## Abstract

### Background

It is important to quantify the dose response for a drug in phase 2a clinical trials so the optimal doses can then be selected for subsequent late phase trials. In a phase 2a clinical trial of new lead drug being developed for the treatment of rheumatoid arthritis (RA), a U-shaped dose response curve was observed. In the light of this result further research was undertaken to design an efficient phase 2a proof of concept (PoC) trial for a follow-on compound using the lessons learnt from the lead compound.

### Methods

The planned analysis for the Phase 2a trial for GSK123456 was a Bayesian *Emax* model which assumes the dose-response relationship follows a monotonic sigmoid “S” shaped curve. This model was found to be suboptimal to model the U-shaped dose response observed in the data from this trial and alternatives approaches were needed to be considered for the next compound for which a Normal dynamic linear model (NDLM) is proposed. This paper compares the statistical properties of the Bayesian *Emax* model and NDLM model and both models are evaluated using simulation in the context of adaptive Phase 2a PoC design under a variety of assumed dose response curves: linear, *Emax* model, U-shaped model, and flat response.

### Results

It is shown that the NDLM method is flexible and can handle a wide variety of dose-responses, including monotonic and non-monotonic relationships. In comparison to the NDLM model the *Emax* model excelled with higher probability of selecting ED90 and smaller average sample size, when the true dose response followed *Emax* like curve. In addition, the type I error, probability of incorrectly concluding a drug may work when it does not, is inflated with the Bayesian NDLM model in all scenarios which would represent a development risk to pharmaceutical company.

The bias, which is the difference between the estimated effect from the *Emax* and NDLM models and the simulated value, is comparable if the true dose response follows a placebo like curve, an *Emax* like curve, or log linear shape curve under fixed dose allocation, no adaptive allocation, half adaptive and adaptive scenarios. The bias though is significantly increased for the *Emax* model if the true dose response follows a U-shaped curve.

### Conclusions

In most cases the Bayesian *Emax* model works effectively and efficiently, with low bias and good probability of success in case of monotonic dose response. However, if there is a belief that the dose response could be non-monotonic then the NDLM is the superior model to assess the dose response.