Pattern-Mixture Models for Multivariate Incomplete Data with Covariates

Abstract

Pattern-mixture models stratify incomplete data by the pattern of missing values and formulate distinct models within each stratum. Pattern-mixture models are developed for analyzing a random sample on continuous variables y(1), y(2) when values of y(2) are nonrandomly missing. Methods for scalar y(1) and y(2) are here generalized to vector y(1) and y(2) with additional fixed covariates x. Parameters in these models are identified by alternative assumptions about the missing-data mechanism. Models may be underidentified (in which case additional assumptions are needed), just-identified, or overidentified. Maximum likelihood and Bayesian methods are developed for the latter two situations, using the EM and SEM algorithms, direct and interactive simulation methods. The methods are illustrated on a data set involving alternative dosage regimens for the treatment of schizophrenia using haloperidol and on a regression example. Sensitivity to alternative assumptions about the missing-data mechanism is assessed, and the new methods are compared with complete-case analysis and maximum likelihood for a probit selection model.

Parametric latent class joint model for a longitudinal biomarker and recurrent events

“…In this setting, for example, pattern mixture models [32,33] would represent the biomarker conditional upon the event occurrence pattern, and selection models [34,35] and related joint models [36,37] typically consider the event hazard conditional upon the current, possibly imputed, biomarker value.…”

Effects of Physical Activity on Teen Smoking Cessation

“…16 Popular methods for dealing with missing data to produce complete data sets have serious drawbacks. 35 List-wise deletion can introduce biased estimates and reduced power, and simple mean replacement leads to reduction of the SE estimates. Similar to procedures used by Joffe et al 16 in a 2-armed randomized trial of N-O-T, the multiple-imputation procedure described by Rubin 36 replaces missing values with a set of plausible values, eliminating uncertainty about which are the correct values to impute.…”

“…Following the recommendations of Rubin, 35 we regarded these data as missing at random or missing completely at random. Our reference sample included 233 qualified participants.…”

“…35 We included the dependent variable in the imputation model to reduce any artificial inflation of the relationship between the independent and dependent variables. The imputed values of the dependent variable did not provide additional error.…”

Sensitivity Analysis for Causal Inference under Unmeasured Confounding and Measurement Error Problems

“…Estimation of the parameter of interest ψ f 0 is then carried out for a set of possible values of α 0 through a model-dependent and often complex estimator, and a decision about the original question of interest is made based on these estimates together with auxiliary subject-matter expert information about α 0 . Approaches that implement this idea but use ML estimators have been also proposed by several authors, including Rosenbaum and Rubin [18], Little [19], Little and Wang [20], Verbeke et al [21]. Bayesian versions of this approach have also been explored by various authors, including Gustafson et al [22], McCandless et al [23].…”