Software for semiparametric shared gamma and log-normal frailty models: An overview

Hirsch, Karin; Wienke, Andreas

doi:10.1016/j.cmpb.2011.05.004

Cited by 28 publications

(22 citation statements)

References 13 publications

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“…Because clustering exists within the data (patients nested within hospital trusts), we fitted a multilevel survival model by extending the Cox regression model to include a frailty term with a Gaussian distribution. [27] This inclusion allowed adjustment for evidence of unexplained variation across hospital trusts. The proportional hazards assumption was assessed using Shoenfelds residuals.…”

Section: Methodsmentioning

confidence: 99%

Mortality rates at 10 years after metal-on-metal hip resurfacing compared with total hip replacement in England: retrospective cohort analysis of hospital episode statistics

Kendal

Prieto-Alhambra

Arden

et al. 2013

BMJ

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Objectives To compare 10 year mortality rates among patients undergoing metal-on-metal hip resurfacing and total hip replacement in England.Design Retrospective cohort study.Setting English hospital episode statistics database linked to mortality records from the Office for National Statistics.Population All adults who underwent primary elective hip replacement for osteoarthritis from April 1999 to March 2012. The exposure of interest was prosthesis type: cemented total hip replacement, uncemented total hip replacement, and metal-on-metal hip resurfacing. Confounding variables included age, sex, Charlson comorbidity index, rurality, area deprivation, surgical volume, and year of operation.Main outcome measures All cause mortality. Propensity score matching was used to minimise confounding by indication. Kaplan-Meier plots estimated the probability of survival up to 10 years after surgery. Multilevel Cox regression modelling, stratified on matched sets, described the association between prosthesis type and time to death, accounting for variation across hospital trusts.Results 7437 patients undergoing metal-on-metal hip resurfacing were matched to 22 311 undergoing cemented total hip replacement; 8101 patients undergoing metal-on-metal hip resurfacing were matched to 24 303 undergoing uncemented total hip replacement. 10 year rates of cumulative mortality were 271 (3.6%) for metal-on-metal hip resurfacing versus 1363 (6.1%) for cemented total hip replacement, and 239 (3.0%) for metal-on-metal hip resurfacing versus 999 (4.1%) for uncemented total hip replacement. Patients undergoing metal-on-metal hip resurfacing had an increased survival probability (hazard ratio 0.51 (95% confidence interval 0.45 to 0.59) for cemented hip replacement; 0.55 (0.47 to 0.65) for uncemented hip replacement). There was no evidence for an interaction with age or sex.Conclusions Patients with hip osteoarthritis undergoing metal-on-metal hip resurfacing have reduced mortality in the long term compared with those undergoing cemented or uncemented total hip replacement. This difference persisted after extensive adjustment for confounding factors available in our data. The study results can be applied to matched populations, which exclude patients who are very old and have had complex total hip replacements. Although residual confounding is possible, the observed effect size is large. These findings require validation in external cohorts and randomised clinical trials. IntroductionTotal hip replacement was introduced in the 1960s and has developed into one of the most successful treatments in modern medicine. [1] [2] Historically, the operation involves replacingCorrespondence to: A Carr andrew.carr@ndorms.ox.ac.uk Extra material supplied by the author (see

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Section: Methodsmentioning

confidence: 99%

Mortality rates at 10 years after metal-on-metal hip resurfacing compared with total hip replacement in England: retrospective cohort analysis of hospital episode statistics

Kendal

Prieto-Alhambra

Arden

et al. 2013

BMJ

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“…frailtyEM fits a gamma frailty model using the expectation‐maximization algorithm, whereas coxme relies on penalized likelihood . A comparison of R packages for fitting semiparametric frailty models is given in the work of Hirsch and Wienke; other possible packages that support semiparametric shared frailty models (using different estimation algorithms) are frailtySurv and frailtyHL . The fully parametric shared frailty models can be fitted using the parfm package for either a gamma or a lognormal frailty; models are fit using full likelihood, and Laplace integration is used when required .…”

Section: A Simulation Studymentioning

confidence: 99%

Impact of model misspecification in shared frailty survival models

Gasparini

Clements

Abrams

et al. 2019

Statistics in Medicine

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Survival models incorporating random effects to account for unmeasured heterogeneity are being increasingly used in biostatistical and applied research. Specifically, unmeasured covariates whose lack of inclusion in the model would lead to biased, inefficient results are commonly modeled by including a subject‐specific (or cluster‐specific) frailty term that follows a given distribution (eg, gamma or lognormal). Despite that, in the context of parametric frailty models, little is known about the impact of misspecifying the baseline hazard or the frailty distribution or both. Therefore, our aim is to quantify the impact of such misspecification in a wide variety of clinically plausible scenarios via Monte Carlo simulation, using open‐source software readily available to applied researchers. We generate clustered survival data assuming various baseline hazard functions, including mixture distributions with turning points, and assess the impact of sample size, variance of the frailty, baseline hazard function, and frailty distribution. Models compared include standard parametric distributions and more flexible spline‐based approaches; we also included semiparametric Cox models. The resulting bias can be clinically relevant. In conclusion, we highlight the importance of fitting models that are flexible enough and the importance of assessing model fit. We illustrate our conclusions with two applications using data on diabetic retinopathy and bladder cancer. Our results show the importance of assessing model fit with respect to the baseline hazard function and the distribution of the frailty: misspecifying the former leads to biased relative and absolute risk estimates, whereas misspecifying the latter affects absolute risk estimates and measures of heterogeneity.

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“…According to Hirsch and Wienke (2011), none of the other software packages with estimation routines for shared-frailty models allows for left-truncation, with the exception of an R package called Frailtypack. This uses the semi-parametric Rondeau and Gonzales (2005) estimator which uses a full likelihood function that does take account of the interplay between dynamic selection and left-truncation (their estimator penalizes non-smoothness of the baseline hazard function λ(t)).…”

Section: Likelihood Specification With Left-truncated Duration Data Amentioning

confidence: 99%

“…The main survival model estimation command streg also captures the shared-frailty model, by invoking the option shared() to indicate which individuals share the same value of v. Gutierrez (2002) gives an overview of parametric shared-frailty models in Stata. See Hirsch and Wienke (2011) for an overview of software packages with estimation routines for sharedfrailty models.…”

Section: Introductionmentioning

confidence: 99%

Inference for Shared-Frailty Survival Models with Left-Truncated Data

Berg

Drepper

2015

Econometric Reviews

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Shared-frailty survival models specify that systematic unobserved determinants of duration outcomes are identical within groups of individuals. We consider random-effects likelihood-based statistical inference if the duration data are subject to left-truncation. Such inference with left-truncated data can be performed in the Stata software package. We show that with left-truncated data, the commands ignore the weeding-out process before the left-truncation points, affecting the distribution of unobserved determinants among group members in the data, that is, among the group members who survive until their truncation points. We critically examine studies in the statistical literature on this issue as well as published empirical studies that use the commands. Simulations illustrate the size of the (asymptotic) bias and its dependence on the degree of truncation. We provide a Stata command file that maximizes the likelihood function that properly takes account of the interplay between truncation and dynamic selection.

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Software for semiparametric shared gamma and log-normal frailty models: An overview

Cited by 28 publications

References 13 publications

Mortality rates at 10 years after metal-on-metal hip resurfacing compared with total hip replacement in England: retrospective cohort analysis of hospital episode statistics

Mortality rates at 10 years after metal-on-metal hip resurfacing compared with total hip replacement in England: retrospective cohort analysis of hospital episode statistics

Impact of model misspecification in shared frailty survival models

Inference for Shared-Frailty Survival Models with Left-Truncated Data

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