68 Chapter 4 its value such that it is linear on the log-hazard scale used by the Cox model (21). We included the complementary log-log of this updated prognosis as a main effect, the main effect for treatment and the treatment-by-prognosis interaction effect in the pooled Cox model. The weighting procedure was adjusted slightly for this analysis because the difference in prognosis between groups was adjusted for by adding it to the model as a main effect (22), (see also the Supplementary Materials). For three hypothetical couples, we visually depicted the relationship between their worsening prognoses and the accompanying 6-month cumulative predicted probability of conception following expectant management or starting IUI-OS, as treatment is initiated later. The first example is a couple referred by their general practitioner, where the female partner is nulliparous and 32 years old, the couple has 1 year of subfertility at the time of completion of the fertility workup and the semen analysis showed 37% progressively motile sperm. In this case, the estimated prognosis of natural conception over the first 6 cycles is 25%. A second couple with the same characteristics except for a 2 year duration of subfertility at the completion of the fertility workup has a prognosis of 20% while a third couple with the same characteristics but for a 3.5-year duration of subfertility has a prognosis of 15%. At the time of the completion of their fertility workup, these couples have prognoses of 25%, 20% and 15% respectively over 6 cycles, which translates to approximately 40%, 32% and 25% respectively over 13 cycles i.e. one year (18). The chances of natural conception for these three hypothetical couples decrease over time based on the number of unsuccessful menstrual cycles between the diagnosis/HSG and the start of a landmark. Estimated cumulative probabilities of ongoing pregnancy from this model are derived from the separate mimicked trials that all have different observed conception rates, thus although predictions are expected to decrease over time, our estimates may fluctuate. We considered an absolute difference of more than five percentage points between estimates of the cumulative ongoing pregnancy rates, estimated at completion of the fertility workup, to indicate a benefit of IUI-OS. In addition to modelling the impact of prognosis and consecutive failed natural cycles on the effect of treatment, we assessed if the effect of IUI-OS depends on the time of initiation of treatment by adding an additional interaction between treatment and landmark time point to the pooled Cox model already including treatment, prognosis and the treatment-by-prognosis interaction. If the interaction between prognosis and treatment yielded a better fit, we also added a three-way interaction between treatment,
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