MMRM
Outline
SAS MMRM equivalence model in R
SAT, and AR(1)
Note: unstructured covariance is not available in SAS when Hessian maxtrix=0
data <- df %>%
mutate(trt = case_when(
trt == "NKTR" ~ "Drug",
TRUE ~ trt
))
data$subjid <- factor(data$subjid)
data$visit <- factor(data$visit)
data$trt <- factor(data$trt)
MMRM SAS code
1 MMRM
# Make sure variables are in class factors, UN can adjust to AR1, CS, VS, etc.
# method can adjust to Kenward-Roger, Satterthwaite, etc.
mm1 <- mmrm(pchg ~ trt + visit + trt*visit + us(visit|subjid), data=data, method='Satterthwaite')
# Least square Estimation
em1 <- emmeans(mm1, ~ trt | visit, adjust='none')
# Adjust Confidence level to :90% CI
cf1 <- summary(confint(em1, level=0.9))
# Disply the P-value and Difference between the two groups
pvs <- summary(pairs(em1, adjust='none'))## mmrm fit
##
## Formula: pchg ~ trt + visit + trt * visit + us(visit | subjid)
## Data: data (used 14400 observations from 1800 subjects with maximum 8
## timepoints)
## Covariance: unstructured (36 variance parameters)
## Inference: REML
## Deviance: 136847.2
##
## Coefficients:
## (Intercept) trtPlacebo visitWK12
## -43.051644 22.064432 -9.083422
## visitWK14 visitWK16 visitWK2
## -15.114512 -20.757179 29.469798
## visitWK4 visitWK6 visitWK8
## 21.933821 14.389944 7.081255
## trtPlacebo:visitWK12 trtPlacebo:visitWK14 trtPlacebo:visitWK16
## 2.869635 5.746693 4.914482
## trtPlacebo:visitWK2 trtPlacebo:visitWK4 trtPlacebo:visitWK6
## -12.500529 -10.015894 -6.012974
## trtPlacebo:visitWK8
## -4.113608
##
## Model Inference Optimization:
## Converged with code 0 and message: convergence: rel_reduction_of_f <= factr*epsmch
MMRM SAS estimation
## visit = WK10:
## trt emmean SE df lower.CL upper.CL
## Drug -43.05 1.225 1798 -45.5 -40.65
## Placebo -20.99 1.501 1798 -23.9 -18.04
##
## visit = WK12:
## trt emmean SE df lower.CL upper.CL
## Drug -52.14 1.163 1798 -54.4 -49.85
## Placebo -27.20 1.424 1798 -30.0 -24.41
##
## visit = WK14:
## trt emmean SE df lower.CL upper.CL
## Drug -58.17 1.147 1798 -60.4 -55.92
## Placebo -30.36 1.405 1798 -33.1 -27.60
##
## visit = WK16:
## trt emmean SE df lower.CL upper.CL
## Drug -63.81 1.106 1798 -66.0 -61.64
## Placebo -36.83 1.355 1798 -39.5 -34.17
##
## visit = WK2:
## trt emmean SE df lower.CL upper.CL
## Drug -13.58 0.909 1798 -15.4 -11.80
## Placebo -4.02 1.113 1798 -6.2 -1.83
##
## visit = WK4:
## trt emmean SE df lower.CL upper.CL
## Drug -21.12 1.252 1798 -23.6 -18.66
## Placebo -9.07 1.534 1798 -12.1 -6.06
##
## visit = WK6:
## trt emmean SE df lower.CL upper.CL
## Drug -28.66 1.251 1798 -31.1 -26.21
## Placebo -12.61 1.532 1798 -15.6 -9.61
##
## visit = WK8:
## trt emmean SE df lower.CL upper.CL
## Drug -35.97 1.201 1798 -38.3 -33.61
## Placebo -18.02 1.471 1798 -20.9 -15.13
##
## Confidence level used: 0.95
MMRM SAS code
## visit = WK10:
## contrast estimate SE df t.ratio p.value
## Drug - Placebo -22.06 1.94 1798 -11.390 <.0001
##
## visit = WK12:
## contrast estimate SE df t.ratio p.value
## Drug - Placebo -24.93 1.84 1798 -13.563 <.0001
##
## visit = WK14:
## contrast estimate SE df t.ratio p.value
## Drug - Placebo -27.81 1.81 1798 -15.336 <.0001
##
## visit = WK16:
## contrast estimate SE df t.ratio p.value
## Drug - Placebo -26.98 1.75 1798 -15.425 <.0001
##
## visit = WK2:
## contrast estimate SE df t.ratio p.value
## Drug - Placebo -9.56 1.44 1798 -6.656 <.0001
##
## visit = WK4:
## contrast estimate SE df t.ratio p.value
## Drug - Placebo -12.05 1.98 1798 -6.084 <.0001
##
## visit = WK6:
## contrast estimate SE df t.ratio p.value
## Drug - Placebo -16.05 1.98 1798 -8.118 <.0001
##
## visit = WK8:
## contrast estimate SE df t.ratio p.value
## Drug - Placebo -17.95 1.90 1798 -9.450 <.0001Particular visit
## contrast visit estimate SE df t.ratio p.value
## Drug - Placebo WK16 -27 1.75 1798 -15.425 <.0001