Medium matters: modeling the impact of solid medium performance on tuberculosis trial sample size requirements

Abstract

Setting: Two-month solid medium culture conversion is a commonly used, if suboptimal, endpoint for phase 2 anti-tuberculosis treatment trials.

Objective and design: To model the effect of the performance characteristics (sensitivity and contamination rate) of solid medium on required sample size for a two-arm clinical trial with 85% true (gold standard) culture conversion in the control and 95% in the experimental arm.

Results: Increasing sensitivity and decreasing contamination reduced the sample size from 239 subjects/arm (60% sensitivity, 30% contamination) to 138 subjects/arm (95% sensitivity, 1% contamination).

Conclusion: Optimizing solid medium has significant potential to reduce sample size and increase the efficiency of tuberculosis clinical trials.

Figure 1

Hypothetical 2-arm study design comparing solid media performance for two-month culture conversion with two sputum specimens between a control arm with 85% “true” culture conversion using solid media to an experimental arm with 95% “true” culture conversion. Probabilities in all nodes are conditional probabilities that sum to 1 given the condition in the attached node to the left. For example, the conditional probabilities of the three nodes to the right of the “15% remain positive” node in the control arm, assuming 20% contamination would equal 0.2 for “1^st sputum contaminated”, (0.7 × (1−0.2))=0.56 for “1^st sputum positive” if the sensitivity of the medium were 70%, and ((1−0.7) × (1−0.2))=0.24 for “1^st sputum negative.” The conditional probabilities (0.2 + 0.56 + 0.24) sum to 1, and the actual probabilities of observing each of these outcomes would be 0.15 multiplied by the conditional probabilities.

Figure 2

Number of subjects/arm required for hypothetical study design with varying fixed sensitivities and contamination rates for solid media (varying the contamination rate between 1–30% and sensitivity between 60–95%). The top chart displays the number of subjects/arm using solid media with a sensitivity of 60–95% and fixed contamination rates of 5%, 10%, 15%, 20%, and 30%, while the bottom chart displays the number of subjects/arm using solid media with a contamination rate of 1–17% and fixed sensitivities of 75%, 85%, 90%, and 95%.