Regression with bivariate grouped data

The problem of accounting for the grouping of continuous, bivariate data in regression analyses is considered. Reasons why grouping must be taken seriously are advanced, and a strategy for accounting for grouping is demonstrated. The specific model asserts that, in the absence of grouping, the data would be bivariate normal. This model is used to adjust estimates of parameters in a regression relating disease severity to a grouped exposure variable, using data on pneumoconiosis in English coal miners (Ashford, 1959, Biometrics 15, 573-581). The choice of computing methods is discussed and likelihood formulas are presented.     

Distribution-free regression analysis of grouped survival data

Methods based on regression models for logarithmic hazard functions, Cox models, are given for analysis of grouped and censored survival data. By making an approximation it is possible to obtain explicitly a maximum likelihood function involving only the regression parameters. This likelihood function is a convenient analog to Cox's partial likelihood for ungrouped data. The method is applied to data from a toxicological experiment.     

Regression analysis of multivariate interval-censored failure time data with application to tumorigenicity experiments

This paper discusses multivariate interval-censored failure time data that occur when there exist several correlated survival times of interest and only interval-censored data are available for each survival time. Such data occur in many fields. One is tumorigenicity experiments, which usually concern different types of tumors, tumors occurring in different locations of animals, or together. For regression analysis of such data, we develop a marginal inference approach using the additive hazards model and apply it to a set of bivariate interval-censored data arising from a tumorigenicity experiment. Simulation studies are conducted for the evaluation of the presented approach and suggest that the approach performs well for practical situations.     

Regression with frailty in survival analysis

In studies of survival, the hazard function for each individual may depend on observed risk variables but usually not all such variables are known or measurable. This unknown factor of the hazard function is usually termed the individual heterogeneity or frailty. When survival is time to the occurrence of a particular type of event and more than one such time may be obtained for each individual, frailty is a common factor among such recurrence times. A model including frailty is fitted to such repeated measures of recurrence times.     

Modeling clustered, discrete, or grouped time survival data with covariates

We have developed methods for modeling discrete or grouped time, right-censored survival data collected from correlated groups or clusters. We assume that the marginal hazard of failure for individual items within a cluster is specified by a linear log odds survival model and the dependence structure is based on a gamma frailty model. The dependence can be modeled as a function of cluster-level covariates. Likelihood equations for estimating the model parameters are provided. Generalized estimating equations for the marginal hazard regression parameters and pseudolikelihood methods for estimating the dependence parameters are also described. Data from two clinical trials are used for illustration purposes.     

Analysis of doubly-censored survival data, with application to AIDS

This paper proposes nonparametric and weakly structured parametric methods for analyzing survival data in which both the time origin and the failure event can be right- or interval-censored. Such data arise in clinical investigations of the human immunodeficiency virus (HIV) when the infection and clinical status of patients are observed only at several time points. The proposed methods generalize the self-consistency algorithm proposed by Turnbull (1976, Journal of the Royal Statistical Society, Series B 38, 290-295) for singly-censored univariate data, and are illustrated with the results from a study of hemophiliacs who were infected with HIV by contaminated blood factor.     

Tests of proportional hazards and proportional odds models for grouped survival data

In this paper, we derive score test statistics to discriminate between proportional hazards and proportional odds models for grouped survival data. These models are embedded within a power family transformation in order to obtain the score tests. In simple cases, some small-sample results are obtained for the score statistics using Monte Carlo simulations. Score statistics have distributions well approximated by the chi-squared distribution. Real examples illustrate the proposed tests.     

A computer program for the generalized chi-square analysis of competing risks grouped survival data (CRISCAT)

CRISCAT is a computer program for the analysis of grouped survival data with competing risks via weighted least squares methods. Competing risks adjustments are obtained from general matrix operations using many of the strategies employed in a previously developed program (GENCAT) for multivariate categorical data. CRISCAT computes survival rates at several time points for multiple causes of failure, where each rate is adjusted for other causes in the sense that failure due to these other causes has been eliminated as a risk. The program can generate functions of the adjusted survival rates, to which asymptotic regression models may be fit. CRISCAT yields test statistics for hypotheses involving either these functions or estimated model parameters. Thus, this computational algorithm links competing risks theory to linear models methods for contingency table analysis and provides a unified approach to estimation and hypothesis testing of functions involving competing risks adjusted rates.     

Semiparametric Bayesian estimation of quantile function for breast cancer survival data with cured fraction

Existing cure‐rate survival models are generally not convenient for modeling and estimating the survival quantiles of a patient with specified covariate values. This paper proposes a novel class of cure‐rate model, the transform‐both‐sides cure‐rate model (TBSCRM), that can be used to make inferences about both the cure‐rate and the survival quantiles. We develop the Bayesian inference about the covariate effects on the cure‐rate as well as on the survival quantiles via Markov Chain Monte Carlo (MCMC) tools. We also show that the TBSCRM‐based Bayesian method outperforms existing cure‐rate models based methods in our simulation studies and in application to the breast cancer survival data from the National Cancer Institute's Surveillance, Epidemiology, and End Results (SEER) database.     

Control of data quality for population-based cancer survival analysis

BackgroundPopulation-based cancer survival is an important measure of the overall effectiveness of cancer care in a population. Population-based cancer registries collect data that enable the estimation of cancer survival. To ensure accurate, consistent and comparable survival estimates, strict control of data quality is required before the survival analyses are carried out. In this paper, we present a basis for data quality control for cancer survival.MethodsWe propose three distinct phases for the quality control. Firstly, each individual variable within a given record is examined to identify departures from the study protocol; secondly, each record is checked and excluded if it is ineligible or logically incoherent for analysis; lastly, the distributions of key characteristics in the whole dataset are examined for their plausibility.ResultsData for patients diagnosed with bladder cancer in England between 1991 and 2010 are used as an example to aid the interpretation of the differences in data quality. The effect of different aspects of data quality on survival estimates is discussed.ConclusionsWe recommend that the results of data quality procedures should be reported together with the findings from survival analysis, to facilitate their interpretation.     

Maximum likelihood estimation for a special type of grouped data with an application to a dose-response problem.

A short-cut method is given for calculating grouped maximum likelihood (ML) estimates when the data are relatively coarsely grouped in some directions, but more finely grouped in others. The algebraic details are then worked out for a dose-response problem that generates data of this kind. The situation envisaged is a variation on the usual quantal response problem in that dosage levels are taken to be random but grouped. Finally, the method is applied both to real and simulated response data conforming to this pattern and shown to work well in practice.     

Dimension reduction methods for microarrays with application to censored survival data

MOTIVATION: Recent research has shown that gene expression profiles can potentially be used for predicting various clinical phenotypes, such as tumor class, drug response and survival time. While there has been extensive studies on tumor classification, there has been less emphasis on other phenotypic features, in particular, patient survival time or time to cancer recurrence, which are subject to right censoring. We consider in this paper an analysis of censored survival time based on microarray gene expression profiles. RESULTS: We propose a dimension reduction strategy, which combines principal components analysis and sliced inverse regression, to identify linear combinations of genes, that both account for the variability in the gene expression levels and preserve the phenotypic information. The extracted gene combinations are then employed as covariates in a predictive survival model formulation. We apply the proposed method to a large diffuse large-B-cell lymphoma dataset, which consists of 240 patients and 7399 genes, and build a Cox proportional hazards model based on the derived gene expression components. The proposed method is shown to provide a good predictive performance for patient survival, as demonstrated by both the significant survival difference between the predicted risk groups and the receiver operator characteristics analysis. AVAILABILITY: R programs are available upon request from the authors. SUPPLEMENTARY INFORMATION: http://dna.ucdavis.edu/~hli/bioinfo-surv-supp.pdf.