Bayesian joint modeling of patient-reported longitudinal data on frequency and duration of migraine

Year 2023, Volume: 52 Issue: 3, 795 - 807, 30.05.2023

Gül İnan

https://doi.org/10.15672/hujms.993075

Abstract

In this methodological study, we address the joint modeling of longitudinal data on the frequency and duration migraine attacks collected from patients in a clinical study in which patients were repeatedly asked at each hospital visit to report the number of days of migraine attacks they had in the last $30$ days and the corresponding average duration of attacks. In our motivating data set, the migraine frequency outcome is a count variable inflated at multiples of $5$ and $10$ days, whereas the migraine duration outcome is reported entirely in discrete hours, including $0$ for non-migraine days and inflated at multiples of $12$ hours. In our study, we propose a joint modeling approach that models each migraine outcome by a multiple inflated negative binomial model with random effects and assumes a bivariate normal distribution for the random effects. We estimate the model parameters under Bayesian inference. We examine the performance of the proposed joint model using a Monte Carlo simulation study and compare its performance with a separate modeling approach in which each longitudinal count outcome is modeled separately. Finally, we present the results of the analysis of migraine data.

Keywords

Count outcomes, migraine days, migraine duration, multiple inflation, self-reported outcomes.

Supporting Institution

Istanbul Technical University

Project Number

41881

Thanks

Authors would like to thank to Prof. Dr. Aynur Ozge from Neurology Department, School of Medicine at Mersin University in Turkey and Dr. Osman Ozgur Yalin from Neurology Department at Istanbul Education and Research Hospital, Turkey for giving the permission to use the migraine data.

References

• [1] C.M. Allen, S.D. Griffith, S. Shiffman and D.F. Heitjan, Proximity and gravity: Modeling heaped self-reports, Stat. Med. 36 (20), 3200–3215, 2017.
• [2] L. Bermúdez, D. Karlis and M. Santolino, A finite mixture of multiple discrete distributions for modelling heaped count data, Comput. Statist. Data Anal. 112, 14–23, 2017.
• [3] E. Buta, S.S. O’Malley and R. Gueorguieva, Bayesian joint modelling of longitudinal data on abstinence, frequency and intensity of drinking in alcoholism trials, J. Roy. Statist. Soc. Ser. A 81 (3), 869–888, 2018.
• [4] C.G. Camarda, P.H. Eilers and J. Gampe, Modelling trends in digit preference patterns, J. R. Stat. Soc. Ser. C. Appl. Stat. 66 (5), 893–918, 2017.
• [5] F.W. Crawford, R.E. Weiss and M.A. Suchard, Sex, lies and self-reported counts: Bayesian mixture models for heaping in longitudinal count data via birth-death processes, Ann. Appl. Stat. 9 (2), 572–596, 2015.
• [6] J. Drechsler and H. Kiesl, Beat the heap: An imputation strategy for valid inferences from rounded income data, J. Surv. Stat. Methodol. 4 (1), 22–42, 2015.
• [7] A. Gelman, J. Hwang and A. Vehtari, Understanding predictive information criteria for Bayesian models, Stat. Comput. 24 (6), 997–1016, 2014.
• [8] R. Gueorguieva, A multivariate generalized linear mixed model for joint modelling of clustered outcomes in the exponential family, Stat. Model. 1 (3), 177–193, 2001.
• [9] D.F. Heitjan and D.B. Rubin, Inference from coarse data via multiple imputation with application to age heaping, J. Amer. Statist. Assoc. 85 (410), 304–314, 1990.
• [10] E. Juarez-Colunga, G.L. Silva and C.B. Dean, Joint modeling of zero-inflated panel count and severity outcomes, Biometrics 73 (4), 1413–1423, 2017.
• [11] W. Kassahun, T. Neyens, G. Molenberghs, C. Faes and G. Verbeke, A joint model for hierarchical continuous and zero-inflated overdispersed count data, J. Stat. Comput. Simul. 85 (3), 552–571, 2015.
• [12] H. Li, J. Staudenmayer, T. Wang, S.K. Keadle and R.J. Carroll, Three-part joint modeling methods for complex functional data mixed with zero-and-one-inflated proportions and zero-inflated continuous outcomes with skewness, Stat. Med. 37 (4), 611–626, 2018.
• [13] Q. Li, J. Pan and J. Belcher, Bayesian inference for joint modelling of longitudinal continuous, binary and ordinal events, Stat. Methods Med. Res. 25 (6), 2521–2540, 2016.
• [14] Q. Li, G.K. Tso, Y. Qin, T.I. Lovejoy, T.G. Heckman and Y. Li, Penalized multiple inflated values selection method with application to SAFER data, Stat. Methods Med. Res. 28 (10-11), 3205–3225, 2019.
• [15] B.E. Magnus and D. Thissen, Item response modeling of multivariate count data with zero inflation, maximum inflation, and heaping, J. Educ. Behav. Stat. 42 (5), 531– 558, 2017.
• [16] C. McCulloch, Joint modelling of mixed outcome types using latent variables, Stat. Methods Med. Res. 17 (1), 53–73, 2008.
• [17] F.E. Messlaki, Making use of multiple imputation to analyze heaped data, Master’s thesis, Utrecht University, 2010.
• [18] M. Plummer, JAGS: Just another Gibbs sampler, http://mcmc-jags.sourceforge.net/, 2017.
• [19] M. Plummer, A. Stukalov and M. Denwood, Package “rjags: Bayesian graphical models using MCMC”, R package version: 4-13, 2022.
• [20] M. Plummer, N. Best, K. Cowles and K. Vines, Package “CODA: Convergence diagnosis and output analysis for MCMC”, R package version: 0.19-4, 2022.
• [21] J. Van der Laan and L. Kuijvenhoven, Imputation of rounded data, Technical report, Statistics Netherlands, 2011.
• [22] H. Wang and D.F. Heitjan, Modeling heaping in self-reported cigarette counts, Stat. Med. 27 (19), 3789–3804, 2008.
• [23] H. Wang, S. Shiffman, S.D. Griffith and D.F. Heitjan, Truth and memory: Linking instantaneous and retrospective self-reported cigarette consumption, Ann. Appl. Stat. 6 (4), 1689–1706, 2012.
• [24] S. Watanabe, Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory, J. Mach. Learn Res. 11, 3571–3594, 2010.
• [25] O.O. Yalin, A. Ozge, M. Turkegun, B. Tasdelen and D. Uluduz, Course of migraine with aura: A follow-up study, J. Neurol. Sci-Turk. 33 (2), 254–263, 2016.
• [26] S. Zinn and A. Würbach, A statistical approach to address the problem of heaping in self-reported income data, J. Appl. Stat. 43 (4), 682–703, 2016.