An Evaluation of Statistical Methods for Analyzing Follow-Up Gaussian Laboratory Data with a Lower Quantification Limit

Laboratory data with a lower quantification limit (censored data) are sometimes analyzed by replacing non-quantifiable values with a single value equal to or less than the quantification limit, yielding possibly biased point estimates and variance estimates that are too small. Motivated by a three-period, three-treatment crossover study of a candidate vaginal microbicide in human immunodeficiency virus (HIV)-infected women, we consider four analysis methods for censored Gaussian data with a single follow-up measurement: nonparametric methods, mixed models, mixture models, and dichotomous measures of a treatment effect. We apply these methods to the crossover study data and use simulation to evaluate the statistical properties of these methods in analyzing the treatment effect in a two-treatment parallel-arm or crossover study with censored Gaussian data. Our simulated data and our mixed and mixture models consider treated follow-up data with the same variance as the baseline data or with an inflated variance. Mixed models have the correct type I error, the best power, the least biased Gaussian parameter treatment-effect estimates, and appropriate confidence interval coverage for these estimates. A crossover study analysis with a period effect can greatly increase the required study sample size. For both designs and both variance assumptions, published sample-size estimation methods do not yield a good estimate of the sample size to obtain the stated power.