Locally efficient semiparametric estimators for a class of Poisson models with measurement error

Abstract

The presence of measurement error may cause bias in parameter estimation and can lead to incorrect conclusions in data analyses. Despite a large body of literature on general measurement error problems, relatively few works exist to handle Poisson models. In this article we thoroughly study Poisson models with errors in covariates and propose consistent and locally efficient semiparametric estimators. We assess the finite sample performance of the estimators through extensive simulation studies and illustrate the proposed methodologies by analyzing data from the Stroke Recovery in Underserved Populations Study. The Canadian Journal of Statistics 47: 157–181; 2019 © 2019 Statistical Society of Canada

A semiparametric method for evaluating causal effects in the presence of error‐prone covariates

“…In fact, the method we proposed leads to a locally efficient semiparametric estimator that is always consistent. If happens to be the true conditional expectation, then the estimators will be semiparametric efficient (Liu et al., 2017; Liu & Ma, 2019; Ma & Zhu, 2012; Tsiatis & Ma, 2004). We state the consistency and locally efficiency properties in Theorem 1.…”

“…We apply the proposed method using a dataset from the Stroke Recovery in Underserved Populations (SRUP) study. As discussed in Liu & Ma (2019), in addition to chronic pain among patients with stroke history, there is statistical evidence that a negative attitude toward life has a larger adversarial impact on stroke recovery among the underserved populations after discharge from a rehabilitation facility. In fact, it is well known that an optimistic attitude could be a critical self‐healing tool for those who had experienced a severe life crisis and/or even a fatal illness (Gable & Haidt, 2005; Sheldon & King, 2001).…”

A model‐averaging treatment of multiple instruments in Poisson models with errors

“…Stefanski & Carroll (1987) and Ma & Tsiatis (2006) studied consistent estimators for generalized linear models based on conditional score functions under the assumption of normal measurement errors or an unknown measurement error distribution. Liu & Ma (2019) focused on the Poisson model with covariate errors. None of these works studied instrumental variables.…”