Likelihood-Based Inference for Semi-Parametric Transformation Cure Models with Interval Censored Data

A simple yet effective way of modeling survival data with cure fraction is by considering Box-Cox transformation cure model (BCTM) that unifies mixture and promotion time cure models. In this article, we numerically study the statistical properties of the BCTM when applied to interval censored data. Time-to-events associated with susceptible subjects are modeled through proportional hazards structure that allows for non-homogeneity across subjects, where the baseline hazard function is estimated by distribution-free piecewise linear function with varied degrees of non-parametricity. Due to missing cured statuses for right censored subjects, maximum likelihood estimates of model parameters are obtained by developing an expectation-maximization (EM) algorithm. Under the EM framework, the conditional expectation of the complete data log-likelihood function is maximized by considering all parameters (including the Box-Cox transformation parameter $\alpha$) simultaneously, in contrast to conventional profile-likelihood technique of estimating $\alpha$. The robustness and accuracy of the model and estimation method are established through a detailed simulation study under various parameter settings, and an analysis of real-life data obtained from a smoking cessation study.Comment: 20 page

An overall strategy based on regression models to estimate relative survival and model the effects of prognostic factors in cancer survival studies.

Relative survival provides a measure of the proportion of patients dying from the disease under study without requiring the knowledge of the cause of death. We propose an overall strategy based on regression models to estimate the relative survival and model the effects of potential prognostic factors. The baseline hazard was modelled until 10 years follow-up using parametric continuous functions. Six models including cubic regression splines were considered and the Akaike Information Criterion was used to select the final model. This approach yielded smooth and reliable estimates of mortality hazard and allowed us to deal with sparse data taking into account all the available information. Splines were also used to model simultaneously non-linear effects of continuous covariates and time-dependent hazard ratios. This led to a graphical representation of the hazard ratio that can be useful for clinical interpretation. Estimates of these models were obtained by likelihood maximization. We showed that these estimates could be also obtained using standard algorithms for Poisson regression

Incidence of HIV-related anal cancer remains increased despite long-term combined antiretroviral treatment: results from the french hospital database on HIV.

PURPOSE: To study recent trends in the incidence of anal cancer in HIV-infected patients receiving long-term combined antiretroviral treatment (cART) compared with the general population. PATIENTS AND METHODS: From the French Hospital Database on HIV, we identified 263 cases of invasive anal squamous cell carcinoma confirmed histologically between 1992 and 2008. We compared incidence rates of anal cancer across four calendar periods: 1992-1996 (pre-cART period), 1997-2000 (early cART period), and 2001-2004 and 2005-2008 (recent cART periods). Standardized incidence ratios (SIRs) were calculated by using general population incidence data from the French Network of Cancer Registries. RESULTS: In HIV-infected patients, the hazard ratio (HR) in the cART periods versus the pre-cART period was 2.5 (95% CI, 1.28 to 4.98). No difference was observed across the cART calendar periods (HR, 0.9; 95% CI, 0.6 to 1.3). In 2005-2008, HIV-infected patients compared with the general population had an excess risk of anal cancer, with SIRs of 109.8 (95% CI, 84.6 to 140.3), 49.2 (95% CI, 33.2 to 70.3), and 13.1 (95% CI, 6.8 to 22.8) for men who have sex with men (MSM), other men, and women, respectively. Among patients with CD4 cell counts above 500/μL for at least 2 years, SIRs were 67.5 (95% CI, 41.2 to 104.3) when the CD4 nadir was less than 200/μL for more than 2 years and 24.5 (95% CI, 17.1 to 34.1) when the CD4 nadir was more than 200/μL. CONCLUSION: Relative to that in the general population, the risk of anal cancer in HIV-infected patients is still extremely high, even in patients with high current CD4 cell counts. cART appears to have no preventive effect on anal cancer, particularly in MSM

Flexible Regression Models for Survival Data

Survival analysis is a branch of statistics to analyze the time-to-event data or survival data. One important feature of survival data is censoring, which means that not all the subjects’ survival time are observed directly. Among all the survival data, right-censored data are the most common type and consist of some exactly observed survival times and some right-censored observations. In this dissertation, we focus on studying flexible regression models for complicated right-censored survival data when the classical proportional hazards (PH) assumption is not satisfied. Flexible semiparametric regression models can largely avoid misspecification of parametric distributions and thus provide more modeling flexibility. Cure models are studied in this dissertation to analyze survival data, for which there is a cured group in the study population and this is evidenced by a level-off at the end of the nonparametric survival estimate. In addition, we also incorporate background mortality in the cure models to improve estimation accuracy in this research. Considering the background mortality is important based on the fact that patients dying from other causes also benefit from the treatment of the disease of interest as shown in the SEER cancer studies. In Chapter 2, a semiparametric estimation approach is proposed based on EM algorithm under the mixture cure proportional hazards model with background mortality (MCPH+BM). In Chapter 3, a promotion time cure proportional hazards model with background mortality (PTPH+BM) is proposed, and its extension to the semiparametric transformation model is under further exploration. Both models are validated via comprehensive simulation studies and real data analysis. Another perspective on non-proportional hazards is to explore a more general model than the Cox PH model such as the generalized odds-rate (GOR) models (Dabrowska and Doksum, 1988). In Chapter 4, the identifiability problems and the estimation of parameters in the GOR models are discussed

Maximum likelihood estimation in a partially observed stratified regression model with censored data

The stratified proportional intensity model generalizes Cox's proportional intensity model by allowing different groups of the population under study to have distinct baseline intensity functions. In this article, we consider the problem of estimation in this model when the variable indicating the stratum is unobserved for some individuals in the studied sample. In this setting, we construct nonparametric maximum likelihood estimators for the parameters of the stratified model and we establish their consistency and asymptotic normality. Consistent estimators for the limiting variances are also obtained