Sample size recalculation based on the overall success rate in a randomized test-treatment trial with restricting randomization to discordant pairs

Abstract

Background: Randomized test-treatment studies are performed to evaluate the clinical effectiveness of diagnostic tests by assessing patient-relevant outcomes. The assumptions for a sample size calculation for such studies are often uncertain.

Methods: An adaptive design with a blinded sample size recalculation based on the overall success rate in a randomized test-treatment trial with restricting randomization to discordant pairs is proposed and evaluated by a simulation study. The results of the adaptive design are compared to those of the fixed design.

Results: The empirical type I error rate is sufficiently controlled in the adaptive design as well as in the fixed design and the estimates are unbiased. The adaptive design achieves the desired theoretical power, whereas the fixed design tends to be over- or under-powered.

Conclusions: It may be advisable to consider blinded recalculation of sample size in a randomized test-treatment study with restriction of randomization to discordant pairs in order to improve the conduct of the study. However, there are a number of study-related limitations that affect the implementation of the method which need to be considered.

Keywords: Adaptive design; Diagnostic test; Discordance design; Overall success rate; Sample size recalculation.

Fig. 1

Results for the empirical type I error vs. the difference between true and initially assumed overall success rate for the 144 scenarios ($\pi ϵ\left\{0.1,,,0.2,,,0.3\right\},\omega ϵ\left\{0.05,,,0.1,,,0.15\right\},S{e}_A,S{p}_Aϵ\left\{0.8,,,0.9\right\},S{e}_B,S{p}_Bϵ\left\{0.6,,,0.7,,,0.8\right\}$) using minimal discordant rate, stratified by the prevalence. The empirical type I error rates for the fixed design and the adaptive design containing a re-estimation of the overall success rate are compared to each other. The black dotted line marks the desired theoretical type I error rate of 5% and the black solid lines mark the respective 95% prediction interval based on the Monte Carlo standard error in the simulation

Fig. 2

Results for the empirical power vs. the difference between true and initially assumed overall success rate for the 144 scenarios ($\pi ϵ\left\{0.1,,,0.2,,,0.3\right\},\omega ϵ\left\{0.05,,,0.1,,,0.15\right\},S{e}_A,S{p}_Aϵ\left\{0.8,,,0.9\right\},S{e}_B,S{p}_Bϵ\left\{0.6,,,0.7,,,0.8\right\}$) using minimal discordant rate, stratified by the prevalence. The empirical power in the fixed design is compared to the adaptive design containing a re-estimation of the overall success rate. The black dotted line marks the desired theoretical power of 80%

Fig. 3

Results of the calculated initial, adjusted and true sample sizes of discordant cases vs. the difference between true and initially assumed overall success rate for the 144 scenarios ($\pi ϵ\left\{0.1,,,0.2,,,0.3\right\},\omega ϵ\left\{0.05,,,0.1,,,0.15\right\},S{e}_A,S{p}_Aϵ\left\{0.8,,,0.9\right\},S{e}_B,S{p}_Bϵ\left\{0.6,,,0.7,,,0.8\right\}$) using minimal discordant rate (based on data generated under the null hypothesis), stratified by the prevalence