Introduction

The Kalamazoo River drains an approximately 2000-square-mile watershed including nearly 400 miles of tributaries in Southwest Michigan. The lower approximately 80 miles of the river are part of the Allied Paper, Inc./Portage Creek/Kalamazoo River Superfund Site. Portage Creek is a tributary joining the Kalamazoo River at Kalamazoo, Michigan, the lower three miles of which are also included in the Site. The presence of polychlorinated biphenyls (PCB) was first reported in the Kalamazoo River and biota of the river in 1971. This consequently resulted in consumption advisories for fish from the Kalamazoo River and Portage Creek. Several subsequent studies have documented the presence of PCB within the surface water, sediments, floodplain soil, and biota of both the Kalamazoo River and Portage Creek, as well as in landfills adjacent to both surface water bodies. In an effort to monitor human-health and ecological risk on the river system, samples of carp and smallmouth bass were collected at several sites within the Kalamazoo River and Portage Creek. Among these sites, the greatest sampling effort occurred at Plainwell Impoundment and Lake Allegan, the most upstream- and downstream-impoundments, respectively, within the superfund site.

Assessment of the efficacy of remedial alternatives on the Kalamazoo River system requires evaluation of future risks to human and ecological health, and quantification of uncertainty in those predictions. Risks result from contact between ecological and human receptors that are of sufficient duration and intensity to elicit adverse effects (EPA, 1992). In this region, human health risks from chlorinated organic compounds such as PCB are primarily associated with ingestion of contaminated fish tissue (Birmingham et al., 1989; Newhook et al., 1988; Fitzgerald et al., 1996). Quantification of human health risks requires prediction of future fish-tissue PCB concentrations and quantification of uncertainty in those predictions.

Temporal trends of the mean or median PCB concentration in fish tissue are typically nonlinear and often modeled as a first order decay process. Stow et al. (1999) pointed out that the first order assumption requires that concentrations decay to zero, thereby precluding the possibility that contaminant concentrations may ultimately reach some steady state nonzero equilibrium or that decay rates may vary temporally. In an effort to correct this weakness, they considered two models for median PCB concentration in fish tissue; a first order decay model with nonzero asymptote (NZA) and a mixed order model (MO).

Following Stow, et al. (1999) we use a mixed-order model for the decay rate of PCB concentrations in fish tissue samples taken from the Kalamazoo River. Although this model offers more flexibility than first order decay, it comes at a statistical cost. The most straightforward methods for prediction and quantification of uncertainty cannot be applied to these models because neither can be transformed into a linear model and analyzed (Neter et al., 1996), nor are they in the class of generalized linear models (McCullagh and Nelder, 1989) for which a significant amount of theory has been developed. Stow, et al. (1999) used non-linear least squares methods to fit the model to their data, but we found this method to be inadequate for quantifying the uncertainty of our predictions because there was no effective way to generate confidence limits. In an effort to avoid these difficulties, we used profile likelihood methods (Venzon and Moolgavkar, 1988) and performed simulations to evaluate the robustness of these methods.