Deals with Sample Size calculation in common situations in Clinical Research.

1. Sample Size in Clinical Research
Inaamul Haq
Assistant Professor
Department of Community Medicine
Government Medical College, Srinagar

2. “One of the questions most commonly
asked about the planning of a statistical
study, and one of the most difficult to
answer, is: how many observations should
be made?”
[Armitage P, Berry G, Matthews JNS. Statistical Methods in
Medical Research, 4th Edition, pp. 137-8]

3. “Samples which are too small can prove
nothing. Samples which are too large can
prove anything.”[Sackett DL]

4. Proportion Mean
Difference between
two proportions
Difference between
two means
p = expected prevalence
q = 100 – p
d = allowable error
s = expected standard deviation
d = allowable error
P = Average of two expected
proportions
Q = 100 – P
D = expected difference between
two proportions
[proportions as percentages;
Calculates sample for each group]
s = expected standard deviation
d = expected difference
between two means

5. Q: Calculate sample size if expected
prevalence (proportion) is 20%.
p = 20%
q = (100-20)=80%
d = 4%
Sample size =
4x20x80/(4x4)=6400/16=400

6. Q: Calculate sample size if expected
proportion in (cases) = 40% and in
(controls) = 70%
P = (40+70)/2=55%
Q = (100-55)=45%
D = (70-40)=30
Sample size =(16x55x45)/(30x30)=44
[44 cases and 44 controls]

7. 1.Introduction
2.Background terms
3.Analytical Studies
4.Descriptive Studies

8. 1.Introduction
2.Background terms
3.Analytical Studies
4.Descriptive Studies

9. Why do we select a sample?
Economical
Less resources
Less time

10. How large should a sample be?
Too small – Less precision
Too large – Wastage of resources

11. 1.Introduction
2.Background terms
3.Analytical Studies
4.Descriptive Studies

12. Background terms to understand sample size calculations
A.Hypothesis
B.Effect Size
C.Type I and Type II errors and Power
of a study

13. The hypothesis should be simple
and specific
A. Hypothesis
Simple = Only one exposure and one outcome;
Specific = Level of measurement of variables should be explicit

14. The expected magnitude of the
association in the population.
B. Effect Size
The size of the association in the
population that the investigator
wishes to detect in the sample.
A clinically significant effect.

15. The difference in the proportion exposed among
cases versus proportion exposed among controls.
B. Effect Size
The difference in the proportion developed disease
among exposed versus proportion developed
disease among non-exposed.
Difference in the cure rate among intervention
group versus control group.

16. C. Type I and Type II errors and Power
Coronil Prednisolone
1 2

17. C. Type I and Type II errors and Power
Truth about the treatment
New treatment
does not work
New treatment
works
Our
conclusion
based
on
the
study
New treatment
does not work
False Negative
Type II Error
Beta Error
New treatment
works
False Positive
Type I Error
Alpha Error

18. C. Type I and Type II errors and Power

19. C. Type I and Type II errors and Power
Truth about the treatment
New treatment
does not work
New treatment
works
Our
conclusion
based
on
the
study
New treatment
does not work
False Negative
Type II Error
Beta Error
New treatment
works
False Positive
Type I Error
Alpha Error

20. C. Type I and Type II errors and Power
The “Power” of a study is its ability to detect a difference when it
exists in the population.
The “Power” of a study is its ability to conclude that a new treatment
is effective when the new treatment is actually good and effective
“The ability to correctly conclude that a new treatment works”.
Conventionally, The Type I Error is set at 5%,
the Type II Error is set at 20%, and
Power is set at 80%.

21. 1.Introduction
2.Background terms
3.Analytical Studies
4.Descriptive Studies

22. The most common situation is
clinical research is where the
outcome is dichotomous and the
exposure also is dichotomous.

23. Case-Control Study
Percentage of cases
exposed &
Percentage of controls
exposed

24. Cohort Study
Percentage of exposed
developed disease &
Percentage of non-exposed
developed disease

25. RCT
Percentage of
Intervention group
patients cured &
Percentage of control
Group patients cured

26. 1.Formulae
2.Online calculators/Softwares
3.Available/Published Tables
3 WAYS TO CALCULATE SAMPLE SIZE

27. Openepi
www.openepi.com
Online Calculators/Software programs

28. Online Calculators/Software programs
Case-Control Studies
Cohort Studies, RCTs,
Analytical Cross-
sectional Studies
Prevalence Studies
Continuous exposure
(Difference in means)

29. An investigator conducts a case-control study to
find out the relationship between obesity
(BMI≥30Kg/m2) and breast cancer. The
prevalence of obesity in the population was
known to be 40% from a pervious study. The
investigator expected that the prevalence of
obesity among breast cancer cases will be 60%
(based on a study in a similar population).
Case-Control Study

30. Case-Control Study

31. Case-Control Study
16 × 50 × 50
20 × 20
= 100

33. An investigator conducts a cohort study to find
out the relationship between late marriage
(married after 30 years of age) and congenital
malformations in the first born. The incidence
of congenital malformations in the unexposed
group is known to be 2%; the incidence of
congenital malformations in the exposed group
(late marriage group) is expected to be 10%.
Cohort Study

34. Cohort Study

35. Cohort Study
16 × 6 × 94
8 × 8
= 141

36. Cohort Study

37. An investigator conducts a clinical trial to
evaluate the efficacy of a new, short-course,
drug regimen to treat Helicobacter Pylori
infection against a standard regimen. The
treatment success rate of the standard regimen
is 65%. The new regimen is expected to
improve the treatment success rate by 10% (i.e.,
the new drug regimen is expected to have a
treatment success rate of 75%).
RCT

38. RCT

39. RCT
16 × 70 × 30
10 × 10
= 336

41. 1.Introduction
2.Background terms
3.Analytical Studies
4.Descriptive Studies

42. Prevalence Studies
An investigator plans to estimate the
prevalence of glaucoma in a population.
Based on findings from a similar
population, the investigator expects that
the prevalence of glaucoma in his
population will be 5%. He wants to
estimate the prevalence of glaucoma
within an error of 1% (absolute precision).

43. Prevalence Study

44. Prevalence Study
4 × 5 × 95
1 × 1
= 1900

45. Questions????

46. Thank You