Browse
Submit Data
Databases
API
Help

Dataset Information

0 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Survival analysis-part 2: Cox proportional hazards model.

ABSTRACT: Learning objectives: 1. To understand the log-rank test and limitations of the log-rank test in comparing survival between groups. 2. To understand the fundamental concepts of the proportional hazards assumption. 3. To understand basic steps in the development of the Cox proportional hazards model and reported hazard ratios. 4. To understand how results of a Cox model run using STATA© (a commonly used proprietary statistical software) can be understood and interpreted.

Supplementary information

The online version contains supplementary material available at 10.1007/s12055-020-01108-7.

SUBMITTER: Deo SV

PROVIDER: S-EPMC7876211 | biostudies-literature | 2021 Mar

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Survival analysis-part 2: Cox proportional hazards model.

Deo Salil Vasudeo SV Deo Vaishali V Sundaram Varun V

Indian journal of thoracic and cardiovascular surgery 20210102 2

Learning objectives: 1. To understand the log-rank test and limitations of the log-rank test in comparing survival between groups. 2. To understand the fundamental concepts of the proportional hazards assumption. 3. To understand basic steps in the development of the Cox proportional hazards model and reported hazard ratios. 4. To understand how results of a Cox model run using STATA© (a commonly used proprietary statistical software) can be understood and interpreted.<h4>Supplementary informati ...[more]

PMID: 33642726

Similar Datasets

A double-Cox model for non-proportional hazards survival analysis with frailty.

Project description:The Cox regression, a semi-parametric method of survival analysis, is extremely popular in biomedical applications. The proportional hazards assumption is a key requirement in the Cox model. To accommodate non-proportional hazards, we propose to parameterize the shape parameter of the baseline hazard function using the additional, separate Cox-regression term which depends on the vector of the covariates. This parametrization retains the general form of the hazard function over the strata and is similar to one in Devarajan and Ebrahimi (Comput Stat Data Anal. 2011;55:667-676) in the case of the Weibull distribution, but differs for other hazard functions. We call this model the double-Cox model. We formally introduce the double-Cox model with shared frailty and investigate, by simulation, the estimation bias and the coverage of the proposed point and interval estimation methods for the Gompertz and the Weibull baseline hazards. For real-life applications with low frailty variance and a large number of clusters, the marginal likelihood estimation is almost unbiased and the profile likelihood-based confidence intervals provide good coverage for all model parameters. We also compare the results from the over-parametrized double-Cox model to those from the standard Cox model with frailty in the case of the scale-only proportional hazards. The model is illustrated on an example of the survival after a diagnosis of type 2 diabetes mellitus. The R programs for fitting the double-Cox model are available on Github.

| S-EPMC10946853 | biostudies-literature

Moving beyond the Cox proportional hazards model in survival data analysis: a cervical cancer study.

Project description:ObjectivesThis study explored the prognostic factors and developed a prediction model for Chinese-American (CA) cervical cancer (CC) patients. We compared two alternative models (the restricted mean survival time (RMST) model and the proportional baselines landmark supermodel (PBLS model, producing dynamic prediction)) versus the Cox proportional hazards model in the context of time-varying effects.Setting and data sourcesA total of 713 CA women with CC and available covariates (age at diagnosis, International Federation of Gynecology and Obstetrics (FIGO) stage, lymph node metastasis and radiation) from the Surveillance, Epidemiology and End Results database were included.DesignWe applied the Cox proportional hazards model to analyse the all-cause mortality with the proportional hazards assumption. Additionally, we applied two alternative models to analyse covariates with time-varying effects. The performances of the models were compared using the C-index for discrimination and the shrinkage slope for calibration.ResultsOlder patients had a worse survival rate than younger patients. Advanced FIGO stage patients showed a relatively poor survival rate and low life expectancy. Lymph node metastasis was an unfavourable prognostic factor in our models. Age at diagnosis, FIGO stage and lymph node metastasis represented time-varying effects from the PBLS model. Additionally, radiation showed no impact on survival in any model. Dynamic prediction presented a better performance for 5-year dynamic death rates than did the Cox proportional hazards model.ConclusionsWith the time-varying effects, the RMST model was suggested to explore diagnosis factors, and the PBLS model was recommended to predict a patient's w-year dynamic death rate.

| S-EPMC7371360 | biostudies-literature

High-dimensional, massive sample-size Cox proportional hazards regression for survival analysis.

Project description:Survival analysis endures as an old, yet active research field with applications that spread across many domains. Continuing improvements in data acquisition techniques pose constant challenges in applying existing survival analysis methods to these emerging data sets. In this paper, we present tools for fitting regularized Cox survival analysis models on high-dimensional, massive sample-size (HDMSS) data using a variant of the cyclic coordinate descent optimization technique tailored for the sparsity that HDMSS data often present. Experiments on two real data examples demonstrate that efficient analyses of HDMSS data using these tools result in improved predictive performance and calibration.

| S-EPMC3944969 | biostudies-literature

Fitting the Cox proportional hazards model to big data.

Project description:The semiparametric Cox proportional hazards model, together with the partial likelihood principle, has been widely used to study the effects of potentially time-dependent covariates on a possibly censored event time. We propose a computationally efficient method for fitting the Cox model to big data involving millions of study subjects. Specifically, we perform maximum partial likelihood estimation on a small subset of the whole data and improve the initial estimator by incorporating the remaining data through one-step estimation with estimated efficient score functions. We show that the final estimator has the same asymptotic distribution as the conventional maximum partial likelihood estimator using the whole dataset but requires only a small fraction of computation time. We demonstrate the usefulness of the proposed method through extensive simulation studies and an application to the UK Biobank data.

| S-EPMC10946235 | biostudies-literature

Bayesian Cox Proportional Hazards Model in Survival Analysis of HACE1 Gene with Age at Onset of Alzheimer's Disease.

Project description:Alzheimer's disease (AD), the most common form of dementia, is a chronic neurodegenerative disease. The HECT domain and ankyrin repeat containing E3 ubiquitin protein ligase 1 (HACE1) gene is expressed in human brain and may play a role in the pathogenesis of neurodegenerative disorders. Till now, no previous study has reported the association of the HACE1 gene with the risk and age at onset (AAO) of AD; while few studies have checked the proportional hazards assumption in the survival analysis of AAO of AD using Cox proportional hazards model. In this study, we examined the associations of 14 single nucleotide polymorphisms (SNPs) in the HACE1 gene with the risk and the AAO of AD using 791 AD patients and 782 controls. Multiple logistic regression model identified one SNP (rs9499937 with p = 1.8×10-3) to be associated with the risk of AD. For survival analysis of AAO, both classic Cox regression model and Bayesian survival analysis using the Cox proportional hazards model were applied to examine the association of each SNP with the AAO. The hazards ratio (HR) with its 95% confidence interval (CI) was estimated. Survival analysis using the classic Cox regression model showed that 4 SNPs were significantly associated with the AAO (top SNP rs9499937 with HR=1.33, 95%CI=1.13-1.57, p=5.0×10-4). Bayesian Cox regression model showed similar but a slightly stronger associations (top SNP rs9499937 with HR=1.34, 95%CI=1.11-1.55) compared with the classic Cox regression model. Using an independent family-based sample, one SNP rs9486018 was associated with the risk of AD (p=0.0323) and the T-T-G haplotype from rs9786015, rs9486018 and rs4079063 showed associations with both the risk and AAO of AD (p=2.27×10-3 and 0.0487, respectively). The findings of this study provide first evidence that several genetic variants in the HACE1 gene were associated with the risk and AAO of AD.

| S-EPMC5806706 | biostudies-literature

An online framework for survival analysis: reframing Cox proportional hazards model for large data sets and neural networks.

Project description:In many biomedical applications, outcome is measured as a "time-to-event" (e.g., disease progression or death). To assess the connection between features of a patient and this outcome, it is common to assume a proportional hazards model and fit a proportional hazards regression (or Cox regression). To fit this model, a log-concave objective function known as the "partial likelihood" is maximized. For moderate-sized data sets, an efficient Newton-Raphson algorithm that leverages the structure of the objective function can be employed. However, in large data sets this approach has two issues: (i) The computational tricks that leverage structure can also lead to computational instability; (ii) The objective function does not naturally decouple: Thus, if the data set does not fit in memory, the model can be computationally expensive to fit. This additionally means that the objective is not directly amenable to stochastic gradient-based optimization methods. To overcome these issues, we propose a simple, new framing of proportional hazards regression: This results in an objective function that is amenable to stochastic gradient descent. We show that this simple modification allows us to efficiently fit survival models with very large data sets. This also facilitates training complex, for example, neural-network-based, models with survival data.

| S-EPMC10724274 | biostudies-literature

Exposure assessment for Cox proportional hazards cure models with interval-censored survival data.

Project description:Mixture cure models have been developed as an effective tool to analyze failure time data with a cure fraction. Used in conjunction with the logistic regression model, this model allows covariate-adjusted inference of an exposure effect on the cured probability and the hazard of failure for the uncured subjects. However, the covariate-adjusted inference for the overall exposure effect is not directly provided. In this paper, we describe a Cox proportional hazards cure model to analyze interval-censored survival data in the presence of a cured fraction and then apply a post-estimation approach by using model-predicted estimates difference to assess the overall exposure effect on the restricted mean survival time scale. For baseline hazard/survival function estimation, simple parametric models as fractional polynomials or restricted cubic splines are utilized to approximate the baseline logarithm cumulative hazard function, or, alternatively, the full likelihood is specified through a piecewise linear approximation for the cumulative baseline hazard function. Simulation studies were conducted to demonstrate the unbiasedness of both estimation methods for the overall exposure effect estimates over various baseline hazard distribution shapes. The methods are applied to analyze the interval-censored relapse time data from a smoking cessation study.

| S-EPMC8752467 | biostudies-literature

Survival time prediction by integrating cox proportional hazards network and distribution function network.

Project description:BackgroundThe Cox proportional hazards model is commonly used to predict hazard ratio, which is the risk or probability of occurrence of an event of interest. However, the Cox proportional hazard model cannot directly generate an individual survival time. To do this, the survival analysis in the Cox model converts the hazard ratio to survival times through distributions such as the exponential, Weibull, Gompertz or log-normal distributions. In other words, to generate the survival time, the Cox model has to select a specific distribution over time.ResultsThis study presents a method to predict the survival time by integrating hazard network and a distribution function network. The Cox proportional hazards network is adapted in DeepSurv for the prediction of the hazard ratio and a distribution function network applied to generate the survival time. To evaluate the performance of the proposed method, a new evaluation metric that calculates the intersection over union between the predicted curve and ground truth was proposed. To further understand significant prognostic factors, we use the 1D gradient-weighted class activation mapping method to highlight the network activations as a heat map visualization over an input data. The performance of the proposed method was experimentally verified and the results compared to other existing methods.ConclusionsOur results confirmed that the combination of the two networks, Cox proportional hazards network and distribution function network, can effectively generate accurate survival time.

| S-EPMC8050908 | biostudies-literature

Causal Mediation Analysis for the Cox Proportional Hazards Model with a Smooth Baseline Hazard Estimator.

Project description:An important problem within the social, behavioral, and health sciences is how to partition an exposure effect (e.g. treatment or risk factor) among specific pathway effects and to quantify the importance of each pathway. Mediation analysis based on the potential outcomes framework is an important tool to address this problem and we consider the estimation of mediation effects for the proportional hazards model in this paper. We give precise definitions of the total effect, natural indirect effect, and natural direct effect in terms of the survival probability, hazard function, and restricted mean survival time within the standard two-stage mediation framework. To estimate the mediation effects on different scales, we propose a mediation formula approach in which simple parametric models (fractional polynomials or restricted cubic splines) are utilized to approximate the baseline log cumulative hazard function. Simulation study results demonstrate low bias of the mediation effect estimators and close-to-nominal coverage probability of the confidence intervals for a wide range of complex hazard shapes. We apply this method to the Jackson Heart Study data and conduct sensitivity analysis to assess the impact on the mediation effects inference when the no unmeasured mediator-outcome confounding assumption is violated.

| S-EPMC5604250 | biostudies-literature

Multiple imputation of missing covariates for the Cox proportional hazards cure model.

Project description:We explore several approaches for imputing partially observed covariates when the outcome of interest is a censored event time and when there is an underlying subset of the population that will never experience the event of interest. We call these subjects 'cured', and we consider the case where the data are modeled using a Cox proportional hazards (CPH) mixture cure model. We study covariate imputation approaches using fully conditional specification. We derive the exact conditional distribution and suggest a sampling scheme for imputing partially observed covariates in the CPH cure model setting. We also propose several approximations to the exact distribution that are simpler and more convenient to use for imputation. A simulation study demonstrates that the proposed imputation approaches outperform existing imputation approaches for survival data without a cure fraction in terms of bias in estimating CPH cure model parameters. We apply our multiple imputation techniques to a study of patients with head and neck cancer. Copyright © 2016 John Wiley & Sons, Ltd.

| S-EPMC5053880 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data