Efficacy Evaluation for Monotherapies in Two-by-Two Factorial Trials

Abstract

For factorial clinical trials in which two monotherapy treatments under study can interact only in the presence of treatment effects for each treatment, the always-pooled test statistic using data from all four groups has a correct size in detecting the simple effect of an individual treatment used alone. However, this test statistic may have an unbounded bias in estimation of the simple effect. The never-pooled test statistic that uses only data from the treatment group not receiving the other treatment has poor precision for estimating the simple effect. Two alternative test statistics under consideration are the two-stage statistic involving a preliminary test of treatment interaction and the maximum test statistic taking the larger of the always-pooled and the never-pooled statistics. The power, bias, and mean square error of all four tests are compared. When negative interactions exist, the two-stage and maximum statistics are generally superior to the always-pooled statistic and compare reasonably well with the never-pooled statistic; the maximum statistic seems slightly more favorable than the two-stage statistic. The two-stage statistic is the best choice when a treatment interaction can be large.

Economic evaluation of factorial randomised controlled trials: challenges, methods and recommendations

“…By contrast, excluding interactions will bias NMB estimates whenever treatment effects are not genuinely additive 13, 15, 16, 17. Non‐qualitative interactions in NMB will change the magnitude of differences between treatments, while qualitative interactions will change the ranking of treatments.…”

“…Analyses allowing for interactions give unbiased estimates of the difference between 0 and a 16, 17 and therefore unbiased estimates of the expected NMB of each treatment. By implication, this means that allowing for interactions and considering the four cells as mutually exclusive alternatives must give the correct ranking of cells by NMB and therefore correctly identify the treatment with highest NMB.…”

“…This term has been used by several recent factorial trials citing that review (e.g. 18, 19), although the earlier literature tends to refer only to analyses of this type as those estimating ‘simple effects’ 16, 17, 20, 21 or conducting comparisons between cell means without reference to a specific term 21. (considering each combination of factors as a separate treatment) and regression analyses including interaction term(s) almost always have lower statistical power than at‐the‐margins analysis 17 but are always unbiased 16, 17. …”

“…They therefore produce biased estimates whenever the true interaction is not zero 13, 15, 16, 17. 2

Bias is a systematic tendency to over‐ or underestimate the parameter of interest.

…”

“…This term has been used by several recent factorial trials citing that review (e.g. 18, 19), although the earlier literature tends to refer only to analyses of this type as those estimating ‘simple effects’ 16, 17, 20, 21 or conducting comparisons between cell means without reference to a specific term 21.…”