In mmrm: Mixed Models for Repeated Measures

library(mmrm)

This package supports estimation of one- and multi-dimensional contrasts (t-test and F-test calculation) with the df_1d() and df_md() functions. Both functions utilize the chosen adjustment method from the initial mmrm call for the calculation of degrees of freedom and (for Kenward-Roger methods) the variance estimates for the test-statistics.

One-dimensional contrasts

Compute the test of a one-dimensional (vector) contrast for a mmrm object with Satterthwaite degrees of freedom.

fit <- mmrm(
  formula = FEV1 ~ RACE + SEX + ARMCD * AVISIT + us(AVISIT | USUBJID),
  data = fev_data
)

contrast <- numeric(length(component(fit, "beta_est")))
contrast[3] <- 1

df_1d(fit, contrast)

This works similarly when choosing a Kenward-Roger adjustment:

fit_kr <- mmrm(
  formula = FEV1 ~ RACE + SEX + ARMCD * AVISIT + us(AVISIT | USUBJID),
  data = fev_data,
  method = "Kenward-Roger"
)

df_1d(fit_kr, contrast)

We see that because this is a one-dimensional contrast, the degrees of freedoms are identical for Satterthwaite and Kenward-Roger. However, the standard errors are different and therefore the p-values are different.

Additional options for the degrees of freedom method are Residual and Between-Within.

Multi-dimensional contrasts

Compute the test of a multi-dimensional (matrix) contrast for the above defined mmrm object with Satterthwaite degrees of freedom:

contrast <- matrix(data = 0, nrow = 2, ncol = length(component(fit, "beta_est")))
contrast[1, 2] <- contrast[2, 3] <- 1

df_md(fit, contrast)

And for the Kenward-Roger adjustment:

df_md(fit_kr, contrast)

We see that for the multi-dimensional contrast we get slightly different denominator degrees of freedom for the two adjustment methods.

Also the simpler Residual and Between-Within method choices can be used of course together with multidimensional contrasts.

Support for emmeans

This package includes methods that allow mmrm objects to be used with the emmeans package. emmeans computes estimated marginal means (also called least-square means) for the coefficients of the MMRM. For example, in order to see the least-square means by visit and by treatment arm:

library(emmeans)
lsmeans_by_visit <- emmeans(fit, ~ ARMCD | AVISIT)
lsmeans_by_visit

Note that the degrees of freedom choice is inherited here from the initial mmrm fit. Furthermore, we can also obtain the differences between the treatment arms for each visit by applying pairs() on the object returned by emmeans() earlier:

pairs(lsmeans_by_visit, reverse = TRUE)

(This is similar like the pdiff option in SAS PROC MIXED.) Note that we use here the reverse argument to obtain treatment minus placebo results, instead of placebo minus treatment results.

To further obtain the confidence interval of the least square mean differences, we can apply confint() on the result returned by pairs() .

This is similar to the LSMEANS in SAS, with CL and DIFF options.

confint(pairs(lsmeans_by_visit, reverse = TRUE))

Support for car

This package includes methods that allow mmrm objects to be used with the car::Anova function. Anova conducts type II/III hypothesis testing for the effect in mmrm models. For example, in order to see if the used covariates are related to the response:

library(car)
Anova(fit, type = "II")

Note that the degrees of freedom choice is inherited here from the initial mmrm fit. In addition, please note that if you see results that are slightly different from SAS, it could be because the reference level is set differently for categorical covariates. We can also use type III hypothesis testing: