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Broomfield J, Abrams KR, Freeman S, Latimer N, Rutherford MJ, Crowther MJ. Modeling the multi-state natural history of rare diseases with heterogeneous individual patient data: A simulation study. Stat Med 2024; 43:184-200. [PMID: 37932874 DOI: 10.1002/sim.9949] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2023] [Revised: 09/05/2023] [Accepted: 10/16/2023] [Indexed: 11/08/2023]
Abstract
Multi-state survival models are used to represent the natural history of a disease, forming the basis of a health technology assessment comparing a novel treatment to current practice. Constructing such models for rare diseases is problematic, since evidence sources are typically much sparser and more heterogeneous. This simulation study investigated different one-stage and two-stage approaches to meta-analyzing individual patient data (IPD) in a multi-state survival setting when the number and size of studies being meta-analyzed are small. The objective was to assess methods of different complexity to see when they are accurate, when they are inaccurate and when they struggle to converge due to the sparsity of data. Biologically plausible multi-state IPD were simulated from study- and transition-specific hazard functions. One-stage frailty and two-stage stratified models were estimated, and compared to a base case model that did not account for study heterogeneity. Convergence and the bias/coverage of population-level transition probabilities to, and lengths of stay in, each state were used to assess model performance. A real-world application to Duchenne Muscular Dystrophy, a neuromuscular rare disease, was conducted, and a software demonstration is provided. Models not accounting for study heterogeneity were consistently out-performed by two-stage models. Frailty models struggled to converge, particularly in scenarios of low heterogeneity, and predictions from models that did converge were also subject to bias. Stratified models may be better suited to meta-analyzing disparate sources of IPD in rare disease natural history/economic modeling, as they converge more consistently and produce less biased predictions of lengths of stay.
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Affiliation(s)
- Jonathan Broomfield
- Biostatistics Research Group, Department of Population Health Sciences, University of Leicester, Leicester, UK
| | - Keith R Abrams
- Department of Statistics, University of Warwick, Coventry, UK
- Centre for Health Economics, University of York, York, UK
| | - Suzanne Freeman
- Biostatistics Research Group, Department of Population Health Sciences, University of Leicester, Leicester, UK
| | - Nicholas Latimer
- School of Health and Related Research (ScHARR), University of Sheffield, Sheffield, UK
| | - Mark J Rutherford
- Biostatistics Research Group, Department of Population Health Sciences, University of Leicester, Leicester, UK
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2
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Meng R, Soper B, Lee HK, Nygård JF, Nygård M. Hierarchical continuous-time inhomogeneous hidden Markov model for cancer screening with extensive followup data. Stat Methods Med Res 2022; 31:2383-2399. [PMID: 36039541 DOI: 10.1177/09622802221122390] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Continuous-time hidden Markov models are an attractive approach for disease modeling because they are explainable and capable of handling both irregularly sampled, skewed and sparse data arising from real-world medical practice, in particular to screening data with extensive followup. Most applications in this context consider time-homogeneous models due to their relative computational simplicity. However, the time homogeneous assumption is too strong to accurately model the natural history of many diseases including cancer. Moreover, cancer risk across the population is not homogeneous either, since exposure to disease risk factors can vary considerably between individuals. This is important when analyzing longitudinal datasets and different birth cohorts. We model the heterogeneity of disease progression and regression using piece-wise constant intensity functions and model the heterogeneity of risks in the population using a latent mixture structure. Different submodels under the mixture structure employ the same types of Markov states reflecting disease progression and allowing both clinical interpretation and model parsimony. We also consider flexible observational models dealing with model over-dispersion in real data. An efficient, scalable Expectation-Maximization algorithm for inference is proposed with the theoretical guaranteed convergence property. We demonstrate our method's superior performance compared to other state-of-the-art methods using synthetic data and a real-world cervical cancer screening dataset from the Cancer Registry of Norway. Moreover, we present two model-based risk stratification methods that identify the risk levels of individuals.
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Affiliation(s)
- Rui Meng
- 8787University of California, Santa Cruz, CA, USA
| | - Braden Soper
- 4578Lawrence Livermore National Laboratory, Livermore, CA, USA
| | | | | | - Mari Nygård
- 11315Cancer Registry of Norway, Oslo, Norway
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3
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Cheung LC, Albert PS, Das S, Cook RJ. Multistate models for the natural history of cancer progression. Br J Cancer 2022; 127:1279-1288. [PMID: 35821296 DOI: 10.1038/s41416-022-01904-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Revised: 06/21/2022] [Accepted: 06/28/2022] [Indexed: 11/09/2022] Open
Abstract
BACKGROUND Multistate models can be effectively used to characterise the natural history of cancer. Inference from such models has previously been useful for setting screening policies. METHODS We introduce the basic elements of multistate models and the challenges of applying these models to cancer data. Through simulation studies, we examine (1) the impact of assuming time-homogeneous Markov transition intensities when the intensities depend on the time since entry to the current state (i.e., the process is time-inhomogenous semi-Markov) and (2) the effect on precancer risk estimation when observation times depend on an unmodelled intermediate disease state. RESULTS In the settings we examined, we found that misspecifying a time-inhomogenous semi-Markov process as a time-homogeneous Markov process resulted in biased estimates of the mean sojourn times. When screen-detection of the intermediate disease leads to more frequent future screening assessments, there was minimal bias induced compared to when screen-detection of the intermediate disease leads to less frequent screening. CONCLUSIONS Multistate models are useful for estimating parameters governing the process dynamics in cancer such as transition rates, sojourn time distributions, and absolute and relative risks. As with most statistical models, to avoid incorrect inference, care should be given to use the appropriate specifications and assumptions.
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Affiliation(s)
- Li C Cheung
- Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institutes of Health, Rockville, MD, USA.
| | - Paul S Albert
- Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institutes of Health, Rockville, MD, USA
| | - Shrutikona Das
- Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institutes of Health, Rockville, MD, USA
| | - Richard J Cook
- Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada
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Cook RJ, Lawless JF. Life history analysis with multistate models: A review and some current issues. CAN J STAT 2022. [DOI: 10.1002/cjs.11711] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Richard J. Cook
- Department of Statistics and Actuarial Science University of Waterloo 200 University Avenue West Waterloo Ontario Canada N2L 3G1
| | - Jerald F. Lawless
- Department of Statistics and Actuarial Science University of Waterloo 200 University Avenue West Waterloo Ontario Canada N2L 3G1
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Akwiwu EU, Klausch T, Jodal HC, Carvalho B, Løberg M, Kalager M, Berkhof J, H. Coupé VM. A progressive three-state model to estimate time to cancer: a likelihood-based approach. BMC Med Res Methodol 2022; 22:179. [PMID: 35761181 PMCID: PMC9235269 DOI: 10.1186/s12874-022-01645-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 05/30/2022] [Indexed: 11/24/2022] Open
Abstract
Background To optimize colorectal cancer (CRC) screening and surveillance, information regarding the time-dependent risk of advanced adenomas (AA) to develop into CRC is crucial. However, since AA are removed after diagnosis, the time from AA to CRC cannot be observed in an ethically acceptable manner. We propose a statistical method to indirectly infer this time in a progressive three-state disease model using surveillance data. Methods Sixteen models were specified, with and without covariates. Parameters of the parametric time-to-event distributions from the adenoma-free state (AF) to AA and from AA to CRC were estimated simultaneously, by maximizing the likelihood function. Model performance was assessed via simulation. The methodology was applied to a random sample of 878 individuals from a Norwegian adenoma cohort. Results Estimates of the parameters of the time distributions are consistent and the 95% confidence intervals (CIs) have good coverage. For the Norwegian sample (AF: 78%, AA: 20%, CRC: 2%), a Weibull model for both transition times was selected as the final model based on information criteria. The mean time among those who have made the transition to CRC since AA onset within 50 years was estimated to be 4.80 years (95% CI: 0; 7.61). The 5-year and 10-year cumulative incidence of CRC from AA was 13.8% (95% CI: 7.8%;23.8%) and 15.4% (95% CI: 8.2%;34.0%), respectively. Conclusions The time-dependent risk from AA to CRC is crucial to explain differences in the outcomes of microsimulation models used for the optimization of CRC prevention. Our method allows for improving models by the inclusion of data-driven time distributions. Supplementary Information The online version contains supplementary material available at (10.1186/s12874-022-01645-2).
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Soper BC, Nygård M, Abdulla G, Meng R, Nygård JF. A hidden Markov model for population-level cervical cancer screening data. Stat Med 2020; 39:3569-3590. [PMID: 32854166 DOI: 10.1002/sim.8681] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Revised: 06/02/2020] [Accepted: 06/11/2020] [Indexed: 12/19/2022]
Abstract
The Cancer Registry of Norway has been administrating a national cervical cancer screening program since 1992 by coordinating triennial cytology exam screenings for the female population between 25 and 69 years of age. Up to 80% of cancers are prevented through mass screening, but this comes at the expense of considerable screening activity and leads to overtreatment of clinically asymptomatic precancers. In this article, we present a continuous-time, time-inhomogeneous hidden Markov model which was developed to understand the screening process and cervical cancer carcinogenesis in detail. By leveraging 1.7 million individual's multivariate time-series of medical exams performed over a 25-year period, we simultaneously estimate all model parameters. We show that an age-dependent model reflects the Norwegian screening program by comparing empirical survival curves from observed registry data and data simulated from the proposed model. The model can be generalized to include more detailed individual-level covariates as well as new types of screening exams. By utilizing individual screening histories and covariate data, the proposed model shows potential for improving strategies for cancer screening programs by personalizing recommended screening intervals.
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Affiliation(s)
- Braden C Soper
- Computing Directorate, Lawrence Livermore National Laboratory, Livermore, California, USA
| | - Mari Nygård
- Research Department, Cancer Registry of Norway, Oslo, Norway
| | - Ghaleb Abdulla
- Computing Directorate, Lawrence Livermore National Laboratory, Livermore, California, USA
| | - Rui Meng
- Department of Statistics, University of California, Santa Cruz, California, USA
| | - Jan F Nygård
- Registry Informatics Department, Cancer Registry of Norway, Oslo, Norway
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Gasperoni F, Ieva F, Paganoni AM, Jackson CH, Sharples L. Evaluating the effect of healthcare providers on the clinical path of heart failure patients through a semi-Markov, multi-state model. BMC Health Serv Res 2020; 20:533. [PMID: 32532254 PMCID: PMC7291648 DOI: 10.1186/s12913-020-05294-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2020] [Accepted: 05/05/2020] [Indexed: 11/16/2022] Open
Abstract
Background Investigating similarities and differences among healthcare providers, on the basis of patient healthcare experience, is of interest for policy making. Availability of high quality, routine health databases allows a more detailed analysis of performance across multiple outcomes, but requires appropriate statistical methodology. Methods Motivated by analysis of a clinical administrative database of 42,871 Heart Failure patients, we develop a semi-Markov, illness-death, multi-state model of repeated admissions to hospital, subsequent discharge and death. Transition times between these health states each have a flexible baseline hazard, with proportional hazards for patient characteristics (case-mix adjustment) and a discrete distribution for frailty terms representing clusters of providers. Models were estimated using an Expectation-Maximization algorithm and the number of clusters was based on the Bayesian Information Criterion. Results We are able to identify clusters of providers for each transition, via the inclusion of a nonparametric discrete frailty. Specifically, we detect 5 latent populations (clusters of providers) for the discharge transition, 3 for the in-hospital to death transition and 4 for the readmission transition. Out of hospital death rates are similar across all providers in this dataset. Adjusting for case-mix, we could detect those providers that show extreme behaviour patterns across different transitions (readmission, discharge and death). Conclusions The proposed statistical method incorporates both multiple time-to-event outcomes and identification of clusters of providers with extreme behaviour simultaneously. In this way, the whole patient pathway can be considered, which should help healthcare managers to make a more comprehensive assessment of performance.
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Affiliation(s)
- Francesca Gasperoni
- MRC Biostatistics Unit, University of Cambridge, Forvie Site, Robinson Way, Cambridge, CB2 0SR, UK.
| | - Francesca Ieva
- MOX laboratory, Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci, 32, Milan, 20133, Italy.,CADS-Center for Analysis, Decisions and Society, Human Technopole, Via Cristina Belgioioso, 171, Milan, 20157, Italy.,CHRP-National Center for Healthcare Research and Pharmacoepidemiology, University of Milano-Bicocca, Via Bicocca degli Arcimboldi, 8, Milan, 20126, Italy
| | - Anna Maria Paganoni
- MOX laboratory, Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci, 32, Milan, 20133, Italy.,CADS-Center for Analysis, Decisions and Society, Human Technopole, Via Cristina Belgioioso, 171, Milan, 20157, Italy.,CHRP-National Center for Healthcare Research and Pharmacoepidemiology, University of Milano-Bicocca, Via Bicocca degli Arcimboldi, 8, Milan, 20126, Italy
| | - Christopher H Jackson
- MRC Biostatistics Unit, University of Cambridge, Forvie Site, Robinson Way, Cambridge, CB2 0SR, UK
| | - Linda Sharples
- Department of Medical Statistics, London School of Hygiene & Tropical Medicine, Keppel Street, London, WC1E 7HT, UK
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O'Keeffe AG, Su L, Farewell VT. Correlated multistate models for multiple processes: an application to renal disease progression in systemic lupus erythematosus. J R Stat Soc Ser C Appl Stat 2018; 67:841-860. [PMID: 31105343 PMCID: PMC6517283 DOI: 10.1111/rssc.12257] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Bidirectional changes over time in the estimated glomerular filtration rate and in urine protein content are of interest for the treatment and management of patients with lupus nephritis. Although these processes may be modelled by separate multistate models, the processes are likely to be correlated within patients. Motivated by the lupus nephritis application, we develop a new multistate modelling framework where subject-specific random effects are introduced to account for the correlations both between the processes and within patients over time. Models are fitted by using bespoke code in standard statistical software. A variety of forms for the random effects are introduced and evaluated by using the data from the Systemic Lupus International Collaborating Clinics.
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Affiliation(s)
| | - Li Su
- University of Cambridge, UK
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9
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Jiang F, Haneuse S. A Semi-parametric Transformation Frailty Model for Semi-competing Risks Survival Data. Scand Stat Theory Appl 2016; 44:112-129. [PMID: 28439147 DOI: 10.1111/sjos.12244] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
In the analysis of semi-competing risks data interest lies in estimation and inference with respect to a so-called non-terminal event, the observation of which is subject to a terminal event. Multi-state models are commonly used to analyse such data, with covariate effects on the transition/intensity functions typically specified via the Cox model and dependence between the non-terminal and terminal events specified, in part, by a unit-specific shared frailty term. To ensure identifiability, the frailties are typically assumed to arise from a parametric distribution, specifically a Gamma distribution with mean 1.0 and variance, say, σ2. When the frailty distribution is misspecified, however, the resulting estimator is not guaranteed to be consistent, with the extent of asymptotic bias depending on the discrepancy between the assumed and true frailty distributions. In this paper, we propose a novel class of transformation models for semi-competing risks analysis that permit the non-parametric specification of the frailty distribution. To ensure identifiability, the class restricts to parametric specifications of the transformation and the error distribution; the latter are flexible, however, and cover a broad range of possible specifications. We also derive the semi-parametric efficient score under the complete data setting and propose a non-parametric score imputation method to handle right censoring; consistency and asymptotic normality of the resulting estimators is derived and small-sample operating characteristics evaluated via simulation. Although the proposed semi-parametric transformation model and non-parametric score imputation method are motivated by the analysis of semi-competing risks data, they are broadly applicable to any analysis of multivariate time-to-event outcomes in which a unit-specific shared frailty is used to account for correlation. Finally, the proposed model and estimation procedures are applied to a study of hospital readmission among patients diagnosed with pancreatic cancer.
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Affiliation(s)
- Fei Jiang
- Department of Statistics, University of South Carolina
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10
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Rotolo F, Rondeau V, Legrand C. Incorporation of nested frailties into semiparametric multi-state models. Stat Med 2016; 35:609-21. [PMID: 26381148 DOI: 10.1002/sim.6734] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2013] [Revised: 08/04/2015] [Accepted: 08/26/2015] [Indexed: 12/29/2022]
Abstract
Proportional hazards models are among the most popular regression models in survival analysis. Multi-state models generalize them by jointly considering different types of events and their interrelations, whereas frailty models incorporate random effects to account for unobserved risk factors, possibly shared by clusters of subjects. The integration of multi-state and frailty methodology is an interesting way to control for unobserved heterogeneity in the presence of complex event history structures and is particularly appealing for multicenter clinical trials. We propose the incorporation of correlated frailties in the transition-specific hazard function, thanks to a nested hierarchy. We studied a semiparametric estimation approach based on maximum integrated partial likelihood. We show in a simulation study that the nested frailty multi-state model improves the estimation of the effect of covariates, as well as the coverage probability of their confidence intervals. We present a case study concerning a prostate cancer multicenter clinical trial. The multi-state nature of the model allows us to evidence the effect of treatment on death taking into account intermediate events.
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Affiliation(s)
- Federico Rotolo
- Gustave Roussy, Service de Biostatistique et d'Epidémiologie, Villejuif, F-94805, France.,CESP Centre for Research in Epidemiology and Population Health, INSERM U1018 (Team 2, Methodology and clinical epidemiology in molecular oncology), Université Paris-Sud, Villejuif, F-94805, France.,Dipartimento di Scienze Statistiche, Universitá degli Studi di Padova, Padova, I-35121, Italy.,Institut de Statistique Biostatistique et Sciences Actuarielles, Université catholique de Louvain, Louvain-la-Neuve, B-1348, Belgium
| | - Virginie Rondeau
- INSERM, U897 (Biostatistics), Bordeaux, F-33076, France.,Université Victor Segalen Bordeaux 2, Bordeaux, F-33076, France
| | - Catherine Legrand
- Institut de Statistique Biostatistique et Sciences Actuarielles, Université catholique de Louvain, Louvain-la-Neuve, B-1348, Belgium
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11
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Vink MA, Bogaards JA, van Kemenade FJ, de Melker HE, Meijer CJLM, Berkhof J. Clinical progression of high-grade cervical intraepithelial neoplasia: estimating the time to preclinical cervical cancer from doubly censored national registry data. Am J Epidemiol 2013; 178:1161-9. [PMID: 23897645 DOI: 10.1093/aje/kwt077] [Citation(s) in RCA: 87] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
Little is known about the time span of progression from high-grade cervical intraepithelial neoplasia (CIN2/3) to invasive cervical cancer. Estimation of this duration from longitudinal studies is not permitted, as CIN2/3 should be treated when detected. Cross-sectional data on the age-specific incidence of detected CIN2/3 and cervical cancer cases are readily available in national registries, but these data are difficult to interpret because neither the moment of lesion development nor the onset of invasive cancer is observed. We developed a statistical model for estimating the duration of time between CIN2/3 and preclinical cancer using Dutch national registries for the years 2000-2005. Human papillomavirus (HPV) genotype data were used to separate CIN2/3 and cancer incidences to obtain estimates for HPV-16-positive and HPV-16-negative lesions. The median time from CIN2/3 to cancer was estimated to be 23.5 years (95% confidence interval: 20.8, 26.6), and 1.6% of the lesions progressed to cancer within 10 years. The median duration for HPV-16-positive lesions was similar, but 2.4% of the HPV-16-positive lesions progressed to cancer within 10 years, as compared with 0.6% for HPV-16-negative lesions. Estimated durations of time to cancer are essential for reassessment of the optimal screening interval in light of vaccination and novel screening tests.
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12
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O'Keeffe AG, Tom BDM, Farewell VT. Mixture distributions in multi-state modelling: some considerations in a study of psoriatic arthritis. Stat Med 2012; 32:600-19. [PMID: 22833400 PMCID: PMC3575696 DOI: 10.1002/sim.5529] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2011] [Accepted: 05/14/2012] [Indexed: 11/15/2022]
Abstract
In many studies, interest lies in determining whether members of the study population will undergo a particular event of interest. Such scenarios are often termed ‘mover–stayer’ scenarios, and interest lies in modelling two sub-populations of ‘movers’ (those who have a propensity to undergo the event of interest) and ‘stayers’ (those who do not). In general, mover–stayer scenarios within data sets are accounted for through the use of mixture distributions, and in this paper, we investigate the use of various random effects distributions for this purpose. Using data from the University of Toronto psoriatic arthritis clinic, we present a multi-state model to describe the progression of clinical damage in hand joints of patients with psoriatic arthritis. We consider the use of mover–stayer gamma, inverse Gaussian and compound Poisson distributions to account for both the correlation amongst joint locations and the possible mover–stayer situation with regard to clinical hand joint damage. We compare the fits obtained from these models and discuss the extent to which a mover–stayer scenario exists in these data. Furthermore, we fit a mover–stayer model that allows a dependence of the probability of a patient being a stayer on a patient-level explanatory variable.
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Joly P, Gerds TA, Qvist V, Commenges D, Keiding N. Estimating survival of dental fillings on the basis of interval-censored data and multi-state models. Stat Med 2012; 31:1139-49. [DOI: 10.1002/sim.4459] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2010] [Accepted: 09/28/2011] [Indexed: 11/09/2022]
Affiliation(s)
- Pierre Joly
- INSERM, U-897; Bordeaux, F33076 France
- Univ. Bordeaux; ISPED; Bordeaux, F33076 France
| | - Thomas A. Gerds
- Department of Biostatistics; University of Copenhagen; Copenhagen Denmark
| | - Vibeke Qvist
- Department of Cariology and Endodontics, School of Dentistry, Faculty of Health Sciences; University of Copenhagen; Copenhagen Denmark
| | - Daniel Commenges
- INSERM, U-897; Bordeaux, F33076 France
- Univ. Bordeaux; ISPED; Bordeaux, F33076 France
| | - Niels Keiding
- Department of Biostatistics; University of Copenhagen; Copenhagen Denmark
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Putter H, van Houwelingen HC. Frailties in multi-state models: Are they identifiable? Do we need them? Stat Methods Med Res 2011; 24:675-92. [DOI: 10.1177/0962280211424665] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The inclusion of latent frailties in survival models can serve two purposes: (1) the modelling of dependence in clustered data, (2) explaining lack of fit of univariate survival models, like deviation from the proportional hazards assumption. Multi-state models are somewhere between univariate data and clustered data. Frailty models can help in understanding the dependence in sequential transitions (like in clustered data) and can be useful in explaining some strange phenomena in the effect of covariates in competing risks models (like in univariate data). The (im)possibilities of frailty models will be exemplified on a data set of breast cancer patients with death as absorbing state and local recurrence and distant metastasis as intermediate events.
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Affiliation(s)
- Hein Putter
- Department of Medical Statistics and Bio-informatics, Leiden University Medical Center, PO Box 9600, 2300 RC, Leiden, the Netherlands
| | - Hans C van Houwelingen
- Department of Medical Statistics and Bio-informatics, Leiden University Medical Center, PO Box 9600, 2300 RC, Leiden, the Netherlands
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