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Table 1 Methodological comparison of the four models used for analysis of longitudinal HRQoL score data

From: Handling informative dropout in longitudinal analysis of health-related quality of life: application of three approaches to data from the esophageal cancer clinical trial PRODIGE 5/ACCORD 17

  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)
  1. Legend: LMM Linear Mixed Model, SM Selection Model, PMM Pattern-Mixture Model, SPM Shared-Parameter Model, MCAR Missing Completely At Random; MAR Missing At Random, MNAR Missing Not At Random, HRQoL Health-Related Quality of Life
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