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.     

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.     

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.     

Stochastic properties of the mixed accelerated hazard models

The accelerated hazard model in survival analysis assumes that the covariate effect acts the time scale of the baseline hazard rate. In this paper, we study the stochastic properties of the mixed accelerated hazard model since the covariate is considered basically unobservable. We build dependence structure between the population variable and the covariate, and also present some preservation properties. Using some well-known stochastic orders, we compare two mixed accelerated hazards models arising out of different choices of distributions for unobservable covariates or different baseline hazard rate functions.     

Interactive Hazards Education Program for Youth in a Low SES Community: A Quasi‐Experimental Pilot Study

A pilot study of an interactive hazards education program was carried out in Canberra (Australia), with direct input from youth participants. Effects were evaluated in relation to youths’ interest in disasters, motivation to prepare, risk awareness, knowledge indicators, perceived preparedness levels, planning and practice for emergencies, and fear and anxiety indicators. Parents also provided ratings, including of actual home‐based preparedness activities. Using a single group pretest‐posttest with benchmarking design, a sample of 20 youths and their parents from a low SES community participated. Findings indicated beneficial changes on a number of indicators. Preparedness indicators increased significantly from pre‐ to posttest on both youth (p < 0.01) and parent ratings (p < 0.01). Parent ratings reflected an increase of just under six home‐based preparedness activities. Youth knowledge about disaster mitigation also was seen to increase significantly (p < 0.001), increasing 39% from pretest levels. While personalized risk perceptions significantly increased (p < 0.01), anxiety and worry levels were seen either not to change (generalized anxiety, p > 0.05) or to reduce between pre‐ and posttest (hazards‐specific fears, worry, and distress, ps ranged from p < 0.05 to < 0.001). In terms of predictors of preparedness, a number of variables were found to predict posttest preparedness levels, including information searching done by participants between education sessions. These pilot findings are the first to reflect quasi‐experimental outcomes for a youth hazards education program carried out in a setting other than a school that focused on a sample of youth from a low SES community.     

Development of predictive signatures for treatment selection in precision medicine with survival outcomes

For survival endpoints in subgroup selection, a score conversion model is often used to convert the set of biomarkers for each patient into a univariate score and using the median of the univariate scores to divide the patients into biomarker‐positive and biomarker‐negative subgroups. However, this may lead to bias in patient subgroup identification regarding the 2 issues: (1) treatment is equally effective for all patients and/or there is no subgroup difference; (2) the median value of the univariate scores as a cutoff may be inappropriate if the sizes of the 2 subgroups are differ substantially. We utilize a univariate composite score method to convert the set of patient's candidate biomarkers to a univariate response score. We propose applying the likelihood ratio test (LRT) to assess homogeneity of the sampled patients to address the first issue. In the context of identification of the subgroup of responders in adaptive design to demonstrate improvement of treatment efficacy (adaptive power), we suggest that subgroup selection is carried out if the LRT is significant. For the second issue, we utilize a likelihood‐based change‐point algorithm to find an optimal cutoff. Our simulation study shows that type I error generally is controlled, while the overall adaptive power to detect treatment effects sacrifices approximately 4.5% for the simulation designs considered by performing the LRT; furthermore, the change‐point algorithm outperforms the median cutoff considerably when the subgroup sizes differ substantially.