A zero-inflated log-normal mixture model (which assumes that the data has a probability mass at zero and a continuous response for values greater than zero) with left censoring due to assay measurements falling below detection limits has been applied to compare treatment groups in randomized clinical trials and observational cohort studies. The sample size calculation (for a given type I error rate and a desired statistical power) has not been studied for this type of data under the assumption of equal proportions of true zeros in the treatment and control groups. In this article, we derive the sample sizes based on the expected differences between the non-zero values of individuals in treatment and control groups. Methods for calculation of statistical power are also presented. When computing the sample sizes, caution is needed as some irregularities occur, namely that the location parameter is sometimes underestimated due to the mixture distribution and left censoring. In such cases, the aforementioned methods fail. We calculated the required sample size for a recent randomized chemoprevention trial estimating the effect of oltipraz on reducing aflatoxin. A Monte Carlo simulation study was also conducted to investigate the performance of the proposed methods. The simulation results illustrate that the proposed methods provide adequate sample size estimates. However, when the aforementioned irregularity occurs, our methods are restricted and further research is needed.
Bibliographical noteFunding Information:
The authors are grateful to the Editor, two anonymous referees for many constructive suggestions and comments, which greatly improved the quality of the paper. Dr. Chu and Dr. Cole were supported in part by the National Institutes of Health through the data coordinating centers for the Pediatric Chronic Kidney Disease cohort study (UO1-DK-066116), the Multicenter AIDS Cohort Study (UO1-AI-35043), and the Women's Interagency HIV Study (UO1-AI-42590), and NIH/NIEHS program project grant P01 ES06052.
- Detection limit
- Mixture models
- Sample size
- Statistical power