Treatment comparisons for a partially categorical outcome applied to a biomarker with assay limit.

The plasma level of HIV-RNA has been shown to be a strong prognostic biomarker for clinical progression and death in HIV infected patients and is widely used as the primary outcome in clinical trials to evaluate antiretroviral treatments. Currently approved assays to measure HIV-RNA levels have a lower limit of reliable quantification (LoQ). Current regulatory guidelines recommend using the proportion of patients achieving HIV-RNA levels below the assay limit at a certain time point (e.g. 24 or 48 weeks) as the primary endpoint for regulatory approval. However, a substantial decrease in HIV-RNA that does not go below the LoQ still is considered clinically beneficial for patients with advanced diseases who have failed many other therapies and are unlikely to maximally suppress the virus and achieve HIV-RNA levels below the LoQ. An experimental treatment may not be distinguishable from a control solely in terms of the proportions of patients whose HIV-RNA levels fall below the LoQ. The sensitivity of the comparison between the experimental treatment and the control could be increased by considering as well the difference between the treatments with respect to the HIV-RNA reductions of patients not achieving HIV-RNA levels below the LoQ. In this paper, we introduce a best-rank analysis which assigns the best rank to patients who achieve the HIV-RNA levels below the LoQ and applies the Mann-Whitney-Wilcoxon rank test to compare the two treatment groups. The Mann-Whitney-Wilcoxon statistic is shown to be a weighted sum of two statistics: one to compare the proportions of patients achieving the HIV-RNA levels below the LoQ and one to compare the viral reductions in patients with HIV-RNA levels above the LoQ. The corresponding statistical null and alternative hypotheses and the clinical interpretations of this best-rank test procedure are also discussed. An example is used to illustrate this approach and a simulation study is used to compare this approach with other methods.