Medicine and Health Sciences Commons^™

A Hybrid Newton-Type Method For The Linear Regression In Case-Cohort Studies, Menggang Yu, Bin Nan

The University of Michigan Department of Biostatistics Working Paper Series

Case-cohort designs are increasingly commonly used in large epidemiological cohort studies. Nan, Yu, and Kalbeisch (2004) provided the asymptotic results for censored linear regression models in case-cohort studies. In this article, we consider computational aspects of their proposed rank based estimating methods. We show that the rank based discontinuous estimating functions for case-cohort studies are monotone, a property established for cohort data in the literature, when generalized Gehan type of weights are used. Though the estimating problem can be formulated to a linear programming problem as that for cohort data, due to its easily uncontrollable large scale even for a …

Nonparametric And Semiparametric Inference For Models Of Tumor Size And Metastasis, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

There has been some recent work in the statistical literature for modelling the relationship between the size of primary cancers and the occurrences of metastases. While nonparametric methods have been proposed for estimation of the tumor size distribution at which metastatic transition occurs, their asymptotic properties have not been studied. In addition, no testing or regression methods are available so that potential confounders and prognostic factors can be adjusted for. We develop a unified approach to nonparametric and semiparametric analysis of modelling tumor size-metastasis data in this article. An equivalence between the models considered by previous authors with survival data …

Model Checking Techniques For Regression Models In Cancer Screening, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

There has been much work on developing statistical procedures for associating tumor size with the probability of detecting a metastasis. Recently, Ghosh (2004) developed a unified statistical framework in which equivalences with censored data structures and models for tumor size and metastasis were examined. Based on this framework, we consider model checking techniques for semiparametric regression models in this paper. The procedures are for checking the additive hazards model. Goodness of fit methods are described for assessing functional form of covariates as well as the additive hazards assumption. The finite-sample properties of the methods are assessed using simulation studies.

On Corrected Score Approach For Proportional Hazards Model With Covariate Measurement Error, Xiao Song, Yijian Huang

UW Biostatistics Working Paper Series

In the presence of covariate measurement error with the proportional hazards model, several functional modeling methods have been proposed. These include the conditional score estimator (Tsiatis and Davidian, 2001), the parametric correction estimator (Nakamura, 1992) and the nonparametric correction estimator (Huang and Wang, 2000, 2003) in the order of weaker assumptions on the error. Although they are all consistent, each suffers from potential difficulties with small samples and substantial measurement error. In this article, upon noting that the conditional score and parametric correction estimators are asymptotically equivalent in the case of normal error, we investigate their relative finite sample performance …

Individualized Predictions Of Disease Progression Following Radiation Therapy For Prostate Cancer., Jeremy Taylor, Menggang Yu, Howard M. Sandler

The University of Michigan Department of Biostatistics Working Paper Series

Background: Following treatment for localized prostate cancer, men are monitored with serial PSA measurements. Refining the predictive value of post-treatment PSA determinations may add to clinical management and we have developed a model that predicts for an individual patient future PSA values and estimates the time to future clinical recurrence.

Methods: Data from 934 patients treated for prostate cancer between 1987 and 2000 were used to develop a comprehensive statistical model to fit the clinical recurrence events and pattern of PSA data. A logistic regression model was used for the probability of cure, non-linear hierarchical mixed models were used for …

Piecewise Constant Cross-Ratio Estimation For Association In Bivariate Survival Data With Application To Studying Markers Of Menopausal Transition, Bin Nan, Xihong Lin, Lynda D. Lisabet, Sioban Harlow

The University of Michigan Department of Biostatistics Working Paper Series

A question of significant interest in female reproductive aging is to identify bleeding criteria for the menopausal transition. Although various bleeding criteria, or markers, have been proposed for the menopausal transition, their validity has not been adequately examined. The Tremin Trust data are collected from a long-term cohort study that followed a group of women throughout their whole reproductive life, and provide a unique opportunity for assessing the association between age at onset of a bleeding marker and age onset of menopause. Formal statistical analysis of this dependence is challenging give the fact that both the marker event and menopause …

Individual Prediction In Prostate Cancer Studies Using A Joint Longitudinal-Survival-Cure Model, Menggang Yu, Jeremy Taylor, Howard M. Sandler

The University of Michigan Department of Biostatistics Working Paper Series

For monitoring patients treated for prostate cancer, Prostate Specific Antigen (PSA) is measured periodically after they receive treatment. Increases in PSA are suggestive of recurrence of the cancer and are used in making decisions about possible new treatments. The data from studies of such patients typically consist of longitudinal PSA measurements, censored event times and baseline covariates. Methods for the combined analysis of both longitudinal and survival data have been developed in recent years, with the main emphasis being on modeling and estimation. We analyze data from a prostate cancer study that has been extended by adding a mixture structure …