Correcting for the dependent competing risk of treatment using inverse probability of censoring weighting and copulas in the estimation of natural conception chances

When estimating the probability of natural conception from observational data on couples with an unfulfilled child wish, the start of assisted reproductive therapy (ART) is a competing event that cannot be assumed to be independent of natural conception. In clinical practice, interest lies in the probability of natural conception in the absence of ART, as this probability determines the need for therapy. We thus want to estimate the marginal cumulative pregnancy distribution. Without assumptions on the dependence structure between the two competing events, this marginal distribution is not identifiable. We first use inverse probability of censoring weighting assuming that the factors influencing the choice to start ART are known. Then, we parameterize the event distributions for conception and for start of ART and use copulas to account for the dependency between both events. By using these two ways of correcting for the dependent risk of treatment, we obtain a plausible estimation region for the cumulative pregnancy curve and for the prognostic effect of tubal tests.