1
|
Li W, Rahbar MH, Savitz SI, Zhang J, Lundin SK, Tahanan A, Ning J. Regression analysis of multivariate recurrent event data allowing time-varying dependence with application to stroke registry data. Stat Methods Med Res 2024; 33:309-320. [PMID: 38263734 PMCID: PMC11080814 DOI: 10.1177/09622802231226330] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2024]
Abstract
In multivariate recurrent event data, each patient may repeatedly experience more than one type of event. Analysis of such data gets further complicated by the time-varying dependence structure among different types of recurrent events. The available literature regarding the joint modeling of multivariate recurrent events assumes a constant dependency over time, which is strict and often violated in practice. To close the knowledge gap, we propose a class of flexible shared random effects models for multivariate recurrent event data that allow for time-varying dependence to adequately capture complex correlation structures among different types of recurrent events. We developed an expectation-maximization algorithm for stable and efficient model fitting. Extensive simulation studies demonstrated that the estimators of the proposed approach have satisfactory finite sample performance. We applied the proposed model and the estimating method to data from a cohort of stroke patients identified in the University of Texas Houston Stroke Registry and evaluated the effects of risk factors and the dependence structure of different types of post-stroke readmission events.
Collapse
Affiliation(s)
- Wen Li
- Division of Clinical and Translational Sciences, Department of Internal Medicine the University of Texas McGovern Medical School at Houston, Houston, TX 77030, USA
- Biostatistics/Epidemiology/Research Design (BERD) Component, Center for Clinical and Translational Sciences (CCTS), University of Texas Health Science Center at Houston, Houston, TX 77030, USA
| | - Mohammad H. Rahbar
- Division of Clinical and Translational Sciences, Department of Internal Medicine the University of Texas McGovern Medical School at Houston, Houston, TX 77030, USA
- Biostatistics/Epidemiology/Research Design (BERD) Component, Center for Clinical and Translational Sciences (CCTS), University of Texas Health Science Center at Houston, Houston, TX 77030, USA
- Division of Epidemiology, Human Genetics, and Environmental Sciences (EHGES), University of Texas School of Public Health at Houston, Houston, TX 77030, USA
| | - Sean I. Savitz
- Department of Neurology and Institute for Stroke and Cerebrovascular Disease, The University of Texas Health Science Center, Houston, TX 77030, USA
| | - Jing Zhang
- Biostatistics/Epidemiology/Research Design (BERD) Component, Center for Clinical and Translational Sciences (CCTS), University of Texas Health Science Center at Houston, Houston, TX 77030, USA
- Department of Biostatistics & Data Science, School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX 77030, USA
| | - Sori Kim Lundin
- Biostatistics/Epidemiology/Research Design (BERD) Component, Center for Clinical and Translational Sciences (CCTS), University of Texas Health Science Center at Houston, Houston, TX 77030, USA
- Center for Biomedical Semantics and Data Intelligence, Houston, TX 77030, USA
| | - Amirali Tahanan
- Biostatistics/Epidemiology/Research Design (BERD) Component, Center for Clinical and Translational Sciences (CCTS), University of Texas Health Science Center at Houston, Houston, TX 77030, USA
| | - Jing Ning
- Department of Biostatistics, University of Texas MD Anderson Cancer Center at Houston, TX 77030, USA
| |
Collapse
|
2
|
Abstract
Many medical studies yield data on recurrent clinical events from populations which consist of a proportion of cured patients in the presence of those who experience the event at several times (uncured). A frailty mixture cure model has recently been postulated for such data, with an assumption that the random subject effect (frailty) of each uncured patient is constant across successive gap times between recurrent events. We propose two new models in a more general setting, assuming a multivariate time-varying frailty with an AR(1) correlation structure for each uncured patient and addressing multilevel recurrent event data originated from multi-institutional (multi-centre) clinical trials, using extra random effect terms to adjust for institution effect and treatment-by-institution interaction. To solve the difficulties in parameter estimation due to these highly complex correlation structures, we develop an efficient estimation procedure via an EM-type algorithm based on residual maximum likelihood (REML) through the generalised linear mixed model (GLMM) methodology. Simulation studies are presented to assess the performances of the models. Data sets from a colorectal cancer study and rhDNase multi-institutional clinical trial were analyzed to exemplify the proposed models. The results demonstrate a large positive AR(1) correlation among frailties across successive gap times, indicating a constant frailty may not be realistic in some situations. Comparisons of findings with existing frailty models are discussed.
Collapse
Affiliation(s)
- Richard Tawiah
- 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
| |
Collapse
|
3
|
|
4
|
Belot A, Rondeau V, Remontet L, Giorgi R. A joint frailty model to estimate the recurrence process and the disease-specific mortality process without needing the cause of death. Stat Med 2014; 33:3147-66. [PMID: 24639014 DOI: 10.1002/sim.6140] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2012] [Revised: 01/28/2014] [Accepted: 02/15/2014] [Indexed: 11/12/2022]
Abstract
In chronic diseases, such as cancer, recurrent events (such as relapses) are commonly observed; these could be interrupted by death. With such data, a joint analysis of recurrence and mortality processes is usually conducted with a frailty parameter shared by both processes. We examined a joint modeling of these processes considering death under two aspects: 'death due to the disease under study' and 'death due to other causes', which enables estimating the disease-specific mortality hazard. The excess hazard model was used to overcome the difficulties in determining the causes of deaths (unavailability or unreliability); this model allows estimating the disease-specific mortality hazard without needing the cause of death but using the mortality hazards observed in the general population. We propose an approach to model jointly recurrence and disease-specific mortality processes within a parametric framework. A correlation between the two processes is taken into account through a shared frailty parameter. This approach allows estimating unbiased covariate effects on the hazards of recurrence and disease-specific mortality. The performance of the approach was evaluated by simulations with different scenarios. The method is illustrated by an analysis of a population-based dataset on colon cancer with observations of colon cancer recurrences and deaths. The benefits of the new approach are highlighted by comparison with the 'classical' joint model of recurrence and overall mortality. Moreover, we assessed the goodness of fit of the proposed model. Comparisons between the conditional hazard and the marginal hazard of the disease-specific mortality are shown, and differences in interpretation are discussed.
Collapse
Affiliation(s)
- Aurélien Belot
- Service de Biostatistique, Hospices Civils de Lyon, F-69495 Pierre-Bénite Cedex, France; Université de Lyon, F-69000 Lyon, France; Université Lyon I, Villeurbanne, F-69622, France; CNRS ; UMR 5558, Laboratoire de Biométrie et Biologie Evolutive, Equipe Biostatistique Santé, Pierre-Bénite, F-69495, France; Département des Maladies Chroniques et Traumatismes, Institut de Veille Sanitaire, Saint-Maurice, F-94415, France
| | | | | | | | | |
Collapse
|
5
|
Fong DYT, Rai SN, Lam KSL. Estimating the effect of multiple imputation on incomplete longitudinal data with application to a randomized clinical study. J Biopharm Stat 2013; 23:1004-22. [PMID: 23957512 DOI: 10.1080/10543406.2013.813514] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Abstract
For analyzing incomplete longitudinal data, there has been recent interest in comparing estimates with and without the use of multiple imputation along with mixed effects model and generalized estimating equations. Empirically, the additional use of multiple imputation generally led to overestimated variances and may yield more heavily biased estimates than the use of last observation carried forward. Under ignorable or nonignorable missing values, a mixed effects model or generalized estimating equations alone yielded more unbiased estimates. The different methods were also assessed in a randomized controlled clinical trial.
Collapse
Affiliation(s)
- Daniel Y T Fong
- School of Nursing, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong, PR China.
| | | | | |
Collapse
|
6
|
Lam KF, Wong KY, Zhou F. A semiparametric cure model for interval-censored data. Biom J 2013; 55:771-88. [DOI: 10.1002/bimj.201300004] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2013] [Revised: 03/12/2013] [Accepted: 03/30/2013] [Indexed: 11/09/2022]
Affiliation(s)
- Kwok Fai Lam
- Department of Statistics and Actuarial Science; The University of Hong Kong; Pokfulam Road; Hong Kong
| | - Kin Yau Wong
- Department of Biostatistics; University of North Carolina at Chapel Hill; Chapel Hill; NC 27599; USA
| | - Feifei Zhou
- Department of Statistics and Actuarial Science; The University of Hong Kong; Pokfulam Road; Hong Kong
| |
Collapse
|
7
|
Abstract
BACKGROUND Injuries are often recurrent, with subsequent injuries influenced by previous occurrences and hence correlation between events needs to be taken into account when analysing such data. OBJECTIVE This paper compares five different survival models (Cox proportional hazards (CoxPH) model and the following generalisations to recurrent event data: Andersen-Gill (A-G), frailty, Wei-Lin-Weissfeld total time (WLW-TT) marginal, Prentice-Williams-Peterson gap time (PWP-GT) conditional models) for the analysis of recurrent injury data. METHODS Empirical evaluation and comparison of different models were performed using model selection criteria and goodness-of-fit statistics. Simulation studies assessed the size and power of each model fit. RESULTS The modelling approach is demonstrated through direct application to Australian National Rugby League recurrent injury data collected over the 2008 playing season. Of the 35 players analysed, 14 (40%) players had more than 1 injury and 47 contact injuries were sustained over 29 matches. The CoxPH model provided the poorest fit to the recurrent sports injury data. The fit was improved with the A-G and frailty models, compared to WLW-TT and PWP-GT models. CONCLUSIONS Despite little difference in model fit between the A-G and frailty models, in the interest of fewer statistical assumptions it is recommended that, where relevant, future studies involving modelling of recurrent sports injury data use the frailty model in preference to the CoxPH model or its other generalisations. The paper provides a rationale for future statistical modelling approaches for recurrent sports injury.
Collapse
Affiliation(s)
- Shahid Ullah
- Flinders Centre for Epidemiology and Biostatistics, Faculty of Health Sciences, Flinders University, Adelaide, South Australia, Australia
| | - Tim J Gabbett
- School of Exercise Science, Australian Catholic University, Brisbane, Queensland, Australia School of Human Movement Studies, The University of Queensland, Brisbane, Queensland, Australia
| | - Caroline F Finch
- Australian Centre for Research into Injury in Sport and its Prevention (ACRISP), Monash Injury Research Institute (MIRI), Monash University, Melbourne, Victoria, Australia
| |
Collapse
|
8
|
Darlington GA, Dixon SN. Event-weighted proportional hazards modelling for recurrent gap time data. Stat Med 2012; 32:124-30. [PMID: 22825881 DOI: 10.1002/sim.5522] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2011] [Revised: 05/18/2012] [Accepted: 06/20/2012] [Indexed: 11/11/2022]
Abstract
The analysis of gap times in recurrent events requires an adjustment to standard marginal models. One can perform this adjustment with a modified within-cluster resampling technique; however, this method is computationally intensive. In this paper, we describe a simple adjustment to the standard Cox proportional hazards model analysis that mimics the intent of within-cluster resampling and results in similar parameter estimates. This method essentially weights the partial likelihood contributions by the inverse of the number of gap times observed within the individual while assuming a working independence correlation matrix. We provide an example involving recurrent mammary tumours in female rats to illustrate the methods considered in this paper.
Collapse
Affiliation(s)
- G A Darlington
- Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada.
| | | |
Collapse
|
9
|
Rondeau V, Schaffner E, Corbière F, Gonzalez JR, Mathoulin-Pélissier S. Cure frailty models for survival data: Application to recurrences for breast cancer and to hospital readmissions for colorectal cancer. Stat Methods Med Res 2011; 22:243-60. [DOI: 10.1177/0962280210395521] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Owing to the natural evolution of a disease, several events often arise after a first treatment for the same subject. For example, patients with a primary invasive breast cancer and treated with breast conserving surgery may experience breast cancer recurrences, metastases or death. A certain proportion of subjects in the population who are not expected to experience the events of interest are considered to be ‘cured’ or non-susceptible. To model correlated failure time data incorporating a surviving fraction, we compare several forms of cure rate frailty models. In the first model already proposed non-susceptible patients are those who are not expected to experience the event of interest over a sufficiently long period of time. The other proposed models account for the possibility of cure after each event. We illustrate the cure frailty models with two data sets. First to analyse time-dependent prognostic factors associated with breast cancer recurrences, metastases, new primary malignancy and death. Second to analyse successive rehospitalizations of patients diagnosed with colorectal cancer. Estimates were obtained by maximization of likelihood using SAS proc NLMIXED for a piecewise constant hazards model. As opposed to the simple frailty model, the proposed methods demonstrate great potential in modelling multivariate survival data with long-term survivors (‘cured’ individuals).
Collapse
Affiliation(s)
- Virginie Rondeau
- INSERM, CR897 (Biostatistic), Bordeaux, France
- Université Victor Segalen Bordeaux 2, Bordeaux, France
| | | | - Fabien Corbière
- INSERM, CR897 (Biostatistic), Bordeaux, France
- INRA-UMR 1225, Toulouse, France
| | - Juan R Gonzalez
- Centre for Research in Environmental Epidemiology (CREAL), Barcelona, Spain
| | | |
Collapse
|
10
|
Abstract
Repeated events processes are ubiquitous across a great range of important health, medical, and public policy applications, but models for these processes have serious limitations. Alternative estimators often produce different inferences concerning treatment effects due to bias and inefficiency. We recommend a robust strategy for the estimation of effects in medical treatments, social conditions, individual behaviours, and public policy programs in repeated events survival models under three common conditions: heterogeneity across individuals, dependence across the number of events, and both heterogeneity and event dependence. We compare several models for analysing recurrent event data that exhibit both heterogeneity and event dependence. The conditional frailty model best accounts for the various conditions of heterogeneity and event dependence by using a frailty term, stratification, and gap time formulation of the risk set. We examine the performance of recurrent event models that are commonly used in applied work using Monte Carlo simulations, and apply the findings to data on chronic granulomatous disease and cystic fibrosis.
Collapse
|
11
|
Abstract
In this article, the focus is on the analysis of multivariate survival time data with various types of dependence structures. Examples of multivariate survival data include clustered data and repeated measurements from the same subject, such as the interrecurrence times of cancer tumors. A random effect semiparametric proportional odds model is proposed as an alternative to the proportional hazards model. The distribution of the random effects is assumed to be multivariate normal and the random effect is assumed to act additively to the baseline log-odds function. This class of models, which includes the usual shared random effects model, the additive variance components model, and the dynamic random effects model as special cases, is highly flexible and is capable of modeling a wide range of multivariate survival data. A unified estimation procedure is proposed to estimate the regression and dependence parameters simultaneously by means of a marginal-likelihood approach. Unlike the fully parametric case, the regression parameter estimate is not sensitive to the choice of correlation structure of the random effects. The marginal likelihood is approximated by the Monte Carlo method. Simulation studies are carried out to investigate the performance of the proposed method. The proposed method is applied to two well-known data sets, including clustered data and recurrent event times data.
Collapse
Affiliation(s)
- K F Lam
- Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong.
| | | | | |
Collapse
|