Sample size estimation of skewed distributions in medical research - Vemula, Sadanandam; Dhakshanamoorthy, Kalpanapriya (Brazilian Journal of Biometrics, 2025)
The primary goal of calculating sample size is to ascertain the minimum number of samples required to identify meaningful changes in treatment outcomes, clinical parameters, or associations following data collection. Determining the sample size is the initial and crucial step in organizing a clinical trial. An improper assessment of this number could result in the approval of an ineffective medication or the rejection of an effective one. Sample size estimations should align with the intended analysis methodology. We will use generalized linear models (GLMs) to analyze the data, frequently employing normal approximations for non-normal distributions. The Binomial, Negative Binomial, Poisson, and Gamma families are specific cases where we utilize GLM theory to derive sample size formulas when comparing two means. We evaluated the performance of normal approximations by simulating various distributions using the log-link and identity-link functions. First, we examined the extent of errors in normal approximations for discrete probability distributions. Next, we applied GLM theory to derive sample size equations, which were evaluated through case studies and simulations. The Negative Binomial and Gamma distributions under study are well-suited for calculations on the link function (log) scale, often providing greater accuracy than normal approximations. However, the Binomial and Poisson distributions offer minimal advantage. The proposed method effectively calculates sample sizes when comparing the means of highly skewed outcome variables.