Sample size estimation

1. SAMPLE SIZE CALCULATION IN
DIFFERENT STUDY DESIGNS
Dr Aswathi T

2. Sample Size Estimation
• Scientific research - requires carefully designed methods to produce
valid and relevant results
• Scientifically proven sample size estimation needed for this
• Most crucial methodological part of a research study
• Key questions health researchers are likely to ask is, how much of a
population is needed for valid and reliable study?

3. • Exhaustive survey
• Researchers may choose to study all those within a target population
• Possible when the entire population of interest is small and there are
resources to study them
• Sample size calculation may not be required or may not be applicable
even when estimated
• Not feasible to study the entire subjects or respondents in a
population of interest

4. Sample
• Sub-set of the study population
• Representatives of the study population
• Make an inference from the sample and apply it to the whole
population
• Study the characters of the population by measuring them from a
smaller number of subjects

5. If sample is too large
Good precision
Close to the truth provided
BUT
× Administrative, economical, ethical & some scientific issue
× Wastage of time, money and resources
× More sample – more work – more expenditure
× A small difference in the test parameter value may become
statistically significant ,but it may not have any clinical significance

6. If sample is too small
×Inaccurate results
×Study fails to give meaningful information
×Might have been obtained by chance only
×Power of the study comes down
×Waste of resources on an inaccurate study
×Ethical issues about recruiting patients into a meaningless study
×A substantial difference in the estimates between the groups may
become statistically insignificant, but may have some clinical
significance

7. Incorrect sample size will lead to
• Wrong conclusion
• Poor quality of research
• Loss of money
• Ethical problems
• Delay in completion
Neither too
small nor too big

8. Factors affecting the Sample size
1. Rough estimate of the magnitude of the study variable – existing
literature/pilot study
2. Minimum clinically relevant effect size
To detect small effect size, large sample size is required vice versa

9. Factors affecting the Sample size…
3. Standard Error ( SE ): ( Standard Deviation ) / √n
Larger the sample size - lesser the SE
4. Precision : Reliability or the Consistency of the estimate in repeated
sampling
precision = √n / S.E.
Larger the sample size, smaller will be the SE and Larger will be the
precision

10. Factors affecting the Sample size…
5. Accuracy
• The extent to which the sample estimate is closer to the True value
• When there is no bias or it is negligible, the sample estimate will be
closer to the True value and the estimate will be more accurate

12. Factors affecting the Sample size…
6. Type I and II Errors
Type I : false positive
Reject null hypothesis when it is true (probability of making this error
is α)
Type II : false negative
Accept hypothesis when it is false (probability of making this error is
β)
1- α is the confidence of a study
1-β is the power of a study

13. Factors affecting the Sample size…
Confidence & power
• A minimum of 95 % confidence ( 5% Type-I error) – 95% probability
that true population parameter will be within the calculated interval
• A minimum of 80% power (20% Type-II error) should be fixed for any
type of study – chance of detecting an effect / association if it exists
• Small alpha error means more sample
• Small beta error/high power means more sample size

14. Study Truth Truth (Reality) in the population
Null Hypothesis
False
Null Hypothesis
True
Study results
from sample
Null Rejected Correct decision
(power)
Alpha Error
Null not
Rejected
Beta Error Correct decision

15. Factors affecting the Sample size…
7. Other factors:
• Type of design - CS/CC/C/CT
• Comparative design generally require a larger sample size than
descriptive designs
• One tailed tests will require 30% less sample size than two tailed test
• Dropout rate, lost to follow up, missed data, non compliance to
treatment – all will increase sample size

17. Types Of Variable
Based on what we are measuring
Qualitative
1. Calculating the proportion
2. Calculating the difference of proportions
Quantitative
1. Calculating the mean
2. Calculating the difference in means

18. Qualitative
• Qualitative are those which can be answered as YES or NO, Male or
Female, etc
• We can only measure their numbers, eg: Number of males, Number
of MDR-TB cases among TB patients, etc.
• A set of qualitative data can be expressed as proportions. Eg:
Prevalence, success rate
• In general sample size is higher for qualitative variable

19. Quantitative
• Quantitative are those which can be measured in numbers, like Blood
pressure, Age, Height, Weight, etc
• A set of quantitative date can be expressed in mean and its standard
deviation
• Mean is the average of all variables in the data
• Standard deviation is a measure of the distribution of variables
around the mean
• In general, sample size is low for quantitative variables

20. Estimation of Sample Size for Cross-sectional
or Descriptive Research Studies
• Done to estimate a population parameter like prevalence of some
disease in a community or finding the average value of some
quantitative variable in a population
• Sample size formula for qualitative variable and quantities variable
are different.

21. Cross Sectional Studies…
• For qualitative variable

22. Cross Sectional Studies…
• Example -1
• A researcher wants to carry out a descriptive study to understand the
prevalence or proportion of diabetes mellitus among adults in a city.
A previous study stated that diabetes in the adult population was
40%. At 95% CI and 5% margin of error, calculate the sample required
to conduct other new research?
• p=0.4, q=0.6, d=0.05
• 369
• 10% dropout406

23. Cross Sectional Studies…
• For quantitative variable

24. Cross Sectional Studies…
• Example -2
• A researcher wants to know the average hemoglobin level among
adults in the city at 95% CI and the margin of error is 2 g/dl. From a
previous study, the SD of hemoglobin level among adults was found
to be 4.5 g/dl. How many study subjects will be required to conduct a
new study?
• 𝜎 = SD=4.5, d=2
• 19
• 10% dropout21

25. Sample Estimation for Case–control Studies
• Retrospective
• In case control studies cases (the group with disease/condition under
consideration) are compared with controls (the group without
disease/condition under consideration) regarding exposure to the risk
factor under question

26. Case–control Studies…

27. Case–control Studies…
• Example - 3
• If a researcher wants to conduct a case–control design to identify the
link between deep vein thrombosis and pulmonary embolism. He
decides to work at 95% CI and 80% power of the study. He assumes
expected proportion in case is 40% and control group is 30% and
decides to have a same number of cases in both groups. Find out the
optimum sample size for each group in study.
• P=0.35, P1=0.4, P2=0.3, r=1
• 357
• 10% dropout393 in cases & control group

28. Case–control Studies…

29. Case–control Studies…
• Example – 4
• Suppose a researcher wants to conduct a study to identify the
association between the amount or quantity of alcohol consumption
and liver cirrhosis. From the previous study, he finds that the mean
difference in alcohol consumption between the case and control
groups was 10 ml/day and SD was 18 ml/day. He decides to conduct
the study at 95% CI and fix power of the study at 80%. Find the
sample size to have a equal number in case and control group for
study.

30. Case–control Studies…
• Example – 4
• 𝜎 = 18, d=10, r=1
• 51
• 10% drop out56 in cases & control group

31. Same Size Estimation for Cohort Studies
• Prospective
• Healthy subjects with or without exposure to some risk factor are
observed over a time period to see the event rate in both groups

32. Cohort Studies…

33. Sample size estimation for comparative studies
• Various types of observational study that compare population
proportions (P1 and P2 ) and means (µ1 and µ2 )
• Formerly known as ‘comparative study’
• There is no form of intervention or experimentation

34. Comparative Studies…
• compare population proportions (P1 and P2 ) and means (µ1 and µ2 )

35. Comparative Studies…

36. Sample Size Estimation for Experimental
Studies or Randomized Controlled Trials
• In this investigator provides intervention and study its effect and
compare in experiential and control group
• Superiority trial: The aim of this type of trial is to view that a novice
drug/treatment/intervention is superior to a control treatment.
• Equivalence trial: The aim of this type of trial is to view that novice
treatment/intervention is equally effective to control treatment.
• Non-inferiority trial: The aim of this type trial is to view that novice
treatment/intervention is effective but must not superior than the
control treatment.
Equality trial - hypothesise that there is no clinical difference or
effect between the mean of the new treatment/intervention (µT)
and the mean of the comparator

37. Randomized Controlled Trials…
• The trials can also be one-sided (one-tail) hypothesis
Direction of the difference or the effect is stated (more/greater or
less/lower than)
• Many researchers prefer to adopt two-sided (two-tail) hypothesis
which usually do not state the direction of the differences or effects
expected
This states that there is no difference between the effect of the
treatment/intervention and the comparator (standard/usual/placebo)
• Design variants of the trials such as the parallel, cross-over and
cluster RCTs also have effects on the sample size

40. Sample size formula for animal studies
• E = Total number of animals – Total number of groups
• The value if E should lies within 10 to 20 for optimum sample size.

41. Electronic Resources for Sample Size
Calculation
StatCalc
WinPepi
OpenEpi
Stata
PASS
nMaster
nQuery Adviser