Exposure-Response Analysis of Adverse Events in Clinical Trials Using Zero-Inflated Poisson Modeling With NONMEM®.
Xu (Steven) Xu and Partha Nandy
Global Clinical Pharmacokinetics & Clinical Pharmacology, Johnson & Johnson Pharmaceutical Research & Development, L.L.C., Raritan, New Jersey; Titusville, New Jersey, US.
Background: Count data, typically characterized by the number of occurrences of an event during a specified time interval, often arises in clinical trials and are usually characterized and modeled by Poisson distribution. Often times, such kind of data is associated with adverse events. However, some adverse events may only be observed in a small portion of the study subjects, namely excessive zeros in the data. Exposure-response modeling of such data allows for a better understanding of the relationships between drug exposure and event rate and helps identify potential risk factors that make subjects prone to certain adverse events.
Objectives: The objectives of the analysis were (1) to model event rate of an adverse event following administration of a new investigational drug; (2) to assess the potential relationships between the occurrence of the adverse event and the extent of drug exposure; and (3) to identify potential risk factors that influence the occurrence of the adverse event.
Methods: An exposure-response model was developed using pooled data from several trials of an investigational drug (1069 patients). Since no events during the studies were observed for a large portion of subjects, zero-inflated Poisson (ZIP) regression models [1] were explored and developed using NONMEM® to characterize the zero-rich count data for the adverse event. Alternative modeling strategies, such as regular Poisson and Negative Binomial regression models (implemented in S-PLUS®) were also fitted to the data; and the results were compared to that from the ZIP model. Patient-specific measures of drug exposure were simulated based on a population PK-model of this drug. Drug exposure, demographic variables, and other relevant variables were examined on both logistic and truncated Poisson components of the ZIP model to identify potential risk factors. The ZIP model was evaluated using marginal calibration diagram [2] and used to simulate exposure-adverse event response curves and placebo effect.
Results: ZIP models adequately characterized the distribution of the adverse event, while Poisson and Negative Binomial models tended to underestimate the event rate. Drug exposure was identified as significant risk factor. An Emax model best described the relationship between the occurrence of the adverse event and drug exposure. Certain demographic variables, such as sex and body weight, were also identified as risk factors. Men were found to be less likely to have the adverse event compared to women. The simulation suggested that higher the drug exposure, the more episodes of the adverse event a subject would be expected to experience. The risk of placebo-treated subjects having multiple episodes of the adverse event was virtually insignificant. In placebo group, women reported more incidences of adverse event than men, which may suggest that women are predisposed to the adverse event compared to men.
Conclusions: Exposure-response modeling allows for exploring relationships between drug exposure and occurrence of drug-related adverse events along with identification of risk factors. Zero-inflated Poisson regression can be implemented in NONMEM® and is a useful tool to model the occurrence of an adverse event, where no instance of the adverse event were reported in majority of subjects.
References:
[1] Johnson NL, Kotz S, Kemp AW. Univariate Discrete Distributions, 2nd edn. Wiley: New York, 1992
[2] Czado, C., Gneiting, T., Held, L. (2007) Predictive Model Assessment for Count Data. University of Washington Department of Statistics Technical Report no. 518.
