A Nonstationary Negative Binomial Time Series With Time-Dependent Covariates

Boston Harbor has a history of poor water quality, including contamination by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. Motivated by the ineffectiveness of standard Poisson mixture models and their zero-inflated counterparts, we propose a new negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor. Without further restrictions, this function is not identifiable in the presence of time-dependent covariates; consequently, we use a basis orthogonal to the space spanned by the covariates and use penalized quasi-likelihood (PQL) for estimation. We conclude that Enterococcus counts were greatly reduced near the Nut Island Treatment Plant (NITP) outfalls following the transfer of wastewaters from NITP to the Deer Island Treatment Plant (DITP) and that the transfer of wastewaters from Boston Harbor to the offshore diffusers in Massachusetts Bay reduced the Enterococcus counts near the DITP outfalls.

[1]  M. Levin,et al.  Relationship of microbial indicators to health effects at marine bathing beaches. , 1979, American journal of public health.

[2]  M. Levin,et al.  Swimming-associated gastroenteritis and water quality. , 1982, American journal of epidemiology.

[3]  Alfred P. Dufour,et al.  A marine recreational water quality criterion consistent with indicator concepts and , 1983 .

[4]  R. Tibshirani,et al.  Generalized additive models for medical research , 1986, Statistical methods in medical research.

[5]  A. E. Greenberg,et al.  Standard methods for the examination of water and wastewater : supplement to the sixteenth edition , 1988 .

[6]  S. Zeger.  A regression model for time series of counts , 1988 .

[7]  S. Zeger,et al.  Markov regression models for time series: a quasi-likelihood approach. , 1988, Biometrics.

[8]  Richard P. Signell,et al.  Modeling tidal exchange and dispersion in Boston Harbor , 1992 .

[9]  Diane Lambert,et al.  Zero-inflacted Poisson regression, with an application to defects in manufacturing , 1992 .

[10]  N. Breslow,et al.  Approximate inference in generalized linear mixed models , 1993 .

[11]  N. Breslow,et al.  Bias correction in generalised linear mixed models with a single component of dispersion , 1995 .

[12]  N. Breslow,et al.  Bias Correction in Generalized Linear Mixed Models with Multiple Components of Dispersion , 1996 .

[13]  J. Durbin,et al.  Monte Carlo maximum likelihood estimation for non-Gaussian state space models , 1997 .

[14]  Thomas C. McMonagle,et al.  Toward a Healthy Harbor , 1997 .

[15]  R. Christensen.  Linear Models for Multivariate, Time Series, and Spatial Data , 1997 .

[16]  Awwa,et al.  Standard Methods for the examination of water and wastewater , 1999 .

[17]  Thomas S. Shively,et al.  Variable Selection and Function Estimation in Additive Nonparametric Regression Using a Data-Based Prior , 1999 .

[18]  S. Zeger,et al.  Frequency Domain Log‐linear Models; Air Pollution and Mortality , 1999 .

[19]  David Ruppert,et al.  Variable Selection and Function Estimation in Additive Nonparametric Regression Using a Data-Based Prior: Comment , 1999 .

[20]  Joel Schwartz,et al.  Transitional Regression Models, with Application to Environmental Time Series , 2000 .

[21]  M P Wand,et al.  Negative Binomial Additive Models , 2000, Biometrics.

[22]  J. Hobert.  Automatic Generalized Nonparametric Regression via Maximum Likelihood , 2000 .

[23]  Peiming Wang,et al.  Markov zero-inflated Poisson regression models for a time series of counts with excess zeros , 2001 .

[24]  M. Wand,et al.  Respiratory health and air pollution: additive mixed model analyses. , 2001, Biostatistics.

[25]  B. Silverman,et al.  Functional Data Analysis , 1997 .

[26]  Comparison of water quality in Boston Harbor before and after inter-island transfer , 2001 .

[27]  A. Bergamasco,et al.  Changes in the metal content of surficial sediments of Boston Harbor since the cessation of sludge discharge. , 2001, Marine environmental research.

[28]  J. Schwartz,et al.  Investigating regional differences in short-term effects of air pollution on daily mortality in the APHEA project: a sensitivity analysis for controlling long-term trends and seasonality. , 2001, Environmental health perspectives.

[29]  Investigating regional differences in short-term effects of air pollution on daily mortality in the APHEA project , 2001 .

[30]  P. Albert,et al.  Parametric and semiparametric approaches to testing for seasonal trend in serial count data. , 2002, Biostatistics.

[31]  Jery R. Stedinger,et al.  Improving MCMC Mixing for a GLMM Describing Pathogen Concentrations in Water Supplies , 2002 .

[32]  Jery R. Stedinger,et al.  Modeling the U.S. national distribution of waterborne pathogen concentrations with application to Cryptosporidium parvum , 2003 .

[33]  D. Ruppert,et al.  Likelihood ratio tests in linear mixed models with one variance component , 2003 .

[34]  Yasuhiro Omori.  Estimation for unequally spaced time series of counts with serially correlated random effects , 2003 .

[35]  Herwig Friedl,et al.  Negative binomial loglinear mixed models , 2003 .

[36]  R. Rigby,et al.  Generalized Autoregressive Moving Average Models , 2003 .

[37]  M. Wand,et al.  Geoadditive models , 2003 .

[38]  Kelly A. Coughlin,et al.  Receiver Operating Characteristic Curve Analysis of Beach Water Quality Indicator Variables , 2003, Applied and Environmental Microbiology.

[39]  V. Cabelli.  Microbial indicator systems for assessing water quality , 2004, Antonie van Leeuwenhoek.

[40]  B. Coull,et al.  Modelling spatial intensity for replicated inhomogeneous point patterns in brain imaging , 2004 .

[41]  Louise Ryan,et al.  Cholesky Residuals for Assessing Normal Errors in a Linear Model With Correlated Outcomes , 2004 .

[42]  G. Molenberghs.  Applied Longitudinal Analysis , 2005 .

[43]  Alan Agresti,et al.  Random effect models for repeated measures of zero-inflated count data , 2005 .

[44]  Manfred Deistler,et al.  Linear Models for Multivariate Time Series , 2006 .