Log-binomial regression and its applications to serial survey data
The log-binomial model is simply a binomial generalised linear model (GLM) with a log link function. It is particularly popular in biostatistical and epidemiological applications as an alternative to logistic regression, since the parameters are adjusted relative risks rather than adjusted odds ratios. Although the model is conceptually straightforward, it requires parameter constraints to prevent probabilities exceeding 1, which leads to numerical problems with standard GLM fitting methods. After introducing the model and illustrating its use in relative risk regression, I will discuss its computational challenges and present some methods and software that I and others have developed for overcoming these challenges. Although the log-binomial model is most commonly used for relative risk regression, it also has applications in other areas. One such area is the analysis of serial survey data, where age- and time-specific prevalence may be used to estimate age- and time-specific incidence. An example of serial survey data is the National Drug Strategy Household Surveys (NDSHS), which provide cross-sectional data on the prevalence of prior substance usage, repeated over time. I will discuss the use of log-binomial regression for analysing serial survey data using the NDSHS data over the period 1998-2013 as an example. This is ongoing work but some preliminary results will be presented related to tobacco usage.