Effects of mismodelling and mismeasuring explanatory variables on tests of their association with a response variable

Area of Science:

• Biostatistics
• Statistical Modeling
• Epidemiology

Background:

• Statistical tests assess associations between explanatory and response variables.
• Accurate measurement and modeling of explanatory variables are crucial for reliable results.
• Misinformation or mismeasurement can lead to reduced statistical power and biased conclusions.

Purpose of the Study:

• To quantify the loss in efficiency of common statistical tests due to explanatory variable mismodeling or mismeasurement.
• To evaluate the impact of specific types of errors, including incorrect dose metameters, continuous variable mismodeling, discretization, classification errors, and measurement errors.
• To provide guidance on test selection, result interpretation, and study design when exact explanatory variable measurement is not feasible.

Main Methods:

• Considered three standard statistical tests for binary or survival-time response variables.
• Investigated efficiency loss from mismodeling continuous and discrete explanatory variables.
• Examined consequences of classification and measurement errors for explanatory variables.

Main Results:

• The asymptotic relative efficiency (ARE) loss for all tested statistical tests equals the square of the correlation between the correct and fitted explanatory variable.
• Numerical evaluation demonstrated efficiency reductions across various mis-specification scenarios.
• The degree of efficiency loss is dependent on the type and extent of the explanatory variable error.

Conclusions:

• Explanatory variable accuracy is critical for maintaining statistical test efficiency.
• Understanding the relationship between correct and fitted explanatory variables aids in interpreting results.
• This research informs the design of studies facing challenges in precise explanatory variable measurement.