**Use of a generalized poisson model to describe micturition frequency in patients with overactive bladder disease.**

N.H. Prins(1), K. Dykstra(1), A. Darekar(2), P.H. van der Graaf(2)

(1)qPharmetra LLC, Andover, MA, USA, (2) Pfizer Ltd, Sandwich, UK

**Objectives:** Daily micturition frequency is a key endpoint for assessing overactive bladder disease activity. Micturitions are count data and are commonly modeled assuming the Poisson distribution, which assumes equidispersion, meaning that mean and variance are the same. However, observed within-individual variance is consistently lower than within-individual mean micturition frequency. Being encouraged by a recent study addressing underdispersion in Likert pain rating scales [1], we evaluated model fit attributes of the same structural micturition model while comparing a generalized Poisson (GP) that flexibly describes under and over dispersion versus the standard Poisson (PS) distribution.

**Methods:** Placebo micturition count data from 3058 patients participating in 7 studies were modeled as mict=mict(base)*(1-plmax*(1-exp(-k*t))), in NONMEM7, with METHOD=SAEM followed by MCMC Bayesian. Parameter plmax was logit-transformed to ensure that predicted mict never went below zero. Lognormal between subject variability (BSV) was assumed on λ (PS) or λ1 (GP) and additive BSV was assumed on plmax (PS, GP). In the generalized Poisson equation [2], a λ1 and a dispersion factor λ2 are estimated, where the mean of the distribution is λ1/(1- λ2) and the variance is λ1/(1- λ2)^3. In the special case of λ2=0, the GP model collapses to a PS. Models were compared by Objective Function Value (OFV), ability to capture mean trends and observed variability using Visual Predictive Check (VPC), and precision of parameter estimates.

**Results:** The mean trend in the data was equally well captured by both models. The GP model was significantly better than the PS model as compared by the lower mean OFV (104,822 vs. 93,612) which is a >11,000 point drop. The VPC showed that the PS model under predicted the 5^{th} and over predicted the 95^{th} confidence interval, while the GP model captured them remarkably well. Parameter estimates of the placebo model were 5% (plmax), 51% (k), 19% (BSV λ or λ1), and 32% (BSV plmax) more precise for the GP model than those of the PS model.

**Conclusions:** The GP model was found to be superior to the PS model in describing the variability observed in micturition count data and yielding more precise parameter estimates. The GP model will as such provide more accurate inferences, such as drug efficacy predictions and clinical trial simulations.

**References:**

[1] [1] Plan & Karlsson (2009). New models for handling correlated underdispersed Likert pain scores. PAGE 2009.

[2] Consul & Jain (1973). A Generalization of the Poisson distribution. Technometrics 15, 791-799