Mechanism

X_{3} (PGR)

X_{2} (LN)

X_{5} (TRT)

X_{8} (TS)


MCAR

β_{0}

β_{0} + ln(OR)M_{X3}

β_{0} + ln(OR)M_{X2}

β_{0} + ln(OR)M_{X3}

MAR

ln(0.8)X_{4}

ln(3)X_{1}

ln(0.7)ln(t)

ln(7)X_{7}

MNAR

ln(1.3)X_{3}

ln(0.6) X_{2}

ln(8)X_{5}

ln(0.9)X_{8}

COMBINED
 
ln(0.7)ln(t) +
ln(0.3)X_{5}

ln(3)X_{1}

ln(0.9)X_{8}


Note: A logistic regression model was used to model the probability of missingness for each incomplete covariate. The entries in the table represent the variables associated with the missingness of each incomplete covariate. For MAR, MNAR, and the combined mechanism, the terms given are extra to those for the MCAR mechanism, e.g. the MAR mechanism for X_{2} is
 where β_{0} is the intercept, estimated by solving the above equation using the specified probabilities of missingness for X_{2} and X_{3} and the average covariate value of X_{1}, M_{X3} is the missingness indicator for covariate X_{3}, which equals 1 if an observation is missing and 0 if the value is observed and OR is odds ratio for the relationship between the missingness of X_{2} and X_{3}, and is obtained from Table 3. The coefficients for the variable associated with the mechanism were modified from relationships with missing data seen in another study [27] to provide significant associations. All continuous variables including survival (t) were standardised by dividing by the standard deviation. When the mechanisms included other covariates subjected to missingness, the original complete data were used.