2026-10-06T20:38:00Z https://api.figshare.com/v2/oai

oai:figshare.com:article/32805488 2026-10-01T16:15:41Z portal_1172 item_type_8 month_year_10_2026

Efficient algorithms for nonparametric and semiparametric estimation with interval-censored data Zachary Waller (11600032) PUREID: 676587307 Non-parametric statistics interval-censoring survival analysis optimisation efficient algorithms In clinical settings, researchers are interested in the risk factors and their effect on event-time distributions. Often, exact event-times are unknown and the observed data is interval-censored. This thesis aims to develop techniques for fast and accurate estimation in the presence of interval-censoring and either left-truncation or competing risks. Left-truncation is a form of selection bias where individuals are only sampled if the event has not occurred by some truncation time. Competing-risks involves a number of mutually exclusive event-types. To allow for maximum flexibility, we estimate survival and incidence functions non-parametrically. 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> 2026-10-01T16:15:41Z Text Thesis 10.17034/32805488.v1 https://figshare.com/articles/thesis/Efficient_algorithms_for_nonparametric_and_semiparametric_estimation_with_interval-censored_data/32805488 All Rights Reserved Open Access after 2027-07-31