A Self-Censoring Model for Multivariate Nonignorable Nonmonotone Missing Data

Abstract

We introduce an itemwise modeling approach called “self‐censoring” for multivariate nonignorable nonmonotone missing data, where the missingness process of each outcome can be affected by its own value and associated with missingness indicators of other outcomes, while conditionally independent of the other outcomes. The self‐censoring model complements previous graphical approaches for the analysis of multivariate nonignorable missing data. It is identified under a completeness condition stating that any variability in one outcome can be captured by variability in the other outcomes among complete cases. For estimation, we propose a suite of semiparametric estimators including doubly robust estimators that deliver valid inferences under partial misspecification of the full‐data distribution. We also provide a novel and flexible global sensitivity analysis procedure anchored at the self‐censoring. We evaluate the performance of the proposed methods with simulations and apply them to analyze a study about the effect of highly active antiretroviral therapy on preterm delivery of HIV‐positive mothers.

Accounting for bias due to outcome data missing not at random: comparison and illustration of two approaches to probabilistic bias analysis: a simulation study

“…Monte Carlo NARFCS has two key strengths for non-specialist analysts: (1) the Monte Carlo implementation of a probabilistic bias analysis does not require knowledge about Bayesian inference and specialist statistical software, and (2) it calculates the bias-adjusted estimates using an MNAR-adaption of a popular and readily implemented imputation approach (FCS). However, both the Monte Carlo probabilistic bias analysis and FCS-type imputation have known theoretical weaknesses.…”

“…We specify the following regression models for the joint distribution of W, X, Y, A, D, M Y | Z : where expit{k} = exp{k}/ 1+ exp{k}, M Y is assumed to be independent of W and Z given D, A, Y and X (as specified in figure 1), and δ SM is the bias parameter representing the difference in the log-odds of observing Y between those with Y= 1 and Y= 0, conditional on D, A, Y and X . Let Ψ SM denote the set of all estimable parameters of model (2) (i.e., all except δ SM ), noting Ψ SM includes exposure effect β X .…”

“…We evaluated these methods when the prior distribution for the bias parameter was (i) inaccurate and imprecise, (ii) accurate and reasonably precise, and (iii) accurate and very precise. We repeated the simulation study for (1) β X = 0 and β X = ln 3 and (2) two data generating models: based on the selection model framework (SM data generating model) and the pattern-mixture model framework (PMM data generating model). For all combinations of the simulation settings, we generated 1000 simulated data sets, each with 100,000 observations for the full sample.…”

“…These mechanisms are commonly classified as missing completely at random (probability of missingness is independent of the observed and missing data), missing at random (MAR; probability of missingness is independent of the missing data given the observed) and missing not at random (MNAR; probability of missingness depends on the missing data even after conditioning on the observed data) (1). We focus on a MNAR missingness mechanism where the value of a variable directly affects its own probability of missingness (2). This type of MNAR missingness mechanism commonly occurs when collecting sensitive information (such as information on sexual health, financial matters, and substance-use behaviours) or when the health outcome under study affects participation.…”

“…In the current literature, there is limited guidance on implementing a probabilistic bias analysis to data MNAR. Recent exceptions for cross-sectional analyses include: (1) a pattern-mixture approach where draws from a prior distribution (of the bias parameters) are used to impute a categorical covariate under MNAR (20,21) and (2) a Bayesian implementation of a selection model for a partially observed continuous outcome (22). Additionally, in the context of selection bias due to non-random selection of participants into a study, Banack et al review and compare a Monte Carlo probabilistic bias analysis to an alternative approach that simulates the entire dataset under different assumptions about the selection bias (23) and Jayaweera et al conducted a Monte Carlo probabilistic bias analysis by inversely weighting participants based on their probability of inclusion (i.e., participating and remaining in the study combined) (24).…”