In response to the letter by Strassle et al, we would like to provide a rejoinder regarding some of the salient points raised by these authors. To do so, it would be useful to address each of these issues separately to clarify some of the confusion that may exist about the statistical analyses in our article.1
The first issue raised by Strassle et al concerned the treatment of loss to program in our analysis. Loss to program (also called loss to follow-up or patient dropout), particularly in the low- to middle-income settings where we work, prevents complete observation of a number of patient outcomes. Of most relevance to our article, loss to program limited observation of incident pregnancies but also other relevant factors such as re-engagement in HIV care at programs outside the initial clinical site and mortality after dropout. For this reason, we considered loss to program as a competing risk rather than an event censoring the time until the experience of an incident pregnancy, our endpoint of interest. It is critical here to recognize that this choice has no bearing on the ultimate numerical estimates of the impact of antiretroviral therapy (ART) on the likelihood (hazard) of incident pregnancy but rather affects solely the interpretation of the results. The reason is that, operationally, loss to program abbreviated the follow-up time in all analyses presented and thus resulted in censoring along with all other events limiting complete follow-up such as death and known transfers, in addition to administrative censoring (end of observation due to database closure) resulting in the end of follow-up. When loss to program is modeled as a competing event, ART is considered a risk factor for the cause-specific hazard of experiencing an incident pregnancy versus the cause-specific hazards of experiencing other events such as death, loss to program, or transfer to another care and treatment facility. So, absent some correction on the current estimates resulting from additional data obtained from some or all the dropouts,2,3 or sensitivity analyses based on historical or otherwise external data, our estimates of the effect of ART on incidence pregnancy do not change whether loss to program is viewed as a competing risk or a censoring event.
Strassle et al additionally noted that loss to program may have downwardly biased estimates of the impact of ART on incident pregnancy. Although we concur with this assessment, we do not agree that attenuation of the estimates is necessarily the result of informative censoring induced by loss to program. As is well known,4 even noninformative censoring can attenuate associations between a risk factor and the outcome of interest. Informative censoring, however, may result in underestimation or overestimation of the true effect,4,5 as the authors correctly state. However, their proposed remedy, inverse probability of censoring weighting methods,6 is unlikely to fully address these biases because data in patients lost to program in this setting are, most likely, not missing at random,7 a key assumption in inverse probability of censoring weighting methods. In the presence of data missing not at random, the effect of ART could have been underestimated or overestimated in ways that are not obvious. For example, it could have been underestimated given the propensity of pregnant women to drop out of care at higher rates compared with the general patient population (see for example the references cited by Strassle et al8–11).