Baseline Intensity Function Research Articles

An Additive–Multiplicative Cox–Aalen Regression Model

We propose an additive–multiplicative intensity model that extends the Cox regression model as well as the additive Aalen model. Instead of having a simple baseline intensity the extended model uses an additive Aalen model as its covariate dependent baseline. Approximate maximum likelihood estimators of the baseline intensity functions and the relative risk parameters of the Cox model are suggested by solving the score equations. The derived estimator is efficient. We establish the large sample properties of the estimator. The model provides a simple pragmatic way of including time‐varying covariate effects.

A comparison of some random effect models for parameter estimation in recurrent events

We consider maximum likelihood estimation for multiplicative intensity models with random effects arising from point processes. The methods of estimation include Gauss-Hermite integration based on log-normal random effects and the EM algorithm for nonparametric estimation of the mixing distribution. The former approximates the marginal likelihood by the Gauss-Hermite rule and the latter is most suitable for discrete random effects. We contrast these two methods of estimation with respect to the bias, relative efficiency, and coverage probability of the parameter estimates. We demonstrate, via simulation, that the regression parameter estimates from these two methods have negligible bias and their variance estimates are also valid for practical use. This desirable feature is also robust to misspecification of the mixing. The estimate for the variance parameter under the log-normal random effect model may have small positive bias if the true mixing distribution is highly discrete. In contrast, the EM algorithm for a nonparametric random effect distribution provides practically unbiased estimate for the variance though on occasion it will give an unrealistically large value. We provide empirical evidence that specification of the baseline intensity function as a piecewise constant function is quite robust to misspecification of the baseline intensity function.

Modeling a Poisson forest in variable elevations: a nonparametric Bayesian approach.

A nonparametric Bayesian formulation is given to the problem of modeling nonhomogeneous spatial point patterns influenced by concomitant variables. Only incomplete information on the concomitant variables is assumed, consisting of a relatively small number of point measurements. Residual variation, caused by other unmeasured influential factors, is modeled in terms of a spatially varying baseline intensity function. A Markov chain Monte Carlo scheme is proposed for the simultaneous nonparametric estimation of each unknown function in the model. The suggested method is illustrated by reanalysing a data set in Rathbun (1996, Biometrics 52, 226-242), and the estimated models are compared with those obtained by Rathbun.

Variate generation for a nonhomogeneous poisson process with time dependent covariates

Algorithms are developed for generating a sequence of event times from a nonhomogeneous Poisson process that is influenced by the values of covariates that vary with time. Closed form expressions for random variate generation are shown for several baseline intensity and link functions. Two specific models linking the baseline process to the general model are considered: the accelerated time model and the proportional intensity model. In the accelerated time model, the cumulative intensity function of a nonhomogeneous Poisson process under covariate effects is , where z is a covariate vector, ⋀0(t) is the baseline cumulative intensity function and ψ(z) is the link function. In the proportional intensity model, the cumulative intensity function of a nonhomogeneous Poisson process under covariate effects is , where λ0(t) is the baseline intensity function.

Point process models in asthma attacks for assessing environmental risk factors.

Point process models are reviewed and discussed for assessing the effects of environmental risk factors on asthma attacks. It is pointed out that the logit model and proportional intensity model are useful for analyzing the data based on the diaries recorded consecutively during several months or during a few years. Some covariates that seems to influence upon asthmatics are explored using these models. Further work on estimating the smoothed base-line intensity function is briefly discussed in terms of the Bayes model.

Point Process Models in Asthma Attacks for Assessing Environmental Risk Factors

Point process models are reviewed and discussed for assessing the effects of environmental risk factors on asthma attacks. It is pointed out that the logit model and proportional intensity model are useful for analyzing the data based on the diaries recorded consecutively during several months or during a few years. Some covariates that seems to influence upon asthmatics are explored using these models. Further work on estimating the smoothed base-line intensity function is briefly discussed in terms of the Bayes model.