Methods for non-proportional hazards in clinical trials: A systematic review

For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards (NPH) has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under NPH. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific NPH situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles. We summarized the contents from the literature review in a concise way in the main text and provide more detailed explanations in the supplement (page 29)

The impact of hurricanes on housing prices: evidence from U.S. coastal cities

We investigate the effect of hurricane strikes on housing prices in U.S. coastal cities. To this end, we construct a new index of hurricane destruction which varies over time and space. Using this index and an annual, two equation, dynamic equilibrium correction panel model with area and time fixed effects, we model the effects of hurricanes on real house process and real incomes. In our model hurricanes have a direct effect on house prices and an indirect effect via a fall in local incomes. Our results show that the typical hurricane strike raises real house prices for a number of years, with a maximum effect of between 3 % to 4 % three years after occurrence. There is also a small negative effect on real incomes. These results are stable across models and subsamples.Econometric models ; Housing - Prices

Efficient Semiparametric Estimation of Short-Term and Long-Term Hazard Ratios with Right-Censored Data: Semiparametric Estimation of Short-Term and Long-Term Hazard Ratios

The proportional hazards assumption in the commonly used Cox model for censored failure time data is often violated in scientific studies. Yang and Prentice (2005) proposed a novel semiparametric two-sample model that includes the proportional hazards model and the proportional odds model as sub-models, and accommodates crossing survival curves. The model leaves the baseline hazard unspecified and the two model parameters can be interpreted as the short-term and long-term hazard ratios. Inference procedures were developed based on a pseudo score approach. Although extension to accommodate covariates was mentioned, no formal procedures have been provided or proved. Furthermore, the pseudo score approach may not be asymptotically efficient. We study the extension of the short-term and long-term hazard ratio model of Yang and Prentice (2005) to accommodate potentially time-dependent covariates. We develop efficient likelihood-based estimation and inference procedures. The nonparametric maximum likelihood estimators are shown to be consistent, asymptotically normal, and asymptotically efficient. Extensive simulation studies demonstrate that the proposed methods perform well in practical settings. The proposed method successfully captured the phenomenon of crossing hazards in a cancer clinical trial and identified a genetic marker with significant long-term effect missed by using the proportional hazards model on age-at-onset of alcoholism in a genetic study

Smoothed Rank Regression with Censored Data

A weighted rank estimating function is proposed to estimate the regression parameter vector in an accelerated failure time model with right censored data. In general, rank estimating functions are discontinuous in the regression parameter, creating difficulties in determining the asymptotic distribution of the estimator. A local distribution function is used to create a rank based estimating function that is continuous and monotone in the regression parameter vector. A weight is included in the estimating function to produce a bounded influence estimate. The asymptotic distribution of the regression estimator is developed and simulations are performed to examine its finite sample properties. A lung cancer data set is used to illustrate the methodology

Supervised Dimension Reduction for Large-scale Omics Data with Censored Survival Outcomes Under Possible Non-proportional Hazards

The past two decades have witnessed significant advances in high-throughput ``omics technologies such as genomics, proteomics, metabolomics, transcriptomics and radiomics. These technologies have enabled simultaneous measurement of the expression levels of tens of thousands of features from individual patient samples and have generated enormous amounts of data that require analysis and interpretation. One specific area of interest has been in studying the relationship between these features and patient outcomes, such as overall and recurrence-free survival, with the goal of developing a predictive ``omics profile. Large-scale studies often suffer from the presence of a large fraction of censored observations and potential time-varying effects of features, and methods for handling them have been lacking. In this paper, we propose supervised methods for feature selection and survival prediction that simultaneously deal with both issues. Our approach utilizes continuum power regression (CPR) - a framework that includes a variety of regression methods - in conjunction with the parametric or semi-parametric accelerated failure time (AFT) model. Both CPR and AFT fall within the linear models framework and, unlike black-box models, the proposed prognostic index has a simple yet useful interpretation. We demonstrate the utility of our methods using simulated and publicly available cancer genomics data

A comprehensive spatial-temporal analysis of driving factors of human-caused wildfires in Spain using Geographically Weighted Logistic Regression

Over the last decades, authorities responsible on forest fire have encouraged research on fire triggering factors, recognizing this as a critical point to achieve a greater understanding of fire occurrence patterns and improve preventive measures. The key objectives of this study are to investigate and analyze spatial-temporal changes in the contribution of wildfire drivers in Spain, and provide deeper insights into the influence of fire features: cause, season and size. We explored several subsets of fire occurrence combining cause (negligence/accident and arson), season (summer-spring and winter-fall) and size (100 Ha). The analysis is carried out fitting Geographically Weighted Logistic Regression models in two separate time periods (1988–1992, soon after Spain joined the European Union; and 2006–2010, after several decades of forest management). Our results suggest that human factors are losing performance with climate factors taking over, which may be ultimately related to the success in recent prevention policies. In addition, we found strong differences in the performance of occurrence models across subsets, thus models based on long-term historical fire records might led to misleading conclusions. Overall, fire management should move towards differential prevention measurements and recommendations due to the observed variability in drivers’ behavior over time and space, paying special attention to winter fires.This work has been financed by the Ministerio de Economía y Competitividad; Marcos Rodrigues is a postdoctoral ‘Juan de la Cierva Formación’ research fellow (FJCI-2016-31090); Adrian Jiménez-Ruano is a granted FPU-PhD student (Ref. 13/06618)

Semiparametric Regression During 2003–2007

Semiparametric regression is a fusion between parametric regression and nonparametric regression and the title of a book that we published on the topic in early 2003. We review developments in the field during the five year period since the book was written. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application