Sample size in health sciences - Basics and selected examples

Sample size estimation:
Basics & selected examples Dr. S. A. Rizwan, M.D.
Public Health Specialist
SBCM, Joint Program – Riyadh
Ministry of Health, Kingdom of Saudi Arabia

Learning objectives
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh
• Importance of sample size estimation
• Basic concepts in sample size calculation
• How does sample size relate to study results
• Sample size calculation in specific situations
2

Books and software
• Books
• Sample size determination in health studies - a practical manual
(Lwanga & Lemeshow)
• Sample Size Calculations in Clinical Research (Shein-Chung Chow,
Hansheng Wang, Jun Shao)
• Software
• Epitools, online calculators, Stat cal in Epi Info, G power
• PASS, nmaster, Statsdirect, Stata
• Many others
3

Obligatory opening joke!
Demystifying statistics! SBCM, Joint Program – RiyadhSBCM, Joint Program – Riyadh 4

Rethinking Aesop’s fables…

Let’s play a game!

Sample size:
Basic concepts

Prerequisites for this class
• Understanding of the following basic concepts
• Types of study designs
• Measures of association
• Mean/SD
• Proportion
• Standard error
• Hypothesis testing and types
• Confidence intervals
8

Some related terms
• Significance level
• Power
• Effect size
• Variability
• Precision
Con. level Z α
95% 1.96 (2 sided)
95% 1.64 (1 sided)
99% 2.57 (2 sided)
99% 2.32 (1 sided)
Power Z β
90% 1.282
85% 1.037
80% 0.842
75% 0.675
70% 0.524
9

Sample size & statistical inference
• Two methods of statistical inference
• Hypothesis testing
• Confidence interval estimation
10

Two aspects of a good sample
• The sample size
• If adequate, then good internal
validity
• The sampling method
• If representative, then good
external validity
11

Why calculate sample size?
• Stating the assumptions and
parameters before start of the
study increases the validity of
statistical conclusions made after
the study
• Post-hoc analysis and results are
considered merely exploratory
12

Thought exercise
• I am applying for a job and in the
resume I have stated that my typing
speed is very fast.
• My friend is applying for the same
job and in his resume he stated that
his typing speed was 60 words/min.
Which candidate are you more likely to assess in a valid manner?
13

Why calculate sample size? (contd.)
• Funds and time constraints
• Really not necessary to study the entire
population (ethical problem!)
• Small samples unable to detect clinically
relevant differences
• If a study with small sample finds non-
significant results – what does it mean?
14

Thought exercise
• Study 1: A study was conducted for an anti-
hypertensive drug on 10,000 people which
showed a statistically significant fall in BP of
1mm Hg over 3 months
• Study 2: It was found that there was 30%
reduction in mortality due to propranolol among
MI patients. But that was not significant. 66
cases and 64 controls were studied
State your comment on each of the above scenario.
15

Thought exercise

Then, how large should SS be ?
• Neither too small nor too large
17

Sample size estimated for primary objective
• Sample size is calculated for
‘primary outcome variable’
• If there are >1 primary outcomes
sample size calculated for each
outcome and largest chosen
18

Common scenarios for sample size
• 100s of scenarios for calculation sample size
• Descriptive:
• Proportion, mean/SD
• Analytical:
• Two proportions, 2 means/SD
• Also, risk diff, OR & RR, incidence density
19

Uncommon scenarios for sample size
• Survival
• Regression
• Correlation
• Quality assurance
• Diagnostic test studies
• And many more
20

Further considerations for sample size
• Study design
• Cluster design
• Cross over
• Matched/paired
• Type of hypothesis (inequality,
equivalence, non-inferiority & superiority)
• Fixed follow up duration
• Ratio of controls to cases
• Hypothesis testing or CI estimation?
21

How to approach a SS problem?
1. Convert the research question into a statistical problem statement
2. Determine formula or software command & determine inputs needed
3. Select the sources for the inputs
4. Substitute the values in the formula or enter in the software
5. Factor in non-response/drop-out rate
22

• First: Convert the research question into a
statistical problem statement
• For eg.,
• To estimate the mean birth weight of
neonates born to mothers with anaemia
in the eastern sector of Riyadh
• Estimation of a single mean with stated
precision
23

• Second: Find out the formula or the software
command appropriate for this problem
• For eg.,
• Estimation of a single mean with stated
precision
N = (Zα
2 * S2) / L2
24

• Second: and determine the ingredients you
require to input in the formula
• Exp. proportion, incidence
• Exp. SD
• Exp. RR or OR
• Power, precision
• Confidence level
• Others (DE, ICC, COV, cluster size)
• For eg.,
• Estimate of SD, alfa & precision
25

• Third: Selecting the sources for the inputs
• Match the location as close as possible
• Match the study population as close as possible
• Match the study setting as close as possible
• Match the statistic as close as possible
• Or conduct a pilot study
• For eg.,
• Other sector in Riyadh -> some other city in KSA ->
Middle east -> any developing country -> anywhere
26

• Third (contd.): What sources to use?
• From where
• Published Literature
• Pilot study
• Experts in the field
• Educated guess (gut feeling)
It begs the question that if we already know these inputs then
why conduct the study in the first place!
27

• Third (Contd.): eg., an appropriate source
28

• Fourth: Substitute the values in the
formula or enter in the software
N = (Zα
2 * S2) / L2
N = (1.96*1.96 * 600*600)/100*100
N = 138.2
N = Rounded to 140
29

• Fifth: Factor in non-response/drop-out rate
• Final sample size =
!"#$%& ()*&
+,$&-.&/ 0&($12(& 0".&
• For eg.,
• For a non-response rate of 20%
• Final sample size = 140 / 0.80 = 175
30

Sample size:
Some selected scenarios

Sample size in specific situations
Authors Original research question Simplified problem statement
1. Dr. Nariman
What is the proportion of patients who quit
smoking in a tobacco cessation program?
Estimation of a single proportion
for a special group
2. Dr. Ghadeer
What is the incidence of DM in obese hypertensives
and what is the incidence of DM in non-obese
hypertensive during a five year follow-up period?
Comparison of incidence rates in
two groups in a cohort study
3. Dr. Rahma
What is the proportion of LBW neonates born to
sickle cell mothers and what is the proportion of
LBW neonates born to normal mothers in a cohort
of mothers?
Comparison of two proportions in
a cohort study
4. Dr. Abrar
What is the proportion of ILI absent students in the
handwashing schools and what is the proportion of
ILI absent students in the control schools? Here
schools are the units of randomisation
Comparison of two proportions in
a 2 group cluster RCT
32

Scenario 1:
Estimating a single proportion

Scenario 1 – Step 1
• What is the proportion of patients who quit smoking
in a tobacco cessation program?
• Specifically, what is the proportion of patients with
DM and HTN who quit smoking in a tobacco cessation
program?
• It is a cross-sectional study based on secondary data
analysis
• Estimating a single proportion
34

• SS formula for estimation a difference between two proportions in cohort study
• Inputs required are expected proportion of quitting, precision & confidence level
35

• A thorough literature review and preliminary data analysis showed a wide variation in
the expected proportion – from 10% to 50%
36

• Substituting the values for a number of scenarios in the software
37

• The concept of dropouts or loss to follow-up in
not applicable in this case because it is secondary
data analysis
• So the sample size should be >400 and but need
not be >3500
• Final decision will depend on feasibility
38

Scenario 2:
Comparison of incidence rates in a
two group cohort study

• Hypothesis: the risk of developing (incidence) DM will
be higher in obese hypertensive patients as compared
to non-obese hypertensive patients during a 5 year
follow-up period
• It is a cohort study with two groups
• Exposed is obese hypertensive
• Non-exposed is non-obese hypertensive
• Outcome is incidence of DM
• Estimating a difference between two incidence rates
in a cohort study
40

• This problem can be visualised in a number of ways:
1. Comparing two incidence rates in a cohort study
(Relative Risk – hypothesis test)
(Relative Risk – stated precision)
with small proportion and fixed study duration (Risk
difference – hypothesis test)
4. Comparing two proportions (Risk difference –
hypothesis test)
41

• Method 1: SS formula for estimating RR with stated precision
• Inputs required are expected proportion of disease among exposed & unexposed, RR, Precision,
confidence level
42

• Method 2: SS formula for hypothesis testing of RR
• Inputs required are expected proportion of disease among exposed & unexposed, RR, power,
confidence level
43

• SS formula for difference in two proportions (aka risk difference) can also be used for
this scenario
Risk difference between 2 proportions Risk difference between 2 incidence rates
with fixed study duration
44

• A casual literature review showed that the risk of DM was 5 times among obese HTN as compared to non-
obese HTN, the incidence among non-obese was 5.4 and among obese was 24.2 per 1000 person years
46

• Method 1 & 2: Substituting the values for a number of scenarios in the software
47

• Considering a loss to follow-up of 10%
• Final sample size = 716 / 0.90 = 795 per group
48

Scenario 3:
Comparison of proportions in a two
group cohort study

• Hypothesis: the proportion of LBW neonates will be
higher in the sickle cell mothers as compared to the
non-sickle cell mother
• It is a cohort with two groups
• Exposed is mothers with sickle cell disease
• Non-exposed is normal mothers
• Outcome is proportion of LBW
• Estimating a difference between two proportions in
a cohort study
50

(Relative Risk – hypothesis test)
(Relative Risk – stated precision)
with small proportion and fixed study duration (Risk
difference – hypothesis test)
hypothesis test)
51

• Method 1: SS formula for estimating risk difference (hypothesis test)
• Inputs required are expected proportion of disease among exposed & unexposed, power, confidence level
Difference between 2 proportions
52

• A literature review showed that proportion of LBW among SCD mothers was 16.5% and
in the normal mothers it was 8.3%, with an RR of ~2
53

54

55

Scenario 4:
Comparison of proportions in two
group cluster RCT

• Hypothesis: the proportion of students being absent due
to ILI will be higher in the control schools as compared to
the schools implementing the handwashing program
during a follow up period of 6 weeks
• It is a cluster RCT with two groups
• Exposed is handwashing program
• Non-exposed is no handwashing program
• Outcome is proportion of ILI absenteeism
• School is the unit of randomisation
• Estimating a difference between two proportions in a
cluster RCT
57

hypothesis test using ICC)
hypothesis test using Design Effect)
hypothesis test using Coefficient of variation)
58

• Method 1: SS formula for comparison of proportions using design effect
• Inputs required are proportion of outcome in the exp. group & control group, size of cluster, DE, power,
confidence level
59

• Method 2: SS formula for comparison of proportions using intra cluster correlation coefficient
• Inputs required are proportion of outcome in the exp. group & control group, size of cluster, ICC,
power, confidence level
60

• A literature review showed that incidence of ILI absenteeism was 0.043 in the exp.
group and 0.070 in the control group
61

62

Scenario 4
• Method 3: SS formula for comparison of incidence rates (person time)
• Inputs required are incidence rates (PT) in the exp. group & control group, coeff. of variation, power,
confidence level
63

• No. of clusters required = 1805 / 40 = 45 per group
64

Review
• Why is sample size calculation important?
• What are the five steps to calculate the SS?
• What are the some of the common inputs required
for sample size formulae?
• How will you select an appropriate source for the
inputs of SS formula?
• How will you relate the SS of your study after the
results?
65

Take home messages
• A priori sample size calculation is very
crucial for making valid conclusions
• Follow the stepwise approach
• Sample size estimation does not need to be
very accurate, only adequate
• In case of non-significant findings in a study,
calculate power for deeper understanding
66

Thank you!
Email your queries to sarizwan1986@outlook.com
67

Sample size in health sciences - Basics and selected examples

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