Using marginal standardisation to estimate relative risk without dichotomising continuous outcomes.

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Dichotomizing continuous variables for analysis is common but criticized.
• Logit models are conventionally used for dichotomized outcomes, yielding odds ratios that approximate relative risks (RRs) for rare events.

Purpose of the Study:

• To extend the marginal standardization method to include linear models for continuous outcomes, avoiding variable dichotomization when estimating RRs.
• To compare the statistical properties of estimates from marginal standardization across different models (linear, logit, probit) and compare marginal standardization with the marginal mean method.
• To evaluate the diagnostic performance of different models (probit, logit, linear).

Main Methods:

• Simulation study comparing marginal standardization for linear, logit, and probit models.
• Comparison of marginal standardization with the marginal mean method applied to linear models.
• Assessment of diagnostic tests for model assumption checking.
• Application of methods to a real dataset on inpatient hyperglycemia management.

Main Results:

• Marginal standardization yielded generally unbiased RR estimates across all models.
• The linear model with marginal standardization provided more precise and powerful RR estimates than logit or probit models, particularly at extreme baseline risks.
• Diagnostic tests for the linear model were more powerful in detecting mis-specified error distributions compared to link tests for logit/probit models.
• In the real dataset, the linear model approach showed stronger evidence of reduced hyperglycemia risk post-intervention.

Conclusions:

• The linear model, when used with marginal standardization, offers superior precision and power for estimating RRs compared to traditional dichotomization approaches.
• The linear model's diagnostic tests are more effective at identifying incorrect distributional assumptions than those for logit or probit models.
• This work highlights methods for analyzing continuous outcomes that are represented as binary, advocating for approaches that avoid unnecessary dichotomization.