]. Bysubtracting the total number
of person-years and deaths in the diabetes and/or cancerpopulation,
we obtained the risk time and person-years in the part of the
population notdiagnosed with any of the two diseases (the ”Well”
state in Figure 1.2).
We then modelled all 9 transition rates shown in Figure 1.2
using age-period models withnatural splines [20]. We assumed that
the mortality rates for cancer patients with andwithout diabetes
were proportional, that is differed only by a multiplicative
constant forany combination of age and calendar time.
We used the estimated age-specific rates from these models to
calculate the burden ofdisease in a hypothetical population under
the scenario of age-specific rates equal to theestimated
cross-sectional age-specific rates as of 1 January 2005. The
practical calculationswere done by multiplying a vector of initial
state-distribution (with all persons starting atage 0 in state
“Well”) successively by the age-specific transition matrices
derived from thethe rates for every 1/10 of a year of age.
A complete account of the data acquisition, rate-estimation and
state-probabilitycalculations and graphical displays are available
ashttp://BendixCarstensen.com/DMCa/EpiDMCa/Report.pdf.
We computed the following quantities:
http://BendixCarstensen.com/DMCa/EpiDMCa/Report.pdf
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Article 1.3 Results 5
• The fraction of a population in each of the 9 different states
at any age.
• The fraction of a 50/60/70 year old non-diseased population
that are in each of thestates at any subsequent age.
• The fraction of a 50/60/70 year old population with diabetes
but not cancer that arein each of the states at any subsequent
age.
This approach yields insight into what fraction of the
population that is likely to beaffected by the two diseases, and in
particular how the relationship of cancer incidencerates between
people with and without diabetes translate into population
experience whenthe mortality rates are taken into account.
1.3 Results
Figure 1.3 shows the estimated rates by age and calendar time.
It is seen that both thecancer incidence and, notably, diabetes
rates are increasing, whereas the mortality rates aredecreasing by
calendar time, and more rapidly among people with diabetes.
Moreover, it is seen that mortality rates for persons with
diabetes and/or cancer areconverging by age, so that there are only
minor differences between the three groups ofpersons after age 80.
This is presumably reflecting the fact that persons without
bothdiabetes and cancer in high ages most likely suffer from other
severe diseases.
When using these rates to obtain probabilities of being in one
of the 9 states at any age(Figure 1.4), and derive the probability
of having a diagnosis of cancer, respectivelydiabetes before a
given age (Figure 1.5), we found a lifetime risk of cancer of 44%
for bothmen an women, and corresponding lifetime risk of diabetes
of 35% for men and 33% forwomen. The lifetime risk of both diseases
was 15% for men and 13% for women (Figure1.5).
Of all persons who contracted diabetes in their lifetime, 43% of
men and 41% of womenhad a diagnosis of cancer too; only slightly
less than the figures for the entire population.
Examining the conditional distribution given that a person was
alive and free of bothdiabetes and cancer at age 50, 60 or 70 years
(Figure 1.6, columns 1 & 3), we found thatthe lifetime risk of
cancer were 45, 44 and 38% among men and 41, 37 and 29% amongwomen.
Comparing to persons who were alive and diagnosed with diabetes
only at thesame ages (Figure 1.6, columns 2 & 4), the lifetime
risk of cancer were 37, 36 and 32%among men and 37, 34 and 27%
among women. So the lifetime risk of cancer for a personwith
diabetes at a given age is smaller than for a person without
diabetes at the same age,and this risk decreases by the age
considered.
1.4 Discussion
The risk of cancer increases among persons with diabetes with
increasing severity of thediabetic disease. It is not clear (let
alone discernible) whether this a result of thedisease-processes
associated with diabetes or if latent cancers contribute to
thedeterioration of the diabetic status of patients.
With the exception of liver and pancreatic cancer, it is also
clear that the excess riskamong persons with diabetes is moderate,
in the order of maximum 20-50% higher for
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6 Article Diabetes & Cancer
those cancers for which an increased cancer incidence has been
observed and other cancertypes there is no excess risk.
When incorporating death as a competing risk to cancer
incidence, the excess mortalityamong persons with diabetes is of
quantitatively much larger concern that the excess ofcancers [21,
12].
Our Danish study demonstrated that the life-time cumulative risk
of cancer is smalleramong persons with diabetes than among persons
not suffering from diabetes. This is dueto the higher mortality
rates among persons with diabetes compared to those
withoutdiabetes. In general terms, persons with diabetes die
earlier and thus escape developmentof some cancers.
One limitation of our register-based estimates is that the
calculations were based oncross-sectional rates applied
longitudinally. Nevertheless, this approach is in completeparallel
to classical calculations of life expectancy, and essentially the
only practicableapproach since the time-period covered by the
diabetes register (1995–2012) is too short togive reliable cohort
specific rates over the entire age-range.
Another limitation is that the rates were only modelled by age
and calendar time nottaking duration of diabetes or cancer into
account, as it is known that both incidence ratesand mortality
rates are higher shortly after a diagnosis of either diabetes or
cancer.However, since our focus was on cumulative measures the
impact of ignoring duration ofdiabetes and cancer is likely
small.
1.4.1 Conclusions
• Overall cancer incidence among persons with diabetes is 10-20%
higher than amongthose without diabetes.
• The most elevated incidence rates among persons with diabetes
are found for cancersof the liver or pancreas, and incidence rates
of cancers of the endometrium, kidneyand colon also seem to be
consistently elevated among patients with diabetes
acrossstudies.
• In the general population, the lifetime risk of cancer is
about 45%, and the lifetimerisk of diabetes about 35%, and the
lifetime risk of both diagnoses about 15%. Forboth diseases the
proportions are slightly less for women than for men.
• Persons with diabetes at a given age have a smaller lifetime
risk of cancer thanpersons without diabetes at the same age. This
is attributable to the highermortality rates among persons with
diabetes.
• Differences in cancer occurrence between persons with diabetes
and non-diabetics is aquantitatively smaller problem than the
difference in mortality rates between the twogroups.
• A further decrease in mortality among persons with diabetes
would be expected toincrease the fraction of persons with diabetes
contracting cancer.
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Article 1.4 Discussion 7
0.5 0.7 1.0 1.5 2.0 3.0 4.0 5.0
RR, DM vs. non−DM
Leukaemia
Multiple myeloma
Non−Hodgkin lymphoma
Hodgkins lymphoma
Thyroid
Brain
Urinary bladder
Kidney
Testis
Prostate
Ovary, fallopian tube etc.
Corpus uteri
Cervix uteri
Breast
Melanoma of skin
Lung, bronchus and pleura
Pancreas
Liver
Rectum
Colon
Stomach
Oesophagus
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Figure 1.1: Estimated RRs from different studies. Blue lines for
men, red lines for women.Within each cancer site, estimates are
from the studies mentioned in in table 1.1, in thesame order as in
table 1.1.
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8 Article Diabetes & Cancer
Well
DM
Ca
DM−Ca
Ca−DM
Dead (Well)
Dead (DM)
Dead (Ca)
Dead (DM−Ca)
Dead (Ca−DM)
Well
DM
Ca
DM−Ca
Ca−DM
Dead (Well)
Dead (DM)
Dead (Ca)
Dead (DM−Ca)
Dead (Ca−DM)
Figure 1.2: Transition rates in a population exposed to
occurrence of diabetes and cancer.The red transitions represent
cancer incidence rates and the black ones death after a
cancerdiagnosis.
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Article 1.4 Discussion 9
0.1
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Age Date
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r in
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nce
rate
s pe
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00 P
YM
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rate
s pe
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00 P
Y
Men Women
Figure 1.3: Estimated age-specific incidence and mortality rates
in the Danish population2005, and trends 1995–2010. The coloring of
the lines refer to the state from which the ratesare. The full
lines in the upper panels are cancer incidence rates, the broken
line diabetesincidence rates and the black lines are the
cancer-incidence rate-ratios between persons withand without
diabetes. In the lower panels, the broken red lines are for cancer
patients devel-oping diabetes after cancer, and the dotted red
lines are for cancer patients with pre-existingdiabetes at time of
diagnosis.
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10 Article Diabetes & Cancer
50 60 70 80 90 1000
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Age (years)
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per
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(%
)
Figure 1.4: Fraction of a birth cohort in each state at a given
age, based on Danish ratesas of 2005. The black line is the overall
survival curve, the green part represents those alivewithout
diabetes or cancer, the gray those who died without any of the
diseases. Blue areasare those with diabetes, red those with cancer
and the purple areas those with both diseases.The white line in the
purple area separates those that had diabetes before cancer
(closest tothe diabetes part) from those who had cancer before
diabetes.
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Article 1.4 Discussion 11
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Figure 1.5: Fraction of a birth cohort that gets diabetes (blue)
or cancer (red) before a givenage. These two events are not
exclusive, the fraction suffering both is given in purple. Hencethe
difference between the red and purple curves is the fraction of a
birth cohort that before agiven age gets cancer alone, and the
difference between the blue and the purple curve is thefraction of
a birth cohort that gets diabetes alone.
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12 Article Diabetes & Cancer
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Men, no DM Men, DM Women, no DM Women, DM
Figure 1.6: Fraction of a birth cohort in each state at a given
age, based on Danish data.Colouring as in Figure 1.4. The three
rows of graphs give the conditional probabilities giventhat a
person is alive at age 50, 60 and 70, respectively. The first and
3rd columns areconditional on having neither diabetes nor cancer,
the 2nd and 4th columns are conditionalon having diabetes only.
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2009.
[8] C. Andersson, A. Vaag, C. Selmer, M. Schmiegelow, R.
Sørensen, J. Lindhardsen,G. H. Gislason, L. Køber, and C.
Torp-Pedersen. Risk of cancer in patients usingglucose-lowering
agents: a nationwide cohort study of 3.6 million people. BMJ
Open,2(3), 2012.
[9] B. Carstensen, D. R. Witte, and S. Friis. Cancer occurrence
in Danish diabeticpatients: duration and insulin effects.
Diabetologia, 55(4):948–958, Apr 2012.
[10] J. A. Johnson, S. L. Bowker, K. Richardson, and C. A.
Marra. Time-varying incidenceof cancer after the onset of type 2
diabetes: evidence of potential detection bias.Diabetologia,
54:2263–2271, Sep 2011.
13
-
14 BIBLIOGRAPHY Diabetes & Cancer
[11] K. Ranc, M. E. Jørgensen, S. Friis, and B. Carstensen.
Mortality after cancer amongpatients with diabetes mellitus: effect
of diabetes duration and treatment.Diabetologia, 57(5):927–934, May
2014.
[12] A. G. Renehan, H. C. Yeh, J. A. Johnson, S. H. Wild, E. A.
Gale, H. Møller, and theDiabetes and Cancer Research Consortium.
Diabetes and cancer (2): evaluating theimpact of diabetes on
mortality in patients with cancer. Diabetologia,
55(6):1619–1632,Jun 2012.
[13] S. Sasazuki, H. Charvat, A. Hara, K. Wakai, C. Nagata, K.
Nakamura, I. Tsuji,Y. Sugawara, A. Tamakoshi, K. Matsuo, I. Oze, T.
Mizoue, K. Tanaka, M. Inoue,S. Tsugane, S. Sasazuki, S. Tsugane, M.
Inoue, M. Iwasaki, T. Otani, N. Sawada,T. Shimazu, T. Yamaji, I.
Tsuji, Y. Tsubono, Y. Nishino, A. Tamakoshi, K. Matsuo,H. Ito, K.
Wakai, C. Nagata, T. Mizoue, and K. Tanaka. Diabetes mellitus and
cancerrisk: pooled analysis of eight cohort studies in Japan.
Cancer Sci., 104(11):1499–1507,Nov 2013.
[14] H. Kajüter, A.S. Geier, I. Wellmann, V. Krieg, R. Fricke,
O. Heidinger, and H.-W.Hense. Kohortenstudie zur Krebsinzidenz bei
Patienten mit Diabetes mellitus Typ 2.Bundesgesundheitsblatt,
57:52–59, 2014.
[15] B. B. Barone, H. C. Yeh, C. F. Snyder, K. S. Peairs, K. B.
Stein, R. L. Derr, A. C.Wolff, and F. L. Brancati. Long-term
all-cause mortality in cancer patients withpreexisting diabetes
mellitus: a systematic review and meta-analysis.
JAMA,300:2754–2764, Dec 2008.
[16] B. Carstensen, Christensen J.K., Marcussen M.M., and
Borch-Johnsen K. TheNational Diabetes Register. Scandinavian
Journal of Public Health, 39(7 suppl):58–61,2011.
[17] B. Carstensen, J.K. Kristensen, P. Ottosen, and K.
Borch-Johnsen. The DanishNational Diabetes Register: Trends in
incidence, prevalence and mortality.Diabetologia, 51:2187–2196,
2008.
[18] M. L. Gjerstorff. The Danish Cancer Registry. Scand J
Public Health, 39/7Suppl):42–45, July 2011.
[19] Human Mortality Database. University of California,
Berkeley (USA), and Max PlanckInstitute for Demographic Research
(Germany). available at www.mortality.org orwww.humanmortality.de
(data downloaded on 20 april 2014). Technical report.
[20] B Carstensen. Age-Period-Cohort models for the Lexis
diagram (author’s reply).Statistics in Medicine, 27:1561–1564,
2007.
[21] J. A. Johnson, B. Carstensen, D. Witte, S. L. Bowker, L.
Lipscombe, A. G. Renehan,and the Diabetes and Cancer Research
Consortium. Diabetes and cancer (1):evaluating the temporal
relationship between type 2 diabetes and cancer
incidence.Diabetologia, 55(6):1607–1618, Jun 2012.
www.mortality.orgwww.humanmortality.de
-
Chapter 2
Background calculations
2.1 Comparing cancer RRs from published studies
We have collected data from other studies that on population
basis has estimated theoverall RR of specific cancers among
diabetes patients relative to the non-diabetic part ofthe
population.
> library(Epi)> # Read the keyed-in data> oth str( oth
)
'data.frame': 243 obs. of 7 variables:$ sex : Factor w/ 2 levels
"F","M": 2 1 2 1 2 1 2 1 2 1 ...$ diag : Factor w/ 24 levels "
Brain",..: 22 22 12 12 7 7 2 2 20 20 ...$ author: Factor w/ 7
levels "Adami","Coughlin",..: 7 7 7 7 7 7 7 7 7 7 ...$ RR : num 1.1
1.1 1.3 1 1.2 1.1 1.3 1.1 1.1 1 ...$ lo : num 1.1 1.1 1 0.7 1 1 1.1
1 0.9 0.9 ...$ hi : num 1.1 1.1 1.6 1.5 1.3 1.4 1.4 1.2 1.2 1.2
...$ N : int 4666 4165 67 26 188 131 413 442 235 167 ...
> levels(oth$author)
[1] "Adami" "Coughlin" "Johnson" "Kajuter" "Sasazuki" "Vecchia"
"Wiederoff"
> oth oth$author head( oth )
sex diag author RR lo hi N1 M All malignant neoplasms Wiederoff
1.1 1.1 1.1 46662 F All malignant neoplasms Wiederoff 1.1 1.1 1.1
41653 M Oesophagus Wiederoff 1.3 1.0 1.6 674 F Oesophagus Wiederoff
1.0 0.7 1.5 265 M Stomach Wiederoff 1.2 1.0 1.3 1886 F Stomach
Wiederoff 1.1 1.0 1.4 131
> # Clean up the site names> nn nn nn oth$diag nn nn
[1] "All malignant neoplasms" "Oesophagus"[3] "Stomach"
"Colon"[5] "Rectum " "Liver"[7] "Pancreas" "Lung, bronchus and
pleura"
15
-
16 Background calculations Diabetes & Cancer
[9] "Melanoma of skin" "Other skin"[11] "Breast" "Cervix
uteri"[13] "Corpus uteri" "Ovary, fallopian tube etc."[15]
"Prostate" "Testis"[17] "Kidney" "Urinary bladder"[19] "Brain"
"Thyroid"[21] "Hodgkins lymphoma" "Non-Hodgkin lymphoma"[23]
"Multiple myeloma" "Leukaemia"
> # Make sure they are in the correct order> oth$diag
levels( oth$diag )
[1] "All malignant neoplasms" "Oesophagus"[3] "Stomach"
"Colon"[5] "Rectum " "Liver"[7] "Pancreas" "Lung, bronchus and
pleura"[9] "Melanoma of skin" "Other skin"[11] "Breast" "Cervix
uteri"[13] "Corpus uteri" "Ovary, fallopian tube etc."[15]
"Prostate" "Testis"[17] "Kidney" "Urinary bladder"[19] "Brain"
"Thyroid"[21] "Hodgkins lymphoma" "Non-Hodgkin lymphoma"[23]
"Multiple myeloma" "Leukaemia"
> # Turn it into a 4-dimensional array for plotting> xxx
xxx[xxx==0] dimnames(xxx)[[1]]
[1] "Adami" "Coughlin" "Johnson" "Kajuter" "Sasazuki"
"Wiederoff"
> # dimnames(xxx)[[2]][8] # dimnames(xxx)[[2]][8]> nd #
Get the data from the DK study> load(
file="../../data/ana1i.Rdata" )> dimnames(res)[[1]] str( res
)
num [1:29, 1:2, 1:4, 1:3] 1.19 1.27 1.25 1.32 1.4 ...- attr(*,
"dimnames")=List of 4..$ diag: chr [1:29] "All malignant neoplasms"
"Oesophagus" "Stomach" "Colon incl. rectosigmoideum" .....$ sex :
chr [1:2] "M" "F"..$ type: chr [1:4] "DM/noIns" "DM/Ins" "Ins vs.
noIns" "DM"..$ est : chr [1:3] "Est" "lo" "hi"
> data.frame( 1:29, dimnames(res)[[1]] )
X1.29 dimnames.res...1..1 1 All malignant neoplasms2 2
Oesophagus3 3 Stomach4 4 Colon incl. rectosigmoideum5 5 Ascending
colon6 6 Transverse colon7 7 Descending and sigmoid colon8 8 Other
colon (unspec. or multiple)9 9 Rectum10 10 Colorectal cancer11 11
Liver12 12 Pancreas13 13 Lung, bronchus and pleura14 14 Melanoma of
skin15 15 Breast16 16 Cervix uteri
-
Background calculations 2.1 Comparing cancer RRs from published
studies 17
17 17 Corpus uteri18 18 Ovary, fallopian tube etc.19 19
Prostate20 20 Testis21 21 Kidney22 22 Urinary bladder23 23 Brain24
24 Thyroid25 25 Hodgkin's lymphoma26 26 Non-Hodgkin lymphoma27 27
Multiple myeloma28 28 Leukaemia29 29 Other
> # Check which ones belong to the ones from the keyed-in
data> wh cbind( dimnames(res)[[1]][wh], dimnames(xxx)[[2]] )
[,1] [,2][1,] "All malignant neoplasms" "All malignant
neoplasms"[2,] "Oesophagus" "Oesophagus"[3,] "Stomach"
"Stomach"[4,] "Colon incl. rectosigmoideum" "Colon"[5,] "Rectum"
"Rectum "[6,] "Liver" "Liver"[7,] "Pancreas" "Pancreas"[8,] "Lung,
bronchus and pleura" "Lung, bronchus and pleura"[9,] "Melanoma of
skin" "Melanoma of skin"[10,] "Breast" "Breast"[11,] "Cervix uteri"
"Cervix uteri"[12,] "Corpus uteri" "Corpus uteri"[13,] "Ovary,
fallopian tube etc." "Ovary, fallopian tube etc."[14,] "Prostate"
"Prostate"[15,] "Testis" "Testis"[16,] "Kidney" "Kidney"[17,]
"Urinary bladder" "Urinary bladder"[18,] "Brain" "Brain"[19,]
"Thyroid" "Thyroid"[20,] "Hodgkin's lymphoma" "Hodgkins
lymphoma"[21,] "Non-Hodgkin lymphoma" "Non-Hodgkin lymphoma"[22,]
"Multiple myeloma" "Multiple myeloma"[23,] "Leukaemia"
"Leukaemia"
> # Extract the corresponding ones from data> cwf #
Nullify male breast cancer> xxx[,"Breast","M",]
cwf["Breast","M",,] # Combine to one array> ( dnam
-
18 Background calculations Diabetes & Cancer
$sex[1] "F" "M"
[[4]][1] "RR" "lo" "hi"
> dnam[["author"]] XXX XXX[-1,,,] str( cwf )
num [1:23, 1:2, 1:4, 1:3] 1.19 1.27 1.25 1.32 1.11 ...- attr(*,
"dimnames")=List of 4..$ diag: chr [1:23] "All malignant neoplasms"
"Oesophagus" "Stomach" "Colon incl. rectosigmoideum" .....$ sex :
chr [1:2] "M" "F"..$ type: chr [1:4] "DM/noIns" "DM/Ins" "Ins vs.
noIns" "DM"..$ est : chr [1:3] "Est" "lo" "hi"
> str( XXX[1,,,] )
num [1:23, 1:2, 1:3] NA NA NA NA NA NA NA NA NA NA ...- attr(*,
"dimnames")=List of 3..$ diag: chr [1:23] "All malignant neoplasms"
"Oesophagus" "Stomach" "Colon" .....$ sex : chr [1:2] "F" "M"..$ :
chr [1:3] "RR" "lo" "hi"
> str( cwf[,2:1,4,] )
num [1:23, 1:2, 1:3] 1.202 0.979 1.344 1.204 0.996 ...- attr(*,
"dimnames")=List of 3..$ diag: chr [1:23] "All malignant neoplasms"
"Oesophagus" "Stomach" "Colon incl. rectosigmoideum" .....$ sex :
chr [1:2] "F" "M"..$ est : chr [1:3] "Est" "lo" "hi"
> XXX[1,,,] str( XXX )
num [1:7, 1:23, 1:2, 1:3] 1.2 1.1 NA NA NA ...- attr(*,
"dimnames")=List of 4..$ author: chr [1:7] "Carstensen" "Adami"
"Coughlin" "Johnson" .....$ diag : chr [1:23] "All malignant
neoplasms" "Oesophagus" "Stomach" "Colon" .....$ sex : chr [1:2]
"F" "M"..$ : chr [1:3] "RR" "lo" "hi"
> RRCa str( RRCa )
num [1:7, 1:23, 1:2, 1:3] 1 1.1 NA NA 1.21 ...- attr(*,
"dimnames")=List of 4..$ author: chr [1:7] "Adami" "Wiederoff"
"Coughlin" "Johnson" .....$ diag : chr [1:23] "All malignant
neoplasms" "Oesophagus" "Stomach" "Colon" .....$ sex : chr [1:2]
"M" "F"..$ : chr [1:3] "RR" "lo" "hi"
> save( RRCa, file="./data/RRCa.Rda" )
With this array set up, we can make a comprehensive forest plot
of estimates
> # Plot to compare the studies results to the previous
ones.> par( mar=c(3,1,1,1), mgp=c(3,1,0)/1.6 )> plotEst(
RRCa[1,,"M",1:3], y=nd:1, col="transparent", lwd=1,+ xlog=T,
xlim=c(0.5,5), grid=c(5:19/10,4:10/2),+ vref=1, ylim=c(1,nd),+
xtic=c(0.5,0.7,1,1.5,2:5), xlab="RR, DM vs. non-DM" )> nst for(
i in 1:nst )+ {+ pointsEst( RRCa[i,,"M",1:3],
y=nd:1+(0+i)/(2.3*nst), col="blue",+ lwd=1.5, cex=0.8 )+ pointsEst(
RRCa[i,,"F",1:3], y=nd:1+(i-nst+1)/(2.3*nst), col="red",+ lwd=1.5,
cex=0.8 )+ }
-
Background calculations 2.1 Comparing cancer RRs from published
studies 19
For reference purposes we also print the collected estimates
too:
> load( file="./data/RRCa.Rda" )> dimnames( RRCa )[[2]]
round( ftable( RRCa, row.vars=2:1 ), 2 )
sex M FRR lo hi RR lo hi
diag authorAll malign Adami 1.00 0.90 1.10 1.10 1.00 1.10
Wiederoff 1.10 1.10 1.10 1.10 1.10 1.10Coughlin NA NA NA NA NA
NAJohnson NA NA NA NA NA NACarstensen 1.21 1.19 1.23 1.20 1.18
1.23Sasazuki 1.21 1.15 1.28 1.18 1.08 1.30Kajuter NA NA NA NA NA
NA
Oesophagus Adami 1.60 1.00 2.40 0.80 0.40 1.60Wiederoff 1.30
1.00 1.60 1.00 0.70 1.50Coughlin 1.20 0.94 1.53 NA NA NAJohnson NA
NA NA NA NA NACarstensen 1.27 1.12 1.44 0.98 0.77 1.24Sasazuki 1.07
0.79 1.44 4.70 1.12 19.71Kajuter NA NA NA NA NA NA
Stomach Adami 0.80 0.70 1.00 0.90 0.70 1.20Wiederoff 1.20 1.00
1.30 1.10 1.00 1.40Coughlin 0.99 0.77 1.27 1.25 0.90 1.73Johnson NA
NA NA NA NA NACarstensen 1.28 1.15 1.43 1.34 1.14 1.58Sasazuki 1.03
0.84 1.25 1.22 0.95 1.57Kajuter NA NA NA NA NA NA
Colon Adami 1.20 0.90 1.40 1.00 0.80 1.20Wiederoff 1.30 1.10
1.40 1.10 1.00 1.20Coughlin 1.20 1.06 1.37 1.24 1.07 1.43Johnson
1.24 1.14 1.35 1.24 1.14 1.35Carstensen 1.32 1.24 1.40 1.20 1.13
1.28Sasazuki 1.58 1.32 1.89 0.92 0.66 1.29Kajuter 1.00 0.89 1.12
0.85 0.73 0.98
Rectum Adami 1.30 1.10 1.70 0.90 0.70 1.20Wiederoff 1.10 0.90
1.20 1.00 0.90 1.20Coughlin 1.07 0.75 1.51 0.90 0.57 1.42Johnson NA
NA NA NA NA NACarstensen 1.11 1.03 1.20 1.00 0.89 1.11Sasazuki 1.05
0.80 1.36 1.48 0.76 2.89Kajuter NA NA NA NA NA NA
Liver Adami 1.80 1.40 2.30 1.30 1.00 1.60Wiederoff 4.00 3.50
4.60 2.10 1.60 2.70Coughlin 2.19 1.76 2.72 1.37 0.94 2.00Johnson NA
NA NA NA NA NACarstensen 3.90 3.50 4.35 1.77 1.43 2.19Sasazuki 2.25
1.83 2.76 1.84 1.30 2.60Kajuter 1.88 1.42 2.43 1.82 1.15 2.73
Pancreas Adami 1.40 1.10 1.80 1.50 1.20 1.80Wiederoff 1.70 1.50
2.00 1.60 1.40 1.90Coughlin 1.48 1.27 1.73 1.44 1.21 1.72Johnson NA
NA NA NA NA NACarstensen 2.86 2.64 3.10 2.65 2.43 2.88Sasazuki 1.72
1.30 2.28 2.27 1.33 3.85Kajuter 1.42 1.09 1.82 1.83 1.44 2.30
Lung, bron Adami 1.00 0.80 1.10 1.10 0.80 1.50Wiederoff 1.00
0.90 1.10 0.90 0.80 1.10Coughlin 1.05 0.97 1.14 1.11 0.98
1.25Johnson 1.14 1.06 1.24 1.14 1.06 1.24Carstensen 1.17 1.12 1.23
1.14 1.07 1.20Sasazuki 1.01 0.83 1.22 1.08 0.76 1.54Kajuter 1.20
1.08 1.33 1.25 1.05 1.48
Melanoma o Adami 1.00 0.50 1.60 0.70 0.40 1.20Wiederoff 1.00
0.70 1.20 1.00 0.80 1.30Coughlin 0.93 0.64 1.36 NA NA NA
-
20 Background calculations Diabetes & Cancer
Johnson NA NA NA NA NA NACarstensen 0.92 0.83 1.03 0.78 0.69
0.89Sasazuki NA NA NA NA NA NAKajuter NA NA NA NA NA NA
Breast Adami NA NA NA 0.90 0.80 1.10Wiederoff NA NA NA 1.10 1.10
1.20Coughlin NA NA NA 1.27 1.11 1.45Johnson NA NA NA 1.00 0.92
1.10Carstensen NA NA NA 1.04 1.00 1.09Sasazuki NA NA NA 0.98 0.69
1.38Kajuter NA NA NA 0.91 0.82 1.01
Cervix ute Adami NA NA NA 0.70 0.40 1.10Wiederoff NA NA NA 0.90
0.70 1.10Coughlin NA NA NA NA NA NAJohnson NA NA NA 1.50 1.26
1.77Carstensen NA NA NA 1.08 0.92 1.27Sasazuki NA NA NA 2.08 1.02
4.27Kajuter NA NA NA NA NA NA
Corpus ute Adami NA NA NA 1.50 1.20 1.80Wiederoff NA NA NA 1.40
1.20 1.60Coughlin NA NA NA 1.33 0.92 1.90Johnson NA NA NA 1.63 1.33
1.99Carstensen NA NA NA 1.58 1.45 1.71Sasazuki NA NA NA 1.69 0.87
3.31Kajuter NA NA NA 1.34 1.08 1.65
Ovary, fal Adami NA NA NA 0.90 0.60 1.10Wiederoff NA NA NA 0.90
0.70 1.00Coughlin NA NA NA 1.02 0.80 1.29Johnson NA NA NA 1.19 0.93
1.53Carstensen NA NA NA 1.08 0.97 1.20Sasazuki NA NA NA 1.68 0.68
4.07Kajuter NA NA NA NA NA NA
Prostate Adami 0.70 0.70 0.90 NA NA NAWiederoff 0.90 0.80 1.00
NA NA NACoughlin 0.90 0.80 1.02 NA NA NAJohnson 0.88 0.82 0.95 NA
NA NACarstensen 0.94 0.91 0.98 NA NA NASasazuki 0.98 0.70 1.36 NA
NA NAKajuter 0.72 0.65 0.79 NA NA NA
Testis Adami 1.00 0.40 2.00 NA NA NAWiederoff 1.00 0.60 1.50 NA
NA NACoughlin NA NA NA NA NA NAJohnson NA NA NA NA NA NACarstensen
0.78 0.58 1.06 NA NA NASasazuki NA NA NA NA NA NAKajuter NA NA NA
NA NA NA
Kidney Adami 1.10 0.80 1.40 1.60 1.20 2.00Wiederoff 1.40 1.20
1.60 1.70 1.40 1.90Coughlin 0.82 0.61 1.10 1.12 0.80 1.58Johnson NA
NA NA NA NA NACarstensen 1.53 1.38 1.71 1.83 1.59 2.10Sasazuki 1.48
0.67 3.29 1.28 0.46 3.55Kajuter NA NA NA NA NA NA
Urinary bl Adami 1.00 0.80 1.30 0.90 0.60 1.30Wiederoff 1.00
0.90 1.10 0.90 0.80 1.10Coughlin 1.43 1.14 1.80 1.30 0.85
2.00Johnson NA NA NA NA NA NACarstensen 1.20 1.13 1.27 1.03 0.91
1.16Sasazuki 1.30 0.89 1.91 1.45 0.65 3.22Kajuter NA NA NA NA NA
NA
Brain Adami NA NA NA NA NA NAWiederoff 1.10 0.90 1.40 1.10 0.80
1.30Coughlin 0.96 0.72 1.29 1.03 0.74 1.43Johnson NA NA NA NA NA
NACarstensen 1.15 1.01 1.31 1.26 1.09 1.47Sasazuki NA NA NA NA NA
NA
-
Background calculations 2.1 Comparing cancer RRs from published
studies 21
Kajuter NA NA NA NA NA NAThyroid Adami 1.30 0.50 2.80 1.00 0.60
1.80
Wiederoff 1.30 0.60 2.30 1.20 0.70 1.80Coughlin NA NA NA NA NA
NAJohnson 1.29 0.87 1.91 1.29 0.87 1.91Carstensen 1.38 0.96 1.99
1.22 0.92 1.62Sasazuki NA NA NA NA NA NAKajuter NA NA NA NA NA
NA
Hodgkins l Adami NA NA NA NA NA NAWiederoff NA NA NA NA NA
NACoughlin NA NA NA NA NA NAJohnson NA NA NA NA NA NACarstensen
1.86 1.37 2.53 1.69 1.12 2.55Sasazuki NA NA NA NA NA NAKajuter 0.72
0.51 1.00 0.93 0.67 1.26
Non-Hodgki Adami NA NA NA NA NA NAWiederoff NA NA NA NA NA
NACoughlin 1.21 0.99 1.48 0.93 0.71 1.21Johnson NA NA NA NA NA
NACarstensen 1.16 1.04 1.29 1.16 1.02 1.32Sasazuki 1.73 0.94 3.18
2.16 0.88 5.32Kajuter NA NA NA NA NA NA
Multiple m Adami NA NA NA NA NA NAWiederoff 1.00 0.80 1.40 1.30
1.00 1.70Coughlin 1.27 0.98 1.66 0.87 0.62 1.24Johnson NA NA NA NA
NA NACarstensen 1.06 0.91 1.23 1.02 0.84 1.23Sasazuki NA NA NA NA
NA NAKajuter NA NA NA NA NA NA
Leukaemia Adami NA NA NA NA NA NAWiederoff 1.10 0.90 1.30 1.10
0.90 1.40Coughlin 0.88 0.71 1.10 1.10 0.85 1.44Johnson NA NA NA NA
NA NACarstensen 1.03 0.92 1.16 1.17 1.02 1.34Sasazuki NA NA NA NA
NA NAKajuter NA NA NA NA NA NA
> round( ftable( RRCa, row.vars=1:2 ), 2 )
sex M FRR lo hi RR lo hi
author diagAdami All malign 1.00 0.90 1.10 1.10 1.00 1.10
Oesophagus 1.60 1.00 2.40 0.80 0.40 1.60Stomach 0.80 0.70 1.00
0.90 0.70 1.20Colon 1.20 0.90 1.40 1.00 0.80 1.20Rectum 1.30 1.10
1.70 0.90 0.70 1.20Liver 1.80 1.40 2.30 1.30 1.00 1.60Pancreas 1.40
1.10 1.80 1.50 1.20 1.80Lung, bron 1.00 0.80 1.10 1.10 0.80
1.50Melanoma o 1.00 0.50 1.60 0.70 0.40 1.20Breast NA NA NA 0.90
0.80 1.10Cervix ute NA NA NA 0.70 0.40 1.10Corpus ute NA NA NA 1.50
1.20 1.80Ovary, fal NA NA NA 0.90 0.60 1.10Prostate 0.70 0.70 0.90
NA NA NATestis 1.00 0.40 2.00 NA NA NAKidney 1.10 0.80 1.40 1.60
1.20 2.00Urinary bl 1.00 0.80 1.30 0.90 0.60 1.30Brain NA NA NA NA
NA NAThyroid 1.30 0.50 2.80 1.00 0.60 1.80Hodgkins l NA NA NA NA NA
NANon-Hodgki NA NA NA NA NA NAMultiple m NA NA NA NA NA NALeukaemia
NA NA NA NA NA NA
Wiederoff All malign 1.10 1.10 1.10 1.10 1.10 1.10Oesophagus
1.30 1.00 1.60 1.00 0.70 1.50Stomach 1.20 1.00 1.30 1.10 1.00
1.40
-
22 Background calculations Diabetes & Cancer
Colon 1.30 1.10 1.40 1.10 1.00 1.20Rectum 1.10 0.90 1.20 1.00
0.90 1.20Liver 4.00 3.50 4.60 2.10 1.60 2.70Pancreas 1.70 1.50 2.00
1.60 1.40 1.90Lung, bron 1.00 0.90 1.10 0.90 0.80 1.10Melanoma o
1.00 0.70 1.20 1.00 0.80 1.30Breast NA NA NA 1.10 1.10 1.20Cervix
ute NA NA NA 0.90 0.70 1.10Corpus ute NA NA NA 1.40 1.20 1.60Ovary,
fal NA NA NA 0.90 0.70 1.00Prostate 0.90 0.80 1.00 NA NA NATestis
1.00 0.60 1.50 NA NA NAKidney 1.40 1.20 1.60 1.70 1.40 1.90Urinary
bl 1.00 0.90 1.10 0.90 0.80 1.10Brain 1.10 0.90 1.40 1.10 0.80
1.30Thyroid 1.30 0.60 2.30 1.20 0.70 1.80Hodgkins l NA NA NA NA NA
NANon-Hodgki NA NA NA NA NA NAMultiple m 1.00 0.80 1.40 1.30 1.00
1.70Leukaemia 1.10 0.90 1.30 1.10 0.90 1.40
Coughlin All malign NA NA NA NA NA NAOesophagus 1.20 0.94 1.53
NA NA NAStomach 0.99 0.77 1.27 1.25 0.90 1.73Colon 1.20 1.06 1.37
1.24 1.07 1.43Rectum 1.07 0.75 1.51 0.90 0.57 1.42Liver 2.19 1.76
2.72 1.37 0.94 2.00Pancreas 1.48 1.27 1.73 1.44 1.21 1.72Lung, bron
1.05 0.97 1.14 1.11 0.98 1.25Melanoma o 0.93 0.64 1.36 NA NA
NABreast NA NA NA 1.27 1.11 1.45Cervix ute NA NA NA NA NA NACorpus
ute NA NA NA 1.33 0.92 1.90Ovary, fal NA NA NA 1.02 0.80
1.29Prostate 0.90 0.80 1.02 NA NA NATestis NA NA NA NA NA NAKidney
0.82 0.61 1.10 1.12 0.80 1.58Urinary bl 1.43 1.14 1.80 1.30 0.85
2.00Brain 0.96 0.72 1.29 1.03 0.74 1.43Thyroid NA NA NA NA NA
NAHodgkins l NA NA NA NA NA NANon-Hodgki 1.21 0.99 1.48 0.93 0.71
1.21Multiple m 1.27 0.98 1.66 0.87 0.62 1.24Leukaemia 0.88 0.71
1.10 1.10 0.85 1.44
Johnson All malign NA NA NA NA NA NAOesophagus NA NA NA NA NA
NAStomach NA NA NA NA NA NAColon 1.24 1.14 1.35 1.24 1.14
1.35Rectum NA NA NA NA NA NALiver NA NA NA NA NA NAPancreas NA NA
NA NA NA NALung, bron 1.14 1.06 1.24 1.14 1.06 1.24Melanoma o NA NA
NA NA NA NABreast NA NA NA 1.00 0.92 1.10Cervix ute NA NA NA 1.50
1.26 1.77Corpus ute NA NA NA 1.63 1.33 1.99Ovary, fal NA NA NA 1.19
0.93 1.53Prostate 0.88 0.82 0.95 NA NA NATestis NA NA NA NA NA
NAKidney NA NA NA NA NA NAUrinary bl NA NA NA NA NA NABrain NA NA
NA NA NA NAThyroid 1.29 0.87 1.91 1.29 0.87 1.91Hodgkins l NA NA NA
NA NA NANon-Hodgki NA NA NA NA NA NAMultiple m NA NA NA NA NA
NALeukaemia NA NA NA NA NA NA
-
Background calculations 2.1 Comparing cancer RRs from published
studies 23
Carstensen All malign 1.21 1.19 1.23 1.20 1.18 1.23Oesophagus
1.27 1.12 1.44 0.98 0.77 1.24Stomach 1.28 1.15 1.43 1.34 1.14
1.58Colon 1.32 1.24 1.40 1.20 1.13 1.28Rectum 1.11 1.03 1.20 1.00
0.89 1.11Liver 3.90 3.50 4.35 1.77 1.43 2.19Pancreas 2.86 2.64 3.10
2.65 2.43 2.88Lung, bron 1.17 1.12 1.23 1.14 1.07 1.20Melanoma o
0.92 0.83 1.03 0.78 0.69 0.89Breast NA NA NA 1.04 1.00 1.09Cervix
ute NA NA NA 1.08 0.92 1.27Corpus ute NA NA NA 1.58 1.45 1.71Ovary,
fal NA NA NA 1.08 0.97 1.20Prostate 0.94 0.91 0.98 NA NA NATestis
0.78 0.58 1.06 NA NA NAKidney 1.53 1.38 1.71 1.83 1.59 2.10Urinary
bl 1.20 1.13 1.27 1.03 0.91 1.16Brain 1.15 1.01 1.31 1.26 1.09
1.47Thyroid 1.38 0.96 1.99 1.22 0.92 1.62Hodgkins l 1.86 1.37 2.53
1.69 1.12 2.55Non-Hodgki 1.16 1.04 1.29 1.16 1.02 1.32Multiple m
1.06 0.91 1.23 1.02 0.84 1.23Leukaemia 1.03 0.92 1.16 1.17 1.02
1.34
Sasazuki All malign 1.21 1.15 1.28 1.18 1.08 1.30Oesophagus 1.07
0.79 1.44 4.70 1.12 19.71Stomach 1.03 0.84 1.25 1.22 0.95 1.57Colon
1.58 1.32 1.89 0.92 0.66 1.29Rectum 1.05 0.80 1.36 1.48 0.76
2.89Liver 2.25 1.83 2.76 1.84 1.30 2.60Pancreas 1.72 1.30 2.28 2.27
1.33 3.85Lung, bron 1.01 0.83 1.22 1.08 0.76 1.54Melanoma o NA NA
NA NA NA NABreast NA NA NA 0.98 0.69 1.38Cervix ute NA NA NA 2.08
1.02 4.27Corpus ute NA NA NA 1.69 0.87 3.31Ovary, fal NA NA NA 1.68
0.68 4.07Prostate 0.98 0.70 1.36 NA NA NATestis NA NA NA NA NA
NAKidney 1.48 0.67 3.29 1.28 0.46 3.55Urinary bl 1.30 0.89 1.91
1.45 0.65 3.22Brain NA NA NA NA NA NAThyroid NA NA NA NA NA
NAHodgkins l NA NA NA NA NA NANon-Hodgki 1.73 0.94 3.18 2.16 0.88
5.32Multiple m NA NA NA NA NA NALeukaemia NA NA NA NA NA NA
Kajuter All malign NA NA NA NA NA NAOesophagus NA NA NA NA NA
NAStomach NA NA NA NA NA NAColon 1.00 0.89 1.12 0.85 0.73
0.98Rectum NA NA NA NA NA NALiver 1.88 1.42 2.43 1.82 1.15
2.73Pancreas 1.42 1.09 1.82 1.83 1.44 2.30Lung, bron 1.20 1.08 1.33
1.25 1.05 1.48Melanoma o NA NA NA NA NA NABreast NA NA NA 0.91 0.82
1.01Cervix ute NA NA NA NA NA NACorpus ute NA NA NA 1.34 1.08
1.65Ovary, fal NA NA NA NA NA NAProstate 0.72 0.65 0.79 NA NA
NATestis NA NA NA NA NA NAKidney NA NA NA NA NA NAUrinary bl NA NA
NA NA NA NABrain NA NA NA NA NA NAThyroid NA NA NA NA NA NAHodgkins
l 0.72 0.51 1.00 0.93 0.67 1.26
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24 Background calculations Diabetes & Cancer
Non-Hodgki NA NA NA NA NA NAMultiple m NA NA NA NA NA
NALeukaemia NA NA NA NA NA NA
-
Background calculations 2.2 Overview of rate computation 25
2.2 Overview of rate computation
2.2.1 Data
We merged the diabetes register and the cancer register,
restricting the cancer register tothe first primary tumour in a
person, and excluding non-melanoma skin cancers.
Thus the resulting data set has one record per person, and
comprises persons that have adiagnosis of either cancer or diabetes
(or both). Thus we have follow-up (and deaths) ofpatients in the
Danish population corresponding to all boxes in figure 1.2 except
the “Well”state.
From the human mortality database we extract the no. of deaths
in 1-year Lexistriangles. We also extract the population size,
which is used for calculation of person-yearsin 1-year Lexis
triangles. Thus we have deaths and risk time for the total
population. Wecan obtain the figures for the “Well” state by
subtraction of risk time and deaths in thepatient population from
that in the total population.
First we need to attach the relevant packages:
library( foreign )library( Epi )library( RCurl )# A function to
fish out data from the HMDBsource( "C:/stat/R/BxC/Examples/HMD2R.r"
)# HMD2R
2.2.2 Total population follow-up
Along the same lines we can derive the number of deaths in the
class (“Well”,“DK”) bysubtracting the number of deaths in all other
classes from the total number of deaths in thepopulation. To that
end we first retrieve the total number of deaths from the
humanmortality database:
2.2.2.1 Mortality data from Human Mortality Database
In order to fetch mortality from the HMD in 1× 1 Lexis triangles
we need to provide a userid and a password, which is hidden in the
output here; but they are put in the variablesHMDBusr and HMDBpwd,
respctively.
We can now get the mortality data for Denmark, and reshape them
to our purpose. Firstwe get the deaths in Lexis triangles; note
that we also compute the average age andcalendar time in the Lexis
triangles, since this is going to be used in the modelling:
DK
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26 Background calculations Diabetes & Cancer
names( DK )
-
Background calculations 2.2 Overview of rate computation 27
The data frame Y.dk now have the amount of follow-up time in
Lexis triangles between1995-01-01 and 2008-12-31 in the ages
between 0 and 100. The function N2Y automaticallyreturns the mean
age and period in A and P.
2.2.2.3 Total population data
We can merge the two dataframe to one; recall that the variable
A and P refer to Lexistriangles, and are coded as the mean age and
period in the triangles:
All.dk
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28 Background calculations Diabetes & Cancer
11 * Set the entry and exit dates for the entire follow-up
endeavour ;12 %let truncdate = '01JAN1995'd ;13 %let censdate =
'31DEC2009'd ;14 * Just to check it all wemt well ;15 %put
validdate = &validdate.16 truncdate = &truncdate.17
censdate = &censdate. ;validdate = '01JAN1995'd truncdate =
'01JAN1995'd censdate = '31DEC2009'd18 * Set the selector of
subgroups to analyse ;19 %let dgrp =
21,22,241,242,243,249,251,26,28,20 33,21 51,22 70,23 82,83,84,24
91,92,25 101,103,26 113,27 121,28 131,132,133,139 ;29 %let
diagselect = diag in (&dgrp.) ;30 * Variable names for
tabulation purposes, note DX and D259 here ;31 %let dvars = D0
D99932 D21 D22 D241 D242 D243 D249 D251 D259 D26 D2833 D3334 D5135
D7036 D82 D83 D8437 D91 D9238 D101 D10339 D11340 D12141 D131 D132
D133 D139 ;4243 * Get the formats and the Lexis macro ;44 options
nosource2 ;45 %inc
"c:\bendix\steno\DM-register\NDR\projects\Cancer\sas\CRG-fmts.sas"
;NOTE: Format SEX has been output.NOTE: Format DIAG has been
output.
NOTE: PROCEDURE FORMAT used (Total process time):real time 0.07
secondscpu time 0.03 seconds
130 libname DMCA
"c:\bendix\steno\DM-register\NDR\projects\Cancer\data" ;NOTE:
Libref DMCA was successfully assigned as follows:
Engine: V9Physical Name:
c:\bendix\steno\DM-register\NDR\projects\Cancer\data
131132
*----------------------------------------------------------------------;133
* Preprocessing of the cancer register to first primary tumours
only ;134135 * First take the cancer registry, remove all
non-cancers ;136 data cancer ;137 set DMCA.cancer ;138 doca =
d_diagnosedato ;139 * Remove 'not counted as cancer' and
non-melanoma skin cancer ;140 if ( diag in (52,150) ) then delete
;141 * Recode the leukaemias to one group (139 is a not used value
in formats) ;142 if diag in (134,135,136,137) then diag = 139 ;143
* Recode the colon cancers to the three separate subsites and the
rest ;144 * 24.1 Ascending colon C18.0, C18.1, C18.2145 * 24.2
Transverse colon C18.3, C18.4, C18.5146 * 24.3 Descending and
sigmoid colon C18.6, C18.7, C19, C19.9147 * 24.9 Other colon
(unspec. or multiple)148 * 25.1 Rectum (excl. anus) C20, C209149 *
This means that colorectal cancers are to be taken as the sum of
these150 * 5 groups, but also that the group 24.9 is NOT of
interest per se ;151 if( diag eq 24 ) then diag = 249 ;152 if(
icdpyrs in ("C180","C181","C182") ) then diag = 241 ;153 if(
icdpyrs in ("C183","C184","C185") ) then diag = 242 ;154 if(
icdpyrs in ("C186","C187","C19","C199") ) then diag = 243 ;155 if(
icdpyrs in ("C20","C209") ) then diag = 251 ;156 * Finally make a
single code for the sites not among those to be anlysed ;157 if not
( diag in ( &dgrp. ) ) then diag = 999 ;158 run ;
NOTE: There were 1748815 observations read from the data set
DMCA.CANCER.NOTE: The data set WORK.CANCER has 1286419 observations
and 32 variables.NOTE: DATA statement used (Total process
time):
real time 8.51 secondscpu time 1.70 seconds
159160 * Sort by id and date of diagnosis ;161 proc sort data =
cancer ;162 by id doCA ;163 run ;
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Background calculations 2.2 Overview of rate computation 29
NOTE: There were 1286419 observations read from the data set
WORK.CANCER.NOTE: The data set WORK.CANCER has 1286419 observations
and 32 variables.NOTE: PROCEDURE SORT used (Total process
time):
real time 14.77 secondscpu time 2.54 seconds
164165 * Then merge with the diabetes register ;166 data
DMCR;167 merge cancer168 DMCA.diabetes ;169 by id ;170 keep id sex
diag171 doBT doDM doCA doDD ;172 * Demografic dates collected from
CRG and NDR ;173 doBT = min( D_foddto , D_fdsdato ) ;174 doDD =
min( D_statdato, D_dodsdto ) ;175 * Event-dates ;176 doDM =
D_inkldto ;177 doI = D_ins ;178 doCA = D_diagnosedato ;179 * If
date of diabetes or cancer is equal to date of death, remove it
;180 if doDD gt .z then do;181 if doDM ge doDD then doDM = . ;182
if doCA ge doDD then doCA = . ;183 end ;184 * If date of diabetes
and cancer is the same, diabetes first ;185 if doDM eq doCA then
doDM = doCA - 2 ;186 if doDM > .z or doCA > .z ;187 * Only
persons alive on 1.1.1995 (or born later) ;188 if doDD gt
'31DEC94'd or doDD le .z ;189 * Only persons with one or the other
disease ;190 if doDM > .z or doCA > .z ;191 run ;
NOTE: Missing values were generated as a result of performing an
operation on missing values.Each place is given by: (Number of
times) at (Line):(Column).463041 at 174:10 62702 at 185:36
NOTE: There were 1286419 observations read from the data set
WORK.CANCER.NOTE: There were 437593 observations read from the data
set DMCA.DIABETES.NOTE: The data set WORK.DMCR has 912764
observations and 7 variables.NOTE: DATA statement used (Total
process time):
real time 2.04 secondscpu time 0.99 seconds
192193 * The dataset DMCR now has a record for each person who
has either a194 * a diabetes diagnosis or a cancer diagnosis.
Persons with more than195 * one recorded tumour are represented by
a record for each tumour ;196 * We then construct the records of
follow-up in different states ;197198 data toLex ;199 set DMCR ;200
id = _n_ ;201 keep id sex diag202 doBT doCa doDM doDD203 entry exit
en_st ex_st ;204 length en_st ex_st $5 ;205 *** Only Cancer ;206 if
( doDM le .z ) then do ;207 entry = max( doCa, &truncdate. )
;208 en_st = "Ca" ;209 exit = min( doDD, &censdate ) ;210 if
exit eq doDD then ex_st = "Dead" ; else211 ex_st = en_st ;212 if
entry lt exit then output ;213 end ;214 *** Only diabetes ;215
else216 if ( doCa le .z ) then do ;217 entry = max( doDM,
&truncdate. ) ;218 en_st = "DM" ;219 exit = min( doDD,
&censdate ) ;220 if exit eq doDD then ex_st = "Dead" ; else221
ex_st = en_st ;222 if entry lt exit then output ;223 end ;224 ***
DM before Cancer ;225 else226 if ( doCa gt doDM ) then do ;227 *
from DM to Ca ;228 entry = max( doDM, &truncdate. ) ;229 en_st
= "DM" ;230 exit = min( doCa, &censdate ) ;231 if exit eq doCa
then ex_st = "DM-Ca" ; else232 ex_st = en_st ;
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30 Background calculations Diabetes & Cancer
233 if entry lt exit then output ;234 * from Ca to end ;235
entry = max( doCa, &truncdate. ) ;236 en_st = ex_st ;237 exit =
min( doDD, &censdate ) ;238 if exit eq doDD then ex_st = "Dead"
; else239 ex_st = en_st ;240 if entry lt exit then output ;241 end
;242 *** Cancer before DM ;243 else244 if ( doCa lt doDM ) then do
;245 * from Ca to DM ;246 entry = max( doCa, &truncdate. ) ;247
en_st = "Ca" ;248 exit = min( doDM, &censdate ) ;249 if exit eq
doDM then ex_st = "Ca-DM" ; else250 ex_st = en_st ;251 if entry lt
exit then output ;252 * from DM to end ;253 entry = max( doDM,
&truncdate. ) ;254 en_st = ex_st ;255 exit = min( doDD,
&censdate ) ;256 if exit eq doDD then ex_st = "Dead" ; else257
ex_st = en_st ;258 if entry lt exit then output ;259 end ;260 run
;
NOTE: There were 912764 observations read from the data set
WORK.DMCR.NOTE: The data set WORK.TOLEX has 981476 observations and
11 variables.NOTE: DATA statement used (Total process time):
real time 2.06 secondscpu time 0.51 seconds
261262 libname allPT xport '../data/allPT.xpt' ;NOTE: Libref
ALLPT was successfully assigned as follows:
Engine: XPORTPhysical Name:
C:\Bendix\Steno\DM-register\NDR\projects\Cancer\papers\EpiDMCa\data\allPT.xpt
263 proc copy in = work264 out = allPT ;265 select toLex ;266
run;
NOTE: Copying WORK.TOLEX to ALLPT.TOLEX (memtype=DATA).NOTE:
There were 981476 observations read from the data set
WORK.TOLEX.NOTE: The data set ALLPT.TOLEX has 981476 observations
and 11 variables.NOTE: PROCEDURE COPY used (Total process
time):
real time 26.28 secondscpu time 0.85 seconds
NOTE: SAS Institute Inc., SAS Campus Drive, Cary, NC USA
27513-2414NOTE: The SAS System used:
real time 56.30 secondscpu time 7.12 seconds
The dataset is generated in Lexis-ready-format, so that it can
be put into a Lexis objectanfter a bit of name-grooming and
transformaton of the dates to fractions of calendaryears:
dc
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Background calculations 2.2 Overview of rate computation 31
wh
-
32 Background calculations Diabetes & Cancer
2.2.4 Setting up the analysis data frame
Before we can analyze rates of cancer and diabetes we must
include the part of thepopulation that is without any of the two
diseases. We have the total amount ofperson-years and no. of deaths
in the data frame All.dk. But we must then subtract allrisk time
and deaths that occur subsequent to either DM or Cancer in order to
get theright amount of deaths and PY in the “Well” state.
2.2.4.1 Patient follow-up
In order to get the risk time among patients obtain this we must
split the follow-up in thepatients by age and calendar time. This
is done the classical way, by successivelyaggreating the risk time
and events in tabular form.
The aggredated data frame must be classified by the relevant
factors, and must allowcounting of events of cancer, diabetes and
death.
Agg
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Background calculations 2.2 Overview of rate computation 33
load( file="./data/Agg.Rda" )Ptt.dk
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34 Background calculations Diabetes & Cancer
Finally we merge in the number of DM cancer diagnoses from the
“Well” state:
str( Well )
'data.frame': 6000 obs. of 10 variables:$ A : num 0.333 0.333
0.333 0.333 0.333 ...$ P : num 1996 1996 1997 1997 1998 ...$ sex :
Factor w/ 2 levels "M","F": 2 1 2 1 2 1 2 1 2 1 ...$ U : int 0 0 0
0 0 0 0 0 0 0 ...$ Y.tot: num 16972 17961 16425 17392 16402 ...$
D.tot: num 137 179 134 189 152 172 132 142 95 156 ...$ Y.ptt: num
1.136 2.738 2.567 0.936 2.197 ...$ D.ptt: num 0 3 2 0 4 0 0 0 0 0
...$ Y : num 16971 17958 16423 17391 16399 ...$ D.dd : num 137 176
132 189 148 172 132 142 95 156 ...
str( Inc )
'data.frame': 5972 obs. of 6 variables:$ sex : Factor w/ 2
levels "M","F": 1 2 1 2 1 2 1 2 1 2 ...$ A : num 0.333 0.333 1.333
1.333 2.333 ...$ P : num 1996 1996 1996 1996 1996 ...$ U : num 0 0
0 0 0 0 0 0 0 0 ...$ D.dm: num 1 0 4 2 5 1 3 1 5 1 ...$ D.ca: num 4
3 7 4 3 4 5 2 1 1 ...
Well
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Background calculations 2.2 Overview of rate computation 35
$ U : num 0 0 0 0 0 0 0 0 0 0 ...$ sex : Factor w/ 2 levels
"M","F": 1 2 1 2 1 2 1 2 1 2 ...$ state: Factor w/ 6 levels
"Well","DM","DM-Ca",..: 1 1 1 1 1 1 1 1 1 1 ...$ Y : num 17958
16971 17391 16423 17362 ...$ D.ca : num 4 3 2 3 1 3 4 6 4 3 ...$
D.dm : num 1 0 0 4 1 0 2 0 1 1 ...$ D.dd : num 176 137 189 132 172
148 142 132 156 95 ...
cbind(xtabs( cbind( D.ca, D.dm, D.dd ) ~ state, data=dcd ),
round(xtabs( Y/1000 ~ state, data=dcd ), 1 ) )
D.ca D.dm D.ddWell 382959 289438 431103 75450.8DM 40854 0 93885
2446.8DM-Ca 0 0 28648 97.5Ca 0 27958 289131 2468.4Ca-DM 0 0 18465
138.5Dead 0 0 0 0.0
save( dcd, file="./data/dcd.Rda" )
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36 Background calculations Diabetes & Cancer
2.3 Modelling of rates
First we load the data and chek the number of events of
different types from differentstates:
> library( Epi )> clear()> load( file="./data/dcd.Rda"
)> addmargins( xtabs( cbind(D.dm,D.ca,D.dd) ~ state, data=dcd ),
1 )
state D.dm D.ca D.ddWell 289438 382959 431103DM 0 40854
93885DM-Ca 0 0 28648Ca 27958 0 289131Ca-DM 0 0 18465Dead 0 0 0Sum
317396 423813 861232
From the table we see that we have events for estimating 9
different rates, and also that wehave ample data for estimating
them. To decide how to distribute knots im modelling ofthe
age-effects, we make histograms of the age-distribution of the
events:
> par( mfrow=c(5,3), mar=c(3,1,1,1), mgp=c(3,1,0)/1.6 )>
par( mfg=c(1,1) ) ; with( subset( dcd, state=="Well" ),> hist(
rep(A,D.dm), breaks=0:100,+ col="black", main="", yaxt="n",+
ylab="", xlab="DM | Well" ) )> par( mfg=c(1,2) ) ; with( subset(
dcd, state=="Well" ),> hist( rep(A,D.ca), breaks=0:100,+
col="black", main="", yaxt="n",+ ylab="", xlab="Ca | Well" ) )>
par( mfg=c(1,3) ) ; with( subset( dcd, state=="Well" ),> hist(
rep(A,D.dd), breaks=0:100,+ col="black", main="", yaxt="n",+
ylab="", xlab="Dead | Well" ) )> par( mfg=c(2,2) ) ; with(
subset( dcd, state=="DM" ),> hist( rep(A,D.ca), breaks=0:100,+
col="black", main="", yaxt="n",+ ylab="", xlab="Ca | DM" ) )>
par( mfg=c(2,3) ) ; with( subset( dcd, state=="DM" ),> hist(
rep(A,D.dd), breaks=0:100,+ col="black", main="", yaxt="n",+
ylab="", xlab="Dead | DM" ) )> par( mfg=c(3,3) ) ; with( subset(
dcd, state=="DM-Ca" ),> hist( rep(A,D.dd), breaks=0:100,+
col="black", main="", yaxt="n",+ ylab="", xlab="Dead | DM-Ca" )
)> par( mfg=c(4,1) ) ; with( subset( dcd, state=="Ca" ),>
hist( rep(A,D.dm), breaks=0:100,+ col="black", main="", yaxt="n",+
ylab="", xlab="DM | Ca" ) )> par( mfg=c(4,3) ) ; with( subset(
dcd, state=="Ca" ),> hist( rep(A,D.dd), breaks=0:100,+
col="black", main="", yaxt="n",+ ylab="", xlab="Dead | Ca" ) )>
par( mfg=c(5,3) ) ; with( subset( dcd, state=="Ca-DM" ),> hist(
rep(A,D.dd), breaks=0:100,+ col="black", main="", yaxt="n",+
ylab="", xlab="Dead | Ca-DM" ) )
2.3.1 Prerequisites for the natural splines
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Background calculations 2.3 Modelling of rates 37
> library( Epi )> library( splines )> ( a.kn ( p.kn (
c.kn # Men> cm.w2dm cm.w2ca cm.w2dd cm.dm2ca cm.dm2dd cm.ca2dm
cm.ca2dd # Women> cf.w2dm cf.w2ca cf.w2dd cf.dm2ca cf.dm2dd
cf.ca2dm cf.ca2dd # Men> pm.w2dm pm.w2ca pm.w2dd pm.dm2ca
pm.dm2dd pm.ca2dm pm.ca2dd # Women> pf.w2dm pf.w2ca pf.w2dd
pf.dm2ca pf.dm2dd pf.ca2dm pf.ca2dd round( ci.exp( pf.w2ca ), 3
)
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38 Background calculations Diabetes & Cancer
exp(Est.) 2.5% 97.5%(Intercept) 0.000 0.000 0.000Ns(A, knots =
a.kn)1 2.095 1.832 2.397Ns(A, knots = a.kn)2 5.856 5.384 6.370Ns(A,
knots = a.kn)3 14.181 13.128 15.318Ns(A, knots = a.kn)4 37.612
35.108 40.295Ns(A, knots = a.kn)5 72.677 67.891 77.801Ns(A, knots =
a.kn)6 121.710 113.823 130.142Ns(A, knots = a.kn)7 191.942 178.685
206.184Ns(A, knots = a.kn)8 82.470 72.671 93.590Ns(A, knots =
a.kn)9 170.229 155.709 186.103Ns(P, knots = p.kn)1 1.047 1.029
1.066Ns(P, knots = p.kn)2 1.425 1.378 1.474Ns(P, knots = p.kn)3
1.192 1.178 1.207
> round( ci.exp( pm.ca2dd, subset="state" ), 3 )
exp(Est.) 2.5% 97.5%stateCa 0.497 0.489 0.506stateCa-DM 0.457
0.446 0.470
> round( ci.exp( pf.ca2dd, subset="state" ), 3 )
exp(Est.) 2.5% 97.5%stateCa 0.428 0.420 0.436stateCa-DM 0.415
0.404 0.426
2.3.2 Computing the state probabilities
If we want to compute the fraction of persons in a given state
at a given time that is in anyof the other possible states.
Since we have restricted ourselves to a scenery where we have
only one time scale,namely age we can do the clculations in closed
form by setting up the transition probabilitymatrix for small
intervals (of length int years. For the sake of completeness we
also wealso set up s asimilar matrix for the RR by period; mainly
for showing the estimated RRsby period / cohort:
> int a.pt p.pt c.pt ( states pnam
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Background calculations 2.3 Modelling of rates 39
> p.ref = 2005> c.ref = 1950> aM pR cR pA cA pM cM
TR["Well" ,"DM" ,,"Cross","M",] TR["Well" ,"Ca" ,,"Cross","M",]
TR["Well" ,"D-W" ,,"Cross","M",] TR["DM" ,"DM-Ca",,"Cross","M",]
TR["DM" ,"D-DM" ,,"Cross","M",] TR["Ca" ,"Ca-DM",,"Cross","M",]
TR["Ca" ,"D-Ca" ,,"Cross","M",] TR["DM-Ca","D-DC" ,,"Cross","M",]
TR["Ca-DM","D-CD" ,,"Cross","M",] TR["Well" ,"DM" ,,"Cross","F",]
TR["Well" ,"Ca" ,,"Cross","F",] TR["Well" ,"D-W" ,,"Cross","F",]
TR["DM" ,"DM-Ca",,"Cross","F",] TR["DM" ,"D-DM" ,,"Cross","F",]
TR["Ca" ,"Ca-DM",,"Cross","F",] TR["Ca" ,"D-Ca" ,,"Cross","F",]
TR["DM-Ca","D-DC" ,,"Cross","F",] TR["Ca-DM","D-CD" ,,"Cross","F",]
TR["Well" ,"DM" ,,"Long" ,"M",] TR["Well" ,"Ca" ,,"Long" ,"M",]
TR["Well" ,"D-W" ,,"Long" ,"M",] TR["DM" ,"DM-Ca",,"Long" ,"M",]
TR["DM" ,"D-DM" ,,"Long" ,"M",] TR["Ca" ,"Ca-DM",,"Long" ,"M",]
TR["Ca" ,"D-Ca" ,,"Long" ,"M",] TR["DM-Ca","D-DC" ,,"Long" ,"M",]
TR["Ca-DM","D-CD" ,,"Long" ,"M",] TR["Well" ,"DM" ,,"Long" ,"F",]
TR["Well" ,"Ca" ,,"Long" ,"F",] TR["Well" ,"D-W" ,,"Long" ,"F",]
TR["DM" ,"DM-Ca",,"Long" ,"F",] TR["DM" ,"D-DM" ,,"Long" ,"F",]
TR["Ca" ,"Ca-DM",,"Long" ,"F",] TR["Ca" ,"D-Ca" ,,"Long" ,"F",]
TR["DM-Ca","D-DC" ,,"Long" ,"F",] TR["Ca-DM","D-CD" ,,"Long" ,"F",]
rt round( (exp( log( rt[2,]/rt[1,] ) / 30 )-1)*100, 1 )
M F10.6 7.2
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40 Background calculations Diabetes & Cancer
2.3.4 Secular trends
We the use almost the same code to fill in the RRs associated
with period:
> pRR["Well" ,"DM" ,,"Cross","M",] pRR["Well" ,"Ca"
,,"Cross","M",] pRR["Well" ,"D-W" ,,"Cross","M",] pRR["DM"
,"DM-Ca",,"Cross","M",] pRR["DM" ,"D-DM" ,,"Cross","M",] pRR["Ca"
,"Ca-DM",,"Cross","M",] pRR["Ca" ,"D-Ca" ,,"Cross","M",]
pRR["DM-Ca","D-DC" ,,"Cross","M",] pRR["Ca-DM","D-CD"
,,"Cross","M",] pRR["Well" ,"DM" ,,"Cross","F",] pRR["Well" ,"Ca"
,,"Cross","F",] pRR["Well" ,"D-W" ,,"Cross","F",] pRR["DM"
,"DM-Ca",,"Cross","F",] pRR["DM" ,"D-DM" ,,"Cross","F",] pRR["Ca"
,"Ca-DM",,"Cross","F",] pRR["Ca" ,"D-Ca" ,,"Cross","F",]
pRR["DM-Ca","D-DC" ,,"Cross","F",] pRR["Ca-DM","D-CD"
,,"Cross","F",] cRR["Well" ,"DM" ,,"Long" ,"M",] cRR["Well" ,"Ca"
,,"Long" ,"M",] cRR["Well" ,"D-W" ,,"Long" ,"M",] cRR["DM"
,"DM-Ca",,"Long" ,"M",] cRR["DM" ,"D-DM" ,,"Long" ,"M",] cRR["Ca"
,"Ca-DM",,"Long" ,"M",] cRR["Ca" ,"D-Ca" ,,"Long" ,"M",]
cRR["DM-Ca","D-DC" ,,"Long" ,"M",] cRR["Ca-DM","D-CD" ,,"Long"
,"M",] cRR["Well" ,"DM" ,,"Long" ,"F",] cRR["Well" ,"Ca" ,,"Long"
,"F",] cRR["Well" ,"D-W" ,,"Long" ,"F",] cRR["DM" ,"DM-Ca",,"Long"
,"F",] cRR["DM" ,"D-DM" ,,"Long" ,"F",] cRR["Ca" ,"Ca-DM",,"Long"
,"F",] cRR["Ca" ,"D-Ca" ,,"Long" ,"F",] cRR["DM-Ca","D-DC" ,,"Long"
,"F",] cRR["Ca-DM","D-CD" ,,"Long" ,"F",] rates2RR
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Background calculations 2.3 Modelling of rates 41
> clr # clr ylm rrr par( mfrow=c(2,2), mar=c(3,2,1,3),
oma=c(1,2,1,0),+ mgp=c(3,1,0)/1.6, bty="n", las=1 )> # Cancer
incidence among men> ciw cid diw rrw rrd rrD plci plci()>
text( rep(23,3), (ylm[2]/5)*0.7^(3:2),+ c("Well","DM"),
col=clr[1:2], adj=0, font=2 )> # Cancer incidence among
women> ciw cid diw rrw rrd rrD plci()> # Mortality among
men> mtw mtd mtc mtcd mtdc rrw rrd rrc rrcd rrdc plmt
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42 Background calculations Diabetes & Cancer
+ lwd=rep(c(3,1,1),2), lty=rep(c(1:3),c(9,3,3)),+
col=rep(clr[c(1:3,3,3)],each=3),type="l" )+ axis( side=4,
at=5:20/10 * rrr, labels=FALSE, tcl=-0.3 )+ axis( side=4,
at=c(0.5,1,2) * rrr, labels=c(0.5,1,2) )+ axis( side=4, at=3 * rrr,
labels="RR", tcl=0 )+ axis( side=1, at=seq( 20,100, 5), labels=F )+
axis( side=1, at=seq( 20,100,20) )+ axis( side=1,
at=seq(105,120,5), labels=F )+ axis( side=1, at=seq(110,120,10),
labels=c(2000,2010) )+ mtext( c("Age","Date"), at=c(60,112.5),
side=1, line=3/1.6 )+ }> plmt()> text( rep(23,3),
ylm[2]*0.7^(3:1),+ c("Well","DM","Cancer"), col=clr[1:3], adj=0,
font=2 )> # Mortality among women> mtw mtd mtc mtcd mtdc rrw
rrd rrc rrcd rrdc plmt()> mtext( "DM / Cancer incidence rates
per 1000 PY",+ side=2, line=1/1.6, at=0.75, las=0, outer=TRUE )>
mtext( "Mortality rates per 1000 PY",+ side=2, line=1/1.6, at=0.25,
las=0, outer=TRUE )> mtext( "Men" , side=3, line=-1, at=0.25,
las=0, outer=TRUE )> mtext( "Women", side=3, line=-1, at=0.75,
las=0, outer=TRUE )
2.3.6 Transition probabilities
Now we have the transition rates corresponding to 1/10 year in
the array TR, but we needto fill in the diagonals to get a proper
transition matrix. To this ens we need a functionthat does this
properly; note that the entries in TR are cumulative rates
corresponding to aperiod of length 1/10 year (well, formally int).
Thus if transition cumulatieve rates from agiven state are, say,
Λ1, Λ2 Λ3, the the diagonal element in the row must beexp
(−(Λ1 + Λ2 + Λ3)
)and the off-diagonal elements in the row must be be multiplied
by(
1− exp(−(Λ1 + Λ2 + Λ3)
))/(Λ1 + Λ2 + Λ3). We wrap this calculation in a small
function:
> ci2pr
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Background calculations 2.3 Modelling of rates 43
> TR print.table( round( TR[,,800,1,1] *10^3 ),
zero.print="." )
tofrom Well DM DM-Ca Ca Ca-DM D-W D-DM D-Ca D-DC D-CDWell . 2 .
4 . 5 . . . .DM . . 4 . . . 9 . . .DM-Ca . . . . . . . . 30 .Ca . .
. . 4 . . 18 . .Ca-DM . . . . . . . . . 19D-W . . . . . . . . .
.D-DM . . . . . . . . . .D-Ca . . . . . . . . . .D-DC . . . . . . .
. . .D-CD . . . . . . . . . .
> print.table( round( ci2pr( TR[,,800,1,1] )*10^3 ),
zero.print="." )
tofrom Well DM DM-Ca Ca Ca-DM D-W D-DM D-Ca D-DC D-CDWell 990 2
. 4 . 5 . . . .DM . 987 4 . . . 9 . . .DM-Ca . . 971 . . . . . 29
.Ca . . . 979 4 . . 17 . .Ca-DM . . . . 981 . . . . 19D-W . . . . .
1000 . . . .D-DM . . . . . . 1000 . . .D-Ca . . . . . . . 1000 .
.D-DC . . . . . . . . 1000 .D-CD . . . . . . . . . 1000
> TRp dim( TRp )
[1] 100 1020 2 2
> # Note that apply does not recognize the dim attribute of
FUN argument> dim( TRp ) dimnames( TRp ) print.table( round(
TRp[,,800,1,1]*10^3 ), zero.print="." )
tofrom Well DM DM-Ca Ca Ca-DM D-W D-DM D-Ca D-DC D-CDWell 990 2
. 4 . 5 . . . .DM . 987 4 . . . 9 . . .DM-Ca . . 971 . . . . . 29
.Ca . . . 979 4 . . 17 . .Ca-DM . . . . 981 . . . . 19D-W . . . . .
1000 . . . .D-DM . . . . . . 1000 . . .D-Ca . . . . . . . 1000 .
.D-DC . . . . . . . . 1000 .D-CD . . . . . . . . . 1000
The just printed matrix is the transition matrix (multiplied by
1000) from age 80 to 80.1,so in order to get the probability
distribution at 80.1, we just multiply thestate-distribution at
time 80.0 (as a row vector) with the transition matrix; this must
ofcourse be looped over all the other dimensions of TR:
> names( dimnames( TRp ) )
[1] "from" "to" "age" "scene" "sex"
> for( sc in dimnames(TRp)[["scene"]] )+ for( sx in
dimnames(TRp)[["sex"]] )+ {+ # Initialize at age 0+
PR[,1,sc,sx]
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44 Background calculations Diabetes & Cancer
+ for( ag in 1:dim(TRp)[3] )+ {+ PR[,ag,sc,sx] summary( PR )
Min. 1st Qu. Median Mean 3rd Qu. Max.0.0000000 0.0003761
0.0116500 0.1000000 0.0746800 0.9997000
> summary( apply( PR, 2:4, sum ) )
Min. 1st Qu. Median Mean 3rd Qu. Max.1 1 1 1 1 1
Now we have the distribution of the persons in the different
states under various scenarios,and we can plot the resulting
distribution of the states as function of time; for eeach of the4
combinations of scenario and sex we can plot the probabilities of
being in each of the 10states, but we must put them in the right
order:
> round( t(PR[,600+1:5,1,1])*100, 1 )
Stateage Well DM DM-Ca Ca Ca-DM D-W D-DM D-Ca D-DC D-CD60.05
71.4 10.7 0.5 4.2 0.2 7.1 1.6 3.8 0.4 0.160.15 71.2 10.8 0.5 4.2
0.2 7.1 1.7 3.9 0.4 0.160.25 71.0 10.8 0.5 4.3 0.2 7.1 1.7 3.9 0.4
0.160.35 70.8 10.9 0.5 4.3 0.2 7.2 1.7 4.0 0.4 0.160.45 70.6 10.9
0.5 4.3 0.2 7.2 1.7 4.0 0.4 0.1
> perm round( t(PR[perm,600+1:5,1,1])*100, 1 )
Stateage DM DM-Ca Ca-DM Ca Well D-W D-Ca D-CD D-DC D-DM60.05
10.7 0.5 0.2 4.2 71.4 7.1 3.8 0.1 0.4 1.660.15 10.8 0.5 0.2 4.2
71.2 7.1 3.9 0.1 0.4 1.760.25 10.8 0.5 0.2 4.3 71.0 7.1 3.9 0.1 0.4
1.760.35 10.9 0.5 0.2 4.3 70.8 7.2 4.0 0.1 0.4 1.760.45 10.9 0.5
0.2 4.3 70.6 7.2 4.0 0.1 0.4 1.7
> CR str( PR )
num [1:10, 1:1020, 1:2, 1:2] 1.00 1.13e-05 0.00 2.72e-05 0.00
...- attr(*, "dimnames")=List of 4..$ State: chr [1:10] "Well" "DM"
"DM-Ca" "Ca" .....$ age : chr [1:1020] "0.05" "0.15" "0.25" "0.35"
.....$ scene: chr [1:2] "Cross" "Long"..$ sex : chr [1:2] "M"
"F"
> str( CR )
num [1:10, 1:1020, 1:2, 1:2] 1.13e-05 1.13e-05 1.13e-05 3.85e-05
1.00 ...- attr(*, "dimnames")=List of 4..$ : chr [1:10] "DM"
"DM-Ca" "Ca-DM" "Ca" .....$ age : chr [1:1020] "0.05" "0.15" "0.25"
"0.35" .....$ scene: chr [1:2] "Cross" "Long"..$ sex : chr [1:2]
"M" "F"
> ftable( round( apply( PR, c(1,3,4), max )*100, 1 ),
col.vars=1 )
State Well DM DM-Ca Ca Ca-DM D-W D-DM D-Ca D-DC D-CDscene
sexCross M 100.0 13.4 1.7 6.9 1.3 35.7 20.1 29.2 9.6 5.4
F 100.0 12.7 1.9 9.1 1.7 36.5 19.8 29.7 7.9 5.6Long M 99.8 15.5
5.4 11.1 6.4 21.6 12.9 25.5 19.7 11.3
F 99.8 16.2 4.9 11.9 6.2 16.9 10.5 26.2 20.6 12.1
> ftable( round( apply( CR, c(1,3,4), max )*100, 1 ),
col.vars=1 )
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Background calculations 2.3 Modelling of rates 45
DM DM-Ca Ca-DM Ca Well D-W D-Ca D-CD D-DC D-DMscene sexCross M
13.4 14.7 15.5 22.4 100.0 100.0 100.0 100.0 100.0 100.0
F 12.7 14.4 15.9 24.9 100.0 100.0 100.0 100.0 100.0 100.0Long M
15.5 19.2 23.8 34.6 99.8 100.0 100.0 100.0 100.0 100.0
F 16.2 20.7 26.5 37.2 99.8 100.0 100.0 100.0 100.0 100.0
> round( t( CR[,800+1:5,"Cross","M"] )*100, 1 )
age DM DM-Ca Ca-DM Ca Well D-W D-Ca D-CD D-DC D-DM80.05 8.6 10.1
11.4 17.1 39.6 60.5 80.2 82.7 88.6 10080.15 8.5 10.0 11.3 17.0 39.3
60.2 80.0 82.5 88.6 10080.25 8.5 9.9 11.2 16.9 38.9 60.0 79.9 82.4
88.5 10080.35 8.4 9.9 11.2 16.7 38.6 59.7 79.7 82.3 88.4 10080.45
8.3 9.8 11.1 16.6 38.2 59.5 79.6 82.2 88.3 100
In order to plot the different probabilities we use the polygon
trick, and in order tovisualize the joint occurrence of diabetes
and cancer we define semi-transparent colors
> nul sx sc aa par( mfrow=c(1,2), mar=c(2,2,1,3),
oma=c(2,2,0,0), mgp=c(3,1,0)/1.6, las=1 )> for( sc in
dimnames(CR)[[3]][1] )+ for( sx in dimnames(CR)[[4]] )+ {+ plot(
NA, xlim=c(50,100), ylim=c(0,100),+ xlab="", ylab="", xaxs="i",
yaxs="i" )+ axis( side=4, lwd=0, lwd.ticks=1 )+ axis( side=4,
lwd=0, lwd.ticks=1, at=seq(10,90,10), labels=F, tcl=-0.4 )+ axis(
side=4, lwd=0, lwd.ticks=1, at=seq( 5,95, 5), labels=F, tcl=-0.3 )+
axis( side=4, lwd=0, lwd.ticks=1, at=1:99, labels=F, tcl=-0.2 )+
polygon( c(aa,rev(aa)), c(CR[1,,sc,sx],rev(nul))*100,+ col =
clr[2], border="transparent")+ polygon( c(aa,rev(aa)),
c(CR[1,,sc,sx],+ rev(CR[3,,sc,sx]))*100,+ col = clr[4],
border="transparent")+ polygon( c(aa,rev(aa)), c(CR[3,,sc,sx],+
rev(CR[4,,sc,sx]))*100,+ col = clr[3], border="transparent")+
polygon( c(aa,rev(aa)), c(CR[4,,sc,sx],+ rev(CR[5,,sc,sx]))*100,+
col = clr[1], border="transparent")+ polygon( c(aa,rev(aa)),
c(CR[5,,sc,sx],+ rev(CR[6,,sc,sx]))*100,+ col = "gray",
border="transparent")+ polygon( c(aa,rev(aa)), c(CR[6,,sc,sx],+
rev(CR[7,,sc,sx]))*100,+ col = clr[3], border="transparent")+
polygon( c(aa,rev(aa)), c(CR[7,,sc,sx],+ rev(CR[9,,sc,sx]))*100,+
col = clr[4], border="transparent")+ polygon( c(aa,rev(aa)),
c(CR[9,,sc,sx],+ rev(CR[10,,sc,sx]))*100,+ col = clr[2],
border="transparent")+ matlines( aa, 100*t(CR[c(2,5,8),,sc,sx]),+
lty=1, col=c("white","black")[c(1,2,1)], lwd=c(1,3,1), type="l" )+
text( 55, 70, sx, font=2, cex=1.5, col="white" )+ mtext( "Age
(years)", side=1, outer=TRUE )+ }> mtext( "Fraction of persons
(%)", side=2, outer=TRUE, las=0 )
We also want to see the cumulative risks of getting DM, cancer
and both before a givenage, so we make graphs of this for men and
women
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46 Background calculations Diabetes & Cancer
> dimnames(PR)[[1]]
[1] "Well" "DM" "DM-Ca" "Ca" "Ca-DM" "D-W" "D-DM" "D-Ca" "D-DC"
"D-CD"
> dmlev calev dclev dimnames(PR)[[1]][dmlev]
[1] "DM" "DM-Ca" "Ca-DM" "D-DM" "D-DC" "D-CD"
> dimnames(PR)[[1]][calev]
[1] "DM-Ca" "Ca" "Ca-DM" "D-Ca" "D-DC" "D-CD"
> dimnames(PR)[[1]][dclev]
[1] "DM-Ca" "Ca-DM" "D-DC" "D-CD"
> par( mfrow=c(1,2), mar=c(2,2,1,3), oma=c(2,2,0,0),
mgp=c(3,1,0)/1.6, las=1 )> for( sc in dimnames(CR)[[3]][1] )+
for( sx in dimnames(CR)[[4]] )+ {+ plot( NA, xlim=c(50,100),
ylim=c(0,50),+ xlab="", ylab="", xaxs="i", yaxs="i" )+ axis(
side=4, lwd=0, lwd.ticks=1 )+ axis( side=4, lwd=0, lwd.ticks=1,
at=seq(10,90,10), labels=F, tcl=-0.4 )+ axis( side=4, lwd=0,
lwd.ticks=1, at=seq( 5,95, 5), labels=F, tcl=-0.3 )+ axis( side=4,
lwd=0, lwd.ticks=1, at=1:99, labels=F, tcl=-0.2 )+ text( 55, 40,
sx, font=2 )+ matlines( aa, cbind( apply( PR[dmlev,,sc,sx]*100, 2,
sum ),+ apply( PR[calev,,sc,sx]*100, 2, sum ),+ apply(
PR[dclev,,sc,sx]*100, 2, sum ) ),+ col=clr[2:4], lty=1, lwd=5 )+
mtext( "Age (years)", side=1, outer=TRUE )+ mtext( "Fraction of
persons (%)", side=2, outer=TRUE, las=0 )+ }
We can of course also make the same exercise conditional being
alive at age 50, 60 etc,but as is seen from figure 2.6 the ultimate
distribution of the fraction of persons that get thetwo diseases is
not dramatically changed by condtioning on survival to ages 50, 60
or 70.
We set up the machinery in parallel for the three conditioning
ages
> DM50
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Background calculations 2.3 Modelling of rates 47
For further comparisons we print the distribution on states at
age 102 years:
> round( ww round( ww[c(7:10),], 1 )
M F M F M F M FD-DM 20.1 19.8 18.6 18.4 16.3 17.3 12.8 14.5D-Ca
29.2 29.7 30.1 29.0 30.5 26.9 28.5 22.6D-DC 9.6 7.9 8.6 6.4 6.8 5.2
4.1 3.2D-CD 5.4 5.6 5.9 5.6 6.1 4.9 5.5 3.5
> round( apply(ww[c(8,9,10),],2,sum), 1 )
M F M F M F M F44.1 43.2 44.6 41.0 43.5 37.0 38.1 29.3
> round( apply(ww[c(7,9,10),],2,sum), 1 )
M F M F M F M F35.1 33.4 33.1 30.4 29.3 27.4 22.4 21.2
> round( apply(ww[c( 9,10),],2,sum), 1 )
M F M F M F M F15.0 13.6 14.5 12.0 13.0 10.1 9.6 6.7
We con compute the fraction of those without disease at
different age and who eventuallygets a DM diagnosis, who also have
a cancer diagnosis:
> round( ww[c(7,9,10),], 1 )
M F M F M F M FD-DM 20.1 19.8 18.6 18.4 16.3 17.3 12.8 14.5D-DC
9.6 7.9 8.6 6.4 6.8 5.2 4.1 3.2D-CD 5.4 5.6 5.9 5.6 6.1 4.9 5.5
3.5
> round( apply(ww[ 9:10 ,],2,sum)/+
apply(ww[c(7,9:10),],2,sum)*100, 1 )
M F M F M F M F42.7 40.6 43.7 39.5 44.3 36.9 42.8 31.6
We can see how the overall fraction of a birth cohort that gets
cancer compares to thefraction among those with diabetes at a given
age that contracts cancer:
> round( cbind( PR[,1020,"Cross",],+ DM50[,1020,"Cross",],+
DM60[,1020,"Cross",],+ DM70[,1020,"Cross",] )*100, 1 )
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48 Background calculations Diabetes & Cancer
M F M F M F M FWell 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.0DM 0.0 0.1
0.0 0.1 0.0 0.1 0.0 0.1DM-Ca 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0Ca 0.0
0.1 0.0 0.0 0.0 0.0 0.0 0.0Ca-DM 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0D-W
35.7 36.5 0.0 0.0 0.0 0.0 0.0 0.0D-DM 20.1 19.8 63.5 62.9 63.5 66.1
67.9 73.4D-Ca 29.2 29.7 0.0 0.0 0.0 0.0 0.0 0.0D-DC 9.6 7.9 36.5
37.0 36.4 33.8 32.0 26.5D-CD 5.4 5.6 0.0 0.0 0.0 0.0 0.0 0.0
We can now plot the comparison between the life-long outloook of
a person with andwithout diabetes:
> CRpl for( sc in dimnames(CR)[[3]][1] )+ for( sx in
dimnames(CR)[[4]] )+ {+ CRpl( PR50, sc, sx, 1:500 )+ CRpl( PR60,
sc, sx, 1:600 )+ CRpl( PR70, sc, sx, 1:700 )+ CRpl( DM50, sc, sx,
1:500, "transparent" )+ CRpl( DM60, sc, sx, 1:600, "transparent" )+
CRpl( DM70, sc, sx, 1:700, "transparent" )
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Background calculations 2.3 Modelling of rates 49
+ }> mtext( "Age (years)", side=1, outer=TRUE )> mtext(
"Fraction of persons (%)", side=2, outer=TRUE, las=0 )> mtext(
"Men, no DM" , side=3, outer=TRUE, las=0, at=1/8 )> mtext( "Men,
DM" , side=3, outer=TRUE, las=0, at=3/8 )> mtext( "Women, no
DM", side=3, outer=TRUE, las=0, at=5/8 )> mtext( "Women, DM" ,
side=3, outer=TRUE, las=0, at=7/8 )
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50 Background calculations Diabetes & Cancer
0.5 0.7 1.0 1.5 2.0 3.0 4.0 5.0
RR, DM vs. non−DM
Leukaemia
Multiple myeloma
Non−Hodgkin lymphoma
Hodgkins lymphoma
Thyroid
Brain
Urinary bladder
Kidney
Testis
Prostate
Ovary, fallopian tube etc.
Corpus uteri
Cervix uteri
Breast
Melanoma of skin
Lung, bronchus and pleura
Pancreas
Liver
Rectum
Colon
Stomach
Oesophagus
All malignant neoplasms ●
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Figure 2.1: Estimated RRs from different studies. Blue lines for
men, red lines for women.Within each group of estimates they are
from the studies, in the same order as in table 1.1.
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Background calculations 2.3 Modelling of rates 51
Well0 0
DM2,447.4
382,477 247,428
DM−Ca97.5
2,030 14,230
Ca2,470.8
522,493 204,878
Ca−DM138.6
5,661 15,132
Dead0 430,993
40,856(16.7)
94,193(38.5)
28,656(293.8)
27,964(11.3)
289,651(117.2)
18,493(133.5)
Well0 0
DM2,447.4
382,477 247,428
DM−Ca97.5
2,030 14,230
Ca2,470.8
522,493 204,878
Ca−DM138.6
5,661 15,132
Dead0 430,993
Well0 0
DM2,447.4
382,477 247,428
DM−Ca97.5
2,030 14,230
Ca2,470.8
522,493