Joint modeling of zero-inflated count and time-to-event data is usually performed by applying the shared random effect model. This kind of joint modeling can be considered as a latent Gaussian model. In this paper, the approach of integrated nested Laplace approximation (INLA) is used to perform approximate Bayesian approach for the joint modeling. We propose a zero-inflated hurdle model under Poisson or negative binomial distributional assumption as sub-model for count data. Also, a Weibull model is used as survival time sub-model. In addition to the usual joint linear model, a joint partially linear model is also considered to take into account the non-linear effect of time on the longitudinal count response. The performance of the method is investigated using some simulation studies and its achievement is compared with the usual approach via the Bayesian paradigm of Monte Carlo Markov Chain (MCMC). Also, we apply the proposed method to analyze two real data sets. The first one is the data about a longitudinal study of pregnancy and the second one is a data set obtained of a HIV study.
MekonnenFHLakewWDTesfayeZD, et al.Statistical models for longitudinal zero-inflated count data: application to seizure attacks. Afr Health Sci2019;
19: 2555–2564.
2.
MaruottiA.A two part mixed effects pattern mixture model to handle zero inflation and incompleteness in a longitudinal setting. Biometric J2011;
53: 716–734.
3.
HurK. A random-effects zero-inflated Poisson regression model for clustered extra-zero count data. 2000.
4.
BuuALiRTanX, et al.Statistical models for longitudinal zero inflated count data with applications to the substance abuse field.Stat Med2012;
31: 4074–4086.
5.
DeSantisSMLazaridisCJiS, et al.Analyzing propensity matched zero-inflated count outcomes in observational studies. J Appl Stat2014;
41: 127–141.
6.
LambertD.Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics1992;
34: 1–4.
7.
RidoutMHindeJDemétrioCG.A score test for testing a zero inflated Poisson regression model against zero inflated negative binomial alternatives.Biometrics2001;
57: 219–223.
8.
MullahyJ.Specification and testing of some modified count data models. J Econometrics1986;
33: 341–365.
9.
ZhuHDeSantisSMLuoS.Joint modeling of longitudinal zero-inflated count and time-to-event data: A Bayesian perspective.Stat Meth Med Res2018;
27: 1258–1270.
BaghfalakiTGanjaliMBerridgeD.Robust joint modeling of longitudinal measurements and time to event data using normal/independent distributions: a Bayesian approach.Biometric J2013;
55: 844–865.
12.
BaghfalakiTGanjaliMBerridgeD.Joint modeling of multivariate longitudinal mixed measurements and time to event data using a Bayesian approach. J Appl Stat2014;
41: 1934–1955.
13.
BaghfalakiTGanjaliM.A Bayesian approach for joint modeling of skew-normal longitudinal measurements and time to event data. REVSTAT-Stat J2015;
13: 169–191.
14.
TsiatisAADavidianM.Joint modeling of longitudinal and time-to-event data: an overview. Statistica Sinica2004; 14(3): 809–834.
15.
ElashoffRLiN.Joint modeling of longitudinal and time-to-event data.
Boca Raton, FL:
CRC Press, 2016.
16.
RizopoulosD.Joint models for longitudinal and time-to-event data: with applications in R.
Boca Raton, FL:
CRC Press, 2012.
17.
AlsefriMSudellMGarcía-FiñanaM, et al.Bayesian joint modelling of longitudinal and time to event data: a methodological review. BMC Med Res Methodol2020;
20: 1–7.
18.
LunnDSpiegelhalterDThomasA, et al.The BUGS project: evolution, critique and future directions.Stat Med2009;
28: 3049–3067.
19.
PlummerM. JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In: Proceedings of the 3rd international workshop on distributed statistical computing, 20 March 2003, pp.1-10.
20.
RueHMartinoS.Approximate Bayesian inference for hierarchical Gaussian Markov random field models. J Stat Plan Inference2007;
137: 3177–3192.
21.
RueHMartinoSChopinN.Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J Royal Stat Soc: Ser B (Statistical Methodology)2009;
71: 319–392.
22.
RueHRieblerASørbyeSH, et al.Bayesian computing with INLA: a review. Annual Rev Stat Appl2017;
4: 395–421.
23.
Van NiekerkJBakkaHRueH. Joint models as latent Gaussian models-not reinventing the wheel. arXiv preprint arXiv:1901.09365. 2019 1--18.
24.
NiekerkJVBakkaHRueH.Competing risks joint models using R-INLA.Stat Model 21(1--2): 56--71.c
25.
KimSZengDTaylorJM.Joint partially linear model for longitudinal data with informative drop outs. Biometrics2017;
73: 72–82.
26.
MahmoodiMMoghimbeigiAMohammadK, et al.Semiparametric models for multilevel overdispersed count data with extra zeros.Stat Meth Med Res2018;
27: 1187–1201.
CzadoCErhardtVMinA, et al.Zero-inflated generalized Poisson models with regression effects on the mean, dispersion and zero-inflation level applied to patent outsourcing rates. Stat Model2007;
7: 125–153.
29.
LewseyJDThomsonWM.The utility of the zero inflated Poisson and zero inflated negative binomial models: a case study of cross sectional and longitudinal DMF data examining the effect of socio economic status.Commun Dentistry Oral Epidemiol2004;
32: 183–189.
30.
MinYAgrestiA.Random effect models for repeated measures of zero-inflated count data. Stat Model2005;
5: 1–9.
31.
NeelonBHO’MalleyAJNormandSL.A Bayesian model for repeated measures zero-inflated count data with application to outpatient psychiatric service use.Stat Model2010;
10: 421–439.
32.
RoseCEMartinSWWannemuehlerKA, et al.On the use of zero-inflated and hurdle models for modeling vaccine adverse event count data.J Biopharmaceut Stat2006;
16: 463–481.
33.
HendersonRDigglePDobsonA.Joint modelling of longitudinal measurements and event time data.Biostatistics2000;
1: 465–480.
34.
RueHHeldL.Gaussian Markov random fields: theory and applications.
Boca Raton, FL:
CRC Press, 2005.
35.
BaghfalakiTGanjaliMHashemiR.Bayesian joint modeling of longitudinal measurements and time-to-event data using robust distributions.J Biopharmaceut Stat2014;
24: 834–855.
36.
Barndorff-NielsenOE.Asymptotic techniques; for use in statistics. 1989.
37.
PerperoglouASauerbreiWAbrahamowiczM, et al.A review of spline function procedures in R.BMC Med Res Methodol2019;
19: 46.
38.
WuHZhangJT.Nonparametric regression methods for longitudinal data analysis: mixed-effects modeling approaches.
John Wiley & Sons, 2006.
39.
De BoorCDe BoorCMathématicienEU, et al.A practical guide to splines.
New York, NY:
Springer-Verlag, 1978.
40.
EilersPHMarxBD.Flexible smoothing with B-splines and penalties.Stat Sci1996; 11(2): 89–102.
41.
ZhangXPeiYFZhangL, et al.Negative Binomial mixed models for analyzing longitudinal microbiome data.Frontiers Microbiol2018;
9: 1683.
42.
LunaPNMansbachJMShawCA.A joint modeling approach for longitudinal microbiome data improves ability to detect microbiome associations with disease.PLOS Computat Biol2020;
16: e1008473.
43.
DiGiulioDBCallahanBJMcMurdiePJ, et al.Temporal and spatial variation of the human microbiota during pregnancy.Proc Natl Acad Sci2015;
112: 11060–11065.
44.
Van den BroekJ.A score test for zero inflation in a Poisson distribution. Biometrics 1995; 51(2): 738–743.
45.
YangZHardinJWAddyCL.Score tests for zero-inflation in overdispersed count data. Commun Stat-Theory Meth2010;
39: 2008–2030.
46.
ChristensenRJohnsonWBranscumA, et al.Bayesian ideas and data analysis: an introduction for scientists and statisticians.
Boca Raton, FL:
CRC Press, 2011.
47.
GelmanACarlinJBSternHS, et al.Bayesian data analysis.
Boca Raton, FL:
CRC Press, 2013.
48.
JeffreysH.The theory of probability.
Oxford:
OUP, 1998.
49.
KassRERafteryAE.Bayes factors. J Am Stat Assoc1995;
90: 773–795.
50.
KassambaraA.Machine learning essentials: practical guide in R. STHDA. 2018.
51.
GuoXCarlinBP.Separate and joint modeling of longitudinal and event time data using standard computer packages.Am Stat2004;
58: 16–24.
52.
RizopoulosD.Joint models for longitudinal and time-to-event data: with applications in R.
Boca Raton, FL:
CRC Press, 2012.
53.
BaghfalakiTGanjaliMVerbekeG.A shared parameter model of longitudinal measurements and survival time with heterogeneous random-effects distribution. J Appl Stat2017;
44: 2813–2836.
54.
GanjaliMBaghfalakiT.A copula approach to joint modeling of longitudinal measurements and survival times using Monte Carlo expectation-maximization with application to AIDS studies.J Biopharmaceut Stat2015;
25: 1077–1099.
55.
NajafabadiMZBahrami SamaniEGanjaliM.Analysis of joint modeling of longitudinal zero-inflated power series and zero-inflated time to event data. J Biopharmaceut Stat2020;
16: 1–9.
