Estimating propensity scores with missing covariate data using general location mixture models

Abstract

Abstract[In many observational studies, researchers estimate causal effects using propensity scores, e.g., by matching or sub-classifying on the scores. Estimation of propensity scores is complicated when some values of the covariates are missing. We propose to use multiple imputation to create completed datasets, from which propensity scores can be estimated, with a general location mixture model. The model assumes that the control units are a latent mixture of (i) units whose covariates are drawn from the same distributions as the treated AbstractIn many observational studies, researchers estimate causal effects using propensity scores, e.g., by matching or sub-classifying on the scores. Estimation of propensity scores is complicated when some values of the covariates are missing. We propose to use multiple imputation to create completed datasets, from which propensity scores can be estimated, with a general location mixture model. The model assumes that the control units are a latent mixture of (i) units whose covariates are drawn from the same distributions as the treated units' covariates and (ii) units whose covariates are drawn from different distributions. This formulation reduces the influence of control units outside the treated units' region of the covariate space on the estimation of parameters in the imputation model, which can result in more plausible imputations and better balance in the true covariate distributions. We illustrate the benefits of 1 the latent class modeling approach with simulations and with an observational study of the effect of breast feeding on children's cognitive abilities.

Long-term immunologic and virologic responses on raltegravir-containing regimens among ART-experienced participants in the HIV Outpatient Study

“…To account for a few covariates with a small fraction of missing data and to avoid bias if these data were not missing completely at random, we used the general location mixture model proposed by Mitra and Reiter. 20 This approach uses multiply imputed data to handle the missing values with an additional covariate that assists in identifying patients who switched to RAL-sparing ART but would have been good candidates for RAL-containing ART. Furthermore, we incorporated a maximum likelihood-based estimation procedure into the logistic regression model 21 to account for baseline HIV RNA values that were undetectable.…”

Causal Inference: A Missing Data Perspective

“…A straightforward approach consists of two independent steps: first impute the missing data and then draw causal inferences from the imputed complete data (e.g. Mitra and Reiter, 2011). However, how the missing values are imputed may have a nontrivial impact on the subsequent causal analysis (e.g.…”

Using mixtures oftdensities to make inferences in the presence of missing data with a small number of multiply imputed data sets

“…We assume that an analyst is interested in determining the relationship between PIATM and the effect of treatment after adjusting for relevant pre-treatment variables. We use the same fourteen background covariates used in Mitra and Reiter (2011). These are the child's race (Hispanic, black or other), the mother's race (Hispanic, black, Asian, white, Hawaiian/Pacific Islander, American Indian or other), the child's sex, indicator variable on whether the child's grandparents were present at birth and another variable indicating the presence of the mother's spouse at birth, the number of years between 1979 and when the mother gave birth (square root transformed), the mother's score on the Armed Forces Qualification Test (square root transformed), the mother's highest educational achievement, the child's birth weight, the number of days spent by the mother in the hospital (log transformed), the number of days spent by the child in the hospital (log transformed), the number of weeks the mother worked in the year preceding to child birth categorised into four groups (0 weeks, 1-47 weeks, 48-51 weeks and 52 weeks), the number of weeks the child was born premature categorised into three groups (0 weeks, 1-4 weeks and >5 weeks preterm), and family income (log transformed) at the time of the birth of the child.…”

“…Following Mitra and Reiter (2011) we dichotomise the variable that measures duration of breastfeeding so as to split units into two groups; the control group, comprises those units who were breastfed for less than 24 weeks, while the treatment group comprises those units who were breastfed for 24 weeks or more. We assume that an analyst is interested in determining the relationship between PIATM and the effect of treatment after adjusting for relevant pre-treatment variables.…”