Choosing near-linear parameters in the four-parameter logistic model for radioligand and related assays

Ten parameters extracted from six currently used parametrizations of the four-parameter logistic model, and one new proposal, were examined for their statistical behavior in nonlinear least-squares estimation in combination with ELISA and RIA data. Those which are adequately near-linear on the basis of the Lowry-Morton lambda statistic were identified and can be recommended for use in practice.     

Stochastic modeling of apoptosis tolerance distributions measured by multivariate flow analysis of human leukemia cells

BACKGROUND: Cytofluorometric analysis allows single-cell resolution of all-or-none programmed cell death (apoptosis) responses and permits direct measurement of cumulative frequency distributions (CFDs) of apoptosis sensitivity from which the median apoptosis tolerance can be estimated. Robust estimation of susceptibility to apoptosis within neoplastic cell populations provides a means of either accurately determining pharmacologically induced changes in apoptosis sensitivity or comparing cell population responses to different apoptosis inducers. METHODS: Experimentally determined CFDs for VP-16 (etoposide)-induced apoptosis were measured by phosphotidylserine surface expression and mitochondrial membrane potential dissipation (DeltaPsi(m)) in BV173 leukemia cells. CFDs were modelled by a modified Hill equation using a four-parameter nonlinear regression from which median apoptosis tolerance (K) was estimated. RESULTS: Median apoptosis tolerance (K) was estimated from nonlinear regression analysis of CFDs for DeltaPsi(m) collapse and loss of membrane asymmetry. The error distribution of K determined from nonlinear regression analysis of 100 simulated CFDs was shown to exhibit an asymmetrical distribution. The asymmetrical likelihood intervals for K were computed iteratively, thereby providing a measure of experimental error. CONCLUSIONS: A distribution-based approach to apoptosis assay using multivariate flow analysis offers a powerful, quantitative technique for investigating the phenotypical basis of neoplastic cell responsiveness to apoptosis therapy, permitting separation of cell populations on the basis of apoptosis susceptibility.     

The five-parameter logistic: a characterization and comparison with the four-parameter logistic

Improvements in assay technology have reduced the amount of random variation in measured responses to the point where even slight asymmetry of the assay data can be more significant than random variation. Use of the five-parameter logistic (5PL) function to fit dose-response data easily accommodates such asymmetry. The 5PL can dramatically improve the accuracy of asymmetric assays over the use of symmetric models such as the four-parameter logistic (4PL) function. Until recently, however, the process of fitting the 5PL function has been difficult, with the result that the 4PL function has continued to be used even for highly asymmetric data. Various ad hoc modifications of the 4PL method have been developed in an attempt to address asymmetric data. However, recent advances in numerical methods and assay analysis software have rendered easier the fitting of the 5PL routine. This paper demonstrates how use of the 5PL function can improve assay performance over the 4PL and its variants. Specifically, the improvement in the accuracy of concentration estimates that can be obtained using the 5PL over the 4PL as a function of the asymmetry present in the data is studied. The behavior of the 5PL curve and how it differs from the 4PL curve are discussed. Common experimental designs, which can lead to ill-conditioned regression problems, are also examined.     

Nomograms Aid Interpretation of Complex Regression Models

ABSTRACT Ecologists often develop complex regression models that include multiple categorical and continuous variables, interactions among predictors, and nonlinear relationships between the response and predictor variables. Nomograms, which are graphical devices for presenting mathematical functions and calculating output values, can aid biologists in interpreting and presenting these complex models. To illustrate benefits of nomograms, we developed a logistic regression model of elk (Cervus elaphus) resource selection. With this model, we demonstrated how a nomogram helps scientists and managers interpret interactions among variables, compare the relative biological importance of variables, and examine predicted shapes of relationships (e.g., linear vs. nonlinear) between response and predictor variables. Although our example focused on logistic regression, nomograms are equally useful for other linear and nonlinear models. Regardless of the approach used for model development, nomograms and other graphical summaries can help scientists and managers develop, interpret, and apply statistical models.     

Offspring-parent regression for a binary trait

Summary Offspring-parent regression is often used to estimate the heritability of a quantitative trait. It is shown that for a purely binary trait, the regression of offspring on one parent is always linear, while that on both parents or mid-parent is generally nonlinear. However, the regressions are linear on a logistic scale.     

Reduction of dimensionality in Bayesian nonlinear regression with a pharmacokinetic application

Application of Bayes's theorem to the analysis of nonlinear regression models is limited by numerical problems associated with calculation of integrals of functions of several variables. For k-parameter models that are linear in l of the parameters, a dimension-reduction procedure is described for factoring the posterior distribution into the product of a multivariate normal density and a function of k-l nonlinear parameters. Integrals can then be calculated with (k-l)-dimensional numerical integration. A four-parameter, two-compartment pharmacokinetic model of lidocaine disposition is analyzed using a change of variables in order to obtain a model that is linear in two parameters. It is shown that a Bayesian analysis, with reduction of dimensionality, applied to this model produces appropriate results with reasonable CPU-time requirements.     

Interaction of interleukin 2 with cells: quantitative analysis of effects

The response of T lymphocytes to interleukin 2 (IL 2) is accurately described by a four-parameter logistic function. Both data generated by a theoretical model of IL 2-driven proliferation and experimental data conformed to this function for all doses of IL 2. Assays measuring either the rate of DNA synthesis or cellular metabolism were well described. The variance of response was not constant but increased in a predictable way. Weighting was therefore included in deriving a nonlinear curve-fitting program. The effects on response of cell density, time, and the T lymphocyte line used were examined. Assays gave reproducible estimates of potency when test preparations were compared with a standard preparation, but not otherwise. A model for IL 2 proliferation was derived on the basis of the two-state model of the cell cycle, with cells leaving a quiescent state randomly and then traversing the other stages of the cell cycle in a determinate way.     

A Simple,Flexible Failure Model

A new failure model is introduced in the form of a four-parameter nonlinear differential equation, with failure probability as the dependent variable and failure time as the independent variable. The first parameter characterizes the location, the second the scale, and the other two the shape of the model. The type of the accompanying hazard function is immediately read off the shape parameters. The new model approximates the classical failure models with rather high precision, but also models cases where the failure density is skewed to the left. It can be used to analyze survival data objectively, based on the shape of the failure distribution. The computation of quantiles and moments is easy and fast. Nonlinear regression methods are used to estimate parameter values.     

Functional relevance of synonymous alleles reflected in allele rareness in the population

We provide theoretical evidence supporting the non-neutrality of synonymous alleles by investigating the rareness of synonymous alleles in the population. We find a significantly greater number of synonymous rare alleles than conventional neutral alleles derived from noncoding regions. A permutation experiment shows that the rareness of synonymous alleles is not a byproduct of random statistical noise. We then compare the frequencies of synonymous rare alleles and common alleles in various functional contexts in which synonymous alleles are known to be involved. Subsequently, we perform logistic regression analysis to elucidate the effect size of each independent factor contributing to the rareness of synonymous alleles. Additionally, we show that changes in optimality caused by synonymous mutations resulting in rare SNPs in the population tend to be biased toward optimality loss. We think that our study will contribute to the development of novel strategies for identifying functional synonymous mutations.     

Estrogen and progesterone measurement and its quality control in breast cancer: a reappraisal

This article illustrates the two main methods for routine measurement of cytoplasmic estrogen receptor status in neoplastic biopsy. The first is the Dextran Coated Charcoal Technique (D.C.C. Assay) which is still the method of choice in the majority of clinical laboratories for its simplicity, reproducibility and low cost. The second is a more advanced technique based on the specific binding, enzymatically displayed, of commercially available antiestrogen monoclonal antibodies (Enzyme Immuno Assay - ABBOTT). The sui generis characteristics of endocrine sensitivity assessment on tumor tissues and the importance of decision-making connected with the assay justify rigorous quality assurance schemes. The quality control design proposed by the Italian Committee concerned the evaluation of several lyophilized preparations with scalar receptor content; this permits the identification through linear regression analysis of systematic and non-systematic errors. The Italian Committee has currently connected 50 labs from most regions of the country.     

Quantitative Risk Assessment in Epidemiological Studies Investigating Threshold Effects

In this paper a method for quantitative risk assessment in epidemiological studies investigating threshold effects is proposed. The simple logistic regression model is used to describe the association between a binary response variable and a continuous risk factor. By defining acceptable levels for the absolute risk and the risk gradient the corresponding benchmark values of the risk factor can be calculated by means of nonlinear functions of the logistic regression coefficients. Standard errors and confidence intervals of the benchmark values are derived by means of the multivariate delta method. The proposed approach is compared with the threshold model of Ulm (1991) for assessing threshold values in epidemiological studies.     

Enzyme-linked immunolysis assay for tumour-specific surface antigens

Expression of the activity of the cytosolic enzyme lactate dehydrogenase released on cell lysis by tumour specific antibodies in the presence of complement was investigated by direct assay of the expression of the occluded enzyme in tumour cell suspensions. This method, called Enzyme Linked Immunolysis Assay (ELILA) was shown to be more sensitive than conventional cytotoxic assays. The data fit well in the linear regression model, so that the technique can be used for quantitation of the antibody titres.     

A sensitive branched DNA HIV-1 signal amplification viral load assay with single day turnaround

Branched DNA (bDNA) is a signal amplification technology used in clinical and research laboratories to quantitatively detect nucleic acids. An overnight incubation is a significant drawback of highly sensitive bDNA assays. The VERSANT® HIV-1 RNA 3.0 Assay (bDNA) (“Versant Assay”) currently used in clinical laboratories was modified to allow shorter target incubation, enabling the viral load assay to be run in a single day. To dramatically reduce the target incubation from 16–18 h to 2.5 h, composition of only the “Lysis Diluent” solution was modified. Nucleic acid probes in the assay were unchanged. Performance of the modified assay (assay in development; not commercially available) was evaluated and compared to the Versant Assay. Dilution series replicates (>950 results) were used to demonstrate that analytical sensitivity, linearity, accuracy, and precision for the shorter modified assay are comparable to the Versant Assay. HIV RNA-positive clinical specimens (n = 135) showed no significant difference in quantification between the modified assay and the Versant Assay. Equivalent relative quantification of samples of eight genotypes was demonstrated for the two assays. Elevated levels of several potentially interfering endogenous substances had no effect on quantification or specificity of the modified assay. The modified assay with drastically improved turnaround time demonstrates the viability of signal-amplifying technology, such as bDNA, as an alternative to the PCR-based assays dominating viral load monitoring in clinical laboratories. Highly sensitive bDNA assays with a single day turnaround may be ideal for laboratories with especially stringent cost, contamination, or reliability requirements.     

International technology transfer of a GCLP-compliant HIV-1 neutralizing antibody assay for human clinical trials

The Collaboration for AIDS Vaccine Discovery/Comprehensive Antibody-Vaccine Immune Monitoring Consortium (CAVD/CA-VIMC) assisted an international network of laboratories in transferring a validated assay used to judge HIV-1 vaccine immunogenicity in compliance with Good Clinical Laboratory Practice (GCLP) with the goal of adding quality to the conduct of endpoint assays for Human Immunodeficiency Virus I (HIV-1) vaccine human clinical trials. Eight Regional Laboratories in the international setting (Regional Laboratories), many located in regions where the HIV-1 epidemic is most prominent, were selected to implement the standardized, GCLP-compliant Neutralizing Antibody Assay for HIV-1 in TZM-bl Cells (TZM-bl NAb Assay). Each laboratory was required to undergo initial training and implementation of the immunologic assay on-site and then perform partial assay re-validation, competency testing, and undergo formal external audits for GCLP compliance. Furthermore, using a newly established external proficiency testing program for the TZM-bl NAb Assay has allowed the Regional Laboratories to assess the comparability of assay results at their site with the results of neutralizing antibody assays performed around the world. As a result, several of the CAVD/CA-VIMC Regional Laboratories are now in the process of conducting or planning to conduct the GCLP-compliant TZM-bl NAb Assay as an indicator of vaccine immunogenicity for ongoing human clinical trials.     

PathogenMip assay: a multiplex pathogen detection assay

The Molecular Inversion Probe (MIP) assay has been previously applied to a large-scale human SNP detection. Here we describe the PathogenMip Assay, a complete protocol for probe production and applied approaches to pathogen detection. We have demonstrated the utility of this assay with an initial set of 24 probes targeting the most clinically relevant HPV genotypes associated with cervical cancer progression. Probe construction was based on a novel, cost-effective, ligase-based protocol. The assay was validated by performing pyrosequencing and Microarray chip detection in parallel experiments. HPV plasmids were used to validate sensitivity and selectivity of the assay. In addition, 20 genomic DNA extracts from primary tumors were genotyped with the PathogenMip Assay results and were in 100% agreement with conventional sequencing using an L1-based HPV genotyping protocol. The PathogenMip Assay is a widely accessible protocol for producing and using highly discriminating probes, with experimentally validated results in pathogen genotyping, which could potentially be applied to the detection and characterization of any microbe.     

A machine‐learning approach for extending classical wildlife resource selection analyses

Resource selection functions (RSFs) are tremendously valuable for ecologists and resource managers because they quantify spatial patterns in resource utilization by wildlife, thereby facilitating identification of critical habitat areas and characterizing specific habitat features that are selected or avoided. RSFs discriminate between known‐use resource units (e.g., telemetry locations) and available (or randomly selected) resource units based on an array of environmental features, and in their standard form are performed using logistic regression. As generalized linear models, standard RSFs have some notable limitations, such as difficulties in accommodating nonlinear (e.g., humped or threshold) relationships and complex interactions. Increasingly, ecologists are using flexible machine‐learning methods (e.g., random forests, neural networks) to overcome these limitations. Herein, we investigate the seasonal resource selection patterns of mule deer (Odocoileus hemionus) by comparing a logistic regression framework with random forest (RF), a popular machine‐learning algorithm. Random forest (RF) models detected nonlinear relationships (e.g., optimal ranges for slope and elevation) and complex interactions which would have been very challenging to discover and characterize using standard model‐based approaches. Compared with standard RSF models, RF models exhibited improved predictive skill, provided novel insights about resource selection patterns of mule deer, and, when projected across a relevant geographic space, manifested notable differences in predicted habitat suitability. We recommend that wildlife researchers harness the strengths of machine‐learning tools like RF in addition to “classical” tools (e.g., mixed‐effects logistic regression) for evaluating resource selection, especially in cases where extensive telemetry data sets are available.     

Homogeneous antibody-based proximity extension assays provide sensitive and specific detection of low-abundant proteins in human blood

Convenient and well-performing protein detection methods for a wide range of targets are in great demand for biomedical research and future diagnostics. Assays without the need for washing steps while still unaffected when analyzing complex biological samples are difficult to develop. Herein, we report a well-characterized nucleic acid proximity-based assay using antibodies, called Proximity Extension Assay (PEA), showing good performance in plasma samples. Target-specific antibody pairs are linked to DNA strands that upon simultaneous binding to the target analyte create a real-time PCR amplicon in a proximity-dependent manner enabled by the action of a DNA polymerase. 3'Exonuclease-capable polymerases were found to be clearly superior in sensitivity over non-3'exonuclease ones. A PEA was set up for IL-8 and GDNF in a user-friendly, homogenous assay displaying femtomolar detection sensitivity, good recovery in human plasma, high specificity and up to 5-log dynamic range in 1 μL samples. Furthermore, we have illustrated the use of a macro-molecular crowding matrix in combination with this homogeneous assay to drive target binding for low-affinity antibodies, thereby improving the sensitivity and increasing affinity reagent availability by lowering assay development dependency on high-affinity antibodies. Assay performance was also confirmed for a multiplex version of PEA.