### Sample size calculation – continuous outcome variable

Jianrong Wu
2018 Southwest Respiratory and Critical Care Chronicles
different outcome variable types. In this issue, we will focus on situations in which the outcome is a continuous variable, e.g. drug concentration in the blood. Statistical power and effect size The majority of clinical trials are designed to answer a specific research question. For example, a study might compare two groups and have both null and alternative hypotheses. In general, the null hypothesis states that there is no difference between groups, and the alternative states that there is a
more » ... significant difference. Based on such a hypothesis, we can define type I and type II errors as follows: A type I error is the probability of rejecting the null hypothesis (no difference) when the null hypothesis is true, while a type II error is the probability of not rejecting the null hypothesis when the null hypothesis is not true. The statistical power is the complement of type II error, i.e., rejection of the null hypothesis when the null hypothesis is not true. In other words, statistical power is the probability of a test identifying a difference when such a difference truly exists. Due to random sampling, type I and type II errors are unavoidable in statistical tests, and the error rates that are acceptable need to be pre-specified in sample size calculation. In general, the type I error rate is often set at 0.05, meaning that 1 out 20 trials will potentially make an incorrect conclusion that a difference exists when the truth is that there is no difference. The statistical power is often set at 80%, meaning that, if there is a true difference, then 80% of the time this difference will be detected by such a trial. Effect size, which is the standardized mean difference between two groups, is another important piece of information needed for sample size calculation: Effect size Difference in mean Standard deviation . = We are planning to conduct a phase III randomized trial to evaluate the difference between daily short infusions and continuous infusions of a chemotherapy drug on the concentration of an active compound in the blood. We understand randomization is important in conducting such a trial. How do we determine the number of patients to be recruited? Sample size/power calculations are a very important aspect of randomized clinical trials and should be performed during the design phase of a study. Incorrect sample size calculation alone sometimes can cause the failure of a trial, including making incorrect conclusions and providing false information for clinical practice. In general, sample size of a trial should be appropriate for answering the research question. If a sample size of a trial is too small, then it might not be able to detect a difference of interest; on the other hand, if the sample size is too large, then the study will take longer and incur greater costs, and it might detect a difference that has no clinical significance. An extreme situation of the latter is to recruit all patients with a certain disease in a trial, so that the entire patient population can be studied. However, such an idea is quite problematic in many aspects, including 1) difficulty in patient recruitment; 2) a longer time to complete the trial; 3) increased costs; and 4) challenges in data analysis. In this article, we will discuss some issues associated with sample size calculation. Formulas and considerations for sample size calculation differ for 14-TTUv6n24-Wu_60-62.indd 60 07/17/18 11:05 AM