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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

From: The impact of moderator by confounder interactions in the assessment of treatment effect modification: a simulation study

  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