Sample size and statistical power assessing the effect of interventions in the context of mixture distributions with detection limits

Often in randomized clinical trials and observational cohort studies, a non-negative continuously distributed response variable is measured in treatment and control groups. In the presence of true zeros for the response variable, a two-part zero-inflated log-normal model (which assumes that the data has a probability mass at zero and a continuous response for values greater than zero) is usually recommended. However, in some environmental health and human immunodeficiency virus (HIV) studies, quantitative assays for metabolites of toxicants, or quantitative HIV RNA measurements are subject to left-censoring due to values falling below the limit of detection (LD). Here, a zero-inflated log-normal mixture model is often suggested since true zeros are indistinguishable from left-censored values due to the LD. When the probabilities of true zeros in the two groups are not restricted to be equal, the information contributed by values falling below LD is used only to estimate the probability of true zeros in the context of mixture distributions. We derived the required sample size to assess the effect of a treatment in the context of mixture models with equal and unequal variances based on the left-truncated log-normal distribution. Methods for calculation of statistical power are also presented. We calculate the required sample size and power for a recent study estimating the effect of oltipraz on reducing urinary levels of the hydroxylated metabolite aflatoxin M₁ (AFM₁) in a randomized, placebo-controlled, double-blind phase IIa chemoprevention trial in Qidong, China. A Monte Carlo simulation study is conducted to investigate the performance of the proposed methods.