Causal inference with multi-state models, applied on estimating the effect of the IUI treatment timing for couples with unexplained subfertility

Abstract

This thesis examines statistical methods to find the right timing of intrauterine insemination treatment relative to the start of the follow-up of the couples. Intrauterine insemination is a fertility treatment conducted by injecting refined sperm into a woman's uterus. Lots of research has been done on timing of steps within one IUI cycle. However, not a lot of research has been done on investigating if couples should be advised to start with the IUI immediately after consulting a fertility clinic, or wait a few more months to see if the pregnancy occurs naturally during this time. To analyze this problem, treatment strategies are defined in the following way: a couple stays on expectant management until some predetermined time when the first IUI cycle is started, unless they become pregnant before that time. Strategies analyzed involve starting the treatment at 0, 3, 6 or 9 months, or not at all until the end of the analysis, which is 1.5 years after diagnosis. Pregnancy probability for each couple is estimated with a multi-state Cox proportional hazards model. Then, the model is connected to the causal inference setting in order to compute the counterfactual pregnancy probability of each couple in the population. This thesis explores how multi-state models can be used to answer causal questions. To do this, a 3-state multi-state model is carefully connected to the causal inference theory and the assumptions this framework relies on are listed and commented upon. Treatment strategies are implemented through making an intervention on the IUI starting time. Then, a causal inference method, G-computation, is used to estimate the expected pregnancy probability of all couples in the population, given that everyone follows the same treatment strategy. Then, individual pregnancy probabilities are averaged in order to obtain the expected pregnancy rates in the population for each strategy. Methodology combining multi-state models and causal inference is new and only one similar study has been found so far in the literature. Multi-state models are currently used mostly for predictive analyses and it is of great interest to use them to answer causal questions as well. The results of this study show that there is no significant effect of the time the IUI has been started on the pregnancy rate in the population after 1.5 years, but there is significant difference between being and not being treated.