Reframing Resilience: Equitable Access to Essential Services

We urgently need to put the concept of resilience into practice if we are to prepare our communities for climate change and exacerbated natural hazards. Yet, despite the extensive discussion surrounding community resilience, operationalizing the concept remains challenging. The dominant approaches for assessing resilience focus on either evaluating community characteristics or infrastructure functionality. While both remain useful, they have several limitations to their ability to provide actionable insight. More importantly, the current conceptualizations do not consider essential services or how access is impaired by hazards. We argue that people need access to services such as food, education, health care, and cultural amenities, in addition to water, power, sanitation, and communications, to get back some semblance of normal life. Providing equitable access to these types of services and quickly restoring that access following a disruption are paramount to community resilience. We propose a new conceptualization of community resilience that is based on access to essential services. This reframing of resilience facilitates a new measure of resilience that is spatially explicit and operational. Using two illustrative examples from the impacts of Hurricanes Florence and Michael, we demonstrate how decisionmakers and planners can use this framework to visualize the effect of a hazard and quantify resilience-enhancing interventions. This “equitable access to essentials” approach to community resilience integrates with spatial planning, and will enable communities not only to “bounce back” from a disruption, but to “bound forward” and improve the resilience and quality of life for all residents.     

A New Estimator for Cox Proportional Hazard Regression Model in Presence of Collinearity

We propose a new approach to estimate the parameters of the Cox proportional hazards model in the presence of collinearity. Generally, a maximum partial likelihood estimator is used to estimate parameters for the Cox proportional hazards model. However, the maximum partial likelihood estimators can be seriously affected by the presence of collinearity since the parameter estimates result in large variances.

In this study, we develop a Liu-type estimator for Cox proportional hazards model parameters and compare it with a ridge regression estimator based on the scalar mean squared error (MSE). Finally, we evaluate its performance through a simulation study.     

Semiparametric regression methods for temporal processes subject to multiple sources of censoring

Process regression methodology is underdeveloped relative to the frequency with which pertinent data arise. In this article, the response-190 is a binary indicator process representing the joint event of being alive and remaining in a specific state. The process is indexed by time (e.g., time since diagnosis) and observed continuously. Data of this sort occur frequently in the study of chronic disease. A general area of application involves a recurrent event with non-negligible duration (e.g., hospitalization and associated length of hospital stay) and subject to a terminating event (e.g., death). We propose a semiparametric multiplicative model for the process version of the probability of being alive and in the (transient) state of interest. Under the proposed methods, the regression parameter is estimated through a procedure that does not require estimating the baseline probability. Unlike the majority of process regression methods, the proposed methods accommodate multiple sources of censoring. In particular, we derive a computationally convenient variant of inverse probability of censoring weighting based on the additive hazards model. We show that the regression parameter estimator is asymptotically normal, and that the baseline probability function estimator converges to a Gaussian process. Simulations demonstrate that our estimators have good finite sample performance. We apply our method to national end-stage liver disease data. The Canadian Journal of Statistics 48: 222–237; 2020 © 2019 Statistical Society of Canada     

Empirical Likelihood for the Additive Hazards Model with Current Status Data

We investigate empirical likelihood for the additive hazards model with current status data. An empirical log-likelihood ratio for a vector or subvector of regression parameters is defined and its limiting distribution is shown to be a standard chi-squared distribution. The proposed inference procedure enables us to make empirical likelihood-based inference for the regression parameters. Finite sample performance of the proposed method is assessed in simulation studies to compare with that of a normal approximation method, it shows that the empirical likelihood method provides more accurate inference than the normal approximation method. A real data example is used for illustration.     

A Proportional Hazards Regression Model for the Subdistribution with Covariates‐adjusted Censoring Weight for Competing Risks Data

With competing risks data, one often needs to assess the treatment and covariate effects on the cumulative incidence function. Fine and Gray proposed a proportional hazards regression model for the subdistribution of a competing risk with the assumption that the censoring distribution and the covariates are independent. Covariate‐dependent censoring sometimes occurs in medical studies. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with proper adjustments for covariate‐dependent censoring. We consider a covariate‐adjusted weight function by fitting the Cox model for the censoring distribution and using the predictive probability for each individual. Our simulation study shows that the covariate‐adjusted weight estimator is basically unbiased when the censoring time depends on the covariates, and the covariate‐adjusted weight approach works well for the variance estimator as well. We illustrate our methods with bone marrow transplant data from the Center for International Blood and Marrow Transplant Research. Here, cancer relapse and death in complete remission are two competing risks.     

The Risk Perception Paradox—Implications for Governance and Communication of Natural Hazards

This article reviews the main insights from selected literature on risk perception, particularly in connection with natural hazards. It includes numerous case studies on perception and social behavior dealing with floods, droughts, earthquakes, volcano eruptions, wild fires, and landslides. The review reveals that personal experience of a natural hazard and trust—or lack of trust—in authorities and experts have the most substantial impact on risk perception. Cultural and individual factors such as media coverage, age, gender, education, income, social status, and others do not play such an important role but act as mediators or amplifiers of the main causal connections between experience, trust, perception, and preparedness to take protective actions. When analyzing the factors of experience and trust on risk perception and on the likeliness of individuals to take preparedness action, the review found that a risk perception paradox exists in that it is assumed that high risk perception will lead to personal preparedness and, in the next step, to risk mitigation behavior. However, this is not necessarily true. In fact, the opposite can occur if individuals with high risk perception still choose not to personally prepare themselves in the face of a natural hazard. Therefore, based on the results of the review, this article offers three explanations suggesting why this paradox might occur. These findings have implications for future risk governance and communication as well as for the willingness of individuals to invest in risk preparedness or risk mitigation actions.     

Exponential tilt models for two-group comparison with censored data

We study application of the Exponential Tilt Model (ETM) to compare survival distributions in two groups. The ETM assumes a parametric form for the density ratio of the two distributions. It accommodates a broad array of parametric models such as the log-normal and gamma models and can be sufficiently flexible to allow for crossing hazard and crossing survival functions. We develop a nonparametric likelihood approach to estimate ETM parameters in the presence of censoring and establish related asymptotic results. We compare the ETM to the Proportional Hazards Model (PHM) in simulation studies. When the proportional hazards assumption is not satisfied but the ETM assumption is, the ETM has better power for testing the hypothesis of no difference between the two groups. And, importantly, when the ETM relation is not satisfied but the PHM assumption is, the ETM can still have power reasonably close to that of the PHM. Application of the ETM is illustrated by a gastrointestinal tumor study.     

Covariate Selection for the Semiparametric Additive Risk Model

Abstract.  This paper considers covariate selection for the additive hazards model. This model is particularly simple to study theoretically and its practical implementation has several major advantages to the similar methodology for the proportional hazards model. One complication compared with the proportional model is, however, that there is no simple likelihood to work with. We here study a least squares criterion with desirable properties and show how this criterion can be interpreted as a prediction error. Given this criterion, we define ridge and Lasso estimators as well as an adaptive Lasso and study their large sample properties for the situation where the number of covariates p is smaller than the number of observations. We also show that the adaptive Lasso has the oracle property. In many practical situations, it is more relevant to tackle the situation with large p compared with the number of observations. We do this by studying the properties of the so-called Dantzig selector in the setting of the additive risk model. Specifically, we establish a bound on how close the solution is to a true sparse signal in the case where the number of covariates is large. In a simulation study, we also compare the Dantzig and adaptive Lasso for a moderate to small number of covariates. The methods are applied to a breast cancer data set with gene expression recordings and to the primary biliary cirrhosis clinical data.     

Hypothesis Testing of Hazard Ratio Parameters in Marginal Models for Multivariate Failure Time Data

Marginal hazard models for multivariate failure time data have been studied extensively in recent literature. However, standard hypothesis test statistics based on the likelihood method are not exactly appropriate for this kind of model. In this paper, extensions of the three commonly used likelihood hypothesis test statistics are discussed. Generalized Wald, generalized score and generalized likelihood ratio tests for hazard ratio parameters in a marginal hazard model for multivariate failure time data are proposed and their asymptotic distributions examined. The finite sample properties of these statistics are studied through simulations. The proposed method is applied to data from Busselton Population Health Surveys.     

Choice of Parametric Accelerated Life and Proportional Hazards Models for Survival Data: Asymptotic Results

We discuss the impact of misspecifying fully parametric proportional hazards and accelerated life models. For the uncensored case, misspecified accelerated life models give asymptotically unbiased estimates of covariate effect, but the shape and scale parameters depend on the misspecification. The covariate, shape and scale parameters differ in the censored case. Parametric proportional hazards models do not have a sound justification for general use: estimates from misspecified models can be very biased, and misleading results for the shape of the hazard function can arise. Misspecified survival functions are more biased at the extremes than the centre. Asymptotic and first order results are compared. If a model is misspecified, the size of Wald tests will be underestimated. Use of the sandwich estimator of standard error gives tests of the correct size, but misspecification leads to a loss of power. Accelerated life models are more robust to misspecification because of their log-linear form. In preliminary data analysis, practitioners should investigate proportional hazards and accelerated life models; software is readily available for several such models.