Multiple imputation for non-monotone missing not at random data using the no self-censoring model

Abstract

Although approaches for handling missing data from longitudinal studies are well-developed when the patterns of missingness are monotone, fewer methods are available for non-monotone missingness. Moreover, the conventional missing at random assumption—a natural benchmark for monotone missingness—does not model realistic beliefs about the non-monotone missingness processes (Robins and Gill, 1997). This has provided the impetus for alternative non-monotone missing not at random mechanisms. The “no self-censoring” model is such a mechanism and assumes the probability an outcome variable is missing is independent of its value when conditioning on all other possibly missing outcome variables and their missingness indicators. As an alternative to “weighting” methods that become computationally demanding with increasing number of outcome variables, we propose a multiple imputation approach under no self-censoring. We focus on the case of binary outcomes and present results of simulation and asymptotic studies to investigate the performance of the proposed imputation approach. We describe a related approach to sensitivity analysis to departure from no self-censoring. We discuss the relationship between missing at random and no self-censoring and prove that one is not a special case of the other. Finally, we discuss extensions to non-binary data settings. The proposed methods are illustrated with application to a substance use disorder clinical trial.

Keywords

Missing at random missing data sensitivity analysis fully conditional specification

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References

Little

Rubin

. Statistical analysis with missing data. 3rd ed. Hoboken, NJ: John Wiley & Sons, 2019.

Molenberghs

Fitzmaurice

Kenward

, et al. Handbook of missing data methodology. Boca Raton, FL: CRC Press, 2014.

Robins

Rotnitzky

Zhao

. Estimation of regression coefficients when some regressors are not always observed. J Am Stat Assoc 1994; 89: 846–866.

Tsiatis

. Semiparametric theory and missing data. New York, NY: Springer, 2006.

Little

Rubin

. Bayes and multiple imputation. Statistical Analysis with Missing Data 2002; 200–220.

Rubin

. Multiple imputation after 18+ years. J Am Stat Assoc 1996; 91: 473–489.

Robins

Gill

. Non-response models for the analysis of non-monotone ignorable missing data. Stat Med 1997; 16: 39–56.

Vansteelandt

Rotnitzky

Robins

. Estimation of regression models for the mean of repeated outcomes under nonignorable nonmonotone nonresponse. Biometrika 2007; 94: 841–860.

Linero

Daniels

. Bayesian approaches for missing not at random outcome data: the role of identifying restrictions. Stat Sci 2018; 33: 198.

10.

Shen

, et al. On weighting approaches for missing data. Stat Methods Med Res 2013; 22: 14–30.

11.

Malinsky

Shpitser

Tchetgen Tchetgen

. Semiparametric inference for nonmonotone missing-not-at-random data: the no self-censoring model. J Am Stat Assoc 2022; 117: 1415–1423.

12.

Robins

Rotnitzky

Scharfstein

. Sensitivity analysis for selection bias and unmeasured confounding in missing data and causal inference models. In Statistical Models in Epidemiology, the Environment, and Clinical Trials, pp. 1–94. Springer, 2000.

13.

Rotnitzky

Robins

Scharfstein

. Semiparametric regression for repeated outcomes with nonignorable nonresponse. J Am Stat Assoc 1998; 93: 1321–1339.

14.

Sadinle

Reiter

. Itemwise conditionally independent nonresponse modelling for incomplete multivariate data. Biometrika 2017; 104: 207–220.

15.

Shpitser

. Consistent estimation of functions of data missing non-monotonically and not at random. Adv Neural Inf Process Syst 2016; 29.

16.

Sun

Tchetgen Tchetgen

. On inverse probability weighting for nonmonotone missing at random data. J Am Stat Assoc 2018; 113: 369–379.

17.

Tchetgen

EJT

Wang

Sun

. Discrete choice models for nonmonotone nonignorable missing data: identification and inference. Stat Sin 2018; 28: 2069.

18.

Zhou

Little

Kalbfleisch

. Block-conditional missing at random models for missing data. Stat Sci 2010; 25: 517–532.

19.

Fletcher Mercaldo

Blume

. Missing data and prediction: the pattern submodel. Biostatistics 2020; 21: 236–252.

20.

Tompsett

Leacy

Moreno-Betancur

, et al. On the use of the not-at-random fully conditional specification (narfcs) procedure in practice. Stat Med 2018; 37: 2338–2353.

21.

Beesley

Bondarenko

Elliot

, et al. Multiple imputation with missing data indicators. Stat Methods Med Res 2021; 30: 2685–2700.

22.

Scharfstein

Steingrimsson

McDermott

, et al. Global sensitivity analysis of randomized trials with nonmonotone missing binary outcomes: application to studies of substance use disorders. Biometrics 2022; 78: 649–659.

23.

National Research Council. The prevention and treatment of missing data in clinical trials. Washington, DC: National Academies Press, 2010.

24.

Van Buuren

. Multiple imputation of discrete and continuous data by fully conditional specification. Stat Methods Med Res 2007; 16: 219–242.

25.

Van Buuren

Brand

Groothuis-Oudshoorn

, et al. Fully conditional specification in multivariate imputation. J Stat Comput Simul 2006; 76: 1049–1064.

26.

Van Buuren

Groothuis-Oudshoorn

. Mice: multivariate imputation by chained equations in R. J Stat Softw 2011; 45: 1–67.

27.

Rubin

. Multiple imputation for nonresponse in surveys. 81. Hoboken, NJ: John Wiley & Sons, 2004.

28.

Heckerman

Chickering

Meek

, et al. Dependency networks for inference, collaborative filtering, and data visualization. J Mach Learn Res 2000; 1: 49–75.

29.

Rubin

. Nested multiple imputation of NMES via partially incompatible MCMC. Stat Neerl 2003; 57: 3–18.

30.

White

Royston

Wood

. Multiple imputation using chained equations: issues and guidance for practice. Stat Med 2011; 30: 377–399.

31.

Van Buuren

. Flexible imputation of missing data. Boca Raton, FL: CRC Press, 2018.

32.

White

Daniel

Royston

. Avoiding bias due to perfect prediction in multiple imputation of incomplete categorical variables. Comput Stat Data Anal 2010; 54: 2267–2275.

33.

Liu

Gelman

Hill

, et al. On the stationary distribution of iterative imputations. Biometrika 2014; 101: 155–173.

34.

Hughes

White

Seaman

, et al. Joint modelling rationale for chained equations. BMC Med Res Methodol 2014; 14: 1–10.

35.

Seaman

Hughes

. Relative efficiency of joint model and full conditional specification multiple imputation when conditional models are compatible: the general location model. Stat Methods Med Res 2018; 27: 1603–1614.

36.

Lin

Lipsitz

Sinha

, et al. Exact Bayesian p-values for a test of independence in a

2 \times 2

contingency table with missing data. Stat Methods Med Res 2018; 27: 3411–3419.

37.

Kim

. Assessment of nonignoralbe log-linear models for an incomplete contingency table. Stat Sin 2018; 28: 1887–1905.

38.

Fitzmaurice

Laird

Rotnitzky

. Regression models for discrete longitudinal responses. Stat Sci 1993; 8: 284–299.

39.

Crits-Christoph

Siqueland

Blaine

, et al. Psychosocial treatments for cocaine dependence: national institute on drug abuse collaborative cocaine treatment study. Arch Gen Psychiatry 1999; 56: 493–502.

40.

American Psychiatric Association. Diagnostic and statistical manual of mental disorders. 4th ed., text rev. Washington, DC: American Psychiatric Association, 2000.

41.

Fitzmaurice

Lipsitz

Weiss

. Sensitivity analysis for non-monotone missing binary data in longitudinal studies: application to the NIDA collaborative cocaine treatment study. Stat Methods Med Res 2019; 28: 3057–3073.

42.

Molenberghs

Beunckens

Sotto

, et al. Every missingness not at random model has a missingness at random counterpart with equal fit. J R Stat Soc: Ser B (Statistical Methodology) 2008; 70: 371–388.

43.

Cox

Donnelly

. Principles of applied statistics. Cambridge, UK: Cambridge University Press, 2011.

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