Reducing sample size needed for cox-proportional hazards model analysis using more efficient sampling method

Abstract

In general, survival data are time-to-event data, such as time to death, time to appearance of a tumor, or time to recurrence of a disease. Models for survival data have frequently been based on the proportional hazards model, proposed by Cox. The Cox model has intensive application in the field of social, medical, behavioral and public health sciences. In this paper we propose a more efficient sampling method of recruiting subjects for survival analysis. We propose using a Moving Extreme Ranked Set Sampling (MERSS) scheme with ranking based on an easy-to-evaluate baseline auxiliary variable known to be associated with survival time. This paper demonstrates that this approach provides a more powerful testing procedure as well as a more efficient estimate of hazard ratio than that based on simple random sampling (SRS). Theoretical derivation and simulation studies are provided. The Iowa 65+ Rural study data are used to illustrate the methods developed in this paper.     

Vulnerabilities and risks in population and environment studies

In the study of risks , different sciences use the same category in different ways, each related to its own ontological assumptions. But many of these fields communicate very little with one another. This article seeks to approximate two of these areas of study that have shown similar concerns and that can mutually strengthen one another, namely, geography and demography. Geography was one of the first disciplines to include risk in its environmental dimension and has had broad experience in simultaneously focusing on social and natural dynamics. Demography, on the other hand, faces greater difficulties because only recently has it incorporated the environmental dimension into its scientific scope. Both have brought the concept of vulnerability into their conceptual framework as complementary to that of risk. Geographers understand vulnerability as a more symbiotic form of the relationship between society and nature, whereas demographers give it a strong socioeconomic component. In this regard, the conceptual discussion on risks and vulnerabilities, in its attempt at approximating these two fields, is a way of conceptually advancing and strengthening the different approaches to empirical work, especially in population–environment studies which is the common ground for the dialogue between the two disciplines.

A simple estimator for a shared frailty regression model

Summary. We propose a simple estimation procedure for a proportional hazards frailty regression model for clustered survival data in which the dependence is generated by a positive stable distribution. Inferences for the frailty parameter can be obtained by using output from Cox regression analyses. The computational burden is substantially less than that of the other approaches to estimation. The large sample behaviour of the estimator is studied and simulations show that the approximations are appropriate for use with realistic sample sizes. The methods are motivated by studies of familial associations in the natural history of diseases. Their practical utility is illustrated with sib pair data from Beaver Dam, Wisconsin.     

A partial score test for difference among heterogeneous populations

In event time data analysis, comparisons between distributions are made by the logrank test. When the data appear to contain crossing hazards phenomena, nonparametric weighted logrank statistics are usually suggested to accommodate different-weighted functions to increase the power. However, the gain in power by imposing different weights has its limits since differences before and after the crossing point may balance each other out. In contrast to the weighted logrank tests, we propose a score-type statistic based on the semiparametric-, heteroscedastic-hazards regression model of Hsieh [2001. On heteroscedastic hazards regression models: theory and application. J. Roy. Statist. Soc. Ser. B 63, 63–79.], by which the nonproportionality is explicitly modeled. Our score test is based on estimating functions derived from partial likelihood under the heteroscedastic model considered herein. Simulation results show the benefit of modeling the heteroscedasticity and power of the proposed test to two classes of weighted logrank tests (including Fleming–Harrington's test and Moreau's locally most powerful test), a Renyi-type test, and the Breslow's test for acceleration. We also demonstrate the application of this test by analyzing actual data in clinical trials.     

Estimation of dependence between paired correlated failure times in the presence of covariate measurement error

Summary. In many biomedical studies, covariates are subject to measurement error. Although it is well known that the regression coefficients estimators can be substantially biased if the measurement error is not accommodated, there has been little study of the effect of covariate measurement error on the estimation of the dependence between bivariate failure times. We show that the dependence parameter estimator in the Clayton–Oakes model can be considerably biased if the measurement error in the covariate is not accommodated. In contrast with the typical bias towards the null for marginal regression coefficients, the dependence parameter can be biased in either direction. We introduce a bias reduction technique for the bivariate survival function in copula models while assuming an additive measurement error model and replicated measurement for the covariates, and we study the large and small sample properties of the dependence parameter estimator proposed.     

The 2003 Heat Wave in France: Dangerous Climate Change Here and Now

In an analysis of the French episode of heat wave in 2003, this article highlights how heat wave dangers result from the intricate association of natural and social factors. Unusually high temperatures, as well as socioeconomic vulnerability, along with social attenuation of hazards, in a general context where the anthropogenic contribution to climate change is becoming more plausible, led to an excess of 14,947 deaths in France, between August 4 and 18, 2003. The greatest increase in mortality was due to causes directly attributable to heat: dehydration, hyperthermia, heat stroke. In addition to age and gender, combinatorial factors included preexisting disease, medication, urban residence, isolation, poverty, and, probably, air pollution. Although diversely impacted or reported, many parts of Europe suffered human and other losses, such as farming and forestry through drought and fires. Summer 2003 was the hottest in Europe since 1500, very likely due in part to anthropogenic climate change. The French experience confirms research establishing that heat waves are a major mortal risk, number one among so-called natural hazards in postindustrial societies. Yet France had no policy in place, as if dangerous climate were restricted to a distant or uncertain future of climate change, or to preindustrial countries. We analyze the heat wave's profile as a strongly attenuated risk in the French context, as well as the causes and the effects of its sudden shift into amplification. Research and preparedness needs are highlighted.     

Variable selection for semiparametric proportional hazards model under progressive Type-II censoring

Variable selection is an effective methodology for dealing with models with numerous covariates. We consider the methods of variable selection for semiparametric Cox proportional hazards model under the progressive Type-II censoring scheme. The Cox proportional hazards model is used to model the influence coefficients of the environmental covariates. By applying Breslow’s “least information” idea, we obtain a profile likelihood function to estimate the coefficients. Lasso-type penalized profile likelihood estimation as well as stepwise variable selection method are explored as means to find the important covariates. Numerical simulations are conducted and Veteran’s Administration Lung Cancer data are exploited to evaluate the performance of the proposed method.     

Additive hazards regression of current status data with auxiliary covariates

This paper discusses the regression analysis of current status failure time data arising from the additive hazards model with auxiliary covariates. As often occurs in practice, it is impossible or impractical to measure the exact magnitude of covariates for all subjects in a study. To compensate the missing information, some auxiliary covariates are utilized instead. We propose two easy-to-implement procedures for estimation of regression parameters by making use of auxiliary information. The asymptotic properties of the resulting estimators are established and extensive numerical studies indicate that both procedures work well in practice.     

Generalizing the standardized hazard ratio to multivariate proportional hazards regression,with an application to clinical~genomic studies

The standardized hazard ratio for univariate proportional hazards regression is generalized as a scalar to multivariate proportional hazards regression. Estimators of the standardized log hazard ratio are developed, with corrections for bias and for regression to the mean in high-dimensional analyses. Tests of point and interval null hypotheses and confidence intervals are constructed. Cohort sampling study designs, commonly used in prospective–retrospective clinical genomic studies, are accommodated.     

An extended semiparametric model for short-term and long-term hazard ratios

In survival analysis, one way to deal with non-proportional hazards is to model short-term and long-term hazard ratios. The existing model of this nature has no control over how fast the hazard ratio is changing over time. We add a parameter to the existing model to allow the hazard ratio to change over time at different speed. A nonparametric maximum likelihood approach is used to estimate the model parameters. The existing model is a special case of the extended model when the speed parameter is 0, which leads naturally to a way of testing the adequacy of the existing model. Simulation results show that there can be substantial bias in the estimation of the short-term and long-term hazard ratio if the speed parameter is fixed incorrectly at 0 rather than estimated. The extended model is fitted to three real data sets to shed new insights, including the observation that converging hazards does not necessarily imply the odds are proportional.