Exploring shared frailty models for cluster-specific risk estimation: A study on diabetes patients with a history of acute coronary syndrome

Yıl 2024, Cilt: 53 Sayı: 4, 1158 - 1177, 27.08.2024

Adedayo Kazeem Adeleke Brıght , Harshal Deshmukh Alan Rigby Thozhukat Sathyapalan Joseph John

https://doi.org/10.15672/hujms.1320996

Öz

This study proposes the use of semiparametric log-normal shared frailty models to analyze time-to-event data for individuals with similar features referred to as clusters. Shared frailty models are useful for modeling and estimating common risk in the lifetimes of individuals in these clusters. While various methods have been proposed for estimating shared frailty models, few studies have explored the use of the pseudo-full-likelihood method. In this study, the pseudo-full-likelihood and hierarchical likelihood approaches were used to construct and estimate parameter estimates and check for asymptotic properties via simulations. Log-normal semiparametric frailty model was used to obtain cluster-specific frailty based on the semiparametric log-normal shared frailty distribution. The results of both methods were compared, and prediction intervals for a random effect were obtained. To further investigate the existence of shared frailty in diabetes patients and a history of acute coronary syndrome (STEMI and NSTEMI), data from UK Biobank was used. The results suggest the presence of frailty within the clusters and indicate cluster time dependence in the study population. Overall, this study highlights the potential benefits of using the pseudo-full-likelihood method in shared frailty modeling and provides insights into the impact of observed variabilities on hazards within clusters.

Anahtar Kelimeler

Log-normal frailty model, pseudo-full-likelihood, shared frailty model, acute coronary syndrome, diabetes mellitus

Destekleyen Kurum

No

Teşekkür

Not supported

Kaynakça

• [1] K.A. Adeleke and G. Grover, Parametric frailty models for clustered survival data: Application to recurrent asthma attack in infants, J. Stat. Appl. Probab. 6, 89-99, 2019.
• [2] S.A. Adham and A.A. AlAhmadi, Gamma and inverse Gaussian frailty models: A comparative study, Journal of Mathematics and Statistics Invention, 2321-4767, 2016.
• [3] T.A. Balan and H. Putter, frailtyEM: An R package for estimating semiparametric shared frailty models, J. Stat. Softw. 90, 1-29, 2019.
• [4] P. Barker and R. Henderson, Small sample bias in the gamma frailty model for univariate survival, Lifetime Data Anal. 11, 265-84, 2005.
• [5] N.J. Christian, I.D. Ha and J.H. Jeong, Hierarchical likelihood inference on clustered competing risks data, Stat. Med. 35 (2), 251-67, 2016.
• [6] D. Clayton and J. Cuzick, Multivariate generalizations of the proportional hazards model, J. Roy. Statist. Soc. Ser. A 148, 82-108, 1985.
• [7] D.G. Clayton, A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence, Biometrika 65, 141-51, 1978.
• [8] R. Collins, What makes UK Biobank special?, Lancet 379 (9822), 1173-1174, 2012.
• [9] DR. Cox, Regression models and lifetables, J. R. Stat. Soc. Ser. B. Stat. Methodol. 34, 187-202, 1972.
• [10] I.L. Do Ha, On estimation of random effect in Poisson HGLMs, J. Kor. Data Anal. Soc. 19 (1), 375-83, 2008.
• [11] L. Duchateau and P. Janssen, The Frailty Model, Springer Verlag, New York, 2008.
• [12] D.G. Enki, A. Noufaily and C.P. Farrington, A time-varying shared frailty model with application to infectious diseases, Ann. Appl. Stat. 8 (1), 430-447 2014.
• [13] W.S. Gachau, Frailty models with applications in medical research: observed and simulated data, PhD Thesis, University of Nairobi, Nairobi, 2014.
• [14] M. Gorfine, D.M. Zucker, and L. Hsu, Prospective survival analysis with a general semiparametric shared frailty model: A pseudo full likelihood approach, Biometrika 93 (3), 735-41, 2006.
• [15] U.S. Govindarajulu, H. Lin, K.L. Lunetta and R.B. D’Agostino Sr, Frailty models: applications to biomedical and genetic studies, Stat. Med. 30 (22), 2754-64, 2011.
• [16] I.D. Ha and G.H. Cho, On prediction of random effects in log-normal frailty models, J. Kor. Data Anal. Soc. 20, 203-209, 2009.
• [17] I.D. Ha, J.H. Jeong and Y. Lee, Statistical Modelling of Survival Data with Random Effects: h-likelihood Approach, Springer, 2017.
• [18] I.D. Ha, Y. Lee and J.K. Song, Hierarchical likelihood approach for frailty models, Biometrika 88 (1), 233, 2001.
• [19] I.D. Ha and Y. Lee, Estimating frailty models via Poisson hierarchical generalized linear models, J. Comput. Graph. Statist. 12 (3), 663-81, 2003.
• [20] D.D. Hanagal and R. Sharma, Analysis of diabetic retinopathy data using shared inverse Gaussian frailty model, Model Assist. Stat. Appl. 8, 103-19, 2013.
• [21] F.K. Ho, S.R. Gray, P. Welsh, F. Petermann-Rocha, H. Foster, H. Waddell, J. Anderson, D. Lyall, N. Sattar, J.M. Gill and J.C. Mathers, Associations of fat and carbohydrate intake with cardiovascular disease and mortality: prospective cohort study of UK Biobank participants, BMJ 368, 2020.
• [22] N. Keyfitz and G. Littman, Mortality in a heterogeneous population, Popul. Stud. 33, 333-342, 1979.
• [23] J.P. Klein, Semiparametric estimation of random effects using the Cox model based on the EM algorithm, Biometrics 1, 795-806, 1992.
• [24] Y. Lee, J.A. Nelder and Y. Pawitan, Generalized Linear Models with Random Effects: Unified Analysis via H-Likelihood, CRC Press, 2018.
• [25] S. Mahmood, B. Zainab, and A.M. Latif, Frailty modeling for clustered survival data: an application to birth interval in Bangladesh, J. Appl. Stat. 40 (12), 2670-80, 2013.
• [26] J.V. Monaco, M. Gorfine and L. Hsu, General semiparametric shared frailty model: estimation and simulation with frailtySurv, J. Stat. Softw. 86, 2018.
• [27] S.A. Murphy, A. W. Van der Vaart, On profile likelihood, J. Am. Stat. Assoc. 95 (450), 449-65, 2000.
• [28] G.G. Nielsen, R.D. Gill, P.K. Andersen and T.I. Sørensen, A counting process approach to maximum likelihood estimation in frailty models, Scand. J. Stat. 1, 25-43, 1992.
• [29] A.W. Oyekunle, K.A. Adeleke and A.A. Olosunde, Gamma and Inverse Gaussian Frailty Models with Time-varying co-variates Based on Some Parametric Baseline Hazards , Afr. Stat. 15 (1), 2199-2224, 2020.
• [30] L.J. Palmer, UK Biobank: bank on it, Lancet 369 (9578), 1980-1982, 2007.
• [31] E. Parner, Asymptotic theory for the correlated gamma-frailty model, Ann. Stat. 26, 183-214, 1998.
• [32] F. Petermann-Rocha, S. Parra-Soto, S. Gray, J. Anderson, P.Welsh, J. Gill, N. Sattar, F.K. Ho, C. Celis-Morales, J.P. Pell, Vegetarians, fish, poultry, and meat-eaters: Who has higher risk of cardiovascular disease incidence and mortality? A prospective study from UK Biobank, Eur. Heart J. 42 (12), 1136-1143, 2021.
• [33] S. Ripatti and J. Palmgren, Estimation of multivariate frailty models using penalized partial likelihood, Biometrics 56 (4), 1016-22, 2000.
• [34] Y.R. Su and J.L. Wang, Semiparametric efficient estimation for shared-frailty models with doubly-censored clustered data, Ann. Stat. 44 (3), 1298, 2016.
• [35] C. Sudlow, J. Gallacher, N. Allen, V. Beral, P. Burton, J. Danesh, P. Downey, P. Elliott, J. Green, M. Landray and B. Liu, UK biobank: an open access resource for identifying the causes of a wide range of complex diseases of middle and old age, PLoS Med. 12 (3), e1001779, 2015.
• [36] F. Vaida and R. Xu, Proportional hazards model with random effects, Stat Med 19 (24), 3309-3324, 2000.
• [37] J.W. Vaupel, K.G. Manton and E. Stallard, The impact of heterogeneity in individual frailty on the dynamics of mortality, Demography 16, 439-54, 1979.
• [38] A. Wienke, Frailty Models in Survival Analysis, Boca Raton: Chapman and Hall/CRC, 2010.
• [39] X. Xue, Multivariate survival data under bivariate frailty: an estimating equation approach, Biometrics 1, 1631-1637, 1998.
• [40] N. Zare and F. Moradi, Parametric frailty and shared frailty models applied to waiting time to first pregnancy, International Conference on Applied Mathematics and Pharmaceutical Sciences, 598-600, 2012.
• [41] D.M. Zucker, M. Gorfine and L. Hsu, Pseudo-full likelihood estimation for prospective survival analysis with a general semiparametric shared frailty model: Asymptotic theory, J. Statist. Plann. Inference 138 (7), 1998-2016, 2008.