1. The Mimix Command
Reference Based Multiple Imputation For Sensitivity Analysis of Longitudinal Trials with Protocol Deviation Suzie Cro EMERGE Meeting 27th March 2015
Improving health worldwide

2. Outline Background Reference based multiple imputation
The mimix command
Example: Sensitivity analysis of a RCT of budesonide versus placebo for treatment of chronic asthma patients

3. Background
Protocol deviations (e.g. treatment withdrawal) are unavoidable during the full course of a longitudinal randomised controlled trial
The results is a missing data problem
Any analysis must make an untestable assumption about the distribution of the unobserved data
A range of analyses which explore how conclusions vary over different assumptions for the missing data should be undertaken

4. Background
Protocol deviations (e.g. treatment withdrawal) are unavoidable during the full course of a longitudinal randomised controlled trial
The results is a missing data problem
Any analysis must make an untestable assumption about the distribution of the unobserved data
A range of analyses which explore how conclusions vary over different assumptions for the missing data should be undertaken
…..Sensitivity Analysis

5. Background
Often sensitivity parameters are specified which relate individuals observed and missing data
Notoriously difficult
In reference based sensitivity analysis statements about the unobserved data are made by reference to other groups of individuals in the study
Qualitative rather than quantitative missing data assumptions

6. Reference Based MI
Carpenter, Roger and Kenward present a collection of reference based Multiple Imputation (MI) procedures
For each treatment arm fit a MVN distribution to the observed data

7. Reference Based MI
For each treatment arm draw a mean vector and variance covariance matrix from the posterior (using MCMC)
Use these draws to form the joint distribution of each deviating individuals pre- and post deviation data by reference to other groups in study
MAR:

8. Reference Based MI
Jump to reference (standard care):

9. Reference Based MI
Last mean carried forward:

10. Reference Based MI
Copy Increments in reference (standard care):

11. Reference Based MI
Copy reference:

12. Reference Based MI
Calculate the conditional distribution of each individuals post deviation data given that observed and sample post deviation data (impute)
5. Repeat steps 2-4 m times (m imputed data sets)
The primary analysis model is retained in sensitivity analysis and fitted to each imputed data set
Rubin’s rules are used to combine estimates across imputed data sets

13. Reference Based MI
Comparison of results under different reference based assumptions allows us to determine the robustness of results to missing post-deviation data
Interim missing observations may often be imputed under on-treatment MAR, or under one of the outlined assumptions

14. Mimix
The mimix command can be used to conduct MI under the 5 distinct assumptions in stata
Optionally allows users to conduct analysis with two in-built analysis options
Data required in long format, syntax:

15. Example
RCT placebo (N=92) versus budesonide (N=91) for treatment of chronic asthma patients

16. Example Primary analysis:
Linear regression of 12 week FEV1 on treatment group, adjusted for baseline FEV1 (N=110)
Treatment Effect = L, p=0.017

17. Example

18. Example

19. Example

20. Example

21. Example

22. Mimix The reference group must be a level of treatvar
But, the reference group need not be a randomised treatment group
Can define an alternative variable to represent the reference group to impute by and use this as the treatvar in mimix
Caution – don’t use regress or mixed analysis option in this case!
Analyse imputed data set by randomised treatment group, use usual mi estimate command (imputed data already mi set)

23. Acknowledgments
Adaptation of a SAS macro written by James Roger who I would to thank
Grateful to Tim Morris for his helpful comments and editions which have helped to improve the programme
James Carpenter, Mike Kenward