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Table 3 Summary statistics of simulationsa with missing data pattern reflecting GERAS study data at 18 monthsb

From: How to deal with missing longitudinal data in cost of illness analysis in Alzheimer’s disease—suggestions from the GERAS observational study

  GERAS-1c GERAS-2d
Imputation method Mean cost (€) Bias (%)e SSE SEE SEE/SSE CP Mean cost (€) Bias (%)e SSE SEE SEE/SSE CP
Complete sample 2101 64 62 0.97 2103 60 61 1.02
Naïve imputation method
 Complete cases 1957 −144 (−7 %) 67 66 0.99 0.38 1689 −414 (−20 %) 52 54 1.04 0.00
Multiple imputation method
 MI MCMC 2037 −64 (−3 %) 74 47 0.64 0.70 1969 −134 (−6 %) 77 41 0.53 0.22
Combination of imputation methods
 Combination Scenario Af 2044 −57 (−3 %) 71 47 0.66 0.73 1947 −157 (−7 %) 69 41 0.59 0.12
 Combination Scenario Bg 2296 195 (9 %) 62 49 0.79 0.02 2075 −28 (−1 %) 49 42 0.86 0.87
  1. Numbers in bold text show the imputation method(s) that perform the best (lowest bias) for each of the two datasets (GERAS-1 and GERAS-2)
  2. Abbreviations: CP coverage probability, MAR missing at random, MCAR missing completely at random, MCMC Markov Chain Monte Carlo, MI multiple imputation, MNAR missing not at random, SEE standard error estimate, SSE sampling standard error
  3. a1000 simulations and sample size 1497
  4. bData missing for 33 % patients at 18 months: 15 % patients institutionalised, 6 % died, 12 % lost to follow-up
  5. cGERAS-1: assumed patients institutionalised were based on a predictive equation (i.e. data MAR)
  6. dGERAS-2: assumed patients institutionalised if their caregiver time was >470 h/month (i.e. data MNAR)
  7. e% bias was calculated as ((estimated−actual)/actual cost × 100), where actual cost was the mean cost for the complete sample
  8. fCombination Scenario A: patients lost to follow-up (data MCAR) had costs imputed using group means method, patients institutionalised (data MAR) were imputed using MI MCMC method (including factors MMSE, ADCS-ADL and caregiver time), and patients who died (data MAR) had costs imputed using the MI MCMC method (including factors MMSE, patient age and ADCS-ADL)
  9. gCombination Scenario B: same imputation methods as Combination Scenario A, but a fixed cost (€2940 per month) was used for patients who were institutionalised (data MNAR)