To the Editor:
Recently, 2 analyses were published from the Hormonal Contraception and Risk of HIV Acquisition Study, a multicenter cohort study specifically designed to evaluate whether hormonal contraceptive use (depot-medroxyprogesterone acetate [DMPA] or combined oral contraceptives [COCs]) alters the risk of HIV acquisition among women.1,2 A detailed description of study participants and methods has been published elsewhere.1 The main study analysis used conventional Cox proportional hazard models with time-varying hormonal contraceptive exposure to adjust for demographic and sexual risk factors. This analysis showed little or no evidence of increased risk of HIV acquisition with either DMPA (hazard ratio = 1.25 [95% confidence interval = 0.89-1.78]) or COCs (0.99 [0.69-1.42]) compared with the nonhormonal group.1 A reanalysis using a marginal structural model (MSM) to accommodate hormonal-contraceptive exposure switching and confounding with the same set of demographic and sexual risk factors found evidence for an increased HIV acquisition risk associated with DMPA (1.48 [1.02-2.15]) but not COC use (1.19 [0.80-1.76]).2
MSMs can appropriately adjust for time-dependent confounding and selection bias using the inverse-probability-of-treatment weighting (IPTW).3 Nevertheless, the model relies on certain assumptions that either cannot be verified (eg, no unmeasured confounders) or could be problematic in the data from this study4 (eg, violation of the positivity assumption due to high association between pregnancy and hormonal contraceptive use).
We conducted several sensitivity analyses to address the above concerns. First, we examined possible model misspecification in the marginal structural model by adding or removing suspected time-varying confounder(s). Second, we investigated the variability of hazard ratios estimated by MSM using a nonparametric bootstrapping procedure to obtain estimates from 1000 with replacement bootstrap samples.5 Finally, we explored possible violations of the positivity assumption when pregnancy status was included in the MSM analyses.
We found a consistently larger effect of DMPA than COCs on HIV acquisition, compared with the nonhormonal group, across various analyses (Table). DMPA also appeared to have a larger effect with MSM analyses than with the conventional Cox model when similar covariates were included in analyses. Model misspecification can cause estimated hazard ratios to vary from 1.24 (0.85-1.80) to 1.51 (1.03-2.22) for DMPA, and from 1.00 (0.69-1.47) to 1.19 (0.80-1.76) for COCs.
Compared with the results in Model 3 (the published results1), the bootstrapped estimates provided similar findings. We also note that the distributions of estimated weights were similar among MSM analyses that did not include pregnancy status; means and standard deviations were approximately 1 and 0.55, respectively, with reasonable ranges from about 0.01 to 2.64. However, when pregnancy status was included in the analysis, the distribution from untruncated weights clearly indicated the violation of positivity assumption because a large standard deviation (16.4) and a wide range of weights (from <0.01 to 3915) were observed. In general, the estimated effect becomes unstable and attenuated under that situation, with a large deviation of weights.
The validity of the MSM analysis depends on the assumption that all confounders were measured and sufficient to adjust for confounding and selection biases. The causal effect estimates could be biased if these assumptions were incorrectly specified. In these analyses, we evaluated the potential issues of model specification and the positivity assumption. These findings parallel the results from a simulation study6 that found that inclusion of more confounders (even in the absence of complete control) resulted in a decrease in bias. This observation suggests that including all possible time-varying confounders in analyses may reduce bias, as long as no finite sample bias is introduced. In addition, because current pregnancy clearly violated the positivity assumption for computing IPTW in the estimation of the hormonal contraceptive effect on HIV acquisition, alternative modeling approaches (such as structural-nested-failure-time models) should be considered.7
Details on time-dependent confounder assessment and MSM specification are available in the eAppendix (http://links.lww.com/EDE/A514).
Biostatistics Department FHI360
Research Triangle Park, NC
Stephen R. Cole
Department of Epidemiology
University of North Carolina
Chapel Hill, NC
Charles S. Morrison
Clinical Sciences Department FHI360
Research Triangle Park, NC
1. Morrison CS, Richardson BA, Mmiro F, et al. Hormonal contraception and the risk of HIV acquisition. AIDS
2. Morrison CS, Chen PL, Kwok C, et al. Hormonal contraception and HIV acquisition: reanalysis using marginal structural modeling. AIDS
3. Robins JM, Hernan MA, Brumback B. Marginal structural models and causal inference in epidemiology. Epidemiology
4. Cole SR, Hernán MA. Constructing inverse probability weights for marginal structural models. Am J Epidemiol
5. Efron B, Tibshirani RJ. An Introduction to the Bootstrap.
London: Chapman-Hall; 1993.
6. Barber JS, Murphy SA, Verbitsky N. Adjusting for Time-varying confounding in survival analysis. Sociol Methodol
7. Robins JM. Structural nested failure time models. In: Armitage P, Colton T, eds. Encyclopedia of Biostatistics
. Chichester, UK: Wiley; 1998.