Table 1 Summary of simulation scenarios

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Base case

x₁, x₂, x₃, x₄, x₅\(\sim Bernoulli (0.5)\)

x₆, x₇, x₈, x₉, x₁₀\(\sim N(\mathrm{0,1})\)

\(Logit\left({p}_{it}\right)= {\alpha }_{0, treat}+{\alpha }_{L}{x}_{1i}+{\alpha }_{M}{x}_{2i}+{\alpha }_{H}{x}_{3i}+\)\({\alpha }_{L}{x}_{4it}+{\alpha }_{H}{x}_{5it}+ {\alpha }_{M}({x}_{4it}{x}_{5it}) +\)\({\alpha }_{L}{x}_{6i}+\)\({\alpha }_{M}{x}_{7i}+\)\({\alpha }_{L}{x}_{7i}^{2}+\)\({\alpha }_{H}{x}_{8i}+\)\({\alpha }_{L}{x}_{9it}^{2}+ {\alpha }_{M}({x}_{6i}{x}_{9it}^{2}) +\)\({\alpha }_{H}{x}_{10it}\)

Autocorrelation:

x₉, x_10: AR(1) Pairwise correlation: ρ = 0

A

Correct functional form

Same as base case

\(Logit\left({p}_{it}\right)= {\alpha }_{0, treat}+{\alpha }_{L}{x}_{1i}+{\alpha }_{M}{x}_{2i}+{\alpha }_{H}{x}_{3i}+\)\({\alpha }_{L}{x}_{4it}+{\alpha }_{H}{x}_{5it}+\)\({\alpha }_{L}{x}_{6i}+\)\({\alpha }_{M}{x}_{7i}+\)\({\alpha }_{H}{x}_{8i}+\)\({\alpha }_{L}{x}_{9it}+\)\({\alpha }_{H}{x}_{10it}\)

Same as base case

B

Weak pairwise correlation

Same as base case

Same as base case

x₉, x_10: AR(1)

All covariates: ρ = 0.2

C

Strong pairwise correlation

Same as base case

Same as base case

x₉, x_10: AR(1)

All covariates: ρ = 0.7

D

Different autocorrelation structure

Same as base case

Same as base case

x₉, x_10: MA(1) ρ = 0

E

Non-standard normal covariate distributions

x₁, x₂, x₃, x₄, x₅\(\sim Bernoulli (0.5)\)

x₆, x₇, x₈\(\sim N(\mathrm{0,1})\)

x₉, x₁₀\(\sim N(\mathrm{2,1})\)

Same as base case

Same as base case

F

Non-normal covariate distributions

x₁, x₂, x₃, x₄, x₅\(\sim Bernoulli (0.5)\)

x₆, x₇, x₈\(\sim N(\mathrm{0,1})\)

x₉\(\sim Poisson(2)\)

x₁₀\(\sim Gamma(\mathrm{2,1})\)

Same as base case

Same as base case