67 IUI success and prognosis of natural conception 4 Adjusting for patient characteristics that differed between treated and untreated couple In our data, couples were not randomized to either expectant management or IUI-OS. Thus, patients starting IUI could differ from those who did not in terms of important predictors of conception such as female age or duration of subfertility. In order to achieve groups that are on average similar, we opted for a statistical technique called applied iterative inverse probability weighting (14-16). By reweighting patients’ contribution to the data, these characteristics are balanced. Details on how we derived the weights to adjust for these differences are given in the Supplementary Data. We chose to balance for the same patient characteristics as in the previous study with the exception of fertility clinic, as that would lead to very unbalanced weights: female age, duration of subfertility, primary or secondary subfertility, total motile sperm count, referral status and the presence of one-sided tubal pathology (17, 18). We calculated the mean weight to assess potential inflation of the effective sample size induced by the weighting, which is ideally around 1 (19). We assessed the degree of balance in patient characteristics before and after weighting using the standardized mean difference between the treated and untreated group in each of the mimicked trial dataset. A lower standardized mean difference between groups represents better balance and a value below 0.10 generally indicates no important difference (14, 15). Statistical analysis We analysed the weighted mimicked trial datasets using a pooled Cox proportional hazards model with IUI-OS or expectant management as a treatment covariate. We calculated an overall hazard ratio by stratifying on the 13 mimicked trials. We used a robust sandwich variance estimator to adjust precision measures since couples can be included in multiple mimicked trial datasets (20). Modification of the estimated effect of IUI-OS by the prognosis of natural conception To address whether the effect of starting IUI-OS depends on the decreasing prognosis of natural conception of the individual couple, we added the prognosis and a treatmentby-prognosis interaction term to the model. We calculated a time-updated prognosis of natural conception over the next 6 cycles at the start of each mimicked trial dataset by using an existing dynamic prediction model that comprises female age, duration of subfertility, primary or secondary subfertility, percentage of progressive motile sperm, referral by a general practitioner or specialist, and the unsuccessful number of menstrual cycles since the fertility workup (18). The prognosis for a couple that we used is thus not one fixed value throughout the study but decreases after consecutive failed natural cycles. We transformed the updated prognosis by taking the complementary log-log of
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