Pseudo-value regression of clustered multistate current status data with informative cluster sizes

Abstract

Multistate current status data presents a more severe form of censoring due to the single observation of study participants transitioning through a sequence of well-defined disease states at random inspection times. Moreover, these data may be clustered within specified groups, and informativeness of the cluster sizes may arise due to the existing latent relationship between the transition outcomes and the cluster sizes. Failure to adjust for this informativeness may lead to a biased inference. Motivated by a clinical study of periodontal disease, we propose an extension of the pseudo-value approach to estimate covariate effects on the state occupation probabilities for these clustered multistate current status data with informative cluster or intra-cluster group sizes. In our approach, the proposed pseudo-value technique initially computes marginal estimators of the state occupation probabilities utilizing nonparametric regression. Next, the estimating equations based on the corresponding pseudo-values are reweighted by functions of the cluster sizes to adjust for informativeness. We perform a variety of simulation studies to study the properties of our pseudo-value regression based on the nonparametric marginal estimators under different scenarios of informativeness. For illustration, the method is applied to the motivating periodontal disease dataset, which encapsulates the complex data-generation mechanism.

Keywords

Current status data multistate models clustered data informative cluster size estimating equations

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References

Andersen

Keiding

. Multi-state models for event history analysis. Stat Methods Med Res 2002; 11: 91–115.

Mitani

Kaye

Nelson

. Marginal analysis of multiple outcomes with informative cluster size. Biometrics 2021; 77: 271–282.

Lan

Bandyopadhyay

Datta

. Non-parametric regression in clustered multistate current status data with informative cluster size. Stat Neerl 2017; 71: 31–57.

Fernandes

Wiegand

Salinas

, et al. Periodontal disease status in Gullah African Americans with type 2 diabetes living in South Carolina. J Periodontol 2009; 80: 1062–1068.

Mdala

Olsen

Haffajee

, et al. Comparing CAL and PD for predicting periodontal disease progression in healthy sites of patients with chronic periodontitis using multi-state Markov models. J Clin Periodontol 2014; 41: 837.

Jewell

van der Laan

. Current status data: Review, recent developments and open problems. Handbook Stat 2003; 23: 625–642.

Shiboski

. Generalized additive models for current status data. Lifetime Data Anal 1998; 4: 29–50.

Sun

. The Statistical Analysis of Interval-Censored Failure Time Data. New York: Springer, 2006.

Chen

Tong

Sun

. A frailty model approach for regression analysis of multivariate current status data. Stat Med 2009; 28: 3424–3436.

10.

Sun

, et al. A new approach for regression analysis of multivariate current status data with informative censoring. Commun Math Stat 2022; 1–20. In press.

11.

Andersen

Klein

Rosthøj

. Generalised linear models for correlated pseudo-observations, with applications to multi-state models. Biometrika 2003; 90: 15–27.

12.

Datta

Sundaram

. Nonparametric estimation of stage occupation probabilities in a multistage model with current status data. Biometrics 2006; 62: 829–837.

13.

Anyaso-Samuel

Datta

. Adjusting for informative cluster size in pseudo-value based regression approaches with clustered time to event data. Stat Med 2023. In press.

14.

Barlow

Bartholomew

Bremner

, et al. Statistical Inference Under Order Restrictions: The Theory and Application of Isotonic Regression. New York, N.Y.: J. Wiley, 1972.

15.

Mukerjee

. Monotone nonparametric regression. Ann Stat 1988; 16: 741–750.

16.

Nadaraya

. On estimating regression. Theory Probab Appl 1964; 9: 141–142.

17.

Watson

. Smooth regression analysis. Sankhyā: Indian J Stat, Ser A 1964; 26: 359–372.

18.

Wand

Jones

. Kernel smoothing. London: Chapman & Hall, 1995.

19.

Andersen

Borgan

Gill

, et al. Statistical models based on counting processes. New York: Springer-Verlag, 1993.

20.

Datta

Satten

. Validity of the Aalen–Johansen estimators of stage occupation probabilities and Nelson–Aalen estimators of integrated transition hazards for non-Markov models. Stat Probab Lett 2001; 55: 403–411.

21.

Klein

Andersen

. Regression modeling of competing risks data based on pseudovalues of the cumulative incidence function. Biometrics 2005; 61: 223–229.

22.

Andersen

Pohar Perme

. Pseudo-observations in survival analysis. Stat Methods Med Res 2010; 19: 71–99.

23.

Wang

Kong

Datta

. Inference for marginal linear models for clustered longitudinal data with potentially informative cluster sizes. Stat Methods Med Res 2011; 20: 347–367.

24.

Liang

Zeger

. Longitudinal data analysis using generalized linear models. Biometrika 1986; 73: 13–22.

25.

Williamson

Datta

Satten

. Marginal analyses of clustered data when cluster size is informative. Biometrics 2003; 59: 36–42.

26.

Dutta

Datta

. A rank-sum test for clustered data when the number of subjects in a group within a cluster is informative. Biometrics 2016; 72: 432–440.

27.

Huang

Leroux

. Informative cluster sizes for subcluster-level covariates and weighted generalized estimating equations. Biometrics 2011; 67: 843–851.

28.

Armitage

. Development of a classification system for periodontal diseases and conditions. Ann Periodontol 1999; 4: 1–6.

29.

Chapple

Genco

and working group 2 of the joint EFP/AAP workshop. Diabetes and periodontal diseases: consensus report of the joint EFP/AAP workshop on periodontitis and systemic diseases. J Periodontol 2013; 84: S106–S112.

30.

Ambrogi

Biganzoli

Boracchi

. Estimates of clinically useful measures in competing risks survival analysis. Stat Med 2008; 27: 6407–6425.

31.

Chaganty

. An alternative approach to the analysis of longitudinal data via generalized estimating equations. J Stat Plan Inference 1997; 63: 39–54.

32.

Lam

Lee

Wong

, et al. Marginal analysis of current status data with informative cluster size using a class of semiparametric transformation cure models. Stat Med 2021; 40: 2400–2412.

33.

Hoffman

Sen

Weinberg

. Within-cluster resampling. Biometrika 2001; 88: 1121–1134.

34.

Jacobsen

Martinussen

. A note on the large sample properties of estimators based on generalized linear models for correlated pseudo-observations. Scand J Stat 2016; 43: 845–862.

35.

Overgaard

Parner

Pedersen

. Asymptotic theory of generalized estimating equations based on jack-knife pseudo-observations. Ann Stat 2017; 45: 1988–2015.

36.

Overgaard

Parner

Pedersen

. Estimating the variance in a pseudo-observation scheme with competing risks. Scand J Stat 2018; 45: 923–940.

37.

Nevalainen

Datta

Oja

. Inference on the marginal distribution of clustered data with informative cluster size. Stat Pap 2014; 55: 71–92.

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