Meg Bennetts
Pfizer Ltd, Sandwich, Kent, UK
Objectives: Longitudinal model based meta-analysis (MBMA) is performed, using all the relevant in-house and published data, to better understand efficacy and safety characteristics of competitor drugs alongside compounds in development. However, in the Drug Development process new compounds often need to show differentiation from standard of care for a Landmark endpoint to meet strategy decisions.
To compare four different methods for producing a landmark prediction and confidence interval from a longitudinal model
Methods: A non-linear longitudinal model was fitted to NIH CPSI (National Institute of Health Chronic Prostatitis Symptom Index) Total Score data for the three As of accepted care (A1 Adreno-receptor antagonist, Anti-Inflammatory & NSAID) and placebo. The final model was a 3 parameter Emax model over time and was performed using NONMEM.
Differentiation from standard of care would be required at 6 hours post dose for a drug in development.
Four methods were employed and compared to calculate the landmark prediction for standard of care:
- Simulation in NONMEM, altering the model file to incorporate parameter uncertainty.
- Calculating the Delta Method formulae for the model and implementing using matrix multiplication in R.
- A simple simulation in R using parameter uncertainty.
- Utilising the delta method function in the R msm package.
Results: All four methods produced similar results.
|
| Difference | StdErr | 95% Lower | 95% Upper |
| Delta Matrix Multiplication | -3.733389 | 1.297707 | -6.276896 | -1.189883 |
| Delta Function | -3.733389 | 1.297707 | -6.276896 | -1.189883 |
| NONMEM Simulation | -3.736108 | 1.281891 | -6.23505 | -1.15085 |
| Simple Simulation | -3.72785 | 1.303936 | -6.283564 | -1.172136 |
Conclusion: The Delta Method is a quick method to produce prediction standard errors. Although a black box the Delta Method function in R gives the same result and removes the need for differentiation and computer intensive simulation.
References:
Oehlert, G. W. A note on the delta method. American Statistician 46(1), 1992
Christopher H. Jackson (2011). Multi-State Models for Panel Data: The msm Package for R. Journal of Statistical Software, 38(8), 1-29
Reference: PAGE 21 (2012) Abstr 2423 [www.page-meeting.org/?abstract=2423]
Poster: Other Modelling Applications