SUMMARYTo assess water quality standards, measurements of water quality under the Clean Water Act are collected on a regular basis over a period of time. The data are analyzed to evaluate the percentage of samples exceeding the standard. One problem is that current data are limited by the time range and consequently the sample size is inadequate to provide necessary precision in parameter estimation. To address this issue, we present a Bayesian approach using a power prior to incorporate historical data and/or the data collected at adjacent stations. We develop a modified power prior approach and discuss its properties under the normal mean model. Several sets of water quality data are studied to illustrate the implementation of the power prior approach and its differences from alternative methods.

The data sets and kinetic models described here are available from http://www.vbi.vt.edu/~mendes/AGN/as biochemical dynamic models in SBML and Gepasi formats.

Estimating the number of clusters in a data set is a crucial step in cluster analysis. In this article, motivated by the gap method (Tibshirani, Walther, and Hastie, 2001, Journal of the Royal Statistical Society B63, 411-423), we propose the weighted gap and the difference of difference-weighted (DD-weighted) gap methods for estimating the number of clusters in data using the weighted within-clusters sum of errors: a measure of the within-clusters homogeneity. In addition, we propose a "multilayer" clustering approach, which is shown to be more accurate than the original gap method, particularly in detecting the nested cluster structure of the data. The methods are applicable when the input data contain continuous measurements and can be used with any clustering method. Simulation studies and real data are investigated and compared among these proposed methods as well as with the original gap method.

BackgroundIdentifying the best markers to judge the adequacy of lipid‐lowering treatment is increasingly important for coronary heart disease (CHD) prevention given that several novel, potent lipid‐lowering therapies are in development. Reductions in LDL‐C, non‐HDL‐C, or apoB can all be used but which most closely relates to benefit, as defined by the reduction in events on statin treatment, is not established.Methods and ResultsWe performed a random‐effects frequentist and Bayesian meta‐analysis of 7 placebo‐controlled statin trials in which LDL‐C, non‐HDL‐C, and apoB values were available at baseline and at 1‐year follow‐up. Summary level data for change in LDL‐C, non‐HDL‐C, and apoB were related to the relative risk reduction from statin therapy in each trial. In frequentist meta‐analyses, the mean CHD risk reduction (95% CI) per standard deviation decrease in each marker across these 7 trials were 20.1% (15.6%, 24.3%) for LDL‐C; 20.0% (15.2%, 24.7%) for non‐HDL‐C; and 24.4% (19.2%, 29.2%) for apoB. Compared within each trial, risk reduction per change in apoB averaged 21.6% (12.0%, 31.2%) greater than changes in LDL‐C (P<0.001) and 24.3% (22.4%, 26.2%) greater than changes in non‐HDL‐C (P<0.001). Similarly, in Bayesian meta‐analyses using various prior distributions, Bayes factors (BFs) favored reduction in apoB as more closely related to risk reduction from statins compared with LDL‐C or non‐HDL‐C (BFs ranging from 484 to 2380).ConclusionsUsing both a frequentist and Bayesian approach, relative risk reduction across 7 major placebo‐controlled statin trials was more closely related to reductions in apoB than to reductions in either non‐HDL‐C or LDL‐C.

The authors examine family purchase-decision dynamics to shed light on enhancing marketing communication effectiveness. In particular, the authors are interested in understanding the temporal nature of spousal behavioral interaction in family decision making to help marketers target communication messages, shape brand choice, and guide personal selling activities. The authors calibrate a dynamic simultaneous equations model to investigate spousal family purchase-decision behavior: What are spousal behavioral interactions in a discrete purchase decision, and what are the temporal aspects of spousal decision behavior across decisions? The results indicate that spouses tend both not to reciprocate coercion in a discrete decision and to adjust influence strategies over time. The authors also investigate the effectiveness of influence strategies and spousal satisfaction with decisions and their impacts on spousal subsequent decision behaviors from a postdecision perspective as a mechanism to explain why spouses revise decision behaviors across purchase decisions. The authors discuss marketing implications of their findings and present ideas about how to use these findings creatively to target advertising and sales messages to influential spouses in specific decision contexts.

No abstract

Section 303(d) of the Clean Water Act requires states to assess the condition of their waters and to implement plans to improve the quality of waters identified as impaired. U.S. Environmental Protection Agency guidelines require a stream segment to be listed as impaired when greater than 10% of the measurements of water quality conditions exceed numeric criteria. This can be termed a "raw score" assessment approach. Water quality measurements are samples taken from a population of water quality conditions. Concentrations of pollutants vary naturally, measurement errors may be made, and occasional violations of a standard may be tolerable. Therefore, it is reasonable to view the assessment process as a statistical decision problem. Assessment of water quality conditions must be cognizant of the possibility of type I (a false declaration of standards violation) and type II (a false declaration of no violation) errors. The raw score approach is shown to have a high type I error rate. Alternatives to the raw score approach are the Binomial test and the Bayesian Binomial approach. These methods use the same information to make decisions but allow for control of the error rates. The two statistical methods differ based on consideration of prior information about violation. Falsely concluding that a water segment is impaired results in unnecessary planning and pollution control implementation costs. On the other hand, falsely concluding that a segment is not impaired may pose a risk to human health or to the services of the aquatic environment. An approach that recognizes type I and type II error in the water quality assessment process is suggested.

Comparative calibration is the broad statistical methodology used to assess the calibration of a set of p instruments, each designed to measure the same characteristic, on a common group of individuals. Different from the usual calibration problem, the true underlying quantity measured is unobservable. Many authors have shown that this problem, in general, does not have a unique solution. Most commonly used assumptions to obtain a unique solution are (i) one instrument is the gold standard (that is, unbiased) and (ii) the measurement errors of the p instruments are independent. Such constraints, however, may not be valid for many clinical applications, for example, the universal standardization project for dual X-ray absorptiometry (DXA) scanners. In this paper, we propose a new approach to resolve the comparative calibration problem when a gold standard is unavailable. Instead of the usual assumptions, we use external information in addition to data from the p instruments, to solve the problem. We address statistical estimation, hypothesis testing and missing data problems. We apply the new method specifically to the universal standardization project data where a group of individuals have been measured for bone mineral density (BMD) by three DXA scanners. We compare the results of the new method to currently used methods and show that they have better statistical properties.