Efficient algorithms for nonparametric and semiparametric estimation with interval-censored data

This approach faces computational challenges which we overcome with novel algorithms and implementations. We present a fast algorithm for calculating the non-parametric maximum likelihood estimate of survival curves for interval-censored and left-truncated data. This Expectation Maximisation (EM) algorithm allows left-truncation to be handled in one step.

By combining this EM algorithm with an Iterative Convex Minorant (ICM) step we further improve performance. We compare this method with others from the literature, all of which we have efficiently implemented, and find it order of magnitudes faster and less prone to numeric errors or premature halting.<br><br>We extend this method to include covariates under the proportional hazards assumption for interval-censored and left-truncated data.

This method combines EM and ICM algorithms and new implementation strategies to improve performance. We compare results to an existing spline-based technique and find that our method is generally faster and avoids the need to specify spline parameters. Finally, we introduce an ICM method for calculating the proportional sub-distribution hazards model for interval-censored competing-risks data.Through simulation we find that the resulting estimates are unbiased.

We also experiment with introducing a logarithmic barrier function to ensure the sub-distribution functions are constrained but find limited applicability due to its detrimental impact on computing time.<br><br><i>Thesis is embargoed until 31 July 2027.</i><br>