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Multi-parameter regression survival modelling with random effects. STAT MODEL 2022. [DOI: 10.1177/1471082x221117377] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
We consider a parametric modelling approach for survival data where covariates are allowed to enter the model through multiple distributional parameters (i.e., scale and shape). This is in contrast with the standard convention of having a single covariate-dependent parameter, typically the scale. Taking what is referred to as a multi-parameter regression (MPR) approach to modelling has been shown to produce flexible and robust models with relatively low model complexity cost. However, it is very common to have clustered data arising from survival analysis studies, and this is something that is under developed in the MPR context. The purpose of this article is to extend MPR models to handle multivariate survival data by introducing random effects in both the scale and the shape regression components. We consider a variety of possible dependence structures for these random effects (independent, shared and correlated), and estimation proceeds using a h-likelihood approach. The performance of our estimation procedure is investigated by a way of an extensive simulation study, and the merits of our modelling approach are illustrated through applications to two real data examples, a lung cancer dataset and a bladder cancer dataset.
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Ha ID, Lee Y. A review of h-likelihood for survival analysis. JAPANESE JOURNAL OF STATISTICS AND DATA SCIENCE 2021. [DOI: 10.1007/s42081-021-00125-z] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
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3
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Park E, Kwon S, Kwon J, Sylvester R, Ha ID. Penalized h‐likelihood approach for variable selection in AFT random‐effect models. STAT NEERL 2019. [DOI: 10.1111/stan.12179] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Eunyoung Park
- Department of StatisticsPukyong National University Busan South Korea
| | - Sookhee Kwon
- Department of StatisticsPukyong National University Busan South Korea
| | - Jihoon Kwon
- Department of Clinical Pharmacology and Therapeutics, College of MedicineSeoul National University Hospital Seoul South Korea
| | - Richard Sylvester
- European Organisation for Research and Treatment of Cancer Brussels Belgium
| | - Il Do Ha
- Department of StatisticsPukyong National University Busan South Korea
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Park E, Ha ID. Penalized variable selection for accelerated failure time models with random effects. Stat Med 2019; 38:878-892. [PMID: 30411376 DOI: 10.1002/sim.8023] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Revised: 09/22/2018] [Accepted: 10/11/2018] [Indexed: 11/07/2022]
Abstract
Accelerated failure time (AFT) models allowing for random effects are linear mixed models under the log-transformation of survival time with censoring and describe dependence in correlated survival data. It is well known that the AFT models are useful alternatives to frailty models. To the best of our knowledge, however, there is no literature on variable selection methods for such AFT models. In this paper, we propose a simple but unified variable-selection procedure of fixed effects in the AFT random-effect models using penalized h-likelihood (HL). We consider four penalty functions (ie, least absolute shrinkage and selection operator (LASSO), adaptive LASSO, smoothly clipped absolute deviation (SCAD), and HL). We show that the proposed method can be easily implemented via a slight modification to existing h-likelihood estimation procedures. We thus demonstrate that the proposed method can also be easily extended to AFT models with multilevel (or nested) structures. Simulation studies also show that the procedure using the adaptive LASSO, SCAD, or HL penalty performs well. In particular, we find via the simulation results that the variable selection method with HL penalty provides a higher probability of choosing the true model than other three methods. The usefulness of the new method is illustrated using two actual datasets from multicenter clinical trials.
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Affiliation(s)
- Eunyoung Park
- Department of Statistics, Pukyong National University, Busan, South Korea
| | - Il Do Ha
- Department of Statistics, Pukyong National University, Busan, South Korea
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5
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Penalized variable selection for accelerated failure time models. COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS 2018. [DOI: 10.29220/csam.2018.25.6.591] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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6
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Tawiah R, Yau KKW, McLachlan GJ, Chambers SK, Ng SK. Multilevel model with random effects for clustered survival data with multiple failure outcomes. Stat Med 2018; 38:1036-1055. [PMID: 30474216 DOI: 10.1002/sim.8041] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2018] [Revised: 10/18/2018] [Accepted: 10/27/2018] [Indexed: 12/27/2022]
Abstract
We present a multilevel frailty model for handling serial dependence and simultaneous heterogeneity in survival data with a multilevel structure attributed to clustering of subjects and the presence of multiple failure outcomes. One commonly observes such data, for example, in multi-institutional, randomized placebo-controlled trials in which patients suffer repeated episodes (eg, recurrent migraines) of the disease outcome being measured. The model extends the proportional hazards model by incorporating a random covariate and unobservable random institution effect to respectively account for treatment-by-institution interaction and institutional variation in the baseline risk. Moreover, a random effect term with correlation structure driven by a first-order autoregressive process is attached to the model to facilitate estimation of between patient heterogeneity and serial dependence. By means of the generalized linear mixed model methodology, the random effects distribution is assumed normal and the residual maximum likelihood and the maximum likelihood methods are extended for estimation of model parameters. Simulation studies are carried out to evaluate the performance of the residual maximum likelihood and the maximum likelihood estimators and to assess the impact of misspecifying random effects distribution on the proposed inference. We demonstrate the practical feasibility of the modeling methodology by analyzing real data from a double-blind randomized multi-institutional clinical trial, designed to examine the effect of rhDNase on the occurrence of respiratory exacerbations among patients with cystic fibrosis.
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Affiliation(s)
- Richard Tawiah
- School of Medicine and Menzies Health Institute Queensland, Griffith University, Queensland, Australia
| | - Kelvin K W Yau
- Department of Management Sciences, City University of Hong Kong, Hong Kong
| | | | - Suzanne K Chambers
- School of Medicine and Menzies Health Institute Queensland, Griffith University, Queensland, Australia
| | - Shu-Kay Ng
- School of Medicine and Menzies Health Institute Queensland, Griffith University, Queensland, Australia
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Wang Z, Chen Z, Chen Z. H-relative error estimation for multiplicative regression model with random effect. Comput Stat 2018. [DOI: 10.1007/s00180-018-0798-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Ha ID, Sylvester R, Legrand C, Mackenzie G. Frailty modelling for survival data from multi-centre clinical trials. Stat Med 2011; 30:2144-59. [PMID: 21563206 DOI: 10.1002/sim.4250] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2010] [Accepted: 02/28/2011] [Indexed: 11/05/2022]
Abstract
Despite the use of standardized protocols in, multi-centre, randomized clinical trials, outcome may vary between centres. Such heterogeneity may alter the interpretation and reporting of the treatment effect. Below, we propose a general frailty modelling approach for investigating, inter alia, putative treatment-by-centre interactions in time-to-event data in multi-centre clinical trials. A correlated random effects model is used to model the baseline risk and the treatment effect across centres. It may be based on shared, individual or correlated random effects. For inference we develop the hierarchical-likelihood (or h-likelihood) approach which facilitates computation of prediction intervals for the random effects with proper precision. We illustrate our methods using disease-free time-to-event data on bladder cancer patients participating in an European Organization for Research and Treatment of Cancer trial, and a simulation study. We also demonstrate model selection using h-likelihood criteria.
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Affiliation(s)
- Il Do Ha
- Department of Asset Management, Daegu Haany University, Gyeongsan 712-715, South Korea.
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10
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Wang N, Xu S, Fang J. Hierarchical likelihood approach for the Weibull frailty model. J STAT COMPUT SIM 2011. [DOI: 10.1080/00949650903348148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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11
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Abstract
Correlated survival times can be modelled by introducing a random effect, or frailty component, into the hazard function. For multivariate survival data, we extend a non-proportional hazards (PH) model, the generalized time-dependent logistic survival model, to include random effects. The hierarchical likelihood procedure, which obviates the need for marginalization over the random effect distribution, is derived for this extended model and its properties are discussed. The extended model leads to a robust estimation result for the regression parameters against the misspecification of the form of the basic hazard function or frailty distribution compared to PH-based alternatives. The proposed method is illustrated by two practical examples and a simulation study which demonstrate the advantages of the new model.
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Affiliation(s)
- Il Do Ha
- Department of Asset Management, Daegu Haany University, South Korea
| | - Gilbert MacKenzie
- Centre of Biostatistics, Department of Mathematics & Statistics, University of Limerick, Ireland and ENSAI, Rennes, France
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Ha ID. A General Mixed Linear Model with Left-Censored Data. COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS 2008. [DOI: 10.5351/ckss.2008.15.6.969] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Ha ID, Lee Y, Pawitan Y. Genetic mixed linear models for twin survival data. Behav Genet 2007; 37:621-30. [PMID: 17401640 DOI: 10.1007/s10519-007-9150-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2006] [Accepted: 03/01/2007] [Indexed: 10/23/2022]
Abstract
Twin studies are useful for assessing the relative importance of genetic or heritable component from the environmental component. In this paper we develop a methodology to study the heritability of age-at-onset or lifespan traits, with application to analysis of twin survival data. Due to limited period of observation, the data can be left truncated and right censored (LTRC). Under the LTRC setting we propose a genetic mixed linear model, which allows general fixed predictors and random components to capture genetic and environmental effects. Inferences are based upon the hierarchical-likelihood (h-likelihood), which provides a statistically efficient and unified framework for various mixed-effect models. We also propose a simple and fast computation method for dealing with large data sets. The method is illustrated by the survival data from the Swedish Twin Registry. Finally, a simulation study is carried out to evaluate its performance.
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Affiliation(s)
- Il Do Ha
- Department of Asset Management, Daegu Haany University, Gyeongsan 712-715, Korea.
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Abstract
In medical research recurrent event times can be analysed using a frailty model in which the frailties for different individuals are independent and identically distributed. However, such a homogeneous assumption about frailties could sometimes be suspect. For modelling heterogeneity in frailties we describe dispersion frailty models arising from a new class of models, namely hierarchical generalized linear models. Using the kidney infection data we illustrate how to detect and model heterogeneity among frailties. Stratification of frailty models is also investigated.
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Affiliation(s)
- Maengseok Noh
- Department of Statistics, Seoul National University, Seoul 151-747, Korea
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Ha ID, Noh M, Yoon S. Genetic Mixed Effects Models for Twin Survival Data. COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS 2005. [DOI: 10.5351/ckss.2005.12.3.759] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Kang W, Lee MS, Lee Y. HGLM versus conditional estimators for the analysis of clustered binary data. Stat Med 2005; 24:741-52. [PMID: 15696505 DOI: 10.1002/sim.1772] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
Clustered binary data arise frequently in medical research such as cross-over clinical trials and twin studies. For the analysis of such data either a random-effects model or a conditional likelihood approach can be used. In this paper, we compare numerically the random-effects model estimator and the conditional likelihood estimator and discuss their relative merits for the analysis of binary data.
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Affiliation(s)
- Weechang Kang
- Department of Information and Statistics, Daejeon University, Daejeon 300-716, Korea
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Abstract
For the analysis of correlated survival data mixed linear models are useful alternatives to frailty models. By their use the survival times can be directly modelled, so that the interpretation of the fixed and random effects is straightforward. However, because of intractable integration involved with the use of marginal likelihood the class of models in use has been severely restricted. Such a difficulty can be avoided by using hierarchical-likelihood, which provides a statistically efficient and fast fitting algorithm for multilevel models. The proposed method is illustrated using the chronic granulomatous disease data. A simulation study is carried out to evaluate the performance.
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Affiliation(s)
- Il Do Ha
- Faculty of Information Science, Daegu Haany University, Kyungsan, 712-240, South Korea.
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Yun S, Lee Y. Comparison of hierarchical and marginal likelihood estimators for binary outcomes. Comput Stat Data Anal 2004. [DOI: 10.1016/s0167-9473(03)00033-1] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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22
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Ha ID, Lee Y. Estimating Frailty Models via Poisson Hierarchical Generalized Linear Models. J Comput Graph Stat 2003. [DOI: 10.1198/1061860032256] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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