Table 1 Methodological comparison of the four models used for analysis of longitudinal HRQoL score data
| Â | 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 (β0, β1, and β2) | Fixed effects (β0, β1, and β2) Logistic regression coefficients (ψ0, ψ1, and ψ2) | (Fixed effects overall patterns (β0, β1, and β2)) Fixed effects in each pattern k (\( {\beta}_0^k \), \( {\beta}_1^k \), and \( {\beta}_2^k \)) Proportion in each pattern (πk) | Fixed effects (β0, β1, and β2) 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 ψ2 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) |