Regression analysis of data with correlated errors: an example from the NHLBI twin study

Area of Science:

• Biostatistics
• Epidemiology
• Genetics

Background:

• Epidemiologic studies frequently analyze genetically related individuals, spouses, or repeated measures.
• Correlated residuals in regression analysis can impact standard error estimates of regression coefficients.

Purpose of the Study:

• To investigate the effects of correlated errors on regression coefficient estimates in epidemiologic studies.
• To compare the performance of different regression techniques when residuals are correlated.

Main Methods:

• Analysis of pulmonary function data from a twin study.
• Application of three distinct regression techniques.
• Comparison of regression coefficients and standard errors across methods.

Main Results:

• Ordinary least squares (OLS) may yield suboptimal estimates (minimum variance) when residuals are correlated.
• Generalized least squares (GLS), also known as weighted least squares, is more appropriate for correlated errors when the error covariance matrix is known or estimable.
• Illustrative comparisons highlight the impact of correlated errors on statistical inference.

Conclusions:

• Accounting for correlated errors is crucial in regression analyses of clustered or related data.
• Generalized least squares provides a more robust approach for estimating regression coefficients and their standard errors in the presence of correlated errors.
• The findings underscore the importance of employing appropriate statistical methods to ensure valid conclusions in epidemiologic research involving dependent observations.