bio statistics for clinical research

Statistical Methods in Clinical Research

Dr Ranjith P

DNB Resident ACME Pariyaram , Kerala

Overview Data types

Summarizing data using descriptive statistics

Standard error

Confidence Intervals

Overview P values

Alpha and Beta errors

Statistics for comparing 2 or more groups with continuous data

Non-parametric tests

Overview Regression and Correlation

Risk Ratios and Odds Ratios

Survival Analysis

Cox Regression

Forest plot

PICOT

overview

Types of Data Discrete Data-limited number of choices

Binary: two choices (yes/no) Dead or alive Disease-free or not

Categorical: more than two choices, not ordered Race Age group

Ordinal: more than two choices, ordered Stages of a cancer Likert scale for response

E.G. strongly agree, agree, neither agree or disagree, etc.

Types of data Continuous data

Theoretically infinite possible values (within physiologic limits) , including fractional values

Height, age, weight Can be interval

Interval between measures has meaning. Ratio of two interval data points has no meaning Temperature in celsius, day of the year).

Can be ratio Ratio of the measures has meaning Weight, height

Types of Data Why important? The type of data defines:

The summary measures used Mean, Standard deviation for continuous data Proportions for discrete data

Statistics used for analysis: Examples:

T-test for normally distributed continuous Wilcoxon Rank Sum for non-normally distributed

continuous

Descriptive Statistics Characterize data set

Graphical presentation Histograms Frequency distribution Box and whiskers plot

Numeric description Mean, median, SD, interquartile range

HistogramContinuous Data

No segmentation of data into groups

Frequency Distribution

Segmentation of data into groupsDiscrete or continuous data

Box and Whiskers Plots

Box and Whisker Plots

Popular in Epidemiologic StudiesUseful for presenting comparative data graphically

Numeric Descriptive Statistics Measures of central tendency of data

Mean Median Mode

Measures of variability of data(dispersion) Standard Deviation, mean deviation Interquartile range, variance

Mean Most commonly used measure of central tendency

Best applied in normally distributed continuous data.

Not applicable in categorical data

Definition: Sum of all the values in a sample, divided by the number of

values.

Eg mean Height of 6 adolescent children 146 ,142,150,148,156,140

Ans ?

882/6 =147

Median Used to indicate the “average” in a

skewed population Often reported with the mean

If the mean and the median are the same, sample is normally distributed.

It is the middle value from an ordered listing of the values If an odd number of values, it is the middle

value 1.2.3.4.5 ie 3 If even number of values, it is the average

of the two middle values.1,2,3,4,5,6 ie 3+4/2 = 3.5

Mid-value in interquartile range

Mode Infrequently reported as a value in studies.

Is the most common value eg. 1,3,8,9,5,8,5,6

mode = 5

.

Interquartile range Is the range of data from the 25th percentile

to the 75th percentile

Common component of a box and whiskers plot It is the box, and the line across the box is the

median or middle value Rarely, mean will also be displayed.

Mean deviation(standard deviation )

Mean deviation(SD) = £I X- Ẍ I / n n is the no of observations Ẍ is the mean ,

X each observation

Square mean deviation= variance=

£I X- Ẍ I² / n

Root mean square deviation =√£I X- Ẍ I² / n

Variance Square of SD(standard deviation )

Coefficient of variance = SD/ mean x 100

Eg. If sd is 3 mean is 150

Variance is 9, coefficient of variance is 300/150 = 2

Standard Error A fundamental goal of statistical analysis is to

estimate a parameter of a population based on a sample

The values of a specific variable from a sample are an estimate of the entire population of individuals who might have been eligible for the study.

A measure of the precision of a sample

Standard Error Standard error of the mean

Standard deviation / square root of (sample size) (if sample greater than 60) Sd/ √n

Important: dependent on sample size Larger the sample, the smaller the standard error.

Clarification Standard Deviation measures the

variability or spread of the data in an individual sample.

Standard error measures the precision of the estimate of a population parameter provided by the sample mean or proportion.

Standard Error Significance:

Is the basis of confidence intervals

A 95% confidence interval is defined by Sample mean (or proportion) ± 1.96 X standard error

Since standard error is inversely related to the sample size:

The larger the study (sample size), the smaller the confidence intervals and the greater the precision of the estimate.

Mean +/- 1 sd = 68.27% value Mean +/- 2 sd = 95.49% value

Mean +/- 3 sd = 99.7% value Mean +/- 4 sd = 99.9% value

Confidence Intervals May be used to assess a single point

estimate such as mean or proportion.

Most commonly used in assessing the estimate of the difference between two groups.

Confidence Intervals

Commonly reported in studies to provide an estimate of the precisionof the mean.

P Values The probability that any observation is

due to chance alone assuming that the null hypothesis is true Typically, an estimate that has a p

value of 0.05 or less is considered to be “statistically significant” or unlikely to occur due to chance alone. Null hypothesis rejected

The P value used is an arbitrary value P value of 0.05 equals 1 in 20

chance P value of 0.01 equals 1 in 100

chance P value of 0.001 equals 1 in 1000

chance.

Errors Type I error

Claiming a difference between two samples when in fact there is none.

Remember there is variability among samples- they might seem to come from different populations but they may not.

Also called the error. Typically 0.05 is used

Errors Type II error

Claiming there is no difference between two samples when in fact there is.

Also called a error. The probability of not making a Type II

error is 1 - , which is called the power of the test.

Hidden error because can’t be detected without a proper power analysis

Errors

Null Hypothesis

H0

Alternative Hypothesis

H1

Null Hypothesis

H0

No Error Type I

Alternative Hypothesis

H1

Type II

No Error

Test result

Truth

Sample Size Calculation Also called “power analysis”. When designing a study, one needs to

determine how large a study is needed. Power is the ability of a study to avoid a Type

II error. Sample size calculation yields the number of

study subjects needed, given a certain desired power to detect a difference and a certain level of P value that will be considered significant.

Sample Size Calculation

Depends on: Level of Type I error: 0.05 typical Level of Type II error: 0.20 typical One sided vs two sided: nearly always two Inherent variability of population

Usually estimated from preliminary data The difference that would be meaningful

between the two assessment arms.

One-sided vs. Two-sided Most tests should be framed as a two-

sided test. When comparing two samples, we usually

cannot be sure which is going to be be better.

You never know which directions study results will go.

For routine medical research, use only two-sided tests.

Statistical Tests Parametric tests

Continuous data normally distributed

Non-parametric tests Continuous data not normally distributed Categorical or Ordinal data

Comparison of 2 Sample Means Student’s T test

Assumes normally distributed continuous data.

T value = difference between means standard error of difference

T value then looked up in Table to determine significance

Paired T Tests Uses the change before

and after intervention in a single individual

Reduces the degree of variability between the groups

Given the same number of patients, has greater power to detect a difference between groups

Analysis of Variance(ANOVA) Used to determine if two or more

samples are from the same population- If two samples, is the same as

the T test. Usually used for 3 or more

samples.

Non-parametric Tests Testing proportions

(Pearson’s) Chi-Squared (2) Test Fisher’s Exact Test

Testing ordinal variables Mann Whiney “U” Test Kruskal-Wallis One-way ANOVA

Testing Ordinal Paired Variables Sign Test Wilcoxon Rank Sum Test

Use of non-parametric tests Use for categorical, ordinal or non-normally

distributed continuous data May check both parametric and non-

parametric tests to check for congruity Most non-parametric tests are based on

ranks or other non- value related methods Interpretation:

Is the P value significant?

(Pearson’s) Chi-Squared (2) Test

Used to compare observed proportions of an event compared to expected.

Used with nominal data (better/ worse; dead/alive)

If there is a substantial difference between observed and expected, then it is likely that the null hypothesis is rejected.

Often presented graphically as a 2 X 2 Table

Non parametric test

For comparing 2 related samples

-Wilcoxon Signed Rank Test

For comparing 2 unrelated samples

-Mann- Whitney U Test

For comparing >2groups

-Kruskal Walli Test

Mann–Whitney U test  Mann–Whitney–Wilcoxon (MWW), Wilcoxon

rank-sum test, or Wilcoxon–Mann–Whitney test) is a non-parametric test especially that a particular population tends to have larger values than the other.

It has greater efficiency than the t-test on non-normal distributions, such as a mixture of normal distributions, and it is nearly as efficient as the t-test on normal distributions.

STUDENT T TEST A t-test is any statistical hypothesis

test in which the test statistic follows a normal

distri bution if the null hypothesis is supported.

It can be used to determine if two sets of data are significantly different from each other, and is most commonly applied when the test statistic would follow a normal distribution 

The Kaplan–Meier estimator,also known as the product limit estimator, is an estimator for estimating the survival function from lifetime data.

In medical research, it is often used to measure the fraction of patients living for a certain amount of time after treatment.

The estimator is named after Edward L. Kaplan and Paul Meier.

A plot of the Kaplan–Meier estimate of the survival function is a series of horizontal steps of declining magnitude which, when a large enough sample is taken, approaches the true survival function for that population.

ODDS RATIO

In case control study – measure of the strength of the association between risk factor and out come

Odds ratioLung cancer(cases)

No lung cancer (controls)

smokers 33 (a) 55 (b)

Non smokers 2 (c) 27 (d)

TOTAL 35(a+c) 82(b+d)

Odds ratio =ad/bc

=33*27/55*2

=8.1 ie smokers have 8.1 times have the

risk to develop lung cancer than non smokers

RELATIVE RISK

Measure of risk in a cohort study

RR=lncidence of disease among exposed / incidence among non exposed

Cigarette smoking

Developod lung cancer

Not Developod lung cancer

total

Yes 70 (a) 6930 (b) 7000(a+b)

No 3 (c) 2997 (d) 3000(c+d)

Incidence among smokers=70/7000=10/1000

Incidence among non smokers=3/3000=1/1000

Total incidence= 73/10000=7.3/1000

RR=lncidence of disease among exposed/ incidence among non exposed

Relative risk of lung cancer=10/1=10

Incidence of lung cancer is 10 times higher in exposed group (smokers) , ie having a Positive relationship with smoking

Larger RR ,more the strength of association

Attributable risk

It is the difference in incidence rates of disease between exposed group(EG) and non exposed group(NEG)

Often expressed in percent

(Incidence of disease rate in EG-Incidence of disease in NEG/incidence rate in EG ) * 100

. AR= 10-1/10=90%

Ie 90% lung cancers in smokers was due to their smoking

Population attributable Risk It is the incidence of the disease in total

population - the incidence of disease among those who were not exposed to the suspected causal factor/incidence of disease in total population

PAR=7.3-1/7.3=86.3%, ie 86.3 % disease can be avoided if risk factors like cigarettes were avoided

Mortality rates & Ratios Crude Death rate

No of deaths (from all cases )per 1000 estimated mid year population(MYP) in one year in a given place

CDR=(No. deaths during the year /MYP)*1000

CDR in Panchayath A is 15.2/1000

Panchayath B is 8.2/1000 population

Health status of Panchayath B is better than A

Specific Death rate=(No of diseases due to specific diseases during a calendar year/ MYP)*1,000

Can calculate death rate in separate diseases eg . TB, HIV 2/1000, 1/1000 respAge groups 5-20yrs, <5yrs - 1/1000, 3/3000

resp.Sex eg. More in males, Specific months,etc

Case fatality rate(ratio) (Total no of deaths due to a particular

disease/Total no of cases due to same disease)*100

Usually described in A/c infectious diseases

Dengue, cholera, food poisoning etc Represent killing power of the disease

Proportional mortality rate(ratio)

Due to a specific disease=(No of deaths from the specific disease in a year/ Total deaths in an year )*100

Under 5 Mortality rate=(No of deaths under 5 years of age in a given year/Total no of deaths during the same period)*100

Survival rate (Total no of patients alive after 5yrs/Total

no of patients diagnosed or treated)*100

Method of prognosis of certain disease conditions mainly in cancers

Can be used as a yardstick for assessment of standards of therapy

INCIDENCE No of new cases occurring in a defined

population during a specified period of time

(No of new cases of specific disease during a given time period / Population at risk)*1000

Eg 500 new cases of TB in a population of 30000, Incidence is (500/3000)*1000

ie 16.7/1000/yr expressed as incidence rate

Incidence-uses Can be expressed as Special incidence

rate , Attack rate , Hospital admission rate , case rate etc

Measures the rate at which new cases are occurring in a population

Not influenced by duration Generally use is restricted to acute

conditions

PREVALENCE Refers specifically to all current cases (old

& new) existing at a given point of time, or a period of time in a given population

Referred to as a rate , it is really a a ratio

Two types ,point prevalence, Period prevalance

Point prevalence=(No of all currant cases (old& new) of a specified disease existing at a given point of time / Estimated population at the same point of time)*100

Period prevalence=(No of existing cases (old& new) of a specified disease during a given period of time / Estimated mid interval population at risk)*100

Incidence - 3,4,5,8

Point prevalence at jan 1- 1,2& 7

Point prevalence at Dec 31- 1,3,5&8

Period prevalence(jan-Dec)- 1,2,3,4,5,7&8

Relationship b/n Incidence & prevalence

Prevalence=Incidence*Mean duration P=I*D I=P/D D=P/I

Eg: Incidence=10 cases/1000 population/yr

Mean duration 5 yrs Prevalence=10*5 =50/1000 population

PREVALENCE-USES Helps to estimate magnitude of

health/disease problems in the community, & identify potential high risk populations

Prevalence rates are especially useful for administrative and planning purposes

eg: hospital beds, man power needs,rehabilation facilities etc.

Statistical significance

P value (hypothesis)

95% CI (Interval)

P value & its interpretation

“it is the probability of type 1 error”

The chance that, a difference or association is concluded , when actually there is none.

Study of prevalence of obesity in male & female child in a classroom.

50 students

of 25 boys- 10 obese

of 25 girls - 16 obese

p value : 0.02

Null hypothesis: “no difference in obesity among boys & girls in the classroom”

study ,Bubble vs conventional CPAP for prevention of extubation Failure( EF) in preterm very low birth weight infants.

EF bCPAP =4(16)

cCPAP =9(16)

p value-0.14

Null hypothesis: “ no difference in EF among preterm babies treated with bCPAP &cCPAP.”

95% CI

95%CI= Mean ‡1.96SD(2SD)

= Mean ‡ 2SE

1) 100 children attending pediatric OP.

mean wt=15kg SD=2

95%CI =?

Interpretation of 95%CI If a test is repeated 100times , 95 times

the mean value comes between this value.

If CI of 2 variables overlap, the chance of significant difference is very less.

Measures Of Risk case control study- Odds ratio Cohort study -RR,AR

Chi-Squared (2) Test Chi-Squared (2) Formula

Not applicable in small samples If fewer than 5 observations per cell, use

Fisher’s exact test

BREAK

Correlation Assesses the linear relationship between two variables

Example: height and weight Strength of the association is described by a correlation

coefficient- r r = 0 - .2 low, probably meaningless r = .2 - .4 low, possible importance r = .4 - .6 moderate correlation r = .6 - .8 high correlation r = .8 - 1 very high correlation

Can be positive or negative Pearson’s, Spearman correlation coefficient Tells nothing about causation

Correlation

Source: Harris and Taylor. Medical Statistics Made Easy

Correlation

Perfect Correlation

Source: Altman. Practical Statistics for Medical Research

Regression Based on fitting a line to data

Provides a regression coefficient, which is the slope of the line

Y = ax + b Use to predict a dependent variable’s value based on the

value of an independent variable. Very helpful- In analysis of height and weight, for a known

height, one can predict weight. Much more useful than correlation

Allows prediction of values of Y rather than just whether there is a relationship between two variable.

Regression Types of regression

Linear- uses continuous data to predict continuous data outcome

Logistic- uses continuous data to predict probability of a dichotomous outcome

Poisson regression- time between rare events. Cox proportional hazards regression- survival

analysis.

Multiple Regression Models Determining the association between two

variables while controlling for the values of others.

Example: Uterine Fibroids Both age and race impact the incidence of fibroids. Multiple regression allows one to test the impact of

age on the incidence while controlling for race (and all other factors)

Multiple Regression Models In published papers, the multivariable models are

more powerful than univariable models and take precedence.

Therefore we discount the univariable model as it does not control for confounding variables.

Eg: Coronary disease is potentially affected by age, HTN, smoking status, gender and many other factors.

If assessing whether height is a factor: If it is significant on univariable analysis, but not on

multivariable analysis, these other factors confounded the analysis.

Survivial Analysis Evaluation of time to an event (death,

recurrence, recover). Provides means of handling censored data

Patients who do not reach the event by the end of the study or who are lost to follow-up

Most common type is Kaplan-Meier analysis Curves presented as stepwise change from

baseline There are no fixed intervals of follow-up- survival

proportion recalculated after each event.

Survival Analysis

Source: Altman. Practical Statistics for Medical Research

Kaplan-Meier Curve

Source: Wikipedia

Kaplan-Meier Analysis Provides a graphical means of comparing the

outcomes of two groups that vary by intervention or other factor.

Survival rates can be measured directly from curve.

Difference between curves can be tested for statistical significance.

Cox Regression Model Proportional Hazards Survival Model. Used to investigate relationship between an event

(death, recurrence) occurring over time and possible explanatory factors.

Reported result: Hazard ratio (HR). Ratio of the hazard in one group divided the hazard in

another. Interpreted same as risk ratios and odds ratios

HR 1 = no effect HR > 1 increased risk HR < 1 decreased risk

Cox Regression Model Common use in long-term studies

where various factors might predispose to an event. Example: after uterine embolization, which

factors (age, race, uterine size, etc) might make recurrence more likely.

True disease state vs. Test result

not rejected rejected

No disease (D = 0)

specificity

XType I error (False +)

Disease (D = 1) X

Type II error (False -)

Power 1 - ; sensitivity

DiseaseTest

Specific Example

Test Result

Pts Pts with with diseasdiseasee

Pts Pts without without the the diseasedisease

Test Result

Call these patients “negative”

Call these patients “positive”

Threshold

Test Result

Call these patients “negative”

Call these patients “positive”

without the diseasewith the disease

True Positives

Some definitions ...

Test Result

Call these patients “negative”

Call these patients “positive”

without the diseasewith the disease

False Positives

Test Result

Call these patients “negative”

Call these patients “positive”

without the diseasewith the disease

True negatives

Test Result

Call these patients “negative”

Call these patients “positive”

without the diseasewith the disease

False negatives

Test Result

without the diseasewith the disease

‘‘‘‘-’-’’’

‘‘‘‘+’+’’’

Moving the Threshold: right

Test Result

without the diseasewith the disease

‘‘‘‘-’-’’’

‘‘‘‘+’+’’’

Moving the Threshold: left

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0%

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False Positive Rate (1-specificity)

0%

100%

ROC curve

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False Positive Rate0%

100%

Tru

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False Positive Rate0%

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A good test: A poor test:

ROC curve comparison

Best Test: Worst test:T

rue

Po

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0%

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False Positive Rate

0%

100%

Tru

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False Positive Rate

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The distributions don’t overlap at all

The distributions overlap completely

ROC curve extremes

Best Test: Worst test:T

rue

Po

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0%

100%

False Positive Rate

0%

100%

Tru

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0%

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False Positive Rate

0%

100%

The distributions don’t overlap at all

The distributions overlap completely

ROC curve extremes

FOREST PLOT

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An example forest plot of five odds

ratios (squares) with the summary measure (centre line of diamond) and associated confidence intervals (lateral tips of diamond), and solid vertical line of no effect. Names of (fictional) studies are shown on the left, odds ratios and confidence intervals on the right.

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A forest plot (or blobbogram[1]) is a graphical display designed to illustrate the relative strength of treatment effects in multiple quantitative scientific studies addressing the same question. It was developed for use in medical research as a means of graphically representing a meta-analysis of the results of randomized controlled trials.

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i. Probably a small study, with a wide CI, crossing the line of no effect (OR = 1). Unable to say if the intervention works

ii. Probably a small study, wide CI , but does not cross OR = 1; suggests intervention works but weak evidence

iii. Larger study, narrow CI: but crosses OR = 1; no evidence that intervention works

iv. Large study, narrow confidence intervals: entirely to left of OR = 1; suggests intervention works

v. Small study, wide confidence intervals, suggests intervention is detrimental

vi. Meta-analysis of all identified studies: suggests intervention works.

PICOT Used to test evidence based research Population Intervension or issue Comparison with another intervention Outcome Time frame