Zeitschrift für Biometrie und Biostatistik

Piecewise Negative Binomial Regression in Analyzing Hypoglycemic Events with Missing Observations

Abstract

Ming Wang, Junxiang Luo, Haoda Fu and Yongming Qu

In diabetes clinical trials, hypoglycemia can be captured. Negative binomial regression is emerging as a standard method for analyzing hypoglycemic events by considering overdispersion. However, in negative binomial regression for hypoglycemic events, variability of the subjects lost to follow up due to dropout is adjusted through an offset parameter, which assumes that dropout is missing completely at random and constant hypoglycemia rate over time. This assumption is vulnerable because dropout may be due to the excessive observed hypoglycemic events and the hypoglycemic event rate may change over time. In addition, the traditional way of using negative binomial regression to analyze hypoglycemic events only compares the counts of hypoglycemic events during a specified period. However, researchers may be interested in comparing hypoglycemic event rates between treatment groups at different time periods to understand the trend over time. Fitting a negative binomial model for each time period ignoring data from other periods may decrease testing power and introduce bias if the assumption of missing completely at random does not hold. We propose piecewise negative binomial regression to incorporate multiple time periods in one model through a generalized linear mixed-effect model. Due to clinical interest, we considered multiple weighting methods to estimate the overall relative rate of hypoglycemia over multiple periods between treatments. Simulations showed that piecewise negative binomial regression performed better than the traditional negative binomial regression in preserving Type I error. As an illustration, piecewise negative binomial regression was implemented in analyzing real data from a Type 2 diabetes clinical trial.