In Chapter 2, we consider estimation of dynamic models of recurrent events (event histories) in continuous time using censored data. We develop maximum simulated likelihood estimators where missing data are integrated out using Monte Carlo and importance sampling methods. We allow for random effects and integrate out the unobserved heterogeneity using a quadrature rule. In Monte Carlo experiments, we find that maximum simulated likelihood estimation is practically feasible and performs better than both listwise deletion and auxiliary modelling of initial conditions. In an empirical application, we study ischaemic heart disease events for male Maoris in New Zealand.
Chapter 3 describes how the risk of experiencing heart attacks varies across gender and ethnicity in New Zealand. We analyse administrative data and estimate dynamic hazard models using maximum simulated likelihood methods to deal with left-censoring. The models allow risk to vary with age, previous heart attack history, and unobserved individual heterogeneity. We find that the risk of subsequent events is far higher than the risk of the first event, and particularly high within 1 year after an event. In most cases, male Maoris have the highest risk, followed by female Maoris, then male Europeans, while female Europeans have the lowest risk.
Differently from the well-known propensity score (PS), the lesser known `prognostic score (PGS)' balances the potential untreated response. Chapter 4 shows that `double robustness' can be achieved by controlling both PS and PGS in various ways in a method-blind manner.
In Chapter 5, we compares various treatment effect estimators through an extensive simulation study using 64 designs and two empirical examples mimicking experiments. In total, we examine 24 estimators based on matching, weighting, double robustness, regression imputation/adjustment, `complete pairing', and `propensity-score residual'. Our results show that, contrary to the common perception, doubly robust estimators are not necessarily the best. In fact, our findings recommend a couple of non-doubly-robust estimators, with a simple propensity-score-residual-based estimator being the nearly dominant best estimator
