ANALYSIS OF NON-LINEAR COVARIATES EFFECTS AND TEMPORAL TREATMENT EFFECT IN COX-TYPE MODELS

ANALYSIS OF NON-LINEAR COVARIATES EFFECTS AND TEMPORAL TREATMENT EFFECT IN COX-TYPE MODELS

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Title Analysis of non-linear covariates effects and temporal treatment effect in Cox-type models Author(s) Xu, Jiajun; Citation Xu, J. [ ]. (2016). Analysis of non-linear covariates effects and temporal treatment effect in Cox-type models. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Issued Date 2016 URL Rights The author retains all proprietary rights, (such as patent rights) and the right to use in future works.
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ANALYSIS OF NON-LINEAR COVARIATES EFFECTS AND TEMPORAL TREATMENT EFFECT IN COX-TYPE MODELS by Jiajun XU A thesis submitted in partial fulfilment of the requirements for the Degree of Doctor of Philosophy at The University of Hong Kong. August 2016
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Abstract of thesis entitled ANALYSIS OF NON-LINEAR COVARIATES EFFECTS AND TEMPORAL TREATMENT EFFECT IN COX-TYPE MODELS Submitted by Jiajun XU for the Degree of Doctor of Philosophy at The University of Hong Kong. in August 2016 This thesis focuses on the statistical analysis of time to event data that the effects of one or more continuous explanatory variables are not linear or the treatment effect varies over time, say the waning efficacy of some chemo- prevention interventions. Standard Cox proportional hazards model cannot be applied to those situations. Modifications of the standard Cox model to accommodate the above situations are proposed. Motivated by a breast cancer data set, we first consider the estimation of the potentially non-linear age effect based on the generalized partly linear survival models. Appropriate adjustment of the non-linear age effects is warranted to ensure a valid statistical inference on other fixed effects. A simple and efficient sieve maximum likelihood estimation method that can be implemented easily using any standard statistical software is proposed. A data-driven algorithm to
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determine the optimal number and location of the knots in the estimation of the non-linear age effect is adopted. This algorithm is able to identify some possible change points where the investigated covariate effect is very different before and after these points. The performance of the proposed method is evaluated by simulation studies. For illustration purpose, the method is applied to the breast cancer data set from the public domain to study the non-linear effects of age-at-onset on the disease free survival of the patients. The next problem considered is the estimation of a time-varying treat- ment effect probably due to waning of the treatment efficacy. Two special features are attached to this special problem. The first one is the possibility of multiple episodes of the disease from the same subject over time, leading to recurrent events nature of the data. The second one is that the treatment is administered intermittently to the subjects to offer protection for the con- trol of infectious disease. The continual administration of the treatment is mainly because of the waning efficacy of the treatment. The primary goal of this study is to estimate the time-varying treatment effect, which generally declines over time. One main objective of this study is to provide a method
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