Propensity Score Analysis With Latent Covariates: Measurement Error Bias Correction Using the Covariate’s Posterior Mean, aka the Inclusive Factor Score

Abstract

We address measurement error bias in propensity score (PS) analysis due to covariates that are latent variables. In the setting where latent covariate X is measured via multiple error-prone items W , PS analysis using several proxies for X -the W items themselves, a summary score (mean/sum of the items), or the conventional factor score (cFS , i.e., predicted value of X based on the measurement model) -often results in biased estimation of the causal effect, because balancing the proxy (between exposure conditions) does not balance X. We propose an improved proxy: the conditional mean of X given the combination of W , the observed covariates Z, and exposure A, denoted X W ZA . The theoretical support, which applies whether X is latent or not (but is unobserved), is that balancing X W ZA (e.g., via weighting or matching) implies balancing the mean of X. For a latent X, we estimate X W ZA by the inclusive factor score (iFS) -predicted value of X from a structural equation model that captures the joint distribution of (X, W , A) given Z. Simulation shows that PS analysis using the iFS substantially improves balance on the first five moments of X and reduces bias in the estimated causal effect. Hence, within the proxy variables approach, we recommend this proxy over existing ones. We connect this proxy method to known results about weighting/matching functions (Lockwood & McCaffrey, 2016;McCaffrey, Lockwood, & Setodji, 2013). We illustrate the method in handling latent covariates when estimating the effect of out-of-school suspension on risk of later police arrests using Add Health data.

Causal effect analysis in nonrandomized data with latent variables and categorical indicators: The implementation and benefits of EffectLiteR.

“…Further methods for measurement error correction are available that can be used for moderated regression models, but also for PS analysis. The strategies relying either on corrections for reliability estimates (e.g., Fuller, 1987; Lockwood & McCaffrey, 2016; McCaffrey et al, 2013), on simulation extrapolation strategies (e.g., Cook & Stefanski, 1994; Lockwood & McCaffrey, 2015), or sophisticated factor score estimates (Nguyen & Stuart, 2020). We did not include such approaches in our application, but they are promising alternatives to control for measurement error.…”

“…However, PS estimates for subsequent treatment effect estimation and balance checks cannot be obtained from these models—as this requires the (unobserved) individual scores on latent covariates. Alternative strategies are available that use information from cSEM (e.g., reliability estimates or factor score estimates) for implementing PS analysis (see, e.g., Cook & Stefanski, 1994; Lockwood & McCaffrey, 2015; Lockwood & McCaffrey, 2016; McCaffrey et al, 2013; Nguyen & Stuart, 2020).…”

Exposure misclassification in propensity score-based time-to-event data analysis

“…A user-friendly R program implementing the new method is available at http://www.hsph.har vard.edu/molin-wang/software. There are existing methods for dealing with error-prone covariates in the PS model; [5][6][7][8][9] however, all of these methods focus on measurement errors in the potential confounders but not on the exposure. Although a recent paper 10 focuses on error-prone exposures, it includes PS implementations of the subclassification, matching, and IPTW approaches, but not the regression modeling approach; their likelihood-based method also involves the probability function of the outcome variable.…”

“…Methods to deal with error-prone covariates in the PS model include a casual graph model method, 5,6 an inverse probability weighting method for the additive measurement error in covariates, 7 a Bayesian method for differential covariates’ measurement errors across treatment groups, 8 and a more recent proxy variable approach. 9 However, none of the methods above considers the presence of misclassification in the exposure, which is the dependent variable in the PS model. A recent paper 10 focuses on error-prone exposures which are based on PS implementations of the subclassification, matching, and IPTW approaches, but not the regression modeling approach.…”

Propensity Score Analysis with Unreliable Covariates: A comparison of Five Reliability-adjustment Methods

“…This method is implemented by the Mplus 1 software (Muthen & Muthen, 1998. Nguyen and Stuart (2020) proposed the propensity score model with inclusive factor sore (PSIF), which includes observed items, other covariates without measurement errors, and treatment indicator Z, where factor scores are 𝜂𝜂̂= 𝐴𝐴(𝜂𝜂|𝑋𝑋, 𝑊𝑊, 𝑍𝑍). Authors also assumed that there was no interaction between fallible covariates and perfect covariates.…”