### Power and sample size

The power and sample size estimates are indicators of the number of patients required for a study. A majority of clinical studies involve a small sample of patients who have a specific characteristic, rather than the entire population. This sample is then used to infer the entire population.

Statistics inference was used in previous articles published in this series of statistics. This is to establish if the results are real or if they were just random. We can eliminate bias from the study design, such as blinding or randomization, to reduce the chance of results being accidental. The number of patients that were studied can also influence the likelihood that our results could be wrong. We intuitively assume that the larger the population being studied, the more accurate we will be in determining the true population. How many people do we have to study to find the right answer?

### What is power and sample size and why does it matter?

Researchers use power and sample size estimations to estimate the number of subjects required to answer the research question (or null hypothesis).

One example is the case of thrombolysis after acute myocardial injury (AMI). Although clinicians believed that this treatment would be beneficial given the etiology of AMI for many years, subsequent studies have failed to support it. The important, but small benefit of thrombolysis only became evident after the completion of sufficiently powered “mega-trials”.

These trials generally compared thrombolysis with placebo, and often had a primary outcome of mortality at a specific number of days. For example, it could have been possible to compare the day 21 mortality rate of thrombolysis with placebo. Two hypotheses are important to consider.

- The null hypothesis states that there is no mortality difference between treatments.
- Another hypothesis is that the mortality rates of different treatments are different.

There are two types of errors that can be made when trying to decide whether two groups are identical (accepting null hypothesis) and different (accepting alternative hypothesis). These errors are known as type I and type II.

When we incorrectly reject the null hypothesis (that is, it’s true and there’s no difference between them) and report a difference among the two groups being examined, this is called a type I error.

Type II errors are when we incorrectly accept the null hypothesis (that is, false and there is an actual difference between the groups) and then report that there is no difference.

We can use power calculations to determine how many patients we need to avoid making a type I error or type II error.

Power is often used to refer to all research sample sizes. Simply speaking, power refers to how many patients are required to avoid type II errors in a comparative study. The term sample size estimation, which encompasses more than the type II error and can be applied to all types of studies, is more comprehensive. The terms are interchangeable in common parlance.

### What Affects the Power of a Study?

The power of a study can be affected by many factors. These factors should be taken into consideration early in the study’s development. We have some control over certain factors, but not all.

### Precision and variance in measurements of any sample

What is the point of a study that doesn’t find any difference? We can only calculate a probability distribution for any given result from a patient sample that will indicate the true population value. 95% confidence intervals are the best-known example. The number of subjects that were studied determines the size of the confidence interval. The more subjects we study, the more accurate we can be in determining the true population value.

Figure 1 shows that the probability distribution for a single measurement is narrower if there are more subjects. The mean in group 1 is 5, with large confidence intervals (3-7). The confidence intervals (3.5-6.5) have been narrowed by doubling the number patients studied. This gives us a more accurate estimate of the true population average.