Maximum likelihood estimation with missing outcomes: From simplicity to complexity

• Published in: Statistics in medicine Vol. 38; no. 22; pp. 4453 - 4474
• Main Author: Baker, Stuart G.
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 30.09.2019
• Subjects: Bias; composite linear model; Computer Simulation; Data Interpretation, Statistical; double sampling; Humans; Latent class analysis; latent class instrumental variable; Likelihood Functions; Methods; Missing data; missing‐data mechanism; Models, Statistical; perfect fit analysis; Propensity Score; Randomized Controlled Trials as Topic; randomized trial; Survival Analysis; double sampling; perfect fit analysis; missing-data mechanism; composite linear model; randomized trial; latent class instrumental variable
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.8319

Many clinical or prevention studies involve missing or censored outcomes. Maximum likelihood (ML) methods provide a conceptually straightforward approach to estimation when the outcome is partially missing. Methods of implementing ML methods range from the simple to the complex, depending on the type of data and the missing‐data mechanism. Simple ML methods for ignorable missing‐data mechanisms (when data are missing at random) include complete‐case analysis, complete‐case analysis with covariate adjustment, survival analysis with covariate adjustment, and analysis via propensity‐to‐be‐missing scores. More complex ML methods for ignorable missing‐data mechanisms include the analysis of longitudinal dropouts via a marginal model for continuous data or a conditional model for categorical data. A moderately complex ML method for categorical data with a saturated model and either ignorable or nonignorable missing‐data mechanisms is a perfect fit analysis, an algebraic method involving closed‐form estimates and variances. A complex and flexible ML method with categorical data and either ignorable or nonignorable missing‐data mechanisms is the method of composite linear models, a matrix method requiring specialized software. Except for the method of composite linear models, which can involve challenging matrix specifications, the implementation of these ML methods ranges in difficulty from easy to moderate.