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 www.lshtm.ac.uk

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

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

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

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

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

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:

Reference Based MI Jump to reference (standard care):

Reference Based MI Last mean carried forward:

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

Reference Based MI Copy reference:

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

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

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:

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

Example Primary analysis: Linear regression of 12 week FEV1 on treatment group, adjusted for baseline FEV1 (N=110) Treatment Effect = 0.239 L, p=0.017

Example

Example

Example

Example

Example

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)

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