# Determination of Offset Values in Binary Regression Models to Adjust for Misclassification Errors

## TL;DR

This paper introduces a method to correct biases in public health research caused by using inaccurate proxy measures instead of gold-standard data.

## Contribution

The novel approach determines offset values in binary regression models to adjust for misclassification errors using validation samples.

## Key findings

- Offset values eliminate biases in risk difference, relative risk, and odds ratio estimates.
- Simulation studies verified unbiased point estimates and standard errors using the proposed method.

## Abstract

Public health relevance—How does this work relate to a public health issue?
Use of unbiased gold-standard measures is limited in public health or epidemiologic research.Surrogates or proxy measures are more often used despite their vulnerability to measurement or misclassification errors.

Use of unbiased gold-standard measures is limited in public health or epidemiologic research.

Surrogates or proxy measures are more often used despite their vulnerability to measurement or misclassification errors.

Public health significance—Why is this work of significance to public health?
Misclassification errors induce biases in research results.Development of methods for corrections of biases pertinent to given circumstances is thus strived for.

Misclassification errors induce biases in research results.

Development of methods for corrections of biases pertinent to given circumstances is thus strived for.

Public health implications—What are the key implications or messages for practitioners, policy makers and/or researchers in public health?
Biased research results may misdirect public health policies.Careful assessment of the extent of misclassification errors is critical for unbiased results.

Biased research results may misdirect public health policies.

Careful assessment of the extent of misclassification errors is critical for unbiased results.

In randomized clinical trials and observational studies alike, it is difficult and challenging to collect gold-standard outcome measures for all participants. Although it would be ideal to use gold-standard measures, the costs and logistics of collecting them are often prohibitive. Therefore, surrogate or proxy measures or screening survey instruments are more often used to mitigate such difficulties, yet at the expense of misclassification errors and consequent biased statistical inferences. In this paper, when misclassification errors of proxy measures in comparison to a gold-standard measure are available through external or internal validation samples, we determined appropriate offset values in generalized binary regression models as a function of the proxy measure to eliminate biases of estimated effects in terms of risk difference, relative risk, and odds ratio that are incurred due to misclassification errors. Simulation studies were conducted to empirically demonstrate and verify the approach using appropriate offset values specific to each binary effect measure for estimating unbiased effects. Both point estimates of all effect measures and standard errors of regression coefficients obtained from the proposed offset-adjusted binary models were shown to be unbiased.