From: Genetic matching for time-dependent treatments: a longitudinal extension and simulation study
Scenario | Description | Covariate distributions | Treatment assignment model | Correlations |
---|---|---|---|---|
- | 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, x10: 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, x10: AR(1) All covariates: ρ = 0.2 |
C | Strong pairwise correlation | Same as base case | Same as base case | x9, x10: AR(1) All covariates: ρ = 0.7 |
D | Different autocorrelation structure | Same as base case | Same as base case | x9, x10: 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 |