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Nonproportional hazards and unobserved heterogeneity in clustered survival data: When can we tell the difference?

ABSTRACT: Multivariate survival data are frequently encountered in biomedical applications in the form of clustered failures (or recurrent events data). A popular way of analyzing such data is by using shared frailty models, which assume that the proportional hazards assumption holds conditional on an unobserved cluster-specific random effect. Such models are often incorporated in more complicated joint models in survival analysis. If the random effect distribution has finite expectation, then the conditional proportional hazards assumption does not carry over to the marginal models. It has been shown that, for univariate data, this makes it impossible to distinguish between the presence of unobserved heterogeneity (eg, due to missing covariates) and marginal nonproportional hazards. We show that time-dependent covariate effects may falsely appear as evidence in favor of a frailty model also in the case of clustered failures or recurrent events data, when the cluster size or number of recurrent events is small. When true unobserved heterogeneity is present, the presence of nonproportional hazards leads to overestimating the frailty effect. We show that this phenomenon is somewhat mitigated as the cluster size grows. We carry out a simulation study to assess the behavior of test statistics and estimators for frailty models in such contexts. The gamma, inverse Gaussian, and positive stable shared frailty models are contrasted using a novel software implementation for estimating semiparametric shared frailty models. Two main questions are addressed in the contexts of clustered failures and recurrent events: whether covariates with a time-dependent effect may appear as indication of unobserved heterogeneity and whether the additional presence of unobserved heterogeneity can be detected in this case. Finally, the practical implications are illustrated in a real-world data analysis example.

SUBMITTER: Balan TA

PROVIDER: S-EPMC6619282 | biostudies-literature | 2019 Aug

REPOSITORIES: biostudies-literature

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Nonproportional hazards and unobserved heterogeneity in clustered survival data: When can we tell the difference?

Balan Theodor Adrian TA Putter Hein H

Statistics in medicine 20190503 18

Multivariate survival data are frequently encountered in biomedical applications in the form of clustered failures (or recurrent events data). A popular way of analyzing such data is by using shared frailty models, which assume that the proportional hazards assumption holds conditional on an unobserved cluster-specific random effect. Such models are often incorporated in more complicated joint models in survival analysis. If the random effect distribution has finite expectation, then the conditi ...[more]

PMID: 31050028

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Project description:We recently developed a new method random-intercept accelerated failure time model with Bayesian additive regression trees (riAFT-BART) to draw causal inferences about population treatment effect on patient survival from clustered and censored survival data while accounting for the multilevel data structure. The practical utility of this method goes beyond the estimation of population average treatment effect. In this work, we exposit how riAFT-BART can be used to solve two important statistical questions with clustered survival data: estimating the treatment effect heterogeneity and variable selection. Leveraging the likelihood-based machine learning, we describe a way in which we can draw posterior samples of the individual survival treatment effect from riAFT-BART model runs, and use the drawn posterior samples to perform an exploratory treatment effect heterogeneity analysis to identify subpopulations who may experience differential treatment effects than population average effects. There is sparse literature on methods for variable selection among clustered and censored survival data, particularly ones using flexible modeling techniques. We propose a permutation-based approach using the predictor's variable inclusion proportion supplied by the riAFT-BART model for variable selection. To address the missing data issue frequently encountered in health databases, we propose a strategy to combine bootstrap imputation and riAFT-BART for variable selection among incomplete clustered survival data. We conduct an expansive simulation study to examine the practical operating characteristics of our proposed methods, and provide empirical evidence that our proposed methods perform better than several existing methods across a wide range of data scenarios. Finally, we demonstrate the methods via a case study of predictors for in-hospital mortality among severe COVID-19 patients and estimating the heterogeneous treatment effects of three COVID-specific medications. The methods developed in this work are readily available in the R${\textsf {R}}$ package riAFTBART$\textsf {riAFTBART}$ .

Project description:BackgroundIn preventive drug trials such as intermittent preventive treatment for malaria prevention during pregnancy (IPTp), where there is repeated treatment administration, recurrence of adverse events (AEs) is expected. Challenges in modelling the risk of the AEs include accounting for time-to-AE and within-patient-correlation, beyond the conventional methods. The correlation comes from two sources; (a) individual patient unobserved heterogeneity (i.e. frailty) and (b) the dependence between AEs characterised by time-dependent treatment effects. Potential AE-dependence can be modelled via time-dependent treatment effects, event-specific baseline and event-specific random effect, while heterogeneity can be modelled via subject-specific random effect. Methods that can improve the estimation of both the unobserved heterogeneity and treatment effects can be useful in understanding the evolution of risk of AEs, especially in preventive trials where time-dependent treatment effect is expected.MethodsUsing both a simulation study and the Chloroquine for Malaria in Pregnancy (NCT01443130) trial data to demonstrate the application of the models, we investigated whether the lognormal shared frailty models with restricted cubic splines and non-proportional hazards (LSF-NPH) assumption can improve estimates for both frailty variance and treatment effect compared to the conventional inverse Gaussian shared frailty model with proportional hazard (ISF-PH), in the presence of time-dependent treatment effects and unobserved patient heterogeneity. We assessed the bias, precision gain and coverage probability of 95% confidence interval of the frailty variance estimates for the models under varying known unobserved heterogeneity, sample sizes and time-dependent effects.ResultsThe ISF-PH model provided a better coverage probability of 95% confidence interval, less bias and less precise frailty variance estimates compared to the LSF-NPH models. The LSF-NPH models yielded unbiased hazard ratio estimates at the expense of imprecision and high mean square error compared to the ISF-PH model.ConclusionThe choice of the shared frailty model for the recurrent AEs analysis should be driven by the study objective. Using the LSF-NPH models is appropriate if unbiased hazard ratio estimation is of primary interest in the presence of time-dependent treatment effects. However, ISF-PH model is appropriate if unbiased frailty variance estimation is of primary interest.Trial registrationClinicalTrials.gov; NCT01443130.

Project description:BackgroundHeterogeneity has a key role in meta-analysis methods and can greatly affect conclusions. However, true levels of heterogeneity are unknown and often researchers assume homogeneity. We aim to: a) investigate the prevalence of unobserved heterogeneity and the validity of the assumption of homogeneity; b) assess the performance of various meta-analysis methods; c) apply the findings to published meta-analyses.Methods and findingsWe accessed 57,397 meta-analyses, available in the Cochrane Library in August 2012. Using simulated data we assessed the performance of various meta-analysis methods in different scenarios. The prevalence of a zero heterogeneity estimate in the simulated scenarios was compared with that in the Cochrane data, to estimate the degree of unobserved heterogeneity in the latter. We re-analysed all meta-analyses using all methods and assessed the sensitivity of the statistical conclusions. Levels of unobserved heterogeneity in the Cochrane data appeared to be high, especially for small meta-analyses. A bootstrapped version of the DerSimonian-Laird approach performed best in both detecting heterogeneity and in returning more accurate overall effect estimates. Re-analysing all meta-analyses with this new method we found that in cases where heterogeneity had originally been detected but ignored, 17-20% of the statistical conclusions changed. Rates were much lower where the original analysis did not detect heterogeneity or took it into account, between 1% and 3%.ConclusionsWhen evidence for heterogeneity is lacking, standard practice is to assume homogeneity and apply a simpler fixed-effect meta-analysis. We find that assuming homogeneity often results in a misleading analysis, since heterogeneity is very likely present but undetected. Our new method represents a small improvement but the problem largely remains, especially for very small meta-analyses. One solution is to test the sensitivity of the meta-analysis conclusions to assumed moderate and large degrees of heterogeneity. Equally, whenever heterogeneity is detected, it should not be ignored.

Dataset Information

Nonproportional hazards and unobserved heterogeneity in clustered survival data: When can we tell the difference?

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Nonproportional hazards and unobserved heterogeneity in clustered survival data: When can we tell the difference?

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