Borrowing from external data that is misaligned w.r.t. the visit schedule

[chstock]

As discussed recently, when borrowing from external data that is misaligned w.r.t. the visit schedule, linear (additive) mixed models might be helpful to derive priors for MMRMs. In practice, this challenge could occur quite frequently and might be something to be addressed in a future vignette.

The attached file includes a first (very preliminary) exploration of models with spline-based smooths fitted using brms::brm() and mgcv::gam(), and marginal means computed with the {emmeans} package.

Bayesian linear (additive) mixed model with spline-based smooths.pdf

Related to #53.

[yonicd]

Small clarification question.

Am I reading correctly that the true treatment effect (PBO-TRT) is

> fev_data2 <- mutate(
+ fev_data2,
+ FEV1 = ifelse(AVISIT == "VIS1" & ARMCD == "TRT", FEV1 + 2, FEV1), #2
+ FEV1 = ifelse(AVISIT == "VIS2" & ARMCD == "TRT", FEV1 + 6, FEV1), #4
+ FEV1 = ifelse(AVISIT == "VIS3" & ARMCD == "TRT", FEV1 + 8, FEV1), #8
+ FEV1 = ifelse(AVISIT == "VIS4" & ARMCD == "TRT", FEV1 + 10, FEV1), #12
+ FEV1 = ifelse(AVISIT == "VIS5" & ARMCD == "TRT", FEV1 + 12, FEV1) #16
+ )

and the estimated from both methods is

week	brms Est.	brms LCL	brms UCL	mgcv Est	mgcv LCL	mgcv UCL	Diff Est.	Diff LCL	Diff UCL
2	−7.77	−10.93	−4.36	−7.86	−11.14	−4.59	0.09	0.20	0.23
4	−9.68	−12.46	−6.80	−9.72	−12.56	−6.89	0.04	0.10	0.09
8	−13.09	−16.13	−9.93	−13.11	−16.22	−10.00	0.03	0.09	0.07
12	−15.69	−18.82	−12.80	−15.71	−18.70	−12.72	0.02	−0.12	−0.08
16	−17.62	−21.04	−14.06	−17.66	−21.21	−14.11	0.04	0.17	0.05

Why are the estimated contrasts much bigger than the true effect?

(I probably misread something in the beginning that I am not seeing)

[chstock]

Why are the estimated contrasts much bigger than the true effect?

(I probably misread something in the beginning that I am not seeing)

Thanks for having had a look, @yonicd, an sorry for the confusion. I didn't add a table with the simulated differences (which I do not know) or the observed ones, which would probably have made things clearer. The fev_data already assumes a treatment effect, and on top of this difference I added what is shown in the mutate() function above. The idea was just to create an example with very obviously different and non-linear mean trajectories in the two arms. What is shown doesn't yet allow to compare truth (or observed values) and estimation.

[wlandau]

Converting this excellent thread to a discussion as it describes a use case of #40 (as opposed to a built-in package feature).