Statistics

1. Statistics for Medical
Research
Anurag Srivastava
Department of Surgery
AIIMS-New Delhi
dr.anuragsrivastava@gmail.com

2. Sherlock Holmes: “ The grand thing is to be able to
reason backwards. There is nothing more deceptive
than an obvious fact. The temptation to form
premature theories upon insufficient data is the bane of
our profession. It is an error to argue in front of your
data. You find yourself insensibly twisting them round
to fit your theories”.
Sherlock Holmes had it right- reasoning backward
from data to truth is full of traps- Statistics helps to
avoid these traps.

3. Clinical research searches for answers in an
heterogeneous environment. Large variability
between patients and their response to therapy,
physician and patient’s biases for one therapy or
the other are reason for controlled trials.
Statistical rules help in design ,conduct, analysis
and interpretation of RCT.
Florence Nightingale: “ To understand God’s
thought we must study statistics, for these are the
measures of His purpose”.

4. Learning Objectives
• How to design a study?
• Basic data analysis- mean, median, standard deviation
and confidence interval.
• Comparison of means, proportions, odds and risks.
• How to assess a diagnostic test?
• Logistic regression, linear regression and survival
analysis.

5. Study Designs
• Follow up study (cohort) - In this
design information on a patient e.g.
B.P., body weight is recorded initially
and patient is followed for some period
of time, and the same measurement is
repeated. The follow up time may vary
from minutes, hours to years.

6. • The patient should be free from
disease/outcome of interest at the start.
• Cohort study helps in identifying the
probability/risk of a disease. It can help
in identifying cause of a disease.
• Randomized controlled trials are
basically a type of follow up study.
QUESTIONS

7. Case Control Design
• A group of subjects are taken in whom the disease or outcome has
occurred-
The CASES
• A similar group of subjects is taken who are free from the disease
-
The CONTROL
• Both groups are asked/tested for previous exposure to a risk
factor.

8. • The odds of exposure is calculated in cases and
controls.
• The odds ratio is calculated as follow : Odds of
exposure in cases/odds of exposure in control.
• Case control study helps in finding risk factor for
rare disease and where induction time is very
long.
• Causality cannot be confirmed by this design.
• The problem of selection bias and recall bias is
high.

9. Randomized Controlled Trial (RCT)
Q. How many of you have done RCT?
• It is a special type of follow up study in which patients
are given an intervention and followed till an outcome
develops.
• The decision to give an intervention is by the process of
Randomization.
• Randomization ensures equal probability of selection of
subjects into two or more arms without any selection
bias.

10. • Randomization is done by table of random
numbers or computer generated random
numbers.
• Randomization ensures equal distribution of
known and unknown factors influencing the
outcome. (questions)
• Thus any difference in the outcome is most likely
to be due to the intervention.
• The randomization for a multi-center RCT is
done on a central office by phone, fax or internet.

11. Data Presentation
1. Binary Data (questions)
2. Ordinal Data - mild, moderate, severe
3. Continuous Data( show tape)
Why classify data?

12. Measures of Central Tendency
why?
• Mean : sum of all observations
number of observations
• Median : 50th percentile of a set of
measurement
• Mode : set of values that occurs
most frequently

13. Measures of Dispersion
• Range : Range of a group of measurement is the difference
between the largest and the smallest observation.
• Interquartile Range : 75th percentile - 25th percentile
• Variance : quantifies the amount of variability or spread
about the mean of the sample.

14. Measures of Dispersion
• Standard Deviation : Square root of the
variance.
• Confidence Interval: e.g. 95% CI is 5-
20,if an experiment is done 100 times in
95 occasions the truth will lie between
5&20.
Exercise: age of participants

15. Hypothesis Testing
A RCT on operation A Vs Operation B
Hypothesis: operation A is same as operation B,
Null Hypothesis
operation A is better than operation B
Alternate Hypothesis
Comparison of continuous data- steps
• plot the data
• check normality-Example

16. • The normal distribution is a cornerstone of statistics. It is a
distribution of scores
• Characterized by 3 properties:
1) It is unimodal,
2) It is bell-shaped
3) It is symmetric,
• The middle and flip one half over, like a hinge, it would match the
corresponding side. The reason for it's importance is simple: lots
of distributions take on a normal shape Moreover, the normal
distribution has regular properties that make it very easy to work
with

17. • If normal-Student t test
• If skewed-Wilcoxan rank sum test
Comparison of binary data
Chi Square test, Fisher’s exact test- Example
Comparison of ordinal data
Chi square test, Log linear model

18. Alpha And Beta Errors
Defendant
Verdict of Jury Innocent Guilty
Not Guilty Correct
Decision
Incorrect
Decision
Guilty Incorrect
Decision
Correct
Decision
H0 is true H0 is false
H0 is not Correct decision Type II error b
rejected Confidence 1-a
H0 is Type I error a Correct decision
rejected Power1-b

19. Meaning of p Value
It’s the probability of obtaining a result equal to
or more extreme than the observed value if Ho
is true.
It is the probability that observed result is due
to chance alone.

20. Probability
If an experiment is repeated n times under essentially
identical conditions , and if the event A occurs m times
then the probability of A is defined as :
P(A) = m / n
The p lies between 0 and 1
where “0” means that the event will never occur
“1” means that the event will definitely occur -100% of
times.
Explain by apple

21. Sensitivity and Specificity
• The probability of a positive result among diseased is
called the Sensitivity -PID ( Positive in disease).
• The probability of a negative result among nondiseased
is called the Specificity - NIH ( Negative in health).
• The relationship between sensitivity and specificity is
illustrated as an Receiver Operator
Characteristics(ROC) curve Explain by example

22. Relative Risk and Odds Ratio
Relative Risk : Probability of disease in the
exposed group divided by probability of disease
in unexposed group.
Odds Ratio : Odds in favour of disease among
exposed individuals divided by odds among
unexposed.
odds = 1/1-p
p = odds/ 1+odds

23. Box and Whisker Plot
sum age if methods = 0 , detail
Percentiles Smallest
• 1% 18 18
• 5% 20 18
• 10% 22 20 Obs 54
• 25% 25 21 Sum of Wgt. 54
• 50% 30.5 Mean 36.37037
• Largest Std. Dev. 14.41212
• 75% 47 61
• 90% 58 62 Variance 207.7093
• 95% 62 68 Skewness .8255658
• 99% 75 75 Kurtosis 2.643563

24. Regression Analysis
• For binary outcome-Logistic regression
Example on Stata
• For continuos outcome-Linear regression
Example on Stata
• For binary outcome with censored follow up-
Survival or Cox regression
Example on Stata

25. Suggested Readings
• Books: Biostatistical analysis -
by J H Zar
• Basics of Clinical Biostatistics -
by Dawson-Saunders & Trapp
• Journals : Statisitics in Medicine
J. of Clinical Epidemiology
• Internet Websites:
www.amstat.org/publication/jse/

26. Suggested Readings
• www.maths.nott.ac.uk/rsscse/TS/
•
www.amstat.org/publications/jse/secure/v7n3/anderson_cook.cfm
• www.maths.nott.ac.uk/rsscse/TS/
• www.amstat.org/publication/jse/v5n3/falk.html
• http://glass.ed.asu.edu/stats
• Softwares: STATA, SPSS, BMDP, Epiinfo(free),SAS
• STATA address :
• sparker@stata.com , vishvas@vsnl.com