BITE software package has been developed for estimating a subset of nonparametric Bayesian (NPB; Green 1995; Walker et al. 1999) intensity models, which provide a flexible framework for modelling various event history phenomena (e.g. Andersen et al. 1993; Keiding 2014) in continuous time, such as survival analysis.
Time-to-event data is often modeled by conditioning on past events as a dynamic point process (PP) in time characterized by a hazard function (Andersen et al., 1993). Here we assume a non-homogeneous Cox PP, which is specified by the non-negative intensity process of time. The PP response may be independently and non-informatively censored or filtered.
Background factors, which have occurred before the baseline of the study and can influence both the outcome and the risk factor, often need to be adjusted for in the analyses. These adjustments can be more accurate if the timing of these events such as the onset time of an exposure to a risk factor can be incorporated. On the other hand, the adjustment can also become more challenging. These events generate time scales of their own, and the time elapsed from e.g. diagnosis or medical treatment can be important to the risk of death or other future outcomes.
In recent years, the NPB models have provided a flexible alternative to the traditional statistical modeling also in analyzing PP data (Müller and Mitra, 2013). Under NPB paradigm, statistical inference is based on the posterior distribution of infinite dimensional unknown quantity given the observed data. Implementation of posterior inference in NPB models is often challenging and requires numerical methods, such as Markov chain Monte Carlo methods.
In BITE, NPB models are build on the approach proposed by Arjas and Gasbarra (1994) to the estimation of the intensity of a non-homogeneous PP on the real line. Nonparametric part of the intensity model is based on the piecewise constant function used to approximate the hazard function, and Bayesian component incorporates the prior assigned to the jump points and corresponding hazard levels of step function. Importantly, the prior distribution also includes a built-in smoothing and borrowing of strength. Posterior sampling is implemented by using the reversible jump Markov chain Monte Carlo (Green 1995) algorithm described by Härkänen (2003).