LMM | SM | PMM | SPM | |
---|---|---|---|---|
MODELING | ||||
Validity of the model | Under MAR assumption | Under MNAR assumption | Under MNAR assumption | Under MNAR assumption |
Model for the HRQoL outcome Y | LMM | LMM | LMM by pattern | LMM |
Model for the dropout variable | – |
Logistic Dropout at specific time (discrete) |
Multinomial Dropout at specific time (discrete) |
Survival model Dropout at any time (continuous) |
Graphical outputs | Mean HRQoL score over time according to treatment arm | Mean HRQoL score over time according to treatment arm |
(Mean HRQoL score over time according to treatment arm) Mean HRQoL score over time according to treatment arm for each dropout pattern |
Mean HRQoL score over time according to treatment arm Hazard function of dropout according to treatment arm |
ESTIMATIONS AND INTERPRETATION | ||||
Main estimated parameters | Fixed effects (β_{0}, β_{1}, and β_{2}) |
Fixed effects (β_{0}, β_{1}, and β_{2}) Logistic regression coefficients (ψ_{0}, ψ_{1}, and ψ_{2}) |
(Fixed effects overall patterns (β_{0}, β_{1}, and β_{2})) Fixed effects in each pattern k (\( {\beta}_0^k \), \( {\beta}_1^k \), and \( {\beta}_2^k \)) Proportion in each pattern (π_{k}) |
Fixed effects (β_{0}, β_{1}, and β_{2}) Association parameter (α) Effect of arm on instantaneous risk of dropout (γ) |
Interpretation | Improvement/deterioration of the HRQoL |
Improvement/deterioration of the HRQoL Testing MNAR assumption: a non-null ψ_{2} when probability of dropout is associated with unobserved Y |
(Improvement/deterioration of the HRQoL) Improvement/deterioration of the HRQoL in each dropout pattern |
Improvement/deterioration of the HRQoL Risk of dropout over time Testing MNAR assumption: a non-null α when instantaneous risk of dropout is associated with current value of Y |
Underlying assumptions | – | Normality of the complete (observed and unobserved) Y | Extrapolation of the conditional distribution of Y (given the dropout pattern) beyond the dropout to obtain estimations for the marginal distribution of Y |
Conditional independence of Y and T given the random effects Normality assumption of the random effects distribution |
Key limitations | Do not account for informative dropout |
Dropout in discrete time Not directly available in classical statistical software |
Dropout in discrete time Do not directly provide marginal estimates | Computationally challenging to approximate integrals over random effects |
Main software |
R (nlme) SAS (PROC MIXED) Stata (mixed) |
S plus (OSWALD, pcmid function but not currently available) Implemented with R in our application (sophisticated programming) | Implemented with R in our application (easy programming) |
R (JM, JMBayes) SAS (%JM) Stata (stjm) |