Score test for missing at random or not

TL;DR

This paper develops score tests to distinguish between missing at random (MAR) and missing not at random (MNAR) mechanisms, addressing a critical gap in missing data analysis with practical applications and robust performance.

Contribution

It introduces novel score tests for MAR versus MNAR under parametric and semiparametric models that avoid identification issues by only requiring estimation under MAR.

Findings

Tests have well-controlled type I errors.

Tests demonstrate desirable power in simulations.

Application to HIV data shows practical utility.

Abstract

Missing data are frequently encountered in various disciplines and can be divided into three categories: missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR). Valid statistical approaches to missing data depend crucially on correct identification of the underlying missingness mechanism. Although the problem of testing whether this mechanism is MCAR or MAR has been extensively studied, there has been very little research on testing MAR versus MNAR.A critical challenge that is faced when dealing with this problem is the issue of model identification under MNAR. In this paper, under a logistic model for the missing probability, we develop two score tests for the problem of whether the missingness mechanism is MAR or MNAR under a parametric model and a semiparametric location model on the regression function. The score tests require only parameter estimation under the null MAR assumption, which completely circumvents the identification issue. Our simulations and analysis of human immunodeficiency virus data show that the score tests have well-controlled type I errors and desirable powers.