# Table 1 Model coefficient values in the data generation models in the simulation study. The values quantify the effects of the model covariates on both the probability of treatment allocation and the outcome. Three different values for the $${\varvec{T}}\times {\varvec{M}}$$ term in the outcome model, and the $${\varvec{M}}\times {{\varvec{X}}}_{1}$$ term in the probability of treatment model and the outcome model were considered

Propensity Score Model Outcome model
Notation Value Notation Value
Intercept $${\alpha }_{0}$$ 0.1 $${\beta }_{0}$$ 0.25
$${\varvec{T}}$$    $${\beta }_{T}$$ 1.5
$${\varvec{M}}$$ $${\alpha }_{M}$$ 0.3 $${\beta }_{M}$$ 0.5
$${\varvec{T}}\times {\varvec{M}}$$    $${\beta }_{TM}$$ (0.3, 0.6)
$${{\varvec{X}}}_{1}$$ $${\alpha }_{{X}_{1}}$$ 0.3 $${\beta }_{{X}_{1}}$$ 0.5
$${\varvec{M}}\times {{\varvec{X}}}_{1}$$ $${\alpha }_{M{X}_{1}}$$ (0, 0.1, 0.2) $${\beta }_{M{X}_{1}}$$ (0, 0.2, 0.4)
$${{\varvec{X}}}_{2}$$ $${\alpha }_{{X}_{2}}$$ 0.2 $${\beta }_{{X}_{2}}$$ 0.5
$${{\varvec{X}}}_{3}$$ $${\alpha }_{{X}_{3}}$$ -0.1 $${\beta }_{{X}_{3}}$$ -0.3
$${{\varvec{X}}}_{4}$$ $${\alpha }_{{X}_{4}}$$ 0.4 $${\beta }_{{X}_{4}}$$ 1
$${{\varvec{X}}}_{5}$$ $${\alpha }_{{X}_{5}}$$ -0.2 $${\beta }_{{X}_{5}}$$ 0.6
$${{\varvec{X}}}_{6}$$ $${\alpha }_{{X}_{6}}$$ 0.3 $${\beta }_{{X}_{6}}$$ 1