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Rathnayake N, Dai HD, Charnigo R, Schmid K, Meza J. A general class of small area estimation using calibrated hierarchical likelihood approach with applications to COVID-19 data. J Appl Stat 2022; 50:3384-3404. [PMID: 37969889 PMCID: PMC10637197 DOI: 10.1080/02664763.2022.2112556] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2021] [Accepted: 08/07/2022] [Indexed: 10/06/2022]
Abstract
The direct estimation techniques in small area estimation (SAE) models require sufficiently large sample sizes to provide accurate estimates. Hence, indirect model-based methodologies are developed to incorporate auxiliary information. The most commonly used SAE models, including the Fay-Herriot (FH) model and its extended models, are estimated using marginal likelihood estimation and the Bayesian methods, which rely heavily on the computationally intensive integration of likelihood function. In this article, we propose a Calibrated Hierarchical (CH) likelihood approach to obtain SAE through hierarchical estimation of fixed effects and random effects with the regression calibration method for bias correction. The latent random variables at the domain level are treated as 'parameters' and estimated jointly with other parameters of interest. Then the dispersion parameters are estimated iteratively based on the Laplace approximation of the profile likelihood. The proposed method avoids the intractable integration to estimate the marginal distribution. Hence, it can be applied to a wide class of distributions, including generalized linear mixed models, survival analysis, and joint modeling with distinct distributions. We demonstrate our method using an area-level analysis of publicly available count data from the novel coronavirus (COVID-19) positive cases.
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Affiliation(s)
- Nirosha Rathnayake
- Department of Biostatistics, University of Nebraska Medical Center, Omaha, NE, USA
| | - Hongying Daisy Dai
- Department of Biostatistics, University of Nebraska Medical Center, Omaha, NE, USA
| | - Richard Charnigo
- Department of Statistics, University of Kentucky, Lexington, KY, USA
| | - Kendra Schmid
- Department of Biostatistics, University of Nebraska Medical Center, Omaha, NE, USA
| | - Jane Meza
- Department of Biostatistics, University of Nebraska Medical Center, Omaha, NE, USA
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He K, Li Y, Wei Q, Li Y. A Computationally Efficient Approach for Modeling Complex and Big Survival Data. CONTRIBUTIONS TO STATISTICS 2017. [DOI: 10.1007/978-3-319-41573-4_10] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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Biard L, Labopin M, Chevret S, Resche-Rigon M. Investigating covariate-by-centre interaction in survival data. Stat Methods Med Res 2016; 27:920-932. [DOI: 10.1177/0962280216647981] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In survival analysis, assessing the existence of potential centre effects on the baseline hazard or on the effect of fixed covariates on the baseline hazard, such as treatment-by-centre interaction, is a frequent clinical concern in multicentre studies. Survival models with random effects on the baseline hazard and/or on the effect of the covariates of interest have been largely applied, for instance, to investigate potential centre effects. We aimed to develop a procedure to routinely test for multiple random effects in survival analyses. We propose a statistic and a permutation approach to test whether all or a subset of components of the variance-covariance matrix of random effects are non-zero in a mixed-effects Cox model framework. Performances of the proposed permutation tests are examined under different null hypotheses corresponding to the different components of the variance-covariance matrix, i.e ., to the different random effects considered on the baseline hazard and/or on the covariates effects. Several alternative hypotheses are evaluated using simulations. The results indicate that the permutation tests have valid type I error rates under the null and achieve satisfactory power under all alternatives. The procedure is applied to two European cohorts of haematological stem cell transplants in acute leukaemia to investigate the heterogeneity across centres in leukaemia-free survival and the potential heterogeneity in prognostic factors effects across centres.
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Affiliation(s)
- L Biard
- Service de Biostatistique et Information Médicale, AP-HP Hôpital Saint-Louis, Paris, France
- Université Paris Diderot – Paris 7, Sorbonne Paris Cité UMR-S 1153, Paris, France
- ECSTRA Team, INSERM, UMR-S 1153, Paris, France
| | - M Labopin
- Clinical Haematology and Cellular Therapy Department AP-HP, Hôpital Saint Antoine, Paris, France
- EBMT Acute Leukaemia Working Party Office, Hôpital Saint Antoine, Paris, France
- Université Pierre et Marie Curie, Paris, France
- INSERM UMR-S 938, Paris, France
| | - S Chevret
- Service de Biostatistique et Information Médicale, AP-HP Hôpital Saint-Louis, Paris, France
- Université Paris Diderot – Paris 7, Sorbonne Paris Cité UMR-S 1153, Paris, France
- ECSTRA Team, INSERM, UMR-S 1153, Paris, France
| | - M Resche-Rigon
- Service de Biostatistique et Information Médicale, AP-HP Hôpital Saint-Louis, Paris, France
- Université Paris Diderot – Paris 7, Sorbonne Paris Cité UMR-S 1153, Paris, France
- ECSTRA Team, INSERM, UMR-S 1153, Paris, France
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Biard L, Porcher R, Resche-Rigon M. Permutation tests for centre effect on survival endpoints with application in an acute myeloid leukaemia multicentre study. Stat Med 2014; 33:3047-57. [PMID: 24676752 DOI: 10.1002/sim.6153] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2013] [Revised: 02/21/2014] [Accepted: 03/02/2014] [Indexed: 11/10/2022]
Abstract
When analysing multicentre data, it may be of interest to test whether the distribution of the endpoint varies among centres. In a mixed-effect model, testing for such a centre effect consists in testing to zero a random centre effect variance component. It has been shown that the usual asymptotic χ(2) distribution of the likelihood ratio and score statistics under the null does not necessarily hold. In the case of censored data, mixed-effects Cox models have been used to account for random effects, but few works have concentrated on testing to zero the variance component of the random effects. We propose a permutation test, using random permutation of the cluster indices, to test for a centre effect in multilevel censored data. Results from a simulation study indicate that the permutation tests have correct type I error rates, contrary to standard likelihood ratio tests, and are more powerful. The proposed tests are illustrated using data of a multicentre clinical trial of induction therapy in acute myeloid leukaemia patients.
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Affiliation(s)
- L Biard
- Service de Biostatistique et Information Médicale, Hôpital Saint-Louis, AP-HP, F-75010 Paris, France; Université Paris Diderot - Paris 7, Sorbonne Paris Cité, F-75010 Paris, France; INSERM, ECSTRA Team, UMR-S 1153, F-75010 Paris, France
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