27 Duration of the fertility enhancing effect of HSG with oil-based contrast 2 conception leading to an ongoing pregnancy, loss to follow-up or end of study follow-up, whichever occurred first. Median follow-up was calculated as the 50th percentile in all numerical follow-up values. Pain experienced during HSG was reported using a visual analogue scale (VAS) score (range 0.0 to 10.0 in centimetres). Primary analysis For long-term follow-up up to 3 years, first a Cox proportional hazards model was fitted for time to pregnancy data with the randomization allocation, i.e. oil versus water, and the overall hazard. Scaled Schoenfeld residuals were then derived and plotted to visualize the change in log hazard ratio over time; a chi-squared test was applied to the residuals to test the plausibility of the proportional hazards assumption that ‘the relative effect is stable over time’ (14). For these tests and plots, both regular time and log-transformed time were used. The non-linear and linear interactions transformed time were added to the Cox model, and the best fitting model was determined by looking at the P-value for the interaction and/or whether the model had lowest Akaike information criterion (AIC) (15, 16). This best-fitting model was used to quantify the change of effect of oil- versus water-based contrast over time by estimating hazard ratios at different time points during follow-up: at 2 weeks of follow-up (which is directly after HSG), and after 1 month (which is the start of the next menstrual cycle after HSG), 3 months, 6 months, 9 months, 1 year, 2 years and 3 years. The number of pregnancies per group per cycle during the first 6 months after HSG and their relative risks were tabulated to look for a trend over time shortly after HSG. Sensitivity analyses Three sensitivity analyses were conducted. For the first, it was postulated that women might experience pain at HSG when the contrast fluid removed debris or mucus plugs from their Fallopian tubes. If this were the mechanism of action, there might not be any change over time in the effect of oil-based contrast versus water-based contrast in this group. To test this, the steps from the primary statistical analysis were repeated in the subgroup of women who experienced pain during the HSG procedure, defined as a pain score of 6 points or more on the VAS. Second, it was postulated that starting IVF at some point during follow-up might distort the effect of oil versus water given the hypothesis that oil-based contrast would flush debris or mucus plugs, as IVF bypasses the Fallopian tubes. For this reason, follow-up was censored, i.e. stopped, when couples started IVF, and the steps in the primary statistical analysis were repeated.
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