MIXED MODEL REPEATED MEASURES (MMRM)
Background
Repeated measures refer to multiple measurements taken from the same experimental unit, such as serial evaluation over time on the same patient. The mixed model for repeated measures (MMRM) is a popular choice for individually randomized trials with longitudinal continuous outcomes. In the context of randomized controlled trials, fixed effects of time, treatment and their interaction are included in the MMRM model. This model’s appeal is due to avoidance of model misspecification and its unbiasedness for data missing completely at random or at random.
Example data
Consider the following data from a randomized study having three treatment groups – Treatment A, Treatment B and Placebo. PANSS (Positive and Negative Syndrome Scale) was used to assess the effectiveness of the treatment groups in comparison to Placebo. The assessment was repeated on Day 8, 15, 22 and 29 following the initial intake of the study drug
SAS Code
A mixed model repated measures (MMRM) linear regression model is fitted using PROC MIXED with treatment, visit, and treatment-by-visit interaction as fixed effects, and baseline value as covariate. The repeated measures are the change from baseline in PANSS total score obtained at the scheduled visits Days 8, 15, 22 and 29 respectively. An unstructured covariance (UN) matrix is used to model the within-subject errors. The Kenward-Roger (KR) approximation is used to estimate denominator degrees of freedom. LS mean difference with corresponding standard error is estimated.
proc mixed data = panss;
class usubjid trt avisit;
model chg = base trt avisit trt*avisit/ ddfm = KR;
repeated avisit/ subject = usubjid type = UN;
lsmeans trt*avisit/ cl alpha = 0.05 diff e;
ods output lsmeans = lsmeans diffs=diffs;
run;DDFM=KR option performs the degrees of freedom calculations detailed by Kenward and Roger.
TYPE=UN option defines the covariance structure as Unstructured.
DIFF option requests differences of LS means.
E requests that the matrix coefficients for all LSMEANS effects be displayed.
