Statistics and Its Interface

Volume 5 (2012)

Number 2

Additive hazards regression and partial likelihood estimation for ecological monitoring data across space

Pages: 195 – 206



Feng-Chang Lin (Department of Biostatistics, University of North Carolina at Chapel Hill, U.S.A.)

Jun Zhu (Department of Statistics and Department of Entomology, University of Wisconsin at Madison, U.S.A.)


We develop continuous-time models for the analysis of environmental or ecological monitoring data such that subjects are observed at multiple monitoring time points across space. Of particular interest are additive hazards regression models where the baseline hazard function can take on flexible forms.We consider time-varying covariates and take into account spatial dependence via autoregression in space and time. We develop statistical inference for the regression coefficients via partial likelihood. Asymptotic properties, including consistency and asymptotic normality, are established for parameter estimates under suitable regularity conditions. Feasible algorithms utilizing existing statistical software packages are developed for computation. We also consider a simpler additive hazards model with homogeneous baseline hazard and develop hypothesis testing for homogeneity. A simulation study demonstrates that the statistical inference using partial likelihood has sound finite-sample properties and offers a viable alternative to maximum likelihood estimation. For illustration, we analyze data from an ecological study that monitors bark beetle colonization of red pines in a plantation of Wisconsin.


current status data, grouped survival data, maximum likelihood, multiple monitoring times, spatial autoregression, spatial lattice

2010 Mathematics Subject Classification

Primary 62N02. Secondary 62M10.

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