CMS Assess, York, Nov. 2002 ADJUSTED SURVIVAL GRAPHS in SPSS ? by Gilbert MacKenzie & Yasin Al-tawarah Centre for Medical Statistics.
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CMS Assess, York, Nov. 2002
ADJUSTED SURVIVAL GRAPHS in SPSS ?
by
Gilbert MacKenzie & Yasin Al-tawarah
Centre for Medical Statistics
CMS Assess, York, Nov. 2002
Introduction
There is a growing awareness generally of the importance of Evaluation in the Health and Education communities.
A key factor in Evaluation has been the introduction, by Government, of:
League Tables
for example, for schools and hospitals. Formally, such data are observational and classically their statistical evaluation
is by covariate adjustment.
CMS Assess, York, Nov. 2002
Time to Event League Table Data
One key class of data to arise in this context is:
Survival Data
Time to Event Data leading to: Survival Graphs
Adjusted Survival Graphs for crude and adjusted for case-mix comparisons, respectively.
CMS Assess, York, Nov. 2002
Models, Graphs & Software The most common survival model is:
COX’s PH model (1972)
and so we should look at:
PH Adjusted Survival Graph and of course
PH Adjusted Survival Graph in SPSS *Does SPSS do a good job here ?
CMS Assess, York, Nov. 2002
Graphical Sense*
Represent the Process Authentically
Makes Statistical and Mathematical Sense
Reasonable Scales, etc
“Visual and Scientific Truth”
*Recall Alan Reese’s impromptu lecture last conference
CMS Assess, York, Nov. 2002
tt|i
iii
)}n/d(exp{)t(S
i )t(
i)]}ˆxexp(/d[exp{)t(S
i0
}xexp{)t(S)x|t(S 0
Statistical Sense
Kaplan Meier
Adjusted Nelson-Aalen (Breslow variant)
where di is the number of deaths and ni is the number at risk at
time ti, for i =1,…, n subjects.
CMS Assess, York, Nov. 2002
Adjusted Survival
Cox’s is invariant to x-location change (but not scale)
COXREG stores and not as one expects
Need to be clear about basics !
)xx( x
)ˆ)xxexp[()t(S)xx|t(S 0
S0(t), S(t|x) require the x’s used with in the model
CMS Assess, York, Nov. 2002
Adjusted Survival - Categorical
Suppose x = (x1, x2): x1 is categorical & x2 is cont. Suppose x1 has 3 categories: 0, 1 and 2. Then we need to see 3 adjusted survival curves Where the adjustment is made at the mean of x2
ie What are the differences in x1 when ? 22 xx
CMS Assess, York, Nov. 2002
}xxxexp{)t(S)x|t(S 2212121111
0
}xxexp{)t(S)x,,x|t(S 221111
0201 }xxexp{)t(S)x,,x|t(S 221212
0210
Adjusted Survival - Categorical
Fit a model with x11 and x12, using x10 as the reference and include x2.
Regression Model:
2212121111 xx.x
Adjusted Survival
CMS Assess, York, Nov. 2002
Example 1 – Dialysis Survival study of Dialysis Patients n= 306
Fit 2 covariates: x1 = Referral Time, x2= Age.
Categories of x1 : x10 = <3mths (reference), x11 = 3mths-1yr, x12 = 1+yrs Analysis is “time to death or censoring”
CMS Assess, York, Nov. 2002
Unadjusted Survival
Survival Time (years)
6543210
Cu
mu
lative
Pro
po
rtio
n S
urv
ivin
g 1.0
.8
.6
.4
.2
0.0
Referral
1+yrs
3 mnths 1 yr
lt 3 mnths
CMS Assess, York, Nov. 2002
Adusted Survival - Coxreg
Time in Years
6543210
Cu
mu
lative
Pro
po
rtio
n S
urv
ivin
g1.0
.8
.6
.4
.2
0.0
Referral
1+yrs
3 mnths-1 yr
< 3 mnths
CMS Assess, York, Nov. 2002
Adjusted Survival - not Coxreg
Time in Years
76543210
Cu
mu
lative
Pro
po
rtio
n S
urv
ivin
g1.0
.8
.6
.4
.2
0.0
Referral
1+yrs
3 mnths-1 yr
lt 3 mnths
CMS Assess, York, Nov. 2002
What, if anything, is Wrong? 1. Note the first Graph is KM (unadjusted) which shows the jumps of the process in each category 2. The second graph is Cox Adjusted, but it estimates a common 0(t) and so is evaluated at every t, but the
graphical procedure does not respect the jumps in the process in the separate categories – so you are led to think that the process jumps at the same time in every category! This is misleading. Also the follow-up time is wrong. The 3rd graph produced by a macro corrects these mistakes and shows the jumps in each category separately. This is more authentic and the follow-up time is again correct.
CMS Assess, York, Nov. 2002
Example 2 – Elderly Facility
Survival study of Elderly Patients 204 patients admitted to one Facility Between 1996 and 2001 Study conducted in 2002 Survival: Year of Admission adjusted for Age
This is an example of suspicious mortality
CMS Assess, York, Nov. 2002
(KM – SPSS)Unadjusted Survival
Time in Years
6543210
Pro
po
rtio
n S
urv
ivin
g1.0
.8
.6
.4
.2
0.0
YEAR
2001
2000
1999
1998
1997
1996
CMS Assess, York, Nov. 2002
Adjusted Survival by Year
Time in Years
543210
Pro
po
rtio
n S
urv
ivin
g
1.0
.8
.6
.4
.2
0.0
Year
2001
2000
1999
1998
1997
1996
CMS Assess, York, Nov. 2002
Adjusted Survival - not Coxreg
Time in Years
6543210
Cu
mu
lative
Pro
po
rtio
n
Su
rviv
ing
1.0
.8
.6
.4
.2
0.0
YEAR
2001
2000
1999
1998
1997
1996
CMS Assess, York, Nov. 2002
The Same things are wrong again!
1. The first graph is OK
2. The second graph has the same process jumps at each time point in all years of entry to the study – now there is suspicious mortality – clockwork death!! - and propagates the wrong duration (4 years) in each year of entry.
3. The last graph produced by a specially written macro fixes all of these problems.
CMS Assess, York, Nov. 2002
Conclusions The SPSS adjusted survival graph procedure does
not correctly reproduce the jumps in the underlying process in the categories or pattern. The SPSS procedure does not even faithfully represent the time-scale on which the process is measured The Adjusted Survival Graphs produced by SPSS are therefore not authentic and are potentially highly misleading especially in the type of comparisons considered in the last example.
CMS Assess, York, Nov. 2002
What is required ? The realisation by SPSS that
1. what they produce in Coxreg by way of graphical output is not what the user wants and is not helpful
2. their standard adjusted graph with a common 0(t) is not properly produced with respect to time scale or to the jumps in the process in the categories of the pattern variable
3. the user always needs to see the Cox model compared with the data ie the KM curve.
The final question is how long will it take to see these obvious corrections made ?
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