Penalized log-likelihood estimation for partly linear transformation models with current status data

We consider partly linear transformation models applied to current status data. The unknown quantities are the transformation function, a linear regression parameter and a nonparametric regression effect. It is shown that the penalized MLE for the regression parameter is asymptotically normal and efficient and converges at the parametric rate, although the penalized MLE for the transformation function and nonparametric regression effect are only $n^{1/3}$ consistent. Inference for the regression parameter based on a block jackknife is investigated. We also study computational issues and demonstrate the proposed methodology with a simulation study. The transformation models and partly linear regression terms, coupled with new estimation and inference techniques, provide flexible alternatives to the Cox model for current status data analysis.Comment: Published at http://dx.doi.org/10.1214/009053605000000444 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Semiparametric Additive Transformation Model under Current Status Data

We consider the efficient estimation of the semiparametric additive transformation model with current status data. A wide range of survival models and econometric models can be incorporated into this general transformation framework. We apply the B-spline approach to simultaneously estimate the linear regression vector, the nondecreasing transformation function, and a set of nonparametric regression functions. We show that the parametric estimate is semiparametric efficient in the presence of multiple nonparametric nuisance functions. An explicit consistent B-spline estimate of the asymptotic variance is also provided. All nonparametric estimates are smooth, and shown to be uniformly consistent and have faster than cubic rate of convergence. Interestingly, we observe the convergence rate interfere phenomenon, i.e., the convergence rates of B-spline estimators are all slowed down to equal the slowest one. The constrained optimization is not required in our implementation. Numerical results are used to illustrate the finite sample performance of the proposed estimators.Comment: 32 pages, 5 figure

Relaxing Assumptions on the Censoring Mechanism in Survival Link-Based Additive Models

Survival models are frequently encountered in applications. In these models, the response of interest, the time until a particular event occurs, is often right censored. Most estimation methods assume that the event time and the censoring time are stochastically independent and non-informative conditional on covariates. However, these assumptions may be questioned. The aim of this thesis is to relax these assumptions in a class of flexible parametric survival models, called survival link-based additive models. The assumption of non-informative censoring is relaxed by assuming that the marginal survival functions of the event and censoring times have parameters in common. In particular, we provide evidence on the efficiency gains produced by the newly introduced informative estimator when compared to its non-informative counterpart. The independence assumption is relaxed by modelling both the event time and the censoring time simultaneously using copula functions. We provide some preliminary arguments towards model identification although this topic is very challenging and requires more future work. In these survival link-based additive models, the baseline functions are estimated non-parametrically by monotonic P-splines, whereas covariate effects are flexibly determined using additive predictors that allow for a vast variety of effects. Parameter estimation is reliably carried out within a penalised maximum likelihood framework with integrated automatic multiple smoothing parameter selection. We derive the √n-consistency and asymptotic normality of the estimators proposed in this thesis. Their finite sample performance are investigated via Monte Carlo simulation studies, and the approaches illustrated using two cases study based on infants hospitalised for pneumonia as well as prostate cancer data. The R package GJRM has been extended to incorporate the developments discussed in this thesis to facilitate transparent and reproducible researc

Methods for non-proportional hazards in clinical trials: A systematic review

For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards (NPH) has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under NPH. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific NPH situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles. We summarized the contents from the literature review in a concise way in the main text and provide more detailed explanations in the supplement (page 29)