A Generalized Logistic Model for Quantal Response Bioassay

In bioassay, where different levels of the stimulus may represent different doses of a drug, the binary response is the death or survival of an individual receiving a specified dose. In such applications, it is common to model the probability of a positive response P at the stimulus level x by P = F(x′β), where F is a cumulative distribution function and β is a vector of unknown parameters which characterize the response function. The two most popular models used for modelling binary response bioassay involve the probit model [BLISS (1935), FINNEY (1978)], and the logistic model [BERKSON (1944), BROWN (1982)]. However, these models have some limitations. The use of the probit model involves the inverse of the standard normal distribution function, making it rather intractable. The logistic model has a simple form and a closed expression for the inverse distribution function, however, neither the logistic nor the probit can provide a good fit to response functions which are not symmetric or are symmetric but have a steeper or gentler incline in the central probability region. In this paper we introduce a more realistic model for the analysis of quantal response bioassay. The proposed model, which we refer to it as the generalized logistic model, is a family of response curves indexed by shape parameters m₁ and m₂. This family is rich enough to include the probit and logistic models as well as many others as special cases or limiting distributions. In particular, we consider the generalized logistic three parameter model where we assume that m₁ = m, m is a positive real number, and m₂ = 1. We apply this model to various sets of data, comparing the fit results to those obtained previously by other dose-response curves such as the logistic and probit, and showing that the fit can be improved by using the generalized logistic.     

Bayesian Analysis for Linearized Multi-Stage Models in Quantal Bioassay

Bayesian methods for estimating dose response curves from linearized multi-stage models in quantal bioassay are studied. A Gibbs sampling approach with data augmentation is employed to compute the Bayes estimates. In addition, estimation of the “relative additional risk” and the “risk specific dose” is studied. Model selection based on conditional predictive ordinates from cross-validated data is developed. Model adequacy is addressed by means of a posterior predictive tail-area test.     

Estimating the Number of Organisms in Quantal Assays

It has been demonstrated by virologists that, when procedural difficulties can be overcome and host variation can be eliminated, dosage-response data from virus assays conform with the one-particle theory of infection for both plaque counts and tissue cultures. Based on this theory, the number of virus particles from quantal virus assays can be estimated. Here a set of tables is presented from which the number of estimated particles can be obtained directly for several dilution factors and a number of dilution levels. Maximum likelihood estimation of particle counts is also illustrated using a computer program that we have prepared.     

A New Non-radioactive Method for IL-2 Bioassay

An oxidation-reduction (redox) indicator, alamarBlue, was used to measure the bioactivity of interleukin 2 (IL-2). This assay system has several advantages over other bioassays for measuring IL-2. It is a nonradioactive method unlike the conventional tritium-labeled thymidine (^[3H]TdR) incorporation assay. The alamarBlue assay is also easier to use than other colorimetric methods, such as the MTT assay, because the alamarBlue assay does not depend on the extraction of insoluble formazan salt, which is time-consuming, error-prone, and cumbersome. Due to its solubility in culture medium and its nontoxicity to cells, alamarBlue provides an easy method to monitor cellular growth using either a fluorescence- or an absor-bance-based instrument. The alamarBlue assay is not sample-destructive, unlike the thymidine incorporation and MTT methods. This adds another advantage to the alamarBlue method as the measurement of cellular growth by sample-destructive methods requires as many tubes as time points whereas the alamarBlue method requires only one tube for the entire growth period. In this study, alamarBlue was used to measure the proliferation of the IL-2-dependent cytotoxic T cell line, CTLL-2. The colorimetric change of alamarBlue at 570 nm compared to the reference wavelength, 600 nm, was proportional to the number of viable cells. The sensitivity of the IL-2 assay using alamarBlue was comparable to that of the ^[3H]thymidine incorporation method. These results demonstrate that the alamarBlue assay is valid for the IL-2 bioassay and that alamarBlue can replace the ^[3H]thymidine employed in the conventional proliferation assays.     

Use of Quantal Method for Estimation of Agricultural Production

The usual analysis of quantal response data occurring in diverse fields such as economics, medicine, psychology and toxicology use probit and logit models or their extensions with generalised least squares or the principle of likelihood as the method of statistical inference. The quantal method was first used for estimation of agricultural production by S. M. Vidwans (1991). He has collected the data on yield rate of rabi jowar from the farmers for year 1981 in four villages in Shirur taluka and three villages in Daund taluka of Pune district of Maharashtra in India. The probit regression line is fitted. The fit is not good. The estimation is done using truncation of data. Here we observed that a second degree polynomial is a good fit to the data. This will give correct prediction of agricultural production with smaller standard error.     

A Method for Isolation of Pasteuria penetrans Endospores for Bioassay and Genomic Studies

A rapid method for collection of Pasteuria penetrans endospores was developed. Roots containing P. penetrans-infected root-knot nematode females were softened by pectinase digestion, mechanically processed, and filtered to collect large numbers of viable endospores. This method obviates laborious handpicking of Pasteuria-infected females and yields endospores competent to attach to and infect nematodes. Endospores are suitable for morphology studies and DNA preparations.     

Critical Assessment of the C-Optimality Design Criteria for Estimating the Median Effective Dose in Quantal Dose-Response Curves

In this paper the properties of C-optimal designs constructed for estimating the median effective dose within the framework of two-parametric linear logistic models are critically assessed. It is well known that this design criterion which is based on the first-order variance approximation of the exact variance of the maximum likelihood estimate of the ED50 leads to a one-point design where the maximum likelihood theory breaks down. The single dose used in this design is identical with the true but unknown value of the ED50. It will be shown, that at this one-point design the asymptotic variance does not exist. A two-point design in the neighbourhood of the one-point design which is symmetrical about the ED50 and associated with a small dose-distance would be nearly optimal, but extremely nonrobust if the best guess of the ED50 differs from the true value. In this situation the asymptotic variance of the two-point design converging towards the one-point design tends to infinity. Moreover, taking in consideration, that for searching an optimal design the exact variance is of primary interest and the asymptotic variance serves only as an approximation of the exact variance, we calculate the exact variance of the estimator from balanced, symmetric 2-point designs in the neighbourhood of the limiting 1-point design for various dose distances and initial best guesses of the ED50. We compare the true variance of the estimate of the ED50 with the asymptotic variance and show that the approximations generally do not represent suitable substitutes for the exact variance even in case of unrealistically large sample sizes. Kalish (1990) proposed a criterion based on the second-order asymptotic variance of the maximum likelihood estimate of the ED50 to overcome the degenerated 1-point design as the solution of the optimization procedure. In fact, we are able to show that this variance approximation does not perform substantially better than the first–order variance. From these considerations it follows, that the C-optimality criterion is not useful in this estimation problem. Other criteria like the F-optimality should be used.     

A Robust Method for Estimating Optimal Treatment Regimes

Summary A treatment regime is a rule that assigns a treatment, among a set of possible treatments, to a patient as a function of his/her observed characteristics, hence “personalizing” treatment to the patient. The goal is to identify the optimal treatment regime that, if followed by the entire population of patients, would lead to the best outcome on average. Given data from a clinical trial or observational study, for a single treatment decision, the optimal regime can be found by assuming a regression model for the expected outcome conditional on treatment and covariates, where, for a given set of covariates, the optimal treatment is the one that yields the most favorable expected outcome. However, treatment assignment via such a regime is suspect if the regression model is incorrectly specified. Recognizing that, even if misspecified, such a regression model defines a class of regimes, we instead consider finding the optimal regime within such a class by finding the regime that optimizes an estimator of overall population mean outcome. To take into account possible confounding in an observational study and to increase precision, we use a doubly robust augmented inverse probability weighted estimator for this purpose. Simulations and application to data from a breast cancer clinical trial demonstrate the performance of the method.     

A New Method for Estimating Growth Transition Matrices

Summary The vast majority of population models work using age or stage not length but there are many cases where animals cannot be aged sensibly or accurately. For these cases length‐based models form the logical alternative but there has been little work done to develop and compare different methods of estimating growth transition matrices to be used in such models. This article demonstrates how a consistent Bayesian framework for estimating growth parameters and a novel method for constructing length transition matrices accounts for variation in growth in a clear and consistent manner and avoids potential subjective choices required using more established methods. The inclusion of the resultant growth uncertainty in population assessment models and the potential impact on management decisions is also addressed.     

A Noninvasive Method for Estimating Nitrogen Balance in Free-Ranging Primates

The vital role of body protein as an energy reserve has received little focus in studies of wild primates. Owing to the relatively low protein content of fruit, some frugivorous primates could face a protein deficit if body protein is catabolized for energy during periods of low fruit availability. Such an imbalance can be detected if fatty acids, amino acids, and nitrogen (N) catabolites are reincorporated or recycled back to tissues. Here we describe a method to quantify protein recycling by measuring standardized urea concentration and N isotope signatures from urine samples collected from wild Bornean orangutans (Pongo pygmaeus wurmbii). Our overall goal was to explore if concentrations of urea and ??¹⁵N values could be used as indicators of the amount of protein consumed and the degree of protein recycling, respectively, in wild, free-ranging primates. We examine the relationships between urea concentration, ??¹⁵N values, protein intake, and fruit availability. Urea concentration increased with fruit availability, reflecting a slight increase in protein consumption when fruit was abundant. However, we found no relationship between ??¹⁵N values and fruit availability, suggesting that orangutans avert a negative protein balance during periods of low fruit availability. These noninvasive methods complement recent advances in primate energy balance research and will contribute to our understanding of adaptations of primates during periods of fruit shortage.     

一种生长曲线的参数估计方法

本文在现有文献研究的基础上,对生长曲线的参数估计问题又作了进一步研究,给出了一种生长曲线参数估计的方法,并进行了示例计算．     

A Direct Confirmation of the Standard Method of Estimating Intercellular Partial Pressure of CO(2)

The partial pressure of CO₂ inside leaves of several species was measured directly. Small gas exchange chambers were clamped above and below the same section of an amphistomatous leaf. A flowing gas stream through one chamber allowed normal CO₂ and water vapor exchange. The other chamber was in a closed circuit consisting of the chamber, an infrared gas analyzer, and a peristaltic pump. The CO₂ in the closed system rapidly reached a steady pressure which it is believed was identical to the CO₂ pressure inside the leaf, because there was no flux of CO₂ across the epidermis. This measured partial pressure was in close agreement with that estimated from a consideration of the fluxes of CO₂ and vapor at the other surface.     

Regularized Sandwich Estimators for Analysis of High‐Dimensional Data Using Generalized Estimating Equations

Summary A modification of generalized estimating equations (GEEs) methodology is proposed for hypothesis testing of high‐dimensional data, with particular interest in multivariate abundance data in ecology, an important application of interest in thousands of environmental science studies. Such data are typically counts characterized by high dimensionality (in the sense that cluster size exceeds number of clusters, n>K) and over‐dispersion relative to the Poisson distribution. Usual GEE methods cannot be applied in this setting primarily because sandwich estimators become numerically unstable as n increases. We propose instead using a regularized sandwich estimator that assumes a common correlation matrix R , and shrinks the sample estimate of R toward the working correlation matrix to improve its numerical stability. It is shown via theory and simulation that this substantially improves the power of Wald statistics when cluster size is not small. We apply the proposed approach to study the effects of nutrient addition on nematode communities, and in doing so discuss important issues in implementation, such as using statistics that have good properties when parameter estimates approach the boundary (), and using resampling to enable valid inference that is robust to high dimensionality and to possible model misspecification.     

A Rapid Bioassay Method for Gramicidin by Measuring Rubidium Ion Leakage from Streptococcus faecalis

Gramicidin was seen to promote rapid release of Rb⁺ from cells of Streptococcus faecalis ATCC 10541 which had been previously enriched with this cation. This response was logarithmic between gramicidin concentrations of 0.25 μg/ml and 2.5 μg/ml. This efflux was measured by flame emission spectroscopy. The results presented here form the basis for a potential rapid bioassay for gramicidin.     

5-AMINOURACIL TREATMENT : A Method for Estimating G2

Treatment of Vicia faba lateral roots with a range of concentrations of 5-aminouracil (5-AU) indicate that cells are stopped at a particular point in interphase. The timing of the fall in mitotic index suggests that cells are held at the S - G₂ transition. When cells are held at this point, treatments with 5-AU can be used to estimate the duration of G₂ + mitosis/2 of proliferating cells. Treatment with 5-AU can also be used to demonstrate the presence of subpopulations of dividing cells that differ in their G₂ duration. Using this method, 5-AU-induced inhibition, we have confirmed that in V. faba lateral roots there are two populations of dividing cells: (a) a fast-dividing population, which makes up ~85% of the proliferating cell population and has a G₂ + mitosis/2 duration of 3.3 hr, and (b) a slow-dividing population, which makes up ~15% of dividing cells and has a G₂ duration in excess of 12 hr. These estimates are similar to those obtained from percentage labeled mitosis (PLM) curves after incorporation of thymidine-³H.