Regression Models For Survival Data Research Articles

SURVIVAL ANALYSIS FOR RECURRENT EVENT DATA USING COUNTING PROCESS APPROACH: APPLICATION TO DIABETICS

Survival analysis is a branch of statistics for analyzing the duration of time until one or more events occur. Time to recurrence of diabetics including survival data. Diabetes can’t be cured but it can be controlled. Diabetics who don’t maintain their health and lifestyle will experience recurrence. Factors thought to influence the recurrence of diabetics are internal factors such as genetics and external factors such as lifestyle. The recurrence time of an object includes recurrent events because each object can experience the same recurrent event during the follow-up. One of the analysis to determine factors that are thought to influence the recurrence time of diabetics is survival analysis. Survival data can be modeled into a regression model if the survival time of an object is influenced by other factors. One of the regression models for survival data is Cox regression. One of the Cox regression models for recurrent event data is the AG model which uses a counting process approach. This study used data on the recurrence of diabetics at MH Thamrin Cileungsi Hospital. Based on data analysis, factors that influence the recurrence of diabetics are age, gender, and type of complication.

Standardised survival probabilities: a useful and informative tool for reporting regression models for survival data

BackgroundWhen interested in studying the effect of a treatment (or other exposure) on a time-to-event outcome, the most popular approach is to estimate survival probabilities using the Kaplan–Meier estimator. In the presence of confounding, regression models are fitted, and results are often summarised as hazard ratios. However, despite their broad use, hazard ratios are frequently misinterpreted as relative risks instead of relative rates.MethodsWe discuss measures for summarising the analysis from a regression model that overcome some of the limitations associated with hazard ratios. Such measures are the standardised survival probabilities for treated and untreated: survival probabilities if everyone in the population received treatment and if everyone did not. The difference between treatment arms can be calculated to provide a measure for the treatment effect.ResultsUsing publicly available data on breast cancer, we demonstrated the usefulness of standardised survival probabilities for comparing the experience between treated and untreated after adjusting for confounding. We also showed that additional important research questions can be addressed by standardising among subgroups of the total population.DiscussionStandardised survival probabilities are a useful way to report the treatment effect while adjusting for confounding and have an informative interpretation in terms of risk.

Modelling time-varying covariates effect on survival via functional data analysis: application to the MRC BO06 trial in osteosarcoma

Time-varying covariates are of great interest in clinical research since they represent dynamic patterns which reflect disease progression. In cancer studies biomarkers values change as functions of time and chemotherapy treatment is modified by delaying a course or reducing the dose intensity, according to patient’s toxicity levels. In this work, a Functional covariate Cox Model (FunCM) to study the association between time-varying processes and a time-to-event outcome is proposed. FunCM first exploits functional data analysis techniques to represent time-varying processes in terms of functional data. Then, information related to the evolution of the functions over time is incorporated into functional regression models for survival data through functional principal component analysis. FunCM is compared to a standard time-varying covariate Cox model, commonly used despite its limiting assumptions that covariate values are constant in time and measured without errors. Data from MRC BO06/EORTC 80931 randomised controlled trial for treatment of osteosarcoma are analysed. Time-varying covariates related to alkaline phosphatase levels, white blood cell counts and chemotherapy dose during treatment are investigated. The proposed method allows to detect differences between patients with different biomarkers and treatment evolutions, and to include this information in the survival model. These aspects are seldom addressed in the literature and could provide new insights into the clinical research.

Quantile regression models for survival data with missing censoring indicators.

The quantile regression model has increasingly become a useful approach for analyzing survival data due to its easy interpretation and flexibility in exploring the dynamic relationship between a time-to-event outcome and the covariates. In this paper, we consider the quantile regression model for survival data with missing censoring indicators. Based on the augmented inverse probability weighting technique, two weighted estimating equations are developed and corresponding easily implemented algorithms are suggested to solve the estimating equations. Asymptotic properties of the resultant estimators and the resampling-based inference procedures are established. Finally, the finite sample performances of the proposed approaches are investigated in simulation studies and a real data application.

Analisis Survival dengan Model Regresi pada Data Tersensor Berdistribusi Log-Logistik

Survival analysis is an analysis used to determine the length of time required by an object in order to survive. That time is sometimes influenced by several factors called independent variables. One way to know relationship is through a regression model. The dependent variable in this regression model is a survival time which is log-logistic distributed. The data used in this study were right censored survival data. Log-logistic regression models for survival data can be expressed by transformation Y=lnT= θ0+θ1xi1+...+θixij+σԑ. The parameter of the log-logistic regression models for right censored survival data are estimated with the maximum likelihood method. In this study, the application of log-logistic regression model for survival data is in data of lung cancer patients. Based on the data already performed, best log-logistic regression model is obtained yi=1.92458+0.0242393 xi1+0.639037ԑi.

Penalised Cox regression models for survival data

In recent years, the advances in genetic technology have enabled the collection of large amount of genetic information; as a result, analysis tools for microarray data have been in high demand. Among all types of data, survival outcome is particularly of more interest to study. Such data has become very typical in biomedical research or genetic lab. However, typical statistical models do not work for such scenarios; in this paper, several Cox model-based penalised regression approaches will be evaluated.

Penalised Cox regression models for survival data

In recent years, the advances in genetic technology have enabled the collection of large amount of genetic information; as a result, analysis tools for microarray data have been in high demand. Among all types of data, survival outcome is particularly of more interest to study. Such data has become very typical in biomedical research or genetic lab. However, typical statistical models do not work for such scenarios; in this paper, several Cox model-based penalised regression approaches will be evaluated.

Penalized estimation for competing risks regression with applications to high-dimensional covariates.

High-dimensional regression has become an increasingly important topic for many research fields. For example, biomedical research generates an increasing amount of data to characterize patients' bio-profiles (e.g. from a genomic high-throughput assay). The increasing complexity in the characterization of patients' bio-profiles is added to the complexity related to the prolonged follow-up of patients with the registration of the occurrence of possible adverse events. This information may offer useful insight into disease dynamics and in identifying subset of patients with worse prognosis and better response to the therapy. Although in the last years the number of contributions for coping with high and ultra-high-dimensional data in standard survival analysis have increased (Witten and Tibshirani, 2010. Survival analysis with high-dimensional covariates. Statistical Methods in Medical Research 19: (1), 29-51), the research regarding competing risks is less developed (Binder and others, 2009. Boosting for high-dimensional time-to-event data with competing risks. Bioinformatics 25: (7), 890-896). The aim of this work is to consider how to do penalized regression in the presence of competing events. The direct binomial regression model of Scheike and others (2008. Predicting cumulative incidence probability by direct binomial regression. Biometrika 95: (1), 205-220) is reformulated in a penalized framework to possibly fit a sparse regression model. The developed approach is easily implementable using existing high-performance software to do penalized regression. Results from simulation studies are presented together with an application to genomic data when the endpoint is progression-free survival. An R function is provided to perform regularized competing risks regression according to the binomial model in the package timereg (Scheike and Martinussen, 2006. Dynamic Regression models for survival data New York: Springer), available through CRAN.

Telematics and Gender Discrimination: Some Usage-Based Evidence on Whether Men’s Risk of Accidents Differs from Women’s

Pay-as-you-drive (PAYD), or usage-based automobile insurance (UBI), is a policy agreement tied to vehicle usage. In this paper we analyze the effect of the distance traveled on the risk of accidents among young drivers with a PAYD policy. We use regression models for survival data to estimate how long it takes them to have their first accident at fault during the coverage period. Our empirical application with real data is presented and shows that gender differences are mainly attributable to the intensity of use. Indeed, although gender has a significant effect in explaining the time to the first crash, this effect is no longer significant when the average distance traveled per day is introduced in the model. This suggests that gender differences in the risk of accidents are, to a large extent, attributable to the fact that men drive more often than women. Estimates of the time to the first accident for different driver risk types are presented. We conclude that no gender discrimination is necessary if telematics provides enough information on driving habits.

The Dantzig Selector in Cox's Proportional Hazards Model

The Dantzig selector (DS) is a recent approach of estimation in high-dimensional linear regression models with a large number of explanatory variables and a relatively small number of observations. As in the least absolute shrinkage and selection operator (LASSO), this approach sets certain regression coefficients exactly to zero, thus performing variable selection. However, such a framework, contrary to the LASSO, has never been used in regression models for survival data with censoring. A key motivation of this article is to study the estimation problem for Cox's proportional hazards (PH) function regression models using a framework that extends the theory, the computational advantages and the optimal asymptotic rate properties of the DS to the class of Cox's PH under appropriate sparsity scenarios. We perform a detailed simulation study to compare our approach with other methods and illustrate it on a well-known microarray gene expression data set for predicting survival from gene expressions.

Dynamic Regression Models for Survival Data edited by Martinussen, T. and Scheike, T. H.

Dynamic Regression Models for Survival Data edited by Martinussen, T. and Scheike, T. H.

Regression Analysis of Restricted Mean Survival Time Based on Pseudo-Observations

Regression models for survival data are often specified from the hazard function while classical regression analysis of quantitative outcomes focuses on the mean value (possibly after suitable transformations). Methods for regression analysis of mean survival time and the related quantity, the restricted mean survival time, are reviewed and compared to a method based on pseudo-observations. Both Monte Carlo simulations and two real data sets are studied. It is concluded that while existing methods may be superior for analysis of the mean, pseudo-observations seem well suited when the restricted mean is studied.

Cox proportional hazards regression models for survival data in cancer research.

Survival analysis which studies the distribution of life times is one of the most commonly used statistical techniques in cancer research. Most frequently, the Kaplan-Merir (1958) estimator is used to estimate the survival probability and log-rank test is used to compare the survival probabilities between the treatment groups. However, in cancer research, some prognostic factors, such as patient characteristics and treatment-related risk factors, may be associated with outcomes. Patients and biomedical researchers may want to know “which prognostic factors are associated with the outcome?”, “how does the prognostic factors affect the outcome?”, “does the risk factor have the same effect for different treatments?”, “what is the predicted survival probability at a certain time after the treatment for a particular patient?”, or “which treatment has better survival probabilities when adjusted for prognostic factors?”. We can use regression analysis to answer these questions. Cox (1972) proposed a proportional hazards regression model in analyzing the survival data. It has gained enormous popularity. We will discuss the techniques used in fitting a Cox regression model. Most of these techniques have been introduced and discussed in various books. Klein and Moeschberger (1997) gives an introduction and a number of examples to the Cox model. Fleming and Harrington (1991) and Andersen et al (1993) give a detailed theoretical discussions for these techniques.

On a general class of semiparametric hazards regression models

A general class of semiparametric hazards regression models for survival data is proposed and studied. This general class includes some popular classes of models as subclasses, such as Cox's proportional hazards model, the accelerated failure time model and a recently proposed class of models called the accelerated hazards model. In the general class of models, a covariate's effect is identified as having two separate components, namely a time-scale change on hazard progression and a relative hazards ratio. The new model is flexible in modelling survival data and may yield more accurate prediction of an individual's survival process. By way of the nested structure that includes the proportional hazards model, the accelerated failure time model and the accelerated hazards model, the general class of models may provide a numerical tool for determining which of them is more appropriate for a given dataset.

Historical controls and modern survival analysis.

Comparison of observed mortality with 'known,' 'background,' or 'standard' rates has taken place for several hundred years. With the developments of regression models for survival data, an increasing interest has arisen in individualizing the standardisation using covariates of each individual. Also, account sometimes needs to be taken of random variation in the standard group. Emphasizing uses of the Cox regression model, this paper surveys a number of critical choices and pitfalls in this area. The methods are illustrated by comparing survival of liver patients after transplantation with survival after conservative treatment.

Survival analysis and neural nets

We consider feed-forward neural nets and their relation to regression models for survival data. We show how the back-propagation algorithm may be used to obtain maximum likelihood estimates in certain standard regression models for survival data, as well as in various generalizations of these. Examples concerning malignant melanoma and post-partum amenorrhoea during lactation are used as illustration. We conclude that although problems with the substantial number of parameters and their interpretation remain, the feed-forward neural network models are flexible extensions to the standard regression models and thereby candidates for use in prediction and exploratory analyses in larger data sets.

Repeated assessment of risk factors in survival analysis.

Regression models for survival data with time-dependent covariates are considered. We review estimation in the Cox regression model and discuss problems in connection with data requirements for the analysis, with interpretation of results and with prediction based on such a model. In particular, we discuss how the latter problems may be approached within an extended (Markov process) model. A clinical trial in liver cirrhosis is used for illustration.

Discussion of Dr Green's Paper

Discussion of Dr Green's Paper

Graft survival after renal transplantation: Agenda for analysis

Simple life-table analyses have not identified the reasons for the steady improvement over the years in graft survival. The use of more sophisticated multifactorial statistical techniques is indicated to identify prognostic factors and to explore the "center effect" on graft survival. An agenda for retrospective analysis of graft survival is proposed as follows. The first item is organizing and checking both survival and covariate data to provide a general description of the transplant series so that one knows, for example, which covariates are interdependent. Plotting lifetables and the time-specific risk of graft failure for one covariate at a time is the next step. The limitations of such analyses are easy to demonstrate and are illustrated with examples which motivate a multifactorial approach. Standard regression models for survival data, such as the exponential, Weibull, proportional hazards, and log-logistic, are described with the caveat that in medical applications, particularly the relevance of covariates, may be time-dependent, not constant on a particular scale (hazard or log odds). The method which is described for exploring how the relevance of covariates changes with elapsed time since transplantation is a simple step-function extension of the idea of proportional hazards. Because discrepancies in graft survival between centers, the "center effect," may owe something to the patient's rehabilitation before transplantation, a scoring system for rehabilitation or performance status would be useful as a summary covariate. Even careful retrospective analysis will not usually promote or indict a treatment policy without confirmation from randomized comparisons. A survey of renal units to elicit research priorities is suggested and factorial designs are recommended as an efficient way of investigating several specific questions. Multicenter collaboration in clinical trials would ensure that answers were speedily available.