This document discusses sample size calculations for clinical trials. It explains that sample size is determined by key factors like the primary variable, test statistic, null and alternative hypotheses, type I and II error rates, and variability estimates. It provides an example calculation for a trial comparing two analgesics. The document also reviews International Conference on Harmonisation guidelines on justifying sample size estimates and assumptions, investigating the sensitivity of sample size to deviations, and conventions for setting type I and II error rates.

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Balance
Calmness
Serenity
SAMPLE SIZE AND
RELATED ICH
GUIDELINES
Kadiroo Jayaraman
Senior Principal Biostatistician (Consultant)

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OUTLINE
• Rationale of sample size computations
• Some illustrations
• Review ICH Guidelines on sample size

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PREMISE
• In the clinical context, sample size generally refers to the number
of subjects used in a study.
• Sample size is computed in advance of conducting a trial.
• Calculation of sample size is important in many respects.
Human subjects are expensive to be available for a study.
There are ethical considerations to include more subjects
in trials.
• So, we look for just the number of subjects required to detect a
pre-decided difference between the study treatments with respect
the response measure, at a pre-specified risk level.

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SAMPLE SIZE DETERMINANTS
Sample size is usually determined by the primary objective of the
trial. Else, this should be made clear and justified like in the case of
important secondary objectives.
Determination of sample size involves specification of the following:
• A primary variable,
• Test statistic,
• Null and Alternative hypotheses (embodies effect size),
• Probability of type I error,
• Probability of type II error,
• An estimate of between subject variability
• Adjustments towards treatment withdrawals and protocol
violations.

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TYPE I AND TYPE II ERRORS
• Probability of type I error = α = level of significance
• Confidence coefficient = 1- α
• Probability of type II error = β
• Power of the test = 1- β
• Power calculation is as important as calculation of sample size for ethical
and credibility considerations.
Missing data could lead to reduced power; hence efforts to review
CRF, DTA etc so that we plan for high compliant data.

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ILLUSTRATION
Suppose we want to test the following hypothesis in an experiment
with an analgesic.
H0 Mean pain relief is the same with both products
H1 Mean pain relief is not the same for the two products
We assume the following.
The difference to be detected is units in pain relief index
of (0 to 4)
Level of significance α = 0.05 for a two-sided test
Power (1-β) = 0.80
Variability estimate from past studies, within group standard
deviation, s=3.

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CALCULATION OF SAMPLE SIZE
We use the following formula to get sample size per group (N).
With 10% drop out rate, we can choose the same size as 20 per
group.

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TYPES OF HYPOTHESES
• Sample size could differ with the type of hypothesis as well. The three
common type of hypotheses encountered are the following:
• Superiority hypothesis
H0: ∆ = 0
H1: ∆ ≠ 0, or (∆ > 0, or ∆ <0 for one-tailed tests)
where ∆ indicates the treatment difference with respect to the
response variable under consideration.
• Bio-equivalence hypothesis
H0: ∆ > ∆E or ∆ < -∆E
H1: ∆E ≤ ∆ ≤ ∆E where ∆E is a clinically relevant equivalence margin
(usually 10%).
• Non-inferiority hypothesis
H0: ∆ > ∆NI
H1: ∆ ≤ ∆NI where ∆NI is a clinically relevant non-inferiority margin
(usually 10%).

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ICH E9 - 3.5 SAMPLE SIZE
• The method by which the sample size is calculated should be given
in the protocol, together with the estimates of any quantities used in
the calculations (such as variances, mean values, response rates,
event rates, difference to be detected). The basis of these
estimates should also be given.
• The sensitivity of the sample size estimate to a variety of deviations
from these assumptions involved could be investigated. This may
be facilitated by providing a range of sample sizes appropriate for a
reasonable range of deviations from assumptions.
• In confirmatory trials, assumptions should normally be based on
published data or on the results of earlier trials.

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ICH E9 - 3.5
• Conventionally the probability of type I error is set at 5% or less
or as dictated by any adjustments made necessary for
multiplicity considerations;
• The probability of type II error is conventionally set at 10% to
20%;
• These standards could also be set to agree with sponsor’s
interest especially in the case of trials that are difficult or
impossible to repeat.
• The sample size of an equivalence trial or a non-inferiority trial
should normally be based on the objective of obtaining a
confidence interval for the treatment difference that shows that
the treatments differ at most by a clinically acceptable difference.

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THANK YOU
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