Sample size requirements for separating out the effects of combination treatments: randomised controlled trials of combination therapy vs. standard treatment compared to factorial designs for patients with tuberculous meningitis

Abstract

Background: In certain diseases clinical experts may judge that the intervention with the best prospects is the addition of two treatments to the standard of care. This can either be tested with a simple randomized trial of combination versus standard treatment or with a 2 x 2 factorial design.

Methods: We compared the two approaches using the design of a new trial in tuberculous meningitis as an example. In that trial the combination of 2 drugs added to standard treatment is assumed to reduce the hazard of death by 30% and the sample size of the combination trial to achieve 80% power is 750 patients. We calculated the power of corresponding factorial designs with one- to sixteen-fold the sample size of the combination trial depending on the contribution of each individual drug to the combination treatment effect and the strength of an interaction between the two.

Results: In the absence of an interaction, an eight-fold increase in sample size for the factorial design as compared to the combination trial is required to get 80% power to jointly detect effects of both drugs if the contribution of the less potent treatment to the total effect is at least 35%. An eight-fold sample size increase also provides a power of 76% to detect a qualitative interaction at the one-sided 10% significance level if the individual effects of both drugs are equal. Factorial designs with a lower sample size have a high chance to be underpowered, to show significance of only one drug even if both are equally effective, and to miss important interactions.

Conclusions: Pragmatic combination trials of multiple interventions versus standard therapy are valuable in diseases with a limited patient pool if all interventions test the same treatment concept, it is considered likely that either both or none of the individual interventions are effective, and only moderate drug interactions are suspected. An adequately powered 2 x 2 factorial design to detect effects of individual drugs would require at least 8-fold the sample size of the combination trial.

Trial registration: Current Controlled Trials ISRCTN61649292.

Figure 1

Power curves for 2 × 2 factorial designs without an interaction assuming a hazard ratio of combination treatment versus standard treatment of 0.7 and an overall mortality of 35%. Figure legend text: The black, dashed blue, and red lines correspond to the probability that the more potent individual treatment, at least one of the two treatments or both treatments jointly, respectively, reach statistical significance. The orange and green lines correspond to the probability of a significant difference between combination treatment and standard treatment in the factorial trial and in a 2-group trial of combination treatment versus standard treatment with equal sample size, respectively.

Figure 2

Power curves for 2 × 2 factorial designs with an interaction assuming equal individual contributions from both treatments corresponding to hazard ratios of 0.84 and an overall mortality of 35%. Figure legend text: The blue lines correspond to the power of the interaction test (solid line: one-sided 2.5% significance level, dashed line: one-sided 10% significance level), the black line to the power of the main effect for treatment A, and the green line to the power of a 2-group trial of combination treatment versus standard treatment with equal sample size.