Parametric and penalized generalized survival models

2016 ◽  
Vol 27 (5) ◽  
pp. 1531-1546 ◽  
Author(s):  
Xing-Rong Liu ◽  
Yudi Pawitan ◽  
Mark Clements
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Information Criteria ◽  
Parametric Models ◽  
Survival Models ◽  
Link Function ◽  
Proportional Odds ◽  
Linear Predictor ◽  
Time Effects ◽  
Covariate Effects

We describe generalized survival models, where g( S( t| z)), for link function g, survival S, time t, and covariates z, is modeled by a linear predictor in terms of covariate effects and smooth time effects. These models include proportional hazards and proportional odds models, and extend the parametric Royston–Parmar models. Estimation is described for both fully parametric linear predictors and combinations of penalized smoothers and parametric effects. The penalized smoothing parameters can be selected automatically using several information criteria. The link function may be selected based on prior assumptions or using an information criterion. We have implemented the models in R. All of the penalized smoothers from the mgcv package are available for smooth time effects and smooth covariate effects. The generalized survival models perform well in a simulation study, compared with some existing models. The estimation of smooth covariate effects and smooth time-dependent hazard or odds ratios is simplified, compared with many non-parametric models. Applying these models to three cancer survival datasets, we find that the proportional odds model is better than the proportional hazards model for two of the datasets.

scholarly journals A foci cohort analysis to monitor successful and persistent foci under Thailand’s Malaria Elimination Strategy

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Prayuth Sudathip ◽  
Suravadee Kitchakarn ◽  
Jui A. Shah ◽  
Donal Bisanzio ◽  
Felicity Young ◽  
...  
Keyword(s):  
Malaria Elimination ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Forest Disturbance ◽  
Cohort Analysis ◽  
Information Criteria ◽  
Factors Associated ◽  
Malaria Burden ◽  
Hazards Model ◽  
Autochthonous Transmission

Abstract Background Thailand’s success in reducing malaria burden is built on the efficient “1-3-7” strategy applied to the surveillance system. The strategy is based on rapid case notification within 1 day, case investigation within 3 days, and targeted foci response to reduce the spread of Plasmodium spp. within 7 days. Autochthonous transmission is still occurring in the country, threatening the goal of reaching malaria-free status by 2024. This study aimed to assess the effectiveness of the 1-3-7 strategy and identify factors associated with presence of active foci. Methods Data from the national malaria information system were extracted from fiscal years 2013 to 2019; after data cleaning, the final dataset included 81,012 foci. A Cox’s proportional hazards model was built to investigate factors linked with the probability of becoming an active focus from 2015 to 2019 among foci that changed status from non-active to active focus during the study period. We performed a model selection technique based on the Akaike Information Criteria (AIC). Results The number of yearly active foci decreased from 2227 to 2013 to 700 in 2019 (68.5 %), and the number of autochthonous cases declined from 17,553 to 3,787 (78.4 %). The best Cox’s hazard model showed that foci in which vector control interventions were required were 18 % more likely to become an active focus. Increasing compliance with the 1-3-7 strategy had a protective effect, with a 22 % risk reduction among foci with over 80 % adherence to 1-3-7 timeliness protocols. Other factors associated with likelihood to become or remain an active focus include previous classification as an active focus, presence of Plasmodium falciparum infections, level of forest disturbance, and location in border provinces. Conclusions These results identified factors that favored regression of non-active foci to active foci during the study period. The model and relative risk map align with the national malaria program’s district stratification and shows strong spatial heterogeneity, with high probability to record active foci in border provinces. The results of the study may be useful for honing Thailand’s program to eliminate malaria and for other countries aiming to accelerate malaria elimination.

Modelling heterogeneity in survival data

1991 ◽  
Vol 28 (03) ◽  
pp. 695-701 ◽  
Author(s):  
Philip Hougaard
Keyword(s):  
Survival Data ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Mixture Distribution ◽  
Survival Models ◽  
Risk Of Death ◽  
Hazards Model ◽  
Occupational Mortality ◽  
Heterogeneity Distribution ◽  
Biased Estimates

Ordinary survival models implicitly assume that all individuals in a group have the same risk of death. It may, however, be relevant to consider the group as heterogeneous, i.e. a mixture of individuals with different risks. For example, after an operation each individual may have constant hazard of death. If risk factors are not included, the group shows decreasing hazard. This offers two fundamentally different interpretations of the same data. For instance, Weibull distributions with shape parameter less than 1 can be generated as mixtures of constant individual hazards. In a proportional hazards model, neglect of a subset of the important covariates leads to biased estimates of the other regression coefficients. Different choices of distributions for the unobserved covariates are discussed, including binary, gamma, inverse Gaussian and positive stable distributions, which show both qualitative and quantitative differences. For instance, the heterogeneity distribution can be either identifiable or unidentifiable. Both mathematical and interpretational consequences of the choice of distribution are considered. Heterogeneity can be evaluated by the variance of the logarithm of the mixture distribution. Examples include occupational mortality, myocardial infarction and diabetes.

scholarly journals A Flexible Link Function for Discrete-Time Duration Models

2016 ◽  
Vol 236 (4) ◽  
pp. 455-481
Author(s):  
Wolfgang Hess ◽  
Gerhard Tutz ◽  
Jan Gertheiss
Keyword(s):  
Discrete Time ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Link Function ◽  
Flexible Link ◽  
Time Duration ◽  
Special Cases ◽  
Simulation Results

Abstract This paper proposes a discrete-time hazard regression approach based on the relation between hazard rate models and excess over threshold models, which are frequently encountered in extreme value modelling. The proposed duration model employs a flexible link function and incorporates the grouped-duration analogue of the well-known Cox proportional hazards model and the proportional odds model as special cases. The theoretical setup of the model is motivated, and simulation results are reported, suggesting that the model proposed performs well. The simulation results and an empirical analysis of US import durations also show that the choice of link function in discrete hazard models has important implications for the estimation results, and that severe biases in the results can be avoided when using a flexible link function.

A Hierarchical Bayes Analysis and Comparison of PH Weibull and PH Exponential Models for One-Shot Device Testing Experiment

2021 ◽  
pp. 2150036
Author(s):  
Reema Sharma ◽  
Richa Srivastava ◽  
Satyanshu K. Upadhyay
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Real Data ◽  
Hierarchical Bayes ◽  
Information Criteria ◽  
Accelerated Life Tests ◽  
Hazards Model ◽  
Bayes Analysis ◽  
Posterior Predictive Loss ◽  
The One

The one-shot devices are highly reliable and, therefore, accelerated life tests are often employed to perform the experiments on such devices. Obviously, in the process, some covariates are introduced. This paper considers the proportional hazards model to observe the effect of covariates on the failure rates under the assumption of two commonly used models, namely the exponential and the Weibull for the lifetimes. The Bayes implementation is proposed using the hybridization of Gibbs and Metropolis algorithms that routinely extend to missing data situations as well. The entertained models are compared using the Bayesian and deviance information criteria and the expected posterior predictive loss criterion. Finally, the results based on two real data examples are given as an illustration.

Flexible covariate effects in the proportional hazards model

1992 ◽  
Vol 22 (3) ◽  
pp. 241-250 ◽  
Author(s):  
Treyor Hastie ◽  
Lynn Sleeper ◽  
Robert Tibshirani
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Covariate Effects ◽  
Hazards Model

Survival analysis via cox proportional hazards additive models

2017 ◽  
Vol 01 (01) ◽  
pp. 1650003
Author(s):  
Lu Bai ◽  
Daniel Gillen
Keyword(s):  
Survival Data ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Model ◽  
Generalized Additive Models ◽  
Cox Proportional Hazards ◽  
Additive Models ◽  
Cox Proportional Hazards Model ◽  
Linear Predictor ◽  
Censored Survival Data

The Cox proportional hazards model is commonly used to examine the covariate-adjusted association between a predictor of interest and the risk of mortality for censored survival data. However, it assumes a parametric relationship between covariates and mortality risk though a linear predictor. Generalized additive models (GAMs) provide a flexible extension of the usual linear model and are capable of capturing nonlinear effects of predictors while retaining additivity between the predictor effects. In this paper, we provide a review of GAMs and incorporate bivariate additive modeling into the Cox model for censored survival data with applications to estimating geolocation effects on survival in spatial epidemiologic studies.

scholarly journals Competing Risks Copula Models for Unemployment Duration: An Application to a German Hartz Reform

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Simon M.S. Lo ◽  
Gesine Stephan ◽  
Ralf A. Wilke
Keyword(s):  
Competing Risks ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Unemployment Duration ◽  
Copula Models ◽  
Covariate Effects ◽  
Hazards Model ◽  
Special Cases

AbstractThe copula graphic estimator (CGE) for competing risks models has received little attention in empirical research, despite having been developed into a comprehensive research method. In this paper, we bridge the gap between theoretical developments and applied research by considering a general class of competing risks copula models, which nests popular models such as the Cox proportional hazards model, the semiparametric multivariate mixed proportional hazards model (MMPHM), and the CGE as special cases. Analyzing the effects of a German Hartz reform on unemployment duration, we illustrate that the CGE imposes fewer restrictions on partial covariate effects than standard methods do. Differences are less evident when a more flexible difference-in-differences estimator is applied. It is also found that the MMPHM estimates react more strongly to the choice of the copula than the CGE in terms of the shape of the treatment effect function over time. Thus, the MMPHM produces less robust results in our application.

scholarly journals A family of partial-linear single-index models for analyzing complex environmental exposures with continuous, categorical, time-to-event, and longitudinal health outcomes

2020 ◽  
Author(s):  
Yuyan Wang ◽  
Yinxiang Wu ◽  
Melanie H. Jacobson ◽  
Myeonggyun Lee ◽  
Peng Jin ◽  
...  
Keyword(s):  
Environmental Factors ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Nonlinear Effects ◽  
Parametric Models ◽  
Time To Event ◽  
Joint Effects ◽  
Single Index ◽  
Hazards Model ◽  
Partial Linear

Abstract Background: Statistical methods to study the joint effects of environmental factors are of great importance to understand the impact of correlated exposures that may act synergistically or antagonistically on health outcomes. This study proposes a family of statistical models under a unified partial-linear single-index (PLSI) modeling framework, to assess the joint effects of environmental factors for continuous, categorical, time-to-event, and longitudinal outcomes. All PLSI models consist of a linear combination of exposures into a single index for practical interpretability of relative direction and importance, and a nonparametric link function for modeling flexibility. Methods: We presented PLSI linear regression and PLSI quantile regression for continuous outcome, PLSI generalized linear regression for categorical outcome, PLSI proportional hazards model for time-to-event outcome, and PLSI mixed-effects model for longitudinal outcome. These models were demonstrated using a dataset of 800 subjects from NHANES 2003-2004 survey including 8 environmental factors. Serum triglyceride concentration was analyzed as a continuous outcome and then dichotomized as a binary outcome. Simulations were conducted to demonstrate the PLSI proportional hazards model and PLSI mixed-effects model. The performance of PLSI models was compared with their counterpart parametric models. Results: PLSI linear, quantile, and logistic regressions showed similar results that the 8 environmental factors had both positive and negative associations with triglycerides, with a-Tocopherol having the most positive and trans-b-carotene the most negative association. For the time-to-event and longitudinal settings, simulations showed that PLSI models could correctly identify directions and relative importance for the 8 environmental factors. Compared with parametric models, PLSI models got similar results when the link function was close to linear, but clearly outperformed in simulations with nonlinear effects. Conclusions: We presented a unified family of PLSI models to assess the joint effects of exposures on four commonly-used types of outcomes in environmental research, and demonstrated their modeling flexibility and effectiveness, especially for studying environmental factors with mixed directional effects and/or nonlinear effects. Our study has expanded the analytical toolbox for investigating the complex effects of environmental factors. A practical contribution also included a coherent algorithm for all proposed PLSI models with R codes available.

Sign in / Sign up

Export Citation Format

Share Document