Average effect estimation with dichotomized events when the missing data mechanism is not missing at random
Amy M Kwon,1 Dianxu Ren2
1Biostatistics and Bioinformatics Core, James Graham Brown Cancer Center, University of Louisville, Louisville, KY, 2Department of Biostatistics, University of Pittsburgh Center for Research and Evaluation, School of Nursing, University of Pittsburgh, Pittsburgh, PA, USA
Background: The purpose of this work was to estimate the average effect of the covariate of interest when the outcome variable is dichotomized from a continuous variable and data are incomplete, with the missing data not missing at random (NMAR). The motivating example is to estimating the effect of vitamin D levels on secondary hyperparathyroidism among patients with chronic kidney disease.
Methods: The average effect of the covariate of interest is computed by a two-step procedure. In the first step, we identify the conditional distribution of the original variable given the covariates by obtaining the parameter estimates. In the second step, we draw the predictive values from the identified distribution, and create binary values from the predictive values by dichotomizing them at the threshold.
Results: According to the simulation results, the biases of the effects between logistic regression with the complete data and the estimated logistic regression with the converted binary variable are negligible. For the application example, the effect of vitamin D on the occurrence of secondary hyperparathyroidism is highly significant in the complete case analysis, but only a modest effect of vitamin D on secondary hyperparathyroidism is observed under the NMAR assumption.
Conclusion: It is impossible to find consistent estimates without knowing the exact nature of the missing data when the missing data mechanism is NMAR. Also, the outcome variable is binary, so we may be faced with an unidentifiability problem when the missing data mechanism is NMAR. To avoid this problem, we estimated the average effect of the covariate of interest in the framework of a generalized linear model from the relationship between a dichotomized outcome and a continuous original outcome, and the estimated effect showed negligible bias according to this simulation.
Keywords: average effect, NMAR, not missing at random, dichotomized events, secondary hyperparathyroidism
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