Turbidimetric Assays: the Antibiotic Dose-Response Line

Several antibiotics reduced growth of bacteria without killing them when present in the range of concentrations of significance in assaying. The reduction in growth rate was linearly related to concentration of antibiotic. From this fact may be derived an equation of the form log N = A - BC where N is the concentration of bacteria at the end of the incubation period, C is the concentration of antibiotic, and A and B are constants. This equation is used to guide the selection of the best range of concentrations of unknown for assay and to show the large influence of variations of temperature upon an assay.     

Dose-Response Model for Lassa Virus

This article develops dose-response models for Lassa fever virus using data sets found in the open literature. Dose-response data were drawn from two studies in which guinea pigs were given subcutaneous and aerosol exposure to Lassa virus. In one study, six groups of inbred guinea pigs were inoculated subcutaneously with doses of Lassa virus and five groups of out-bred guinea pigs were similarly treated. We found that the out-bred subcutaneously exposed guinea pig did not exhibit a dose-dependent trend in response. The inbred guinea pigs data were best fit by an exponential dose-response model. In a second study, four groups of out-bred guinea pigs were exposed to doses of Lassa virus via the aerosol route. In that study, aerosol diameter was less than 4.5 μ m and both mortality and morbidity were used as endpoints. The log-probit dose-response model provided a somewhat better fit than the Beta-Poisson model for data with mortality as the endpoint, but the Beta-Poisson is considered the best fit model because it can be derived using biological considerations. Morbidity data were best fit with an exponential dose-response model.     

A Linear Dose-Response Curve at the Motor Endplate

The motor endplate of frog sartorius muscle was voltage clamped and the peak current to different concentrations of acetylcholine and carbachol applied in the perfusing fluid was measured. Perfusing fluid was hypertonic in order to suppress contractions. Current responses were smooth and reached a peak value within 2–5 s. The dose-response curve was usually linear even with concentrations of 10^-2 M acetylcholine, indicating that the conductance change was probably proportional to the concentration of acetylcholine or carbachol. With high concentrations nonlinearity sometimes appeared but in these cases the fast onset of desensitization appeared to be preventing the current response from reaching its expected peak amplitude. When the depolarization produced by acetylcholine in a non-voltage-clamped endplate was measured the dose-response curve was hyperbolic. This relationship was imposed by the electrical properties of the endplate membrane and its surrounding sarcolemma, and could be predicted if the input resistance of the fiber was known. Experiments were also done on slow muscle fibers. Depolarizing analogues of acetylcholine had similar effects to acetylcholine. d-Tubocurarine reduced the proportionality constant between concentration of acetylcholine and conductance change, and this resulted in a parallel shift of the log-concentration depolarization curve. A linear dose-response curve was unexpected within the context of current theories of drug action.     

Statistical Dose-Response Models with Hormetic Effects

Monotonically increasing or decreasing functions are often used to model the relationship between the response of an experimental unit and the dose of a given substance. Of late, there has been an increased interest in dose-response relationships that exhibit hormetic effects. These effects may be characterized by an increase in response at low doses instead of the expected decrease in response that is observed at higher doses. Herein, we study the statistical implications of hormesis in several ways. First, we present a broad class of parametric mathematical-statistical models, constructed from standard dose-response models, that allow the incorporation of hormetic effects in such a way that the presence of hormesis can be tested statistically. Second, we consider the impact of model misspecification on effective dose estimation, such as the ED50 and the limiting dose for stimulation, when the hormetic effect is present but ignored in the dose-response model by the researcher (model underspecification) and when an hormetic effect is not present but incorporated into the dose-response model (model overspecification). Our simulation study reveals that it is more damaging to the estimation of effective dose to ignore the hormetic effect through model underspecification than to include the hormetic effect in the model through model overspecification. Third, we develop a nonpara-metric regression technique useful as an exploratory procedure to indicate hormetic effects when present. Finally, both parametric and nonparametric methods are illustrated with an example.     

Univariate Dose-Response Models in Case-Control Studies

For modelling dose-response relationships in case-control studies the multiplicative logistic regression model, assuming the relative risk to be an exponential function of the dose, is widely known. If the relative risk is assumed to be a linear function of the dose, several authors (see e.g. BERRY (1980)) have proposed an additive (linear) model. This model has a better fit with the data if such a linear relation holds. Confidence limits for the relative risk derived from the information matrix, however, appear to be rather inaccurate. Therefore, use of the ‘standard’ logistic model in two different ways was studied: extension with a quadratic term or a logarithmic transformation of the dose. By applying the methods both to an empirical data set and in a simulation experiment, it is shown that appropriate transformation (often logarithmic) of the dosage and then applying the ‘standard’ logistic model is an useful approach if a linear dose-response relationship holds.     

Comprehensive Realism's Weight-of-Evidence Based Distributional Dose-Response Characterization

Challenges to low-dose linearity and other default assumptions in cancer risk assessment and the limitations associated with NOAELs, LOAELs, and constant uncertainty factor values in the evaluation of noncancer health effects have stimulated the continued evolution of risk assessment methodologies. The increasing need for more realistic estimates of the dose-response relationship, better uncertainty characterization, and greater utilization of cost-benefit analyses have also contributed to this evolution. “Comprehensive Realism” is an emerging quantitative weight-of-evidence based risk assessment methodology for both cancer and noncancer health effects which utilizes probability distributions and decision analysis techniques to reflect more of the relevant human exposure data, more of the available and pertinent human and animal dose-response data, and the current state of knowledge about the relative plausibility of alternative dose-response analyses. A tree (like a decision tree and a probability tree) is used to decompose the dose-response assessment into component factors, to provide a structure for explicitly considering multiple alternatives for each factor, and to explicitly incorporate the current state of knowledge about the relative plausibility of these alternatives. Groundbreaking work has demonstrated the feasibility of weight-of-evidence based distributional characterizations, and provided initial examples. Computer software implementations are also available.     

U-Shaped Dose-Response Relationships for Mutation and Cancer

A biologically based mutation model that can be parameterized to reflect U-shaped behavior at low doses of genotoxic substances is derived. The U-shaped behavior results from an efficient, adaptive DNA repair process, by which some endogenous DNA damage that would not be repaired in the absence of the genotoxic substance is repaired when low levels of the substance are present. Hence, the model embodies a type of hormesis. The dose response is U shaped even though the genotoxic mechanism is additive to an existing background mutation process. The risk-assessment implications regarding possible hormetic effects, instead of the generally expected low-dose-linear effects, for agents that are both genotoxic and additive to background are discussed.     

Towards the Development of a Biologically based Dose-Response Model of Lead Neurotoxicity

Biologically-based dose-response (BBDR) paradigms incorporatemechanistic toxicological data in the derivation of quantitativemodels to estimate risk. Developmental lead (Pb) exposure hasbeen long associated with deficits in intellectual ability.To date, direct estimates of toxicant-induced functional alterationsin brain that may underlie cognition have been lacking, obviatingthe utilization of quantitative modeling for toxicological endpointsof higher brain function. The utility of the long-term potentiation(LTP) model of synaptic plasticity in the context of Pb-inducedcognitive deficits is explored in the present paper. In reviewingphysiological and biochemical requirements of LTP that may overlapwith cellular mechanisms of Pb toxicity, a neurobiological schemais constructed upon which we can begin to explore the possibilityof applying BBDR models in neurotoxicology.     

Graphical Methods for Analysing Combination Effects in Dose-Response Experiments

An organbath experiment with bovine tracheal muscle strips with cumulative increases in concentrations of a substance A in the absence and presence of a fixed concentration of a second substance B is considered as an example for demonstrating graphical methods to analyse drug combination effects. The response of each strip is individually described and estimated by a nonlinear dose response curve. From the curves of the combined action theoretical curves of substance A are derived, which were expected if the combination effect was simple similar or independent, respectively. The first graphical method consists in comparing the derived curves for substance A with the curves for substance A directly fitted. It is cheeked by eye if the group of derived curves can clearly be distinguished from the group of directly fitted curves. The second graphical method differs from the first method in so far, as not the curves are visualized but the parameter vectors corresponding to them. In contrast to widely used analytical methods the proposed graphical methods allow to treat individual instead of averaged dose response relationships. The methods can help to decide if the combination effect may be considered as independent, simple similar or none of both.     

Development and Validation of Dose-Response Relationship for Listeria monocytogenes

Listeria monocytogenes is a foodborne pathogen internationally and in the U.S. The objective of this work was to develop and validate a dose-response model for infection by this organism. Only animal data was available in the literature. The beta-Poisson dose response model provided good fit to the data, and one of the two data sets was found to be concordant with attack rates noted in human outbreaks. There are differences, however, between the dose-response relationship and endemic illness rates computed from market basket surveys of the prevalence of L. monocytogenes. Further work to elucidate the bases for this difference is necessary.     

Dose-Response Relationships in an Olfactory Flux Detector Model Revisited

Chemical Senses,     

Dose-Response Envelope for Escherichia coli O157:H7

Escherichia coli O157:H7 is an emerging food and waterborne pathogen in the U.S. and internationally. The objective of this work was to develop a dose-response model for illness by this organism that bounds the uncertainty in the dose-response relationship. No human clinical trial data are available for E. coli O157:H7, but such data are available for two surrogate pathogens: enteropathogenic E. coli (EPEC) and Shigella dysenteriae. E. coli O157:H7 outbreak data provide an initial estimate of the most likely value of the dose-response relationship within the bounds of an envelope defined by beta-Poisson dose-response models fit to the EPEC and S. dysenteriae data. The most likely value of the median effective dose for E. coli O157:H7 is estimated to be approximately 190[emsp4 ]000 colony forming units (cfu). At a dose level of 100[emsp4 ]cfu, the median response predicted by the model is six percent.     

Dose-Response Relationship for Nicotine-Induced Up-Regulation of Rat Brain Nicotinic Receptors

Abstract: The chronic administration of nicotine to animals has been shown to result in an increase in brain nicotinic acetylcholine receptor (nAChR) density. It has been suggested that this agonist-induced receptor up-regulation is a consequence of long-term nAChR desensitization in vivo. In this study, the effects of different nicotine doses and administration schedules as well as the resulting blood and brain nicotine levels were determined to assess the effect of in vivo nicotine concentration on nAChR density in the brain. Rats with indwelling subcutaneous cannulas were infused for 10 days with 0.6–4.8 mg/kg/day nicotine either 2×, 4×, or 8×/day or by constant infusion. The nAChR density in cortical, striatal, and hippocampal tissue measured by [³H]cytisine binding as well as the corresponding plasma and brain nicotine levels measured by GC analysis were determined. The results showed a dose-dependent increase in nAChR density with significant increases achieved at 2.4 mg/kg/day in all three brain areas. It is surprising that at this dose there was little difference between the constant infusion of nicotine and twice-daily administration, whereas more frequent periodic injections were actually less effective at up-regulating nAChRs. An analysis of the blood and brain levels of nicotine compared with the concentrations that produce nAChR desensitization suggests that in vivo desensitization alone is not sufficient for nAChR up-regulation to occur.     

Quantitative Models of the Dose-Response and Time Course of Inhalational Anthrax in Humans

Anthrax poses a community health risk due to accidental or intentional aerosol release. Reliable quantitative dose-response analyses are required to estimate the magnitude and timeline of potential consequences and the effect of public health intervention strategies under specific scenarios. Analyses of available data from exposures and infections of humans and non-human primates are often contradictory. We review existing quantitative inhalational anthrax dose-response models in light of criteria we propose for a model to be useful and defensible. To satisfy these criteria, we extend an existing mechanistic competing-risks model to create a novel Exposure–Infection–Symptomatic illness–Death (EISD) model and use experimental non-human primate data and human epidemiological data to optimize parameter values. The best fit to these data leads to estimates of a dose leading to infection in 50% of susceptible humans (ID₅₀) of 11,000 spores (95% confidence interval 7,200–17,000), ID₁₀ of 1,700 (1,100–2,600), and ID₁ of 160 (100–250). These estimates suggest that use of a threshold to human infection of 600 spores (as suggested in the literature) underestimates the infectivity of low doses, while an existing estimate of a 1% infection rate for a single spore overestimates low dose infectivity. We estimate the median time from exposure to onset of symptoms (incubation period) among untreated cases to be 9.9 days (7.7–13.1) for exposure to ID₅₀, 11.8 days (9.5–15.0) for ID₁₀, and 12.1 days (9.9–15.3) for ID₁. Our model is the first to provide incubation period estimates that are independently consistent with data from the largest known human outbreak. This model refines previous estimates of the distribution of early onset cases after a release and provides support for the recommended 60-day course of prophylactic antibiotic treatment for individuals exposed to low doses.     

Alanine Aminotransferase and Risk of the Metabolic Syndrome: A Linear Dose-Response Relationship

Background

Elevated baseline circulating alanine aminotransferase (ALT) level has been demonstrated to be associated with an increased risk of the metabolic syndrome (MetS), but the nature of the dose-response relationship is uncertain.

Methods

We performed a systematic review and meta-analysis of published prospective cohort studies to characterize in detail the nature of the dose-response relationship between baseline ALT level and risk of incident MetS in the general population. Relevant studies were identified in a literature search of MEDLINE, EMBASE, and Web of Science up to December 2013. Prospective studies in which investigators reported relative risks (RRs) of MetS for 3 or more categories of ALT levels were eligible. A potential nonlinear relationship between ALT levels and MetS was examined using restricted cubic splines.

Results

Of the 489 studies reviewed, relevant data were available on 29,815 non-overlapping participants comprising 2,125 incident MetS events from five prospective cohort studies. There was evidence of a linear association (P for nonlinearity = 0.38) between ALT level and risk of MetS, characterised by a graded increase in MetS risk at ALT levels 6–40 U/L. The risk of MetS increased by 14% for every 5 U/L increment in circulating ALT level (95% CI: 12–17%). Evidence was lacking of heterogeneity and publication bias among the contributing studies.

Conclusions

Baseline ALT level is associated with risk of the MetS in a linear dose-response manner. Studies are needed to determine whether the association represents a causal relationship.     

Unveiling Time in Dose-Response Models to Infer Host Susceptibility to Pathogens

The biological effects of interventions to control infectious diseases typically depend on the intensity of pathogen challenge. As much as the levels of natural pathogen circulation vary over time and geographical location, the development of invariant efficacy measures is of major importance, even if only indirectly inferrable. Here a method is introduced to assess host susceptibility to pathogens, and applied to a detailed dataset generated by challenging groups of insect hosts (Drosophila melanogaster) with a range of pathogen (Drosophila C Virus) doses and recording survival over time. The experiment was replicated for flies carrying the Wolbachia symbiont, which is known to reduce host susceptibility to viral infections. The entire dataset is fitted by a novel quantitative framework that significantly extends classical methods for microbial risk assessment and provides accurate distributions of symbiont-induced protection. More generally, our data-driven modeling procedure provides novel insights for study design and analyses to assess interventions.