48 Chapter 3 Sample size Our hypothesis is that HSG with oil-based contrast will increase the live birth rate with 10% in three infertility groups: (1) women aged 39 years or older, (2) women with ovulation disorders and (3) women who have a high risk for tubal pathology. To detect an increase of 10% in live birth rate from 17 to 27%, 395 women per group are needed (alpha 1%, beta 20%, Z-test with unpooled variances as calculated in PASS 2020). Anticipating a loss to follow-up rate of 15%, the total number of participants required is 930 (465 in each arm of the trial). With this number we have 80% power to study the 10% difference in live birth rate in the intervention versus control group in the stratified design using Cochrane-Mantel-Haenzel. Statistical analysis Categorical data will be reported as absolute numbers and percentages. Normally distributed continuous variables will be summarized as means with standard deviations, and non-normally distributed continuous variables will be reported as medians with interquartile ranges. The primary analyses will done according to the intention to treat (ITT) principle, including all randomised women. Differences in live births will be expressed as crude and stratification adjusted risk ratio and absolute risk difference with associated 95% and 99% confidence intervals (CI) using log-linear binomial regression. We will construct Kaplan-Meier curves, estimating the cumulative probability of conception leading to live birth over time and use the log-rank test to assess differences. Additionally, we will do a cox proportional hazard analysis to evaluate the difference in primary outcomes over time while accounting for the subgroups and evaluating presence of interaction. Continuous outcomes will be measured at multiple time-points and will be analysed with the use of linear mixed models. We will subsequently compare intervention and control treatment within the stratified groups (1) women aged 39 years or older, (2) women with ovulation disorders and (3) women who have a high risk for tubal pathology. Women meeting more than one criterion will be included in the group that comes first in ranking as described earlier. Within these stratified groups pregnancy outcomes will be expressed as risk ratio, risk difference and hazard ratio with 95% CI. Cost-effectiveness analysis The average costs and effects of tubal flushing during HSG with oil-based contrast and water-based contrast during fertility work-up will be compared. Total costs of the HSG, fertility treatments and fertility outcomes (collected using the eCRF) will be evaluated after a follow-up of six months after randomization. These data will be used to calculate the direct medical costs.
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