Using marginal standardisation to estimate relative risk without dichotomising continuous outcomes

Background: Although criticisms regarding the dichotomisation of continuous variables are well known, applying logit model to dichotomised outcomes is the convention because the odds ratios are easily obtained and they approximate the relative risks (RRs) for rare events.

Methods: To avoid dichotomisation when estimating RR, the marginal standardisation method that transforms estimates from logit or probit model to RR estimate is extended to include estimates from linear model in the transformation. We conducted a simulation study to compare the statistical properties of the estimates from: (i) marginal standardisation method between models for continuous (i.e., linear model) and dichotomised outcomes (i.e., logit or probit model), and (ii) marginal standardisation method and distributional approach (i.e., marginal mean method) applied to linear model. We also compared the diagnostic test for probit, logit and linear models. For the real dataset analysis, we applied these analytical approaches to assess the management of inpatient hyperglycaemia in a pilot intervention study.

Results: Although the RR estimates from the marginal standardisation method were generally unbiased for all models in the simulation study, the marginal standardisation method for linear model provided estimates with higher precision and power than logit or probit model, especially when the baseline risks were at the extremes. When comparing approaches that avoid dichotomisation, RR estimates from these approaches had comparable performance. Assessing the assumption of error distribution was less powerful for logit or probit model via link test when compared with diagnostic test for linear model. After accounting for multiple thresholds representing varying levels of severity in hyperglycaemia, marginal standardisation method for linear model provided stronger evidence of reduced hyperglycaemia risk after intervention in the real dataset analysis although the RR estimates were similar across various approaches.

Conclusions: When compared with approaches that do not avoid dichotomisation, the RR estimated from linear model is more precise and powerful, and the diagnostic test from linear model is more powerful in detecting mis-specified error distributional assumption than the diagnostic test from logit or probit model. Our work describes and assesses the methods available to analyse data involving studies of continuous outcomes with binary representations.