Casual Reasoning with Survival Data

Abstract

The hazard rate is the most commonly studied parameter in survival analysis, but it is usually not suitable for causal inference.

This thesis focuses on developing alternatives to hazards for analyzing survival data. The methodology can be useful in situations hazards are difficult to interpret.

Many survival analysis parameters, including the survival function, the restricted mean survival function, and the cumulative incidence function, solve differential equations involving hazards. The differential equation structure allows for the development of a general method for estimation and inference, where hazard models, which are well developed, are used as an intermediary step. Software that makes the method available for applied researchers is described, and worked examples are provided.

The thesis also contributes to the continuous-time Marginal Structural Models (MSMs) both concerning methodology and software. An estimator for the continuous-time weights is proposed, and a result on the weighted additive hazard estimator is provided. The result enables consistent estimation of MSM parameters specified by the mentioned class of differential equations.

The utility and practical feasibility of the continuous-time MSMs are demonstrated through an application on a substantive prostate cancer treatment problem. The treatment regimens radical prostatectomy and radiation therapy are compared over 11 years of follow-up, in a weighted analysis of a cohort from the Cancer Registry of Norway. The analysis fails to distinguish the causal cumulative incidences for prostate cancer death for the two regimens, accounting for the competing risk of death from other causes. The observed difference between the naive cumulative incidences is likely due to confounding and is therefore not causal.