# What to consider when planning the sample size for a non-interventional study

For both, interventional and non-interventional studies, the determination of an “adequate” sample size is an essential part of the statistical planning process. First and foremost, the sample size estimation should relate to the specific **study objectives**.

### The “power approach” for sample size estimations in clinical trials

In randomised clinical trials, the calculation of the required number of patients is generally based on a comparison between the** treatment groups** under investigation. As an example, consider a study designed to show superiority of a test medication over placebo with respect to a specified primary efficacy variable. In this case, the so-called “power approach” is applied: The sample size is calculated in such a way that a pre-defined clinically relevant difference between both treatment groups can be detected with a given high probability. This probability is called the **power of the study** (mostly 80% or 90%).

For the vast majority of non-interventional studies (NIS), this approach is not feasible, simply because it is usually not the objective of a NIS to compare different treatments.

### The justification (rather than calculation) of a sample size in the non-interventional setting

The class of NIS comprises many types of investigations, e.g. observational studies, cross-sectional studies or registries. Accordingly, various possible **objectives and associated approaches** exist for determining a reasonable patient number.

There are many situations where it is not feasible to perform a formal statistical sample size calculation for a NIS. However, it is still required to provide a statement in the protocol justifying that the chosen sample number is **adequate to investigate the objectives of the study**. Sometimes “non-statistical” criteria, like the incidence of the underlying disease in the investigated population or organisational restrictions, have to be taken into consideration. Concerning epidemiological studies, the representativeness of the investigated group of patients could also be an issue. For many NIS, however, it is the lack of a computational basis which appoints the phrase “**sample size justification**” as more appropriate than “sample size calculation”.

### When the aim of a NIS is to measure an effect

However, there are designs and associated objectives of NIS where a statistical sample size estimation is straightforward. Let us consider the most widely used type of NIS, the **post-marketing observational study (PMOS) **designed to investigate a particular medication under practice conditions in a large group of patients.

One common aim of a PMOS is to estimate the proportion of patients who reach a specific treatment goal in the course of the observation period, e.g. the remission of the underlying disease. It is clear that larger sample numbers allow for **higher precision of the estimation**, i.e. the calculated proportion of patients is more stable and more reliable than for smaller patient numbers.

Precision in this context is measured by the length of a so-called **confidence interval** which is calculated from the resulting study data. Higher sample numbers per se lead to smaller confidence intervals which correspond to higher precision of the estimation. The sample size calculation, thus, can be based on the requirement that the length of the confidence interval will not exceed a lower limit, or, in other words, that the estimator is sufficiently precise.

### Calculating the sample size to detect adverse drug reactions

Another classical objective of observational studies is the systematic search for **adverse drug reactions (ADR)**. Due to the restrictions in sample size, phase III clinical trials are at best capable to detect frequent ADRs, mostly by chance, and without providing sufficient data to estimate the underlying incidence rates.

With an observational study, though, it is possible to detect rare ADRs, at least with a pre-specified (high) probability. The** incidence rate** of a specified ADR describes the frequency at which the ADR occurs in the patient population and is often expressed as, e.g., 0.01% or “1 in 10000 patients”. However, an incidence rate of 0.01% does not imply that in 10000 treated patients exactly 1 specific ADR will occur. The incidence rate is just a statistical expression describing what can be expected **with a high probability**. Just by chance it could also happen that no event will be observed.

This means: We cannot be sure that the specific ADR will occur in the sample, but we can **specify a high probability for the ADR to happen.** The higher this probability is, and the more we actually want to be sure, the higher is the resulting sample size.

### Example:

Suppose in an observational study it is planned to detect any adverse drug reactions which have an **incidence rate of at least 0.1%** (which means they are expected to occur once in 1000 treated patients, or more frequently) **with a probability of at least 95%**.

How many patients do we need to achieve this?

The result of the sample size calculation is 2996 patients.

In summary, depending on your type of non-interventional **study design** and your specific **study objectives**, there are different approaches for the planning of your sample size. That is, the decision on **what you want to show** with your NIS also defines the strategy for your sample size estimation.

Picture: Ethan Weil