A general regression framework for a secondary outcome in case-control studies

Tchetgen, Eric J. Tchetgen

doi:10.1093/biostatistics/kxt041

Cited by 42 publications

(59 citation statements)

References 22 publications

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“…When this model is (semi)parametric, our proposed estimator is more efficient than IPW. Interestingly, we show that the new set of estimating equations uses the parameterization proposed by Tchetgen Tchetgen (2014). However, focusing on the identity and log links, our approach is more robust to certain forms of misspecification than the estimator of Tchetgen Tchetgen (2014).…”

Section: Introductionmentioning

confidence: 94%

“…Wei et al (2013) modeled a continuous secondary outcome semi-parametrically and relaxed the distributional assumptions, but assumed that the primary disease is rare, which does not apply in many situations, including the T2D case-control study introduced earlier. Tchetgen Tchetgen (2014) proposed a general model based on a nonparametric parameterization for the secondary outcome conditional on disease status and covariates, for the identity, log, and logit link functions. Under the proposed parameterization, the mean model of the outcome conditional on disease status and covariates is factored into three functions: the mean model of the outcome conditional on covariates, the disease probability model, and a so-called selection bias function.…”

Section: Introductionmentioning

confidence: 99%

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Control Function Assisted Ipw Estimation With a Secondary Outcome in Case-Control Studies

et al. 2017

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Case-control studies are designed towards studying associations between risk factors and a single, primary outcome. Information about additional, secondary outcomes is also collected, but association studies targeting such secondary outcomes should account for the case-control sampling scheme, or otherwise results may be biased. Often, one uses inverse probability weighted (IPW) estimators to estimate population effects in such studies. IPW estimators are robust, as they only require correct specification of the mean regression model of the secondary outcome on covariates, and knowledge of the disease prevalence. However, IPW estimators are inefficient relative to estimators that make additional assumptions about the data generating mechanism. We propose a class of estimators for the effect of risk factors on a secondary outcome in case-control studies that combine IPW with an additional modeling assumption: specification of the disease outcome probability model. We incorporate this model via a mean zero control function. We derive the class of all regular and asymptotically linear estimators corresponding to our modeling assumption, when the secondary outcome mean is modeled using either the identity or the log link. We find the efficient estimator in our class of estimators and show that it reduces to standard IPW when the model for the primary disease outcome is unrestricted, and is more efficient than standard IPW when the model is either parametric or semiparametric.

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Control Function Assisted Ipw Estimation With a Secondary Outcome in Case-Control Studies

et al. 2017

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“…Recently, there has been considerable interest in using case-control data for a separate task, namely examining the interrelationship between covariates, say Y and X , where Y is a scalar and X is potentially multivariate (Jiang et al, 2006; Lin and Zeng, 2009; Li et al, 2010; Wei et al, 2013; Tchetgen, 2014). For example, in Section 6, we describe a case-control study involving breast cancer.…”

Section: Introductionmentioning

confidence: 99%

“…However, this approach can have relatively low efficiency because it ignores the information carried by the cases. A more efficient approach is to adopt a semiparametric framework, assuming a parametric distribution for Y given X , e.g., linear regression with normally distributed and homoscedastic regression errors, as well as known or rare disease rate (Jiang et al, 2006; Lin and Zeng, 2009; Li et al, 2010; Wei et al, 2013; Tchetgen, 2014). This approach improves estimation efficiency compared with the controls only method because both cases and controls are taken into account.…”

Section: Introductionmentioning

confidence: 99%

Dimension reduction and estimation in the secondary analysis of case-control studies

Liang¹,

Carroll

2018

Electron. J. Statist.

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Studying the relationship between covariates based on retrospective data is the main purpose of secondary analysis, an area of increasing interest. We examine the secondary analysis problem when multiple covariates are available, while only a regression mean model is specified. Despite the completely parametric modeling of the regression mean function, the case-control nature of the data requires special treatment and semi-parametric efficient estimation generates various nonparametric estimation problems with multivariate covariates. We devise a dimension reduction approach that fits with the specified primary and secondary models in the original problem setting, and use reweighting to adjust for the case-control nature of the data, even when the disease rate in the source population is unknown. The resulting estimator is both locally efficient and robust against the misspecification of the regression error distribution, which can be heteroscedastic as well as non-Gaussian. We demonstrate the advantage of our method over several existing methods, both analytically and numerically.

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“…Further generalizations of Lin and Zeng’s likelihood approach were proposed by Ghosh et al (2013); Wei et al (2013). He et al (2012) used a Gaussian copula approach to jointly model Y and D , while Tchetgen (2014) considered a careful re-parameterization of the conditional model for Y given D .…”

Section: Introductionmentioning

confidence: 99%

A novel association test for multiple secondary phenotypes from a case-control GWAS

Ray

Basu

2017

Genet. Epidemiol.

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Summary In the past decade, many genome wide association studies (GWASs) have been conducted to explore association of single nucleotide polymorphisms (SNPs) with complex diseases using a case-control design. These GWASs not only collect information on the disease status (primary phenotype, D) and the SNPs (genotypes, X), but also collect extensive data on several risk factors and traits. Recent literature and grant proposals point towards a trend in re-using existing large case-control data for exploring genetic associations of some additional traits (secondary phenotypes, Y) collected during the study. These secondary phenotypes may be correlated, and a proper analysis warrants a multivariate approach. Commonly used multivariate methods are not equipped to properly account for the non-random sampling scheme. Current ad hoc practices include analyses without any adjustment, and analyses with D adjusted as a covariate. Our theoretical and empirical studies suggest that the type I error for testing genetic association of secondary traits can be substantial when X as well as Y are associated with D, even when there is no association between X and Y in the underlying (target) population. Whether using D as a covariate helps maintain type I error or not depends heavily on the disease mechanism and the underlying causal structure (which is often unknown). To avoid grossly incorrect inference, we have proposed proportional odds model adjusted for propensity score (POM-PS). It uses a proportional odds model for X on Y and adjusts estimated conditional probability of being diseased as a covariate. We demonstrate the validity and advantage of POM-PS, and compare to some existing methods in extensive simulation experiments mimicking plausible scenarios of dependency among Y, X, and D. Finally, we use POM-PS to jointly analyze four adiposity traits using a type 2 diabetes (T2D) case-control sample from the population-based Metabolic Syndrome in Men (METSIM) Study. Only POM-PS analysis of the T2D case-control sample seems to provide valid association signals.

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A general regression framework for a secondary outcome in case-control studies

Cited by 42 publications

References 22 publications

Control Function Assisted Ipw Estimation With a Secondary Outcome in Case-Control Studies

Control Function Assisted Ipw Estimation With a Secondary Outcome in Case-Control Studies

Dimension reduction and estimation in the secondary analysis of case-control studies

A novel association test for multiple secondary phenotypes from a case-control GWAS

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