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.     

Analysis of a continuous-time proportional hazard model using discrete duration data

Many economic duration variables are often available only up to intervals, and not up to exact points. However, continuous time duration models are conceptually superior to discrete ones. Hence, in duration analyses, one faces a situation with discrete data and a continuous model. This paper discusses (i) the asymptotic bias of a conventional approximation procedure in which a discrete duration is treated as an exact observation; and (ii) the efficiency of a correct maximum likelihood estimator which appropriately accounts for the discrete nature of the data.     

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.     

On a system of nonhomogeneous components sharing a common frailty

The components of a reliability system subjected to a common random environment usually have dependent lifetimes. This paper studies the stochastic properties of such a system with lifetimes of the components following multivariate frailty models and multivariate mixed proportional reversed hazard rate (PRHR) models, respectively. Through doing stochastic comparison, we devote to throwing a new light on how the random environment affects the number of working components of a reliability system and on assessing the performance of a k-out-of-n system.     

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.     

Perceptions of Risk and Vulnerability Following Exposure to a Major Natural Disaster: The Calgary Flood of 2013

Many studies have examined the general public's flood risk perceptions in the aftermath of local and regional flooding. However, relatively few studies have focused on large‐scale events that affect tens of thousands of people within an urban center. Similarly, in spite of previous research on flood risks, unresolved questions persist regarding the variables that might influence perceptions of risk and vulnerability, along with management preferences. In light of the opportunities presented by these knowledge gaps, the research reported here examined public perceptions of flood risk and vulnerability, and management preferences, within the city of Calgary in the aftermath of extensive flooding in 2013. Our findings, which come from an online survey of residents, reveal that direct experience with flooding is not a differentiating factor for risk perceptions when comparing evacuees with nonevacuees who might all experience future risks. However, we do find that judgments about vulnerability—as a function of how people perceive physical distance—do differ according to one's evacuation experience. Our results also indicate that concern about climate change is an important predictor of flood risk perceptions, as is trust in government risk managers. In terms of mitigation preferences, our results reveal differences in support for large infrastructure projects based on whether respondents feel they might actually benefit from them.