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MI*/MI gives biased estimation, because the imputation model at stage 1 is misspecified.
The row IPW/MI* shows the result of IPW/MI with the same misspecified imputation model at stage 2.
However, when the imputation model at stage 1 or stage 2 is misspecified, MI/MI may be biased.
Misspecification also of the imputation model at stage 2 (MI*/MI*) adds to the bias, especially in θ4.
First, suppose that the imputation model at stage 1 is misspecified as (X2, X3, X4, X5) T ∼ N{ γ2, γ3, γ4, γ5) T, Σ}.
Second, suppose the imputation model at stage 1 is correct but that at stage 2 is misspecified by leaving out the β23 X2 X3, β123 X1 X2 X3, and β5 X5 terms.
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Despite the classical Kocks-Mecking model, valid at stage III, the strain hardening asymptotically decreases resembling a hyperbolic function.
For MI/MI, the imputation model used at stage 1 (to impute X2 and X3) falsely assumed that (Y, X2, X3) was trivariate normal.
Acute disturbances, chronic social difficulties, parental and sibling medical illnesses were designated as inactive covariates as they showed negligible model contribution at stage 1.
For IPW/MI and MI*/MI, the imputation model used at stage 2 (to impute X4) was correctly specified in terms of X1, X2, X3, Y, and certain interactions.
Using this kind of adaptive designs, more information of previous stages are used to update the model at each stage, and more patients may be assigned to better treatments.
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