Daniel Sabanes Bove

(Statistical Engineering, Pharma Product Development Data Sciences, Roche)

12/8/22

Authors:

- Kevin Kunzmann (Boehringer Ingelheim)
- Brian Matthew Lang (MSD)
- Ya Wang (Gilead)
- Julia Dedic (Roche)
- Doug Kelkhoff (Roche)
- Liming Li (Roche)

Thanks to:

- Ben Bolker (McMaster University)
- Software Engineering working group (SWE WG)
- Gonzalo Duran Pacheco (Roche)
- Craig Gower-Page (Roche)
- Dinakar Kulkarni (Roche)
- Davide Garolini (Roche)

- 2 years ago, we thought we had solved the MMRM problem, using
`lme4`

and`lmerTest`

- However in March this year, Gonzalo and Julia told us the bad news: this approach failed on their Ophthalmology data sets (slow, did not converge)
`nlme`

does not give Satterthwaite adjusted degrees of freedom, has convergence issues, and with`emmeans`

it is only approximate- Next we tried to extend
`glmmTMB`

to calculate Satterthwaite adjusted degrees of freedom, but it did not work

- Because
`glmmTMB`

is always using a random effects representation, we cannot have a real unstructured model (uses \(\sigma = \varepsilon > 0\) trick) - We only want to fit a fixed effects model with a structured covariance matrix for each subject
- The idea is then to use the Template Model Builder (
`TMB`

) directly - as it is also underlying`glmmTMB`

- but code the exact model we want - We do this by implementing the log-likelihood in
`C++`

using the`TMB`

provided libraries

`TMB`

- Fast
`C++`

framework for defining objective functions (`Rcpp`

would have been alternative interface) - Automatic differentiation of the log-likelihood as a function of the variance parameters
- We get the gradient and Hessian exactly and without additional coding
- This can be used from the R side with the
`TMB`

interface and plugged into optimizers

- We created an initial prototype quickly and open sourced it on github.com/openpharma/mmrm
- In parallel we assembled multiple other companies - many of them had also struggled to implement MMRM in R (crucial gap in toolbox so far)
- This was the start of the Software Engineering working group (SWE WG)
- Read more at rconsortium.github.io/asa-biop-swe-wg
- Official working group of the ASA Biopharmaceutical section

- Linear model for dependent observations within independent subjects
- Covariance structures for the dependent observations:
- Unstructured, Toeplitz, AR1, compound symmetry, ante-dependence, spatial exponential
- Allows group specific covariance estimates and weights

- REML or ML estimation, using multiple optimizers if needed
`emmeans`

interface for least square means- Satterthwaite adjusted degrees of freedom

`mmrm`

is on CRAN - use this as a starting point:

- Visit openpharma.github.io/mmrm for detailed docs including vignettes
- Consider tern.mmrm for high-level clinical reporting interface, incl. standard tables and graphs

- We still have major features on our backlog:
- Kenward-Roger (improved variance-covariance matrix, degrees of freedom)
- Robust sandwich estimator for covariance matrix (important when not using unstructured covariance)
- Type II and type III ANOVA tests

- Working on comparison to other implementations
- Parameter estimates, computation time, convergence, …

- Please let us know what is missing in
`mmrm`

for you! And try it out :-)