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YSC2019-Rushani Wijesuriya
- 1. Evaluation of approaches for multiple imputation in three-level data structures Rushani Wijesuriya Supervisors : A/Prof Katherine Lee, Dr. Margarita Moreno-Betancur, Prof John Carlin and Dr. Anurika De Silva 02nd of October 2019 1
- 2. … 44 1 2 𝑗44 • Repeated measures within an individual and also clustering by school … … … 1 1 2 𝑗1 2 1 2 𝑗2 Case Study: Childhood to Adolescence Transition Study (CATS) 2 School - 𝒊 Student -𝒋 Wave -𝒌 Three levels of hierarchyor Two levels of clustering
- 3. Age1 Sex SES1 Nap1_Z Dep.4 Dep.6 Napscore_Z.3 Napscore_Z.7Napscore_Z.5 Case Study : Target Analysis and Missing Data 3 Dep.2
- 4. … 1 2 mm-1 Incomplete dataset The first stage : Imputation stage 4 Multiple Imputation
- 5. The second stage : Analysis stage … 𝜽 𝟏 𝜽 𝟐 𝜽 𝒎−𝟏 𝜽 𝒎𝜽𝒊 𝜽 𝑴𝑰 5 Multiple Imputation
- 6. Congeniality 6 • A key consideration in MI : the imputation model needs to preserve all the features of the analysis • Need to incorporate the clustered structure in the imputation model
- 7. How to incorporate the multilevel structure in the imputation model? Multiple Imputation for multilevel data MI approaches based on mixed effects /multilevel models Manipulate the standard (single-level) MI approaches • The Dummy Indicator (DI) approach • Just Another Variable (JAV) approach (if repeated measures are at fixed intervals of time) ID Age Sex Dep_1 Dep_2 Dep_3 1 8 Male 0.4 1.9 0.2 2 7 Female 1.9 - 2.9 3 9 Male 1.0 3.1 - 4 8 Male - 2.6 - 5 10 Female 1.5 0.5 1.5 Wide format one row per individual ID Age Sex Wave Dep 1 8 Male 1 0.4 1 8 Male 2 1.9 1 8 Male 3 0.2 2 7 Female 1 1.9 2 7 Female 2 - 2 7 Female 3 2.9 Long format One row per wave per individual Structure used in the analysis stage 7
- 8. How to impute incomplete three-level data? Multiple Imputation for three-level data Manipulate standard MI approaches to allow for both levels of clustering Remaining level of clustering : JAV or DI One level of clustering : mixed model based MI (specialized for one level of clustering) Mixed model based MI for both levels of clustering 8 School clusters :DI Repeated measures: Mixed model based MI School clusters :Mixed model based MI Repeated measures: JAV School clusters :DI Repeated measures: JAV • Blimp (FCS) • JM-STD • FCS-STD • ML-JM-JAV • ML-FCS-JAV • ML-JM-DI • ML-FCS-DI
- 9. • 1000 datasets were simulated • 40 school clusters (𝑖 = 1, … , 40) were generated • Each school cluster was populated in two ways: Fixed, Varying • Four different strengths of level-2 and level-3 intra-cluster correlations Simulation of Complete Data 9 ICC level 3 (within school) level 2 (within individual ) High-high 0.15 0.5 High-low 0.15 0.2 Low-high 0.05 0.5 Low-low 0.05 0.2
- 10. SDQ.2 SDQ.4 SDQ.6 Dep.4 Dep.6 Napscore_Z.3 Napscore_Z.7Napscore_Z.5 R_Dep.2 R_Dep.4 R_Dep.6 Generation of Missing Data MCAR Missing values assigned completely at random MAR- Strong MAR-Weak 10% 15% 20% 20% 30% 40% Dep.2 Dep.4 Dep.6 10 Dep.2
- 11. Simulation Study-Results 11 Standardized biases for the regression coefficient 𝛽= (-0.5) - MAR (strong) Long Wide (Average estimate-Parameter)/Emp.SE*100
- 12. Key findings 12 • Approaches which imputes in long format (BLIMP, ML-JM-DI, ML-FCS-DI) were the best in estimating the effect estimate • However, ML-JM-DI and ML-FCS-DI can be problematic when the number of clusters is high • ML-JM-JAV and ML-FCS-JAV : good alternatives
- 13. Acknowledgements 13 • Supervisors • VicBiostat • CATS data team Funding • Murdoch Children’s Research Institute (MCRI) • Statistical Society of Australia, Victorian Branch
- 14. 14 You can contact me anytime at : rushani.wijesuriya@mcri.edu.au You can download the slides at : Thank You https://tinyurl.com/YSC2019-Rushani
- 15. Extra Slides 15
- 16. Variable Type Grouping /Range Label Child’s gender Categorical 0 = Female 1 = Male 𝑆𝑒𝑥𝑗𝑘 Child’s age (wave one) Continuous Range [7-11] 𝐴𝑔𝑒1 𝑗𝑘 SES measured by the SEIFA IRSAD quintile (wave 1) Categorical 1st quintile (most disadvantaged) 2nd quintile 3rd quintile 4th quintile 5th quintile (most advantaged) 𝑆𝐸𝑆1𝑗𝑘 NAPLAN numeracy score (wave 1) Continuous Range [0,1000] 𝑁𝑎𝑝1_𝑧𝑗𝑘 NAPLAN numeracy scores (waves 3,5 and 7) Continuous Range [0,1000] 𝑁𝑎𝑝𝑠𝑐𝑜𝑟𝑒_𝑧𝑖𝑗𝑘 Depressive symptom score (waves 2-7) Continuous Range [0,8] 𝐷𝑒𝑝𝑖𝑗𝑘 Overall child behaviour reported by the Strength and Difficulties Questionnaire (SDQ) (waves 2, 4 and 6) Continuous Range [0,40] 𝑆𝐷𝑄𝑖𝑗𝑘 Variables of Interest 16
- 17. Approach Paradigm Type Clustering due to schools Clustering due to repeated Measures JM-STD JM Standard DI JAV FCS-STD FCS Standard DI JAV ML-JM-JAV JM Specialized for one level of clustering RE JAV ML-FCS-JAV FCS Specialized for one level of clustering RE JAV ML-JM-DI JM Specialized for one level of clustering DI RE ML-FCS-DI FCS Specialized for one level of clustering DI RE BLIMP FCS-Blimp Specialized for two levels of clustering RE RE ML.LMER FCS-miceadds Specialized for two levels of clustering RE RE JM:Joint Modelling; FCS:Fully Conditional Spcecification;RE:Random Effects; DI :Dummy Indicators ; JAV: Just Another Variable 17 Available case analysis was also performed Multiple Imputation for three-level data
Editor's Notes
- The impact of bias on intervals and tests depends on how large it is relative to the overall uncertainty in the system. For example, a value of -50% means that the estimate on average falls one halfof a standard error below the parameter, roughly equivalent to one-eighth of the width of a typical confidence interval