Statistical Methods to Extrapolate Time-To-Event Data - Cooney, Philip (Trinity College Dublin. School of Computer Science & Statistics. Discipline of Statistics, 2024)
This thesis investigates methods used to predict long-term survival of observations (typically survival times) beyond the time at which data follow-up is available. Current practice is to use parametric survival models; however, different models can produce different survival predictions, particularly if the lifetimes of many of the observations are censored. We focus on applying novel statistical techniques to improve existing methods to predict survival. One existing predictive approach assumes that after a certain timepoint, the hazards are approximately constant, and a constant hazard after this timepoint is used to estimate long-term survival. The choice of this timepoint is arbitrary and subject to considerable uncertainty. To improve on this methodology we estimate a statistical model known as a change-point survival model. This model allows the observed data to inform the timepoint after which the constant hazard is appropriate. Statistical goodness of fit measures can identify if the addition complexity associated with the inclusion of a change-point is warranted. We also estimate other more complex change-point survival models which allow us to model multiple treatments. Another topic which was investigated is the incorporation of expert opinion with statistical models. In the case of survival predictions, even if the survival is not observed at a timepoint, there are often opinions on the plausible ranges that these values may take. In this thesis, we investigate how these opinions can be incorporated in a robust manner, allowing for the predicted survival to take account of the precision of the expert's opinion and the sample size of the observed data. We also estimate how to quantify the strength of an expert's opinion to allow for appropriate calibration of their opinions at the elicitation stage. We found that the change-point model we estimated can robustly detect the timepoint at which a constant hazard is appropriate. In several real-world applications, it provided the closest predictions to the follow-up survival data. The proposed method for incorporation of expert opinion allowed for the straightforward synthesis of different types of expert opinions with data. We demonstrate by way of a simulation study that including expert opinion can more accurate survival predictions, even when the expert's belief is biased away from the true estimate. By numerically quantifying the strength of expert's beliefs, we more easily identify situations where expert's opinions are overconfident, allowing for re-calibration of their beliefs. The key methods from the thesis are implemented as open-source software packages to allow the methods to be used in practical applications. The ideas in this thesis can also be extended and improved upon in future research. We believe that the methods illustrated in this work will improve the ability of decision makers to model hypotheses relating to the prediction of long-term survival outcomes.
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Keywords: Health Technology Assessment; Extrapolation of time-to-event data; Prediction; Survvial Analysis; Bayesian Methods