Development↦Statistic Methodology↦Study Design↦Sample Size Calculation
What is it? Why is it important?
The aim of a Sample Size Calculation (SSC) is to determine the minimum number of participants needed to address a study question. To calculate and decide on an applicable sample size, two main statistical frameworks are used:
- The hypothesis testing: the primary outcome / endpoint is assessed with a statistical test (e.g. the difference between an intervention and control group). In a hypothesis testing framework, two competing hypotheses are formulated, the:
- Null hypothesis (H0) corresponds to the hypothetical claim that the treatment effect does not exist (e.g. no effect)
- Alternative hypothesis (Ha) - contradicts the null hypothesis (e.g.claims the existence of a treatment effect)
- The Precision-based approach: The aim is to estimate a quantity with a certain accuracy. For example, the frequency of patients with a cardiac event (e.g. with a precision of +/- 2.5%), in other words with a certain width of the Confidence Interval (CI)
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The goal of hypothesis testing is to quantify the extent to which the null hypothesis is plausible in light of the data.
The most widely accepted way of quantifying evidence against the null hypothesis is to use the p-value. Given that the null hypothesis is true, the p-value is defined as the probability of obtaining a result equal to or more extreme than what was observed. The smaller the p-value, the stronger the evidence against the null hypothesis.
For example, a p-value of 0.001 means that if the null hypothesis was true, then we have a chance of 1 out of 1000 to observe a result equal or more extreme as the current one, i.e., the null hypothesis is not compatible with the observed data.
In a hypothesis testing framework, the key ingredients to calculate the sample size of a study are:
- The (minimal) clinically relevant treatment effect (Δ ): the smallest difference of the primary outcome that clinicians and patients would care about, and the effect size we want to minimally detect in a study
- The variability for Δ (σ ): a greater variability of a measurement makes it harder to detect a true effect from noise and then increase the sample size
- The Type I error (α ): also known as a false positive, as it entails the rejection of the null hypothesis when it is actually true. It represents a situation where the researcher concludes that there is a significant effect when, in reality, there is no such effect Type I error is classically set at 5% of the Power (1 - β) : it is the probability of correctly rejecting the null hypothesis (e.g. a cholesterol-lowering drug has an effect on cholesterol levels). It is classically set at 80 or 90%.
What do I need to do?
Aspects to consider:
- It is important for the study SP-INV to understand how important it is to do a proper sample size calculation, and the associated risks when sample size is underestimated (i.e. the study might lack the power to answer the study question, or a potential treatment effect might be missed). As a SP-INV, consult a statistician for the SSC of your study
- The process to get to the number of participants needed for the study bears the risk of frustration for both, the SP-INV and the statistician. The SP-INV just wants to know the number that must be included in a proposal/protocol/grant application, while the statistician cannot provide a number before having received the required information form the SP-INV needed to perform a SSC. A good interdisciplinary collaboration and understanding between study SP-INV and statistician is crucial.
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For a sample size calculation the following information should be provided to the statistician:
- The objective of your study, which will determine the statistical framework of your study
- The primary outcome / endpoint, including variable type (e.g. continuous, categorical, binary, count)
- The variability of your study outcome / endpoint (e.g. expected standard deviation of your continuous variables)
- The (minimal) clinically relevant treatment effect
- The availability and ability to recruit the required number of study participants can be very challenging
- Each additionally recruited participant increases work load and study budget
Where can I get help?
Your local Research Support Centre↧ can assist you with experienced staff regarding this topic
Basel, Departement Klinische Forschung (DKF), dkf.unibas.ch
Lugano, Clinical Trials Unit (CTU-EOC), ctueoc.ch
Bern, Department of Clinical Research (DCR), dcr.unibe.ch
Geneva, Clinical Research Center (CRC), crc.hug.ch
Lausanne, Clinical Research Center (CRC), chuv.ch
St. Gallen, Clinical Trials Unit (CTU), h-och.ch
Zürich, Clinical Trials Center (CTC), usz.ch
SCTO Research Tools & Resources
External Links
- SCTO Platforms: precise –precision based sample size calculation
- Statistical Power and Sample Size Calculation Tools
References
ICH GCP E6(R3) Guideline – see in particular:
- Essential records table: documentation statistical consideration
- 3.11.4.5.4 Monitoring of clinical trials
- 3.16.2 b Statistical programming
- B.10.2 Statistical consideration
ICH Topic E9 statistical Principles for Clinical Trials – see in particular
- 3.5 Sample size
- 4.4 Sample size adjustment
ICH Topic E8(R1) General considerations for clinical studies - see in particular
- 5.1 Study population
- 5.6 Statistical analysis
Swiss Law
ClinO – see in particular article
- Art. 2b Definition of intervention
ClinO-MD – see in particular article
- Art. 2a Definition of clinical intervention
- Art. 2a Definition of performance study
HRO – see in particular article
- Art. 3a Definition of research