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In clinical trials and other medical studies, it has become increasingly common to observe simultaneously an event time of interest and longitudinal covariates. In the literature, joint modelling approaches have been employed to analyse both survival and longitudinal processes and to investigate their association. However, these approaches focus mostly on developing adaptive and flexible longitudinal processes based on a prespecified survival model, most commonly the Cox proportional hazards model. In this paper, we propose a general class of semiparametric hazard regression models, referred to as the extended hazard model, for the survival component. This class includes two popular survival models, the Cox proportional hazards model and the accelerated failure time model, as special cases. The proposed model is flexible for modelling event data, and its nested structure facilitates model selection for the survival component through likelihood ratio tests. A pseudo joint likelihood approach is proposed for estimating the unknown parameters and components via a Monte Carlo em algorithm. Asymptotic theory for the estimators is developed together with theory for the semiparametric likelihood ratio tests. The performance of the procedure is demonstrated through simulation studies. A case study featuring data from a Taiwanese HIV/AIDS cohort study further illustrates the usefulness of the extended hazard model.

Both varying-coe cient and additive models have been studied extensively in the literature as extensions to linear models. They have also been extended to functional response data. However, existing extensions are still not su ciently flexible to reflect the functional feature of the responses. In this paper, we extend both varying-coe cient and additive models to a much more flexible “varying-coe cient additive model” and propose a simple algorithm to estimate the nonparametric additive and varying-coe cient components of this model. We establish the L 2 rate of convergence for each component function and demonstrate the applicability of the new model through tra c data.

SUMMARY The accelerated failure time model is an attractive alternative to the Cox model when the proportionality assumption fails to capture the relationship between the survival time and longitudinal covariates. Several complications arise when the covariates are measured intermittently at different time points for different subjects, possibly with measurement errors, or measurements are not available after the failure time. Joint modelling of the failure time and longitudinal data offers a solution to such complications. We explore the joint modelling approach under the accelerated failure time assumption when covariates are assumed to follow a linear mixed effects model with measurement errors. The procedure is based on maximising the joint likelihood function with random effects treated as missing data. A Monte Carlo EM algorithm is used to estimate all the unknown parameters, including the unknown baseline hazard function. The performance of the proposed procedure is checked in simulation studies. A case study of reproductive egg-laying data for female Mediterranean fruit flies and their relationship to longevity demonstrate the effectiveness of the new procedure.

SUMMARY We address the problem of estimating hazard rates from lifetable data. The central issue is a discretisation bias, which is caused by the aggregation of lifetimes which occurs in lifetable data. Smoothing raw mortalities directly derived from lifetable data leads to severe biases whenever the true hazard rate is large. We propose here a new transformation of smoothed lifetable data which is superior to previous approaches. This is demonstrated by means of large-sample arguments and a simulation study in which several recent approaches are compared. We demonstrate the application of the proposed methods to assess the mortality of medflies.

SUMMARY: Left truncation and right censoring arise frequently in practice for life data. This paper is concerned with the estimation of the hazard rate function for such data. Two types of nonparametric estimators based on kernel smoothing methods are considered. The first one is obtained by convolving a kernel with a cumulative hazard estimator. The second one is in the form of a ratio of two statistics. Local properties including consistency, asymptotic normality and mean squared error expressions are presented for both estimators. These properties facilitate locally adaptive bandwidth choice. The two types of estimators are then compared based on their theoretical and empirical performances. The effect of overlooking the truncation factor is demonstrated through the Channing House data.