Efficient odds ratio estimation under two‐phase sampling using error‐prone data from a multi‐national HIV research cohort

Abstract

Persons living with HIV engage in routine clinical care, generating large amounts of data in observational HIV cohorts. These data are often error‐prone, and directly using them in biomedical research could bias estimation and give misleading results. A cost‐effective solution is the two‐phase design, under which the error‐prone variables are observed for all patients during Phase I, and that information is used to select patients for data auditing during Phase II. For example, the Caribbean, Central, and South America network for HIV epidemiology (CCASAnet) selected a random sample from each site for data auditing. Herein, we consider efficient odds ratio estimation with partially audited, error‐prone data. We propose a semiparametric approach that uses all information from both phases and accommodates a number of error mechanisms. We allow both the outcome and covariates to be error‐prone and these errors to be correlated, and selection of the Phase II sample can depend on Phase I data in an arbitrary manner. We devise a computationally efficient, numerically stable EM algorithm to obtain estimators that are consistent, asymptotically normal, and asymptotically efficient. We demonstrate the advantages of the proposed methods over existing ones through extensive simulations. Finally, we provide applications to the CCASAnet cohort.

Association analysis of self‐reported outcomes with a validated subset

“…Two‐phase stratified sampling has been discussed/used by many authors, for example, 20‐23 ) to select subjects for the collection of additional data, for example, validation data for addressing measurement error problems. Stratification jointly by outcome and covariates, with sampling fractions chosen to enhance efficiency compared with stratification based on the outcome or covariates alone.…”

“…However, this method appears not robust to misspecification of the distribution relating the surrogate to the true outcome, $$$ {P}_{\boldsymbol{\theta}}\left(S|Y,\boldsymbol{X}\right) $$$. Lotspeich et al 20 proposed a robust sieve maximum likelihood estimator employing a nonparametric model for the exposure's measurement errors. Although Lotspeich et al 20 found that logistic regression can be fairly robust to certain types of model misspecification, a proper specification of conditional probability $$$ {P}_{\boldsymbol{\theta}}\left(S|Y,\boldsymbol{X}\right) $$$ was stated to be desirable in their proposed likelihood and discussed it as a limitation in the Discussion Section of the paper.…”

“…Lotspeich et al 20 proposed a robust sieve maximum likelihood estimator employing a nonparametric model for the exposure's measurement errors. Although Lotspeich et al 20 found that logistic regression can be fairly robust to certain types of model misspecification, a proper specification of conditional probability $$$ {P}_{\boldsymbol{\theta}}\left(S|Y,\boldsymbol{X}\right) $$$ was stated to be desirable in their proposed likelihood and discussed it as a limitation in the Discussion Section of the paper. Our simulation results suggested that the WGLM estimates are relatively more robust to misspecification of the model $$$ {P}_{\boldsymbol{\theta}}\left(Y|S,\boldsymbol{X}\right) $$$) than Pepe's method is to misspecification of $$$ {P}_{\boldsymbol{\theta}}\left(S|Y,\boldsymbol{X}\right) $$$; however, the bias in both methods can be appreciable.…”

“…While applying Pepe 7,17,20 's methods need an advanced programming effort to maximize the likelihood, the WGLM method is easy to apply as each of its two stages uses a generalized linear model and can be performed using standard software.…”

“…Association analysis with self‐reported outcomes has been widely discussed in biostatistics and epidemiology literature (eg, 7,9,10,14‐20 ). Most of these methods address binary outcome misclassification, while a few methods have been developed to handle outcome misclassification and covariate measurement error simultaneously 17,20 . A few articles, such as Magder and Hughes 15 and Kowal and Wu, 19 used an expectation‐maximization (EM) algorithm to estimate the coefficients in regression analysis when the outcome is measured with uncertainty, but the use of a validated sample was not considered in their approaches.…”