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Supplemental Material for Two strategies for partner notification and partner HIV self-testing reveal no evident predictors of male partner HIV testing in antenatal settings: A secondary analysis by Andrew Kumwenda, Ann Marie Kathryn Weideman, Lauren Aiko Graybill, Matthew Kevin Dinwiddie, Kellie Freeborn, Mildred M Lusaka, Rose Lungu, Wilbroad Mutale, Nora E Rosenberg, Margaret Kasaro, Katie R. Mollan and Benjamin H Chi in International Journal of STD & AIDS.

In an analysis of randomized trials, use of efavirenz for treatment of human immunodeficiency virus (HIV) infection was associated with increased suicidal thoughts/behaviors. However, analyses of observational data have found no evidence of increased risk. To assess whether population differences might explain this divergence, we transported the effect of efavirenz use from these trials to a specific target population. Using inverse odds weights and multiple imputation, we transported the effect of efavirenz on suicidal thoughts/behaviors in these randomized trials (participants were enrolled in 2001-2007) to a trials-eligible cohort of US adults initiating antiretroviral therapy while receiving HIV clinical care at medical centers between 1999 and 2015. Overall, 8,291 cohort participants and 3,949 trial participants were eligible. Prescription of antidepressants (19% vs. 13%) and injection drug history (16% vs. 10%) were more frequent in the cohort than in the trial participants. Compared with the effect in trials, the estimated hazard ratio for efavirenz on suicidal thoughts/behaviors was attenuated in our target population (trials:hazard ratio (HR) =2.3 (95% confidence interval (CI): 1.2, 4.4); transported: HR=1.8 (95% CI: 0.9, 4.4)), whereas the incidence rate difference was similar (trials: HR=5.1 (95% CI: 1.6, 8.7); transported: HR=5.4 (95% CI: -0.4, 11.4)). In our target population, there was greater than 20% attenuation of the hazard ratio estimate as compared with the trials-only estimate. Transporting results from trials to a target population is informative for addressing external validity.

Accurate power calculations are essential in small studies containing expensive experimental units or high-stakes exposures. Herein, exact power of the Wilcoxon Mann-Whitney rank-sum test of a continuous variable is formulated using a Monte Carlo approach and defining P(X < Y) = p as a measure of effect size, where X and Y denote random observations from two distributions hypothesized to be equal under the null. Effect size p fosters productive communications because researchers understand p = 0.5 is analogous to a fair coin toss, and p near 0 or 1 represents a large effect. This approach is feasible even without background data. Simulations were conducted comparing the exact power approach to existing approaches by Rosner & Glynn (2009), Shieh et al. (2006), Noether (1987), and O'Brien-Castelloe (2006). Approximations by Noether and O'Brien-Castelloe are shown to be inaccurate for small sample sizes. The Rosner & Glynn and Shieh et al. approaches performed well in many small sample scenarios, though both are restricted to location-shift alternatives and neither approach is theoretically justified for small samples. The exact method is recommended and available in the R package wmwpow. KEYWORDS: Mann-Whitney test, Monte Carlo simulation, non-parametric, power analysis, Wilcoxon rank-sum test