Biased Estimation of Adjusted Odds Ratios From Incomplete Covariate Data Due to Violation of the Missing at Random Assumption

We investigate the possible bias due to an erroneous missing at
random assumption if adjusted odds ratios are estimated from
incomplete covariate data using the maximum likelihood principle. A
relation between complete case estimates and maximum likelihood
estimates allows us to identify situations where the bias vanishes.
Numerical computations demonstrate that the bias is most serious if
the degree of the violation of the missing at random assumption
depends on the value of the outcome variable or of the observed
covariate. Implications for the analysis of prospective and
retrospective studies are given.