Mapping water quality by local scoring

The mean density of bacteria in a water body is commonly monitored using quantal assay. This paper describes the use of local scoring in estimating the spatial distribution of mean density from quantal assay results at a set of point locations. An application to estimating the mean density of fecal conform bacteria in a coastal pond is presented. Model diagnostics based on a parametric bootstrap are also presented.     

胸腺素含量的ELISA测定法

用胸腺素免疫新西兰免,获得抗胸腺素抗体,建立了胸腺素ELISA定量测定法．该法检测灵敏度为3．2ng/ml,测定范围3．2～50000ng/ml,批内和批间变异系数分别为4．4％和8．9％,方法特异性鉴定显示与另外七种激素无明显交叉反应．     

Threshold‐free estimation of functional antibody titers of a group B streptococcus opsonophagocytic killing assay

Opsonophagocytic killing assays (OPKA) are routinely used for the quantification of bactericidal antibodies in blood serum samples. Quantification of the OPKA readout, the titer, provides the basis for the statistical analysis of vaccine clinical trials having functional immune response endpoints. Traditional OPKA titers are defined as the maximum serum dilution yielding a predefined bacterial killing threshold value, and they are estimated by fitting a dose‐response model to the dilution‐killing curve. This paper illustrates a novel definition of titer, the threshold‐free titer, which preserves biological interpretability while not depending on any killing threshold or on a postulated shape of the dose‐response curve. These titers are shown to be more precise than the traditional threshold‐based titers when using simulated and experimental group B streptococcus OPKA experimental data. Also, titer linearity is shown to be not measurable when using threshold‐based titers, whereas it becomes measurable using threshold‐free titers. The biological interpretability and operational characteristics demonstrated here indicate that threshold‐free titers are an appropriate tool for the routine analysis of OPKA data. Copyright © 2015 John Wiley & Sons, Ltd.     

Non-Normal Bivariate Distributions with Normal Marginals

The purpose of this note is to indicate that Fieller's Theorem can be expressed in the matrix formulation of the general linear model. The practical consequence is that one general computer program which can estimate the parameters and test the validity of a pertinent model, can also compute confidence limits for the ratios of any linear combinations of the parameters.     

Bayesian Measures of the Minimum Detectable Concentration of an Immunoassay

The minimum detectable concentration (MDC) is one of the most important properties of an assay. It is a statement about the smallest physical quantity an assay can reliably measure, and is used in assay design and quality control assessments. A plethora of measures of the MDC have been reported in a widely scattered literature. Many of these were developed at a time when accuracy and relevance had to be sacrificed for computational feasibility. This paper identifies limitations of existing measures and demonstrates how Bayesian inference may be used to overcome these limitations. Several new measures of the MDC are developed. These are conceptually simpler than existing measures, and are free of analytical approximations. The recent advances in Bayesian computation make them efficient to evaluate. A procedure developed in this paper measures the difference in the quality of two assays and shows that the new Bayesian measures perform better than existing measures.     

Identifying Preferences for Conditional Cooperation Using Individual Beliefs

The relationship between contributions and elicited beliefs in a repeated two-person public good experiment is modeled with the help of a parsimounious random-utility function that allows for conditionally cooperative, opportunistic, and altruistic patterns of behavior. Under standard assumptions, a latent-class mixed logit specification with three sub-populations is shown to capture well heterogeneity in individual contribution levels over time, while also accomodating for different degrees of heteroscedasticity. The estimation results are consistent with the conjecture that the majority of players in public goods games are strongly conditional cooperators, with smaller fractions of the population leaning to opportunistic or altruistic behavior.     

Combining Multivariate Bioassays: Accurate Inference Using Small Sample Asymptotics

For several independent multivariate bioassays performed at different laboratories or locations, the problem of testing the homogeneity of the relative potencies is addressed, assuming the usual slope‐ratio or parallel line assay model. When the homogeneity hypothesis holds, interval estimation of the common relative potency is also addressed. These problems have been investigated in the literature using likelihood‐based methods, under the assumption of a common covariance matrix across the different studies. This assumption is relaxed in this investigation. Numerical results show that the usual likelihood‐based procedures are inaccurate for both of the above problems, in terms of providing inflated type I error probabilities for the homogeneity test, and providing coverage probabilities below the nominal level for the interval estimation of the common relative potency, unless the sample sizes are large, as expected. Correction based on small sample asymptotics is investigated in this article, and this provides significantly more accurate results in the small sample scenario. The results are also illustrated with examples.     

A generalized estimating equation approach to modelling incompatible data formats with covariate measurement error: application to human immunodeficiency virus immune markers

The integration of technological advances into research studies often raises an issue of incompatibility of data. This problem is common to longitudinal and multicentre studies, taking the form of changes in the definitions, acquisition of data or measuring instruments of some study variables. In our case of studying the relationship between a marker of immune response to human immunodeficiency virus and human immunodeficiency virus infection status, using data from the Multi-Center AIDS Cohort Study, changes in the manufactured tests used for both variables occurred throughout the study, resulting in data with different manufactured scales. In addition, the latent nature of the immune response of interest necessitated a further consideration of a measurement error component. We address the general issue of incompatibility of data, together with the issue of covariate measurement error, in a unified, generalized linear model setting with inferences based on the generalized estimating equation framework. General conditions are constructed to ensure consistent estimates and their variances for the primary model of interest, with the asymptotic behaviour of resulting estimates examined under a variety of modelling scenarios. The approach is illustrated by modelling a repeated ordinal response with incompatible formats, as a function of a covariate with incompatible formats and measurement error, based on the Multi-Center AIDS Cohort Study data.     

Relative Potency Estimation in Parallel-Line Assays – Method Comparison and Some Extensions

Relative potency estimations in both multiple parallel-line and slope-ratio assays involve construction of simultaneous confidence intervals for ratios of linear combinations of general linear model parameters. The key problem here is that of determining multiplicity adjusted percentage points of a multivariate t-distribution, the correlation matrix R of which depends on the unknown relative potency parameters. Several methods have been proposed in the literature on how to deal with R . In this article, we introduce a method based on an estimate of R (also called the plug-in approach) and compare it with various methods including conservative procedures based on probability inequalities. Attention is restricted to parallel-line assays though the theory is applicable for any ratios of coefficients in the general linear model. Extension of the plug-in method to linear mixed effect models is also discussed. The methods will be compared with respect to their simultaneous coverage probabilities via Monte Carlo simulations. We also evaluate the methods in terms of confidence interval width through application to data on multiple parallel-line assay.     

Design and analysis of a 3‐arm noninferiority trial with a prespecified margin for the hazard ratio

A 3‐arm trial design that includes an experimental treatment, an active reference treatment, and a placebo is useful for assessing the noninferiority of an experimental treatment. The inclusion of a placebo arm enables the assessment of assay sensitivity and internal validation, in addition to the testing of the noninferiority of the experimental treatment compared with the reference treatment. In 3‐arm noninferiority trials, various statistical test procedures have been considered to evaluate the following 3 hypotheses: (i) superiority of the experimental treatment over the placebo, (ii) superiority of the reference treatment over the placebo, and (iii) noninferiority of the experimental treatment compared with the reference treatment. However, hypothesis (ii) can be insufficient and may not accurately assess the assay sensitivity for the noninferiority of the experimental treatment compared with the reference treatment. Thus, demonstrating that the superiority of the reference treatment over the placebo is greater than the noninferiority margin (the nonsuperiority of the reference treatment compared with the placebo) can be necessary. Here, we propose log‐rank statistical procedures for evaluating data obtained from 3‐arm noninferiority trials to assess assay sensitivity with a prespecified margin Δ. In addition, we derive the approximate sample size and optimal allocation required to minimize the total sample size and that of the placebo treatment sample size, hierarchically.