Skip to main content
Log in

Partitioned method of valid moment marginal model with Bayes interval estimates for correlated binary data with time-dependent covariates

  • Original paper
  • Published:
Computational Statistics Aims and scope Submit manuscript

Abstract

The fit of marginal models to longitudinal data should include modelling all extra variation among responses and covariates. This paper proposes a Partitioned Method of Valid Moments marginal regression model for binary outcomes with Bayes method while using lagged coefficients. Time-dependent covariates are factored in through composite likelihoods. A simulation study highlights the properties of the model coefficients. Modeling cognitive impairment diagnosis in NACC Alzheimer clinical data are demonstrated. Sensitivity analyses are conducted to evaluate the impact of the prior distribution on the posterior inferences.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Beekly DL, Ramos EM, Erin M, et al (2007) The National Alzheimer’s Coordinating Center (NACC) database: the uniform dataset. https://www.alz.washington.edu/.

  • Chandler RE, Bate S (2007) Inference for clustered data using the independence loglikelihood. Biometrika 94(1):167–183

    Article  MathSciNet  Google Scholar 

  • Cox DR, Reid N (2004) A note on pseudolikelihood constructed from marginal densities. Biometrika 91(3):729–737

    Article  MathSciNet  Google Scholar 

  • Efron B (2015) Frequentist accuracy of Bayesian estimates. J R Stat Soc Ser B Stat Methodol 77(3):617–649

    Article  MathSciNet  Google Scholar 

  • Glasbey CA (2001) Non-linear autoregressive time series with multivariate Gaussian mixtures as marginal distributions. J R Stat Soc Ser C Appl Stat 50(2):143–154

    Article  MathSciNet  Google Scholar 

  • Hall AR (2005) Generalized method of moments. Oxford University Press, New York

    MATH  Google Scholar 

  • Hansen LP (1982) Large sample properties of generalized method of moments estimators. Econometrica 50(4):1029–1054

    Article  MathSciNet  Google Scholar 

  • Hansen LP, Heaton J, Yaron A (1996) Finite-sample properties of some alternative GMM estimators. J Bus Econ Stat 14(3):262–280

    Google Scholar 

  • Heagerty PJ (2002) Marginalized transition models and likelihood inference for longitudinal cateogorical data. Biometrics 58(2):342–351

    Article  MathSciNet  Google Scholar 

  • Heagerty PJ, Comstock BA (2013) Exploration of lagged associations using longitudinal data. Biometrics 69(1):197–205

    Article  MathSciNet  Google Scholar 

  • Hoff PD (2009) A first course in bayesian statistical methods. Springer, New York

    Book  Google Scholar 

  • Hogervorst E, Hupper F, Matthews FE, Brayne C (2008) Thyroid function and cognitive decline in the MRC cognitive function and ageing study. Psychoneuroendocrinology 33(7):1013–1022

    Article  Google Scholar 

  • Irimata KM, Wilson JR. (2018) Using SAS to estimate lagged coefficients with the %partitionedGMM macro. In: SAS Global Forum 2018 conference proceedings. Denver.

  • Irimata KM, Broatch J, Wilson JR (2019) Partitioned GMM logistic regression models for longitudinal data. Stat Med 38(12):2171–2183

    Article  MathSciNet  Google Scholar 

  • Joe H (1997) Multivariate models and dependence concepts. Chapman and Hall, London

    Book  Google Scholar 

  • Lai TL, Small D (2007) Marginal regression analysis of longitudinal data with time-dependent covariates: a generalised method of moments approach. J R Stat Soc Ser B 69(1):79–99

    Article  MathSciNet  Google Scholar 

  • Laird NM, Ware JH (1982) Random-effects models for longitudinal data. Biometrics 38(4):963–974

    Article  Google Scholar 

  • Lalonde TL, Wilson JR, Yin J (2014) GMM logistic regression models for longitudinal data with time-dependent covariates. Stat Med 33(27):4756–4769

    Article  MathSciNet  Google Scholar 

  • Liang K-Y, Zeger SL (1986) Longitudinal data analysis using generalized linear models. Biometrika 73(1):13–22

    Article  MathSciNet  Google Scholar 

  • LoBue C, Denney D, Hynan LS et al (2016) Self-reported traumatic brain injury and mild cognitive impairment: Increased risk and earlier age of diagnosis. J Alzheimers Dis 51(3):727–736

    Article  Google Scholar 

  • McFadden D (1989) A method of simulated moments for estimation of discrete response models without numerical integration. Econometrica 57(5):995–1026

    Article  MathSciNet  Google Scholar 

  • Muller H-G, Stadtmuller U (2005) Generalized functional linear models. Ann Stat 33(2):774–805

    Article  MathSciNet  Google Scholar 

  • Obermeier V, Scheipl F, Heumann C, Wassermann J, Küchenhoff H (2015) Flexible distributed lags for modelling earthquake data. J R Stat Soc Ser C Appl Stat 64(2):395–412

    Article  MathSciNet  Google Scholar 

  • Paterniti S, Verdier-Taillefer MH, Dufouil C, Alperovich A (2002) Depressive symptoms and cognitive decline in elderly people. Br J Psychiatry 181:406–410

    Article  Google Scholar 

  • Qu A, Lindsay BG, Li B (2000) Improving generalised estimating equations using quadratic inference functions. Biometrika 87(4):823–836

    Article  MathSciNet  Google Scholar 

  • Rocca WA, Petersen RC, Knopman DS et al (2011) Trends in the incidence and prevalence of Alzheimer’s disease, dementia and cognitive impairment in the United States. Alzheimers Dement 7(1):80–93

    Article  Google Scholar 

  • Roos M, Held L (2011) Sensitivity analysis in Bayesian generalized linear mixed models for binary data. Bayesian Anal 6(2):259–278

    Article  MathSciNet  Google Scholar 

  • Schildcrout JS, Heagerty PJ (2005) Regression analysis of longitudinal binary data with time-dependent environmental covariates: bias and efficiency. Biostatistics 6(4):633–652

    Article  Google Scholar 

  • Skene AM, Shaw JEH, Lee TD (1986) Bayesian modelling and sensitivity analysis. J R Stat Soc Stat 35(2):281–288

    Google Scholar 

  • Stein ML, Chi Z, Welty LJ (2004) Approximating likelihoods for large spatial data sets. J R Stat Soc Ser B Stat Methodol. 66(2):275–296

    Article  MathSciNet  Google Scholar 

  • Tanaka M (2020) Adaptive MCMC for generalized method of moments with many moment conditions.

  • Varin C (2008) On composite marginal likelihoods. AStA Adv Stat Anal 92:1–28

    Article  MathSciNet  Google Scholar 

  • Varin C, Reid N, Firth D (2011) An overview of composite likelihood methods. Stat Sin 21(1):5–42

    MathSciNet  MATH  Google Scholar 

  • Yin G (2009) Bayesian generalized method of moments. Bayesian Anal 4(2):191–207

    MathSciNet  MATH  Google Scholar 

  • Yin G, Ma Y, Liang F, Yuan Y (2011) Stochastic Generalized Method of Moments. J Comput Graph Stat 20(3):714–727

    Article  MathSciNet  Google Scholar 

  • Zeger SL, Liang K-Y (1986) Longitudinal data analysis for discrete and continuous outcomes. Biometrics 42(1):121–130

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jeffrey R. Wilson.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vazquez, E., Wilson, J.R. Partitioned method of valid moment marginal model with Bayes interval estimates for correlated binary data with time-dependent covariates. Comput Stat 36, 2701–2718 (2021). https://doi.org/10.1007/s00180-021-01105-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-021-01105-3

Keywords

Navigation