Regression with incomplete multivariate surrogate responses for a latent covariate

ABSTRACT

We consider the setting in which a categorical exposure variable of interest can only be measured subject to misclassification via surrogate variables. These surrogate variables may represent the classification of an individual via imperfect diagnostic tests. In such settings, a random number of diagnostic tests may be ordered at the discretion of a treating physician with the decision to order further tests made in a sequential fashion based on the results of preliminary test results. Because the underlying latent status is not ascertainable these cheaper but imperfect surrogate test results are used in lieu of the definitive classification in a model for a long-term outcome. Naive use of a single surrogate or functions of the available surrogates can lead to biased estimators of the association and invalid inference. We propose a likelihood-based approach for modeling the effect of the latent variable in the absence of validation data with estimation based on an expectation–maximization (EM) algorithm. The method yields consistent and efficient estimates and is shown to out-perform several common alternative approaches. The performance of the proposed method is demonstrated in simulation studies and its utility is illustrated by applying the proposed method to the stimulating study on breast cancer.

Keywords:

• Expectation–maximization algorithm
• latent variable
• misspecified model
• regression
• surrogate variable

Acknowledgements

The authors thank Dr Xiaolan Feng for permission to use the data from the study of patients with breast cancer at the Foothills Hospital in Calgary and Dr Haocheng Li for the introduction and stimulating the collaboration with Dr Feng.

Disclosure statement

In accordance with Taylor & Francis policy and our ethical obligations as researchers, we are reporting that we have no financial and/or business interests and receive no funding from any company that may be affected by the research reported in the enclosed paper.

Data availability statement

There is a data set associated with the paper. However, data sharing violates the valid privacy and security concerns of the principal investigators, therefore authors do not share or make open the data supporting the results or analyses presented in their paper.

Additional information

Funding

This work was supported by grants from the Natural Sciences and Engineering Research Council of Canada [grant numbers RGPIN 04594 and RGPIN 155849], the Breast Cancer Society of Canada, and startup funds at the University of Calgary.

Notes on contributors

Hua Shen

Hua Shen is an Assistant Professor of Biostatistics in the Department of Mathematics and Statistics and jointly appointed in the Natural Sciences Program at the University of Calgary. Her research interests are on the methodology development and statistical analysis of data arising from public health and medical research. Her current research focuses on developing statistical methods to analyze incomplete lifetime data involving latent processes arising in clinical trials and observational studies.

Richard J. Cook

Richard J. Cook is Professor of Statistics in the Department of Statistics and Actuarial Science at the University of Waterloo with cross-appointments at the School of Public Health and Health Systems at the University of Waterloo and the Faculty of Health Science at McMaster University. His research interests include the analysis of life history data, the design and analysis of clinical and epidemiological studies, and statistical methods for incomplete data.