IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v195y2024ics0167947324000422.html
   My bibliography  Save this article

Semiparametric accelerated failure time models under unspecified random effect distributions

Author

Listed:
  • Seo, Byungtae
  • Ha, Il Do

Abstract

Accelerated failure time (AFT) models with random effects, a useful alternative to frailty models, have been widely used for analyzing clustered (or correlated) time-to-event data. In the AFT model, the distribution of the unobserved random effect is conventionally assumed to be parametric, often modeled as a normal distribution. Although it has been known that a misspecfied random-effect distribution has little effect on regression parameter estimates, in some cases, the impact caused by such misspecification is not negligible. Particularly when our focus extends to quantities associated with random effects, the problem could become worse. In this paper, we propose a semi-parametric maximum likelihood approach in which the random-effect distribution under the AFT models is left unspecified. We provide a feasible algorithm to estimate the random-effect distribution as well as model parameters. Through comprehensive simulation studies, our results demonstrate the effectiveness of this proposed method across a range of random-effect distribution types (discrete or continuous) and under conditions of heavy censoring. The efficacy of the approach is further illustrated through simulation studies and real-world data examples.

Suggested Citation

  • Seo, Byungtae & Ha, Il Do, 2024. "Semiparametric accelerated failure time models under unspecified random effect distributions," Computational Statistics & Data Analysis, Elsevier, vol. 195(C).
  • Handle: RePEc:eee:csdana:v:195:y:2024:i:c:s0167947324000422
    DOI: 10.1016/j.csda.2024.107958
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947324000422
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2024.107958?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fabio, Lizandra C. & Paula, Gilberto A. & Castro, Mário de, 2012. "A Poisson mixed model with nonnormal random effect distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1499-1510.
    2. Agresti, Alan & Caffo, Brian & Ohman-Strickland, Pamela, 2004. "Examples in which misspecification of a random effects distribution reduces efficiency, and possible remedies," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 639-653, October.
    3. John P. Klein & Corey Pelz & Mei-jie Zhang, 1999. "Modeling Random Effects for Censored Data by a Multivariate Normal Regression Model," Biometrics, The International Biometric Society, vol. 55(2), pages 497-506, June.
    4. Byungtae Seo & Sangwook Kang, 2023. "Accelerated failure time modeling via nonparametric mixtures," Biometrics, The International Biometric Society, vol. 79(1), pages 165-177, March.
    5. Wei Pan & Thomas A. Louis, 2000. "A Linear Mixed-Effects Model for Multivariate Censored Data," Biometrics, The International Biometric Society, vol. 56(1), pages 160-166, March.
    6. Yong Wang, 2007. "On fast computation of the non‐parametric maximum likelihood estimate of a mixing distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 185-198, April.
    7. Daowen Zhang & Marie Davidian, 2001. "Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data," Biometrics, The International Biometric Society, vol. 57(3), pages 795-802, September.
    8. John M. Williamson & Somnath Datta & Glen A. Satten, 2003. "Marginal Analyses of Clustered Data When Cluster Size Is Informative," Biometrics, The International Biometric Society, vol. 59(1), pages 36-42, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Leonardo Grilli & Carla Rampichini, 2015. "Specification of random effects in multilevel models: a review," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 967-976, May.
    2. Wang, Yong, 2010. "Fisher scoring: An interpolation family and its Monte Carlo implementations," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1744-1755, July.
    3. Vock, David & Davidian, Marie & Tsiatis, Anastasios, 2014. "SNP_NLMM: A SAS Macro to Implement a Flexible Random Effects Density for Generalized Linear and Nonlinear Mixed Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 56(c02).
    4. Jaeun Choi & Donglin Zeng & Andrew F. Olshan & Jianwen Cai, 2018. "Joint modeling of survival time and longitudinal outcomes with flexible random effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 126-152, January.
    5. Francis K. C. Hui & Samuel Müller & Alan H. Welsh, 2021. "Random Effects Misspecification Can Have Severe Consequences for Random Effects Inference in Linear Mixed Models," International Statistical Review, International Statistical Institute, vol. 89(1), pages 186-206, April.
    6. Tanya P. Garcia & Yanyuan Ma, 2016. "Optimal Estimator for Logistic Model with Distribution-free Random Intercept," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 156-171, March.
    7. Li Liu & Liming Xiang, 2014. "Semiparametric estimation in generalized linear mixed models with auxiliary covariates: A pairwise likelihood approach," Biometrics, The International Biometric Society, vol. 70(4), pages 910-919, December.
    8. Charles E. McCulloch & John M. Neuhaus, 2011. "Prediction of Random Effects in Linear and Generalized Linear Models under Model Misspecification," Biometrics, The International Biometric Society, vol. 67(1), pages 270-279, March.
    9. Reza Drikvandi & Geert Verbeke & Geert Molenberghs, 2017. "Diagnosing misspecification of the random-effects distribution in mixed models," Biometrics, The International Biometric Society, vol. 73(1), pages 63-71, March.
    10. Fabienne Comte & Adeline Samson, 2012. "Nonparametric estimation of random-effects densities in linear mixed-effects model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 951-975, December.
    11. Peng Zhang & Peter X.-K. Song & Annie Qu & Tom Greene, 2008. "Efficient Estimation for Patient-Specific Rates of Disease Progression Using Nonnormal Linear Mixed Models," Biometrics, The International Biometric Society, vol. 64(1), pages 29-38, March.
    12. Zhengxin Zhang & Xiaosheng Si & Changhua Hu & Xiangyu Kong, 2015. "Degradation modeling–based remaining useful life estimation: A review on approaches for systems with heterogeneity," Journal of Risk and Reliability, , vol. 229(4), pages 343-355, August.
    13. Madeleine Cule & Richard Samworth & Michael Stewart, 2010. "Maximum likelihood estimation of a multi‐dimensional log‐concave density," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 545-607, November.
    14. Jaakko Nevalainen & Somnath Datta & Hannu Oja, 2014. "Inference on the marginal distribution of clustered data with informative cluster size," Statistical Papers, Springer, vol. 55(1), pages 71-92, February.
    15. Ye, Rendao & Wang, Tonghui & Gupta, Arjun K., 2014. "Distribution of matrix quadratic forms under skew-normal settings," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 229-239.
    16. Huang, Xianzheng, 2011. "Detecting random-effects model misspecification via coarsened data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 703-714, January.
    17. Manuel Arellano & Stéphane Bonhomme, 2012. "Identifying Distributional Characteristics in Random Coefficients Panel Data Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 987-1020.
    18. Iryna Lobach & Raymond J. Carroll & Christine Spinka & Mitchell H. Gail & Nilanjan Chatterjee, 2008. "Haplotype‐Based Regression Analysis and Inference of Case–Control Studies with Unphased Genotypes and Measurement Errors in Environmental Exposures," Biometrics, The International Biometric Society, vol. 64(3), pages 673-684, September.
    19. Axel Munk & Tatyana Krivobokova, 2009. "Comments on: Goodness-of-fit tests in mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 256-259, August.
    20. Roger Tovar-Falón & Guillermo Martínez-Flórez & Heleno Bolfarine, 2022. "Modelling Asymmetric Data by Using the Log-Gamma-Normal Regression Model," Mathematics, MDPI, vol. 10(7), pages 1-16, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:195:y:2024:i:c:s0167947324000422. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.