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Multiple imputation in Cox regression when there are time-varying effects of covariates.

ABSTRACT: In Cox regression, it is important to test the proportional hazards assumption and sometimes of interest in itself to study time-varying effects (TVEs) of covariates. TVEs can be investigated with log hazard ratios modelled as a function of time. Missing data on covariates are common and multiple imputation is a popular approach to handling this to avoid the potential bias and efficiency loss resulting from a "complete-case" analysis. Two multiple imputation methods have been proposed for when the substantive model is a Cox proportional hazards regression: an approximate method (Imputing missing covariate values for the Cox model in Statistics in Medicine (2009) by White and Royston) and a substantive-model-compatible method (Multiple imputation of covariates by fully conditional specification: accommodating the substantive model in Statistical Methods in Medical Research (2015) by Bartlett et al). At present, neither accommodates TVEs of covariates. We extend them to do so for a general form for the TVEs and give specific details for TVEs modelled using restricted cubic splines. Simulation studies assess the performance of the methods under several underlying shapes for TVEs. Our proposed methods give approximately unbiased TVE estimates for binary covariates with missing data, but for continuous covariates, the substantive-model-compatible method performs better. The methods also give approximately correct type I errors in the test for proportional hazards when there is no TVE and gain power to detect TVEs relative to complete-case analysis. Ignoring TVEs at the imputation stage results in biased TVE estimates, incorrect type I errors, and substantial loss of power in detecting TVEs. We also propose a multivariable TVE model selection algorithm. The methods are illustrated using data from the Rotterdam Breast Cancer Study. R code is provided.

SUBMITTER: Keogh RH

PROVIDER: S-EPMC6220767 | biostudies-literature | 2018 Nov

REPOSITORIES: biostudies-literature

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Multiple imputation in Cox regression when there are time-varying effects of covariates.

Keogh Ruth H RH Morris Tim P TP

Statistics in medicine 20180716 25

In Cox regression, it is important to test the proportional hazards assumption and sometimes of interest in itself to study time-varying effects (TVEs) of covariates. TVEs can be investigated with log hazard ratios modelled as a function of time. Missing data on covariates are common and multiple imputation is a popular approach to handling this to avoid the potential bias and efficiency loss resulting from a "complete-case" analysis. Two multiple imputation methods have been proposed for when t ...[more]

PMID: 30014575

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Project description:BackgroundPatients with hepatitis C virus (HCV) frequently remain at risk for cirrhosis after sustained virologic response (SVR). Existing cirrhosis predictive models for HCV do not account for dynamic antiviral treatment status and are limited by fixed laboratory covariates and short follow up time. Advanced fibrosis assessment modalities, such as transient elastography, remain inaccessible in many settings. Improved cirrhosis predictive models are needed.MethodsWe developed a laboratory-based model to predict progression of liver disease after SVR. This prediction model used a time-varying covariates Cox model adapted to utilize longitudinal laboratory data and to account for antiretroviral treatment. Individuals were included if they had a history of detectable HCV RNA and at least 2 AST-to-platelet ratio index (APRI) scores available in the national Veterans Health Administration from 2000 to 2015, Observation time extended through January 2019. We excluded individuals with preexisting cirrhosis. Covariates included baseline patient characteristics and 16 time-varying laboratory predictors. SVR, defined as permanently undetectable HCV RNA after antiviral treatment, was modeled as a step function of time. Cirrhosis development was defined as two consecutive APRI scores > 2. We predicted cirrhosis development at 1-, 3-, and 5-years follow-up.ResultsIn a national sample of HCV patients (n = 182,772) with a mean follow-up of 6.32 years, 42% (n = 76,854) achieved SVR before 2016 and 16.2% (n = 29,566) subsequently developed cirrhosis. The model demonstrated good discrimination for predicting cirrhosis across all combinations of laboratory data windows and cirrhosis prediction intervals. AUROCs ranged from 0.781 to 0.815, with moderate sensitivity 0.703-0.749 and specificity 0.723-0.767.ConclusionA novel adaptation of time-varying covariates Cox modeling technique using longitudinal laboratory values and dynamic antiviral treatment status accurately predicts cirrhosis development at 1-, 3-, and 5-years among patients with HCV, with and without SVR. It improves upon earlier cirrhosis predictive models and has many potential population-based applications, especially in settings without transient elastography available.

Dataset Information

Multiple imputation in Cox regression when there are time-varying effects of covariates.

Publications

Multiple imputation in Cox regression when there are time-varying effects of covariates.

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