This thesis is devoted to presenting and illustrating a novel estimation method offering a way to reduce confounding bias in time-to-event situations. In order to reduce this bias, without having to observe all of the confounding, one can use instrumental variables (IV). These are observed variables independent of the unknown confounder, correlated with the exposure of interest and affecting the response only through the exposure. Under these assumptions, one can perform a two-stage predictor substitution, that allows for consistent estimation of the hazard difference for Aalen’s additive hazard model, and under the additional assumption of rare outcome, allows for approximate consistent estimation of the hazard ratio for Cox’s proportional hazards model. For the aforementioned models, we then illustrate the consistency of this estimate for varying IV strength, and investigate the meaning of “rare outcome”, by illustrating how inconsistent the estimator can become as the number of outcomes increases. We also found, somewhat surprisingly, that bootstrapping might not necessarily be the best choice for estimating the variance of the IV estimate, as both the aalen function and the coxph function in R already seem to report the correct variance. As for small samples, bootstrapping an estimate of the variance for Cox’s proportional hazard might be cumbersome. Under misspecification of the first stage, only the two-stage predictor substitution for Aalen’s additive hazard model seems to still yield consistent estimates but the resulting variances are very high in comparison to a correctly specified first stage. We thus advise against misspecification. However, for testing the null hypothesis of no causal effect, both Aalen’s additive hazard model and Cox’s proportional hazards model seem to perform well under misspecification of the first stage and with an arbitrary number of outcome. We then perform an analysis of the effect of mothers body mass index (BMI) on the pregnancy duration using data from the Norwegian Mother and Child cohort. Even though previous studies showed a clear effect of the mother’s BMI on premature birth, this analysis shows only a very small overall effect of the mother’s BMI. We hope, however, that this analysis can provide the reader with an illustration on how to apply the method to a real data set.