From: "Balasubramani, G.K." BalaGK@edc.pitt.edu Subject: [NMusers] Missing Covariate values Date: Tue, October 26, 2004 8:43 am Hello all, I have a multivariate data with outcome is a continuous measure and missing occurs in both outcome as well as in covariates and the missing outcome measure follows the assumption of MNAR. We are trying to do the pattern mixture model approach, but I had some difficulty of doing that, since one or more values in the covariates are missing. The data structure I have is of the following four patterns: 1. Non- missing outcome(continuous measure) with all the values of the covariates are available 2. Non-missing outcome with one or more vaues of the covariates are missing 3. Missing outcome with all the values of the covariates are available 4. Missing outcome with one or more vaues of the covariates are missing. I modelled on non-missing outcome using the first two groups and estimated the parameters and using these estimated parameters, I predict the missing outcome, but for only with all the values of the covatiate. I cannot be able to find out the values for the missing outcome with missed covariate values. In this type of situation, how to model this case using the data patterns in 3 and 4. Is there any method available for the missing covarites values for imputation. Any suggestion. Thanks in advance. Bala _______________________________________________________ From: "Nick Holford"
Subject: RE: [NMusers] Missing Covariate values Date: Wed, October 27, 2004 1:05 pm Hi, Methods for dealing with missing covariates include: 1. Naive: Impute the missing value with some central statistic such as the median 2. Multiple Imputation: Estimate the parameters of the covariate distribution e.g. using a multivariate normal. Sample from the MVN for the missing parameters to create datasets with imputed values. Fit several such data sets and use the average of the resulting parameters describing the outcome data. 3. Joint Model: Model the covariates as if they were dependent variables ('outcomes'). This is essentialy equivalent to method 2 but integrates over the covariate distribution for the missing values and does not have to explicitly impute (i.e. make up and use a value as if it was real data). The joint model can be done simultaneously with the outcome data or in a two stage approach with explicit imputation from the first stage (model for the covariates alone). Take a look at this thread which illustrates code for the joint model approach. http://www.cognigencorp.com/nonmem/nm/99jun282004.html This is an example of it's application: Mould DR, Holford NH, Schellens JH, Beijnen JH, Hutson PR, Rosing H, et al. Population pharmacokinetic and adverse event analysis of topotecan in patients with solid tumors. Clinical Pharmacology & Therapeutics. 2002;71(5):334-48 The MEM likelihood approach for modelling outcomes when they are not complete for all subjects makes model based assumptions about the trajectory of the outcomes. If you don't mind making some model based assumptions this is better than making absurd assumptions such as Last Observation Carried Forward. See Jonsson EN, Sheiner LB. More efficient clinical trials through use of scientific model-based statistical tests. Clin Pharmacol Ther 2002;72(6):603-14 and Mallinckrodt CH, Clark SW, Carroll RJ, Molenbergh G. Assessing response profiles from incomplete longitudinal clinical trial data under regulatory considerations. J Biopharm Stat 2003;13(2):179-90 You can also try modelling the missing data mechanism and test if it is Missing Completely At Random, Missing at Random or Not Missing at Random. See Hu C, Sale ME. A joint model for nonlinear longitudinal data with informative dropout. J Pharmacokinet Pharmacodyn 2003;30(1):83-103. This does not help to estimate the outcome data model parameters themselves but could be useful for simulating clinical trials with a model for the missingness mechanism. -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:firstname.lastname@example.org tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ _______________________________________________________