Relaxing the independent censoring assumption in the Cox proportional hazards model using multiple imputation.
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ABSTRACT:
SUBMITTER: Jackson D
PROVIDER: S-EPMC4282781 | biostudies-literature | 2014 Nov
REPOSITORIES: biostudies-literature
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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
Project description: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 informationThe online version contains supplementary material available at 10.1007/s12055-020-01108-7.
| S-EPMC7876211 | biostudies-literature
Project description:BackgroundThe appropriate handling of missing covariate data in prognostic modelling studies is yet to be conclusively determined. A resampling study was performed to investigate the effects of different missing data methods on the performance of a prognostic model.MethodsObserved data for 1000 cases were sampled with replacement from a large complete dataset of 7507 patients to obtain 500 replications. Five levels of missingness (ranging from 5% to 75%) were imposed on three covariates using a missing at random (MAR) mechanism. Five missing data methods were applied; a) complete case analysis (CC) b) single imputation using regression switching with predictive mean matching (SI), c) multiple imputation using regression switching imputation, d) multiple imputation using regression switching with predictive mean matching (MICE-PMM) and e) multiple imputation using flexible additive imputation models. A Cox proportional hazards model was fitted to each dataset and estimates for the regression coefficients and model performance measures obtained.ResultsCC produced biased regression coefficient estimates and inflated standard errors (SEs) with 25% or more missingness. The underestimated SE after SI resulted in poor coverage with 25% or more missingness. Of the MI approaches investigated, MI using MICE-PMM produced the least biased estimates and better model performance measures. However, this MI approach still produced biased regression coefficient estimates with 75% missingness.ConclusionsVery few differences were seen between the results from all missing data approaches with 5% missingness. However, performing MI using MICE-PMM may be the preferred missing data approach for handling between 10% and 50% MAR missingness.
| S-EPMC3019210 | biostudies-literature
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
Project description:BackgroundTo accurately predict the response to treatment, we need a stable and effective risk score that can be calculated from patient characteristics. When we evaluate such risks from time-to-event data with right-censoring, Cox's proportional hazards model is the most popular for estimating the linear risk score. However, the intrinsic heterogeneity of patients may prevent us from obtaining a valid score. It is therefore insufficient to consider the regression problem with a single linear predictor.Methodswe propose the model with a quasi-linear predictor that combines several linear predictors. This provides a natural extension of Cox model that leads to a mixture hazards model. We investigate the property of the maximum likelihood estimator for the proposed model. Moreover, we propose two strategies for getting the interpretable estimates. The first is to restrict the model structure in advance, based on unsupervised learning or prior information, and the second is to obtain as parsimonious an expression as possible in the parameter estimation strategy with cross- L1 penalty. The performance of the proposed method are evaluated by simulation and application studies.ResultsWe showed that the maximum likelihood estimator has consistency and asymptotic normality, and the cross- L1-regularized estimator has root-n consistency. Simulation studies show these properties empirically, and application studies show that the proposed model improves predictive ability relative to Cox model.ConclusionsIt is essential to capture the intrinsic heterogeneity of patients for getting more stable and effective risk score. The proposed hazard model can capture such heterogeneity and achieve better performance than the ordinary linear Cox proportional hazards model.
| S-EPMC7336640 | biostudies-literature
Project description:BackgroundClinical prediction rules (CPRs) should be externally validated by independent researchers. Although there are many cardiovascular CPRs, most have not been externally validated. It is not known why some CPRs are externally validated by independent researchers and others are not.MethodsWe analyzed cardiovascular risk CPRs included in a systematic review. Independent external validations were identified by forward citation searches of derivation studies. Time between the publication of a cardiovascular CPR and the first independent external validation was calculated. We assessed Kaplan-Meier estimates of the probability to have an independent external validation. Using univariable Cox regression, we explored whether characteristics of derivation (design, location, sample size, number of predictors, presentation format, validation in derivation), reporting (participants, predictors, outcomes, performance measure, information for risk calculation), and publication (journal impact factor) are associated with time to the first independent external validation.ResultsOf 125 cardiovascular risk CPRs, 29 had an independent external validation. The median follow-up was 118 months (95% CI, 99-130). The 25th percentile of event time was 122 months (95% CI, 91-299). Cardiovascular risk CPRs from the USA were 4.15 times (95% CI, 1.89-9.13) more likely to have an independent external validation. Increasing the sample size of derivation by ten times was associated with a 2.32-fold (95% CI, 1.37-3.91) increase in the probability of having an independent external validation. CPRs presented with an internal validation tend to get an independent external validation sooner (HR = 1.73, 95% CI, 0.77-3.93). CPRs reporting all the information necessary for calculating individual risk were 2.65 (95% CI, 1.01-6.96) times more likely to have an independent external validation. Publishing a cardiovascular risk CPR in a journal that has one unit higher impact factor was associated with a 6% (95% CI, 3-9) higher likelihood of an independent external validation.ConclusionsThe probability for cardiovascular risk CPRs to get an independent external validation was low even many years after their derivations. Authors of new cardiovascular risk CPRs should consider using adequate sample size, conducting an internal validation, and reporting all the information needed for risk calculation as these features were associated with an independent external validation.
| S-EPMC6460844 | biostudies-literature
Project description:Regularized variable selection is a powerful tool for identifying the true regression model from a large number of candidates by applying penalties to the objective functions. The penalty functions typically involve a tuning parameter that control the complexity of the selected model. The ability of the regularized variable selection methods to identify the true model critically depends on the correct choice of the tuning parameter. In this study we develop a consistent tuning parameter selection method for regularized Cox's proportional hazards model with a diverging number of parameters. The tuning parameter is selected by minimizing the generalized information criterion. We prove that, for any penalty that possesses the oracle property, the proposed tuning parameter selection method identifies the true model with probability approaching one as sample size increases. Its finite sample performance is evaluated by simulations. Its practical use is demonstrated in the Cancer Genome Atlas (TCGA) breast cancer data.
| S-EPMC6107315 | biostudies-literature
Project description:BackgroundSurvival analysis and effect of covariates on survival time is a central research interest. Cox proportional hazards regression remains as a gold standard in the survival analysis. The Cox model relies on the assumption of proportional hazards (PH) across different covariates. PH assumptions should be assessed and handled if violated. Our aim was to investigate the reporting of the Cox regression model details and testing of the PH assumption in survival analysis in total joint arthroplasty (TJA) studies.MethodsWe conducted a review in the PubMed database on 28th August 2019. A total of 1154 studies were identified. The abstracts of these studies were screened for words "cox and "hazard*" and if either was found the abstract was read. The abstract had to fulfill the following criteria to be included in the full-text phase: topic was knee or hip TJA surgery; survival analysis was used, and hazard ratio reported. If all the presented criteria were met, the full-text version of the article was then read. The full-text was included if Cox method was used to analyze TJA survival. After accessing the full-texts 318 articles were included in final analysis.ResultsThe PH assumption was mentioned in 114 of the included studies (36%). KM analysis was used in 281 (88%) studies and the KM curves were presented graphically in 243 of these (87%). In 110 (45%) studies, the KM survival curves crossed in at least one of the presented figures. The most common way to test the PH assumption was to inspect the log-minus-log plots (n = 59). The time-axis division method was the most used corrected model (n = 30) in cox analysis. Of the 318 included studies only 63 (20%) met the following criteria: PH assumption mentioned, PH assumption tested, testing method of the PH assumption named, the result of the testing mentioned, and the Cox regression model corrected, if required.ConclusionsReporting and testing of the PH assumption and dealing with non-proportionality in hip and knee TJA studies was limited. More awareness and education regarding the assumptions behind the used statistical models among researchers, reviewers and editors are needed to improve the quality of TJA research. This could be achieved by better collaboration with methodologists and statisticians and introducing more specific reporting guidelines for TJA studies. Neglecting obvious non-proportionality undermines the overall research efforts since causes of non-proportionality, such as possible underlying pathomechanisms, are not considered and discussed.
| S-EPMC8161573 | biostudies-literature
Project description:An adequate imputation of missing data would significantly preserve the statistical power and avoid erroneous conclusions. In the era of big data, machine learning is a great tool to infer the missing values. The root means square error (RMSE) and the proportion of falsely classified entries (PFC) are two standard statistics to evaluate imputation accuracy. However, the Cox proportional hazards model using various types requires deliberate study, and the validity under different missing mechanisms is unknown. In this research, we propose supervised and unsupervised imputations and examine four machine learning-based imputation strategies. We conducted a simulation study under various scenarios with several parameters, such as sample size, missing rate, and different missing mechanisms. The results revealed the type-I errors according to different imputation techniques in the survival data. The simulation results show that the non-parametric "missForest" based on the unsupervised imputation is the only robust method without inflated type-I errors under all missing mechanisms. In contrast, other methods are not valid to test when the missing pattern is informative. Statistical analysis, which is improperly conducted, with missing data may lead to erroneous conclusions. This research provides a clear guideline for a valid survival analysis using the Cox proportional hazard model with machine learning-based imputations.
| S-EPMC8289437 | biostudies-literature
Project description:BackgroundCox proportional hazard regression (CPH) model relies on the proportional hazard (PH) assumption: the hazard of variables is independent of time. CPH has been widely used to identify prognostic markers of the transcriptome. However, the comprehensive investigation on PH assumption in transcriptomic data has lacked.ResultsThe whole transcriptomic data of the 9,056 patients from 32 cohorts of The Cancer Genome Atlas and the 3 lung cancer cohorts from Gene Expression Omnibus were collected to construct CPH model for each gene separately for fitting the overall survival. An average of 8.5% gene CPH models violated the PH assumption in TCGA pan-cancer cohorts. In the gene interaction networks, both hub and non-hub genes in CPH models were likely to have non-proportional hazards. Violations of PH assumption for the same gene models were not consistent in 5 non-small cell lung cancer datasets (all kappa coefficients < 0.2), indicating that the non-proportionality of gene CPH models depended on the datasets. Furthermore, the introduction of log(t) or sqrt(t) time-functions into CPH improved the performance of gene models on overall survival fitting in most tumors. The time-dependent CPH changed the significance of log hazard ratio of the 31.9% gene variables.ConclusionsOur analysis resulted that non-proportional hazards should not be ignored in transcriptomic data. Introducing time interaction term ameliorated performance and interpretability of non-proportional hazards of transcriptome data in CPH.
| S-EPMC8762368 | biostudies-literature