Correction of the P-value after multiple coding of an explanatory variable in logistic regression

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Logistic regression is widely used for binary outcomes.
• Assessing the significance of transformed explanatory variables requires careful consideration of multiple testing.
• Existing methods for significance level correction may not fully account for correlations between successive tests.

Purpose of the Study:

• To propose a novel method and software for determining significance levels of coded explanatory variables in logistic regression.
• To evaluate different significance level correction methods, including Bonferroni, Efron's, and exact calculations.
• To develop a strategy for selecting the optimal number and type of variable codings.

Main Methods:

• The study considers dichotomous and Box-Cox transformations for explanatory variables.
• Three significance level correction methods are investigated: Bonferroni, Efron's method (using successive test correlations), and exact calculation via numerical integration.
• A simulation study is conducted to compare these methods and inform a selection strategy.

Main Results:

• The simulation study provides insights into the performance of different significance level correction methods.
• A practical strategy is proposed for choosing the number and types of variable codings.
• The developed method is demonstrated using real-world data on cholesterol and dementia.

Conclusions:

• The proposed method and program offer a robust approach to determining significance levels for coded variables in logistic regression.
• The findings guide the selection of appropriate variable transformations and correction methods for improved statistical inference.
• This work facilitates a more accurate analysis of relationships between variables, such as cholesterol levels and dementia risk.