Dose–response relationship from longitudinal data with response‐dependent dose modification using likelihood methods

In some clinical trials or clinical practice, the therapeutic agent is administered repeatedly, and doses are adjusted in each patient based on repeatedly measured continuous responses, to maintain the response levels in a target range. Because a lower dose tends to be selected for patients with a better outcome, simple summarizations may wrongly show a better outcome for the lower dose, producing an incorrect dose–response relationship. In this study, we consider the dose–response relationship under these situations. We show that maximum‐likelihood estimates are consistent without modeling the dose‐modification mechanisms when the selection of the dose as a time‐dependent covariate is based only on observed, but not on unobserved, responses, and measurements are generated based on administered doses. We confirmed this property by performing simulation studies under several dose‐modification mechanisms. We examined an autoregressive linear mixed effects model. The model represents profiles approaching each patient's asymptote when identical doses are repeatedly administered. The model takes into account the previous dose history and provides a dose–response relationship of the asymptote as a summary measure. We also examined a linear mixed effects model assuming all responses are measured at steady state. In the simulation studies, the estimates of both the models were unbiased under the dose modification based on observed responses, but biased under the dose modification based on unobserved responses. In conclusion, the maximum‐likelihood estimates of the dose–response relationship are consistent under the dose modification based only on observed responses.     

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.     

Dose responses for adaption to low doses of (60)Co gamma rays and (3)H beta particles in normal human fibroblasts

The dose response for adaption to radiation at low doses was compared in normal human fibroblasts (AG1522) exposed to either (60)Co gamma rays or (3)H beta particles. Cells were grown in culture to confluence and exposed at either 37 degrees C or 0 degrees C to (3)H beta-particle or (60)Co gamma-ray adapting doses ranging from 0.1 mGy to 500 mGy. These cells, and unexposed control cells, were allowed to adapt during a fixed 3-h, 37 degrees C incubation prior to a 4-Gy challenge dose of (60)Co gamma rays. Adaption was assessed by measuring micronucleus frequency in cytokinesis-blocked, binucleate cells. No adaption was detected in cells exposed to (60)Co gamma radiation at 37 degrees C after a dose of 0.1 mGy given at a low dose rate or to 500 mGy given at a high dose rate. However, low-dose-rate exposure (1-3 mGy/min) to any dose between 1 and 500 mGy from either radiation, delivered at either temperature, caused cells to adapt and reduced the micronucleus frequency that resulted from the subsequent 4-Gy exposure. Within this dose range, the magnitude of the reduction was the same, regardless of the dose or radiation type. These results demonstrate that doses as low as (on average) about one track per cell (1 mGy) produce the same maximum adaptive response as do doses that deposit many tracks per cell, and that the two radiations were not different in this regard. Exposure at a temperature where metabolic processes, including DNA repair, were inactive (0 degrees C) did not alter the result, indicating that the adaptive response is not sensitive to changes in the accumulation of DNA damage within this range. The results also show that the RBE for low doses of tritium beta-particle radiation is 1, using adaption as the end point.     

A Symmetric Extended Logistic Model with Applications to Experimental Toxicity Data

The fit of the logit and probit models for quantal response data can be improved by embedding these classical models within a richer parametric family indexed by one or two shape parameters. In this paper, a symmetric extended logistic model indexed by a shape parameter λ is discussed with application to dose response curves. The usual maximum likelihood method is employed to estimate the parameters of the model. The need to include the shape parameter λ is illustrated by analyzing a set of real experimental data and comparing the fit of the extended logistic model to those obtained by the standard logit and probit models.     

Hormetic effects of curcumin: What is the evidence?

Curcumin (diferuloylmethane), a component of the yellow powder prepared from the roots of Curcuma longa or Zingiberaceae (known as turmeric) is not only widely used to color and flavor food but also used as a pharmaceutical agent. Curcumin demonstrates anti-inflammatory, anticarcinogenic, antiaging, and antioxidant activity, as well as efficacy in wound healing. Notably, curcumin is a hormetic agent (hormetin), as it is stimulatory at low doses and inhibitory at high doses. Hormesis by curcumin could be also a particular function at low doses (i.e., antioxidant behavior) and another function at high dose (i.e., induction of autophagy and cell death). Recent findings suggest that curcumin exhibits biphasic dose–responses on cells, with low doses having stronger effects than high doses; examples being activation of the mitogen-activated protein kinase signaling pathway or antioxidant activity. This indicates that many effects induced by curcumin are dependent on dose and some effects might be greater at lower doses, indicative of a hormetic response. Despite the consistent occurrence of hormetic responses of curcumin in a wide range of biomedical models, epidemiological and clinical trials are needed to assess the nature of curcumin’s dose–response in humans. Fortunately, more than one hundred clinical trials with curcumin and curcumin derivatives are ongoing. In this review, we provide the first comprehensive analysis supportive of the hormetic behavior of curcumin and curcumin derivatives.     

Combining multiple comparisons and modeling techniques in dose-response studies

The analysis of data from dose-response studies has long been divided according to two major strategies: multiple comparison procedures and model-based approaches. Model-based approaches assume a functional relationship between the response and the dose, taken as a quantitative factor, according to a prespecified parametric model. The fitted model is then used to estimate an adequate dose to achieve a desired response but the validity of its conclusions will highly depend on the correct choice of the a priori unknown dose-response model. Multiple comparison procedures regard the dose as a qualitative factor and make very few, if any, assumptions about the underlying dose-response model. The primary goal is often to identify the minimum effective dose that is statistically significant and produces a relevant biological effect. One approach is to evaluate the significance of contrasts between different dose levels, while preserving the family-wise error rate. Such procedures are relatively robust but inference is confined to the selection of the target dose among the dose levels under investigation. We describe a unified strategy to the analysis of data from dose-response studies which combines multiple comparison and modeling techniques. We assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying dose-response curve, while preserving the family-wise error rate. The selected model is then used to provide inference on adequate doses.     

Dose-response model for Burkholderia pseudomallei (melioidosis)

Aims: The objective of this study was development of a dose–response model for exposure to Burkholderia pseudomallei in different animal hosts and analysis of the results. The data sets with which the model was developed were taken from the open literature. Methods and Results: All data sets were initially tested for a trend between dose and outcome using the Cochran–Armitage test. Only data showing a statistically significant trend were subjected to further analysis (fitting with parametric dose–response relationships). Dose–response relationships (exponential, beta-Poisson and log-probit) were fit to data using the method of maximum likelihood estimation. Conclusions: Dose–response analysis of BALB/c mice, C57BL/6 mice, guinea pigs and diabetic rats showed that BALB/c mice exposed intranasally (i.n.) and guinea pigs exposed intraperitoneally (i.p.) are significantly more sensitive to B. pseudomallei than C57BL/6 mice exposed i.n. and diabetic rats exposed i.p. Significance and Impact of the Study: The results confirmed the findings of a study of outbreak data that the diabetic population is more susceptible to infection with B. pseudomallei than the general population. The low dose prediction from best fit dose–response models can be used to draw guidelines for public health decision making processes, including consideration of sensitive subpopulations.     

Partial desiccation augments plant regeneration from irradiated embryogenic cultures of sugarcane

Partial desiccation treatment was applied to improve plant regeneration response in irradiated in vitro cultures. Embryogenic callus cultures of sugarcane cv. Co-671 were exposed to different doses of gamma radiation (0–80 Gy) and radiation effect was evaluated in terms of post-irradiation callus recovery, growth and regeneration of plants. Proliferative capacity of cultures was inversely correlated with radiation dose as the percentage surviving cultures or white proliferating clumps (WPC) decreased as the radiation dose increased up to 80 Gy. LD50 was found to be around 20–30 Gy and at higher doses, poor regeneration frequency was observed after 4–6 weeks of post-irradiation culture. To stimulate regeneration response, irradiated cultures were subjected to partial desiccation for 6 h and the treatment resulted in enhanced plant regeneration response. The study suggests that partial desiccation treatment can be useful in stimulating regeneration response of irradiated in vitro cultures.     

First principle-based models in plant suspension cell cultures: a review

In this work, the development and application of published models for describing the behavior of plant cell cultures is reviewed. The structure of each type of model is analyzed and the new tendencies for the modeling of biotechnological processes that can be applied in plant cell cultures are presented. This review is a tool for clarifying the main features that characterize each type of model in the field of plant cell cultures and can be used as a support on the selection of the more suitable model type, taking into account the purpose of specific research.     

The proliferative response of mouse jejunal crypt cells to radiation-induced cell depletion is not mediated exclusively by transforming growth factor alpha

Several lines of correlative evidence link transforming growth factor alpha (Tgfa, also known as TGF-alpha) to proliferative activity in jejunal crypt cells. It is therefore tempting to hypothesize that, as a ligand of the epidermal growth factor, it mediates the compensatory proliferative burst in the crypts after radiation-induced cell killing. We have tested this hypothesis by comparing the repopulation response of wild-type and Tgfa-null mice, using the microcolony assay. Mice were exposed whole-body to (137)Cs gamma rays at a dose of approximately 1.6 Gy/min. Single doses and equal doses separated by 4 and 54 h were given. The rightward shift of the dose-response curves for 54 h was identical for wild-type and Tgfa-null mice, and there was no indication of a difference in radiosensitivity. This result indicates that Tgfa is not an essential component of the proliferative response of tissue to radiation-induced cell killing.     

Statistical models for low dose exposure

Extrapolation of health risks from high to low doses has received a considerable amount of attention in carcinogenic risk assessment over decades. Fitting statistical dose-response models to experimental data collected at high doses and use of the fitted model for estimating effects at low doses lead to quite different risk predictions. Dissatisfaction with this procedure was formulated both by toxicologists who saw a deficit of biological knowledge in the models as well as by risk modelers who saw the need of mechanistically-based stochastic modeling. This contribution summarizes the present status of low dose modeling and the determination of the shape of dose-response curves. We will address the controversial issues of the appropriateness of threshold models, the estimation of no observed adverse effect levels (NOAEL), and their relevance for low dose modeling. We will distinguish between quantal dose-response models for tumor incidence and models of the more informative age/time dependent tumor incidence. The multistage model and the two-stage model of clonal expansion are considered as dose-response models accounting for biological mechanisms. Problems of the identifiability of mechanisms are addressed, the relation between administered dose and effective target dose is illustrated by examples, and the recently proposed Benchmark Dose concept for risk assessment is presented with its consequences for mechanistic modeling and statistical estimation.     

Characterization of the adaptive response to ionizing radiation induced by low doses of X rays to human lymphocytes

In previous studies we have shown that low doses of radiation from incorporated tritiated thymidine can make human lymphocytes less susceptible to the genetic damage manifested as chromatid breakage induced by a subsequent high dose of X rays. We have also shown that this adaptive response to ionizing radiation can be induced by very low doses of X rays (0.01 Gy; i.e., 1 rad) delivered during S phase of the cell cycle. To see if a low dose of X rays could induce this response in cells at other phases of the cell cycle, human lymphocytes were irradiated with 0.01 or 0.05 Gy before stimulation by phytohemagglutinin (G0) or with 0.01 Gy at various times after stimulation (G1), followed by 1.5 Gy (150 rad) at G2 phase. Although G0 lymphocytes failed to exhibit an adaptive response, G1 cells irradiated as early as 4 h after stimulation did show the response. Experiments were also carried out to determine how long the adaptive response induced by 0.01 Gy could persist. A 0.01-Gy dose was delivered to lymphocytes in the first S phase, followed by 1.5 Gy in the same or subsequent cell cycles. Lymphocytes receiving a 1.5-Gy dose at 40, 48, or 66 h after stimulation exhibited an adaptive response, whereas those receiving a 1.5-Gy dose at 90 or 114 h did not. Duplicate cultures containing bromodeoxyuridine showed that at 40 h all the lymphocytes were in their first cell cycle after stimulation, at 48 h half of the lymphocytes were in their first cell cycle and half in their second, and at 66 h 80% of the lymphocytes were in their third cell cycle. Thus the adaptive response persists for at least three cell cycles after it is induced by 0.01 Gy of X rays. In other experiments, the time necessary for maximal expression of the adaptive response was determined by delivering 0.01 Gy at hourly intervals 1-6 h before the 1.5-Gy dose. While a 4-h interval was enough for expression of the adaptive response, shorter intervals were not.     

Dose-response modeling of life shortening in a retrospective analysis of the combined data from the JANUS program at Argonne National Laboratory

Life shortening was investigated in both sexes of the B6CF1 (C57BL/6 x BALB/c) mouse exposed to fission neutrons and 60Co gamma rays. Three basic exposure patterns for both neutrons and gamma rays were compared: single exposures, 24 equal once-weekly exposures, and 60 equal once-weekly exposures. Ten different dose-response models were fitted to the data for animals exposed to neutrons. The response variable used for all dose-response modeling was mean after-survival. A simple linear model adequately described the response to neutrons for females and males at doses less than or equal to 80 cGy. At higher neutron dose levels a linear-quadratic equation was required to describe the life-shortening response. An effect of exposure pattern was observed prior to the detection of curvature in the dose response for neutrons and emerged as a potentially significant factor at neutron doses in the range of 40-60 cGy. Augmentation of neutron injury with dose protraction was observed in both sexes and began at doses as low as 60 cGy. The life-shortening response for all animals exposed to gamma rays (22-1918 cGy) was linear and inversely dependent upon the protraction period (1 day, 24 weeks, 60 weeks). Depending on the exposure pattern used for the gamma-ray baseline, relative biological effectiveness (RBE) values ranged from 6 to 43. Augmentation, because it occurred only at higher levels of neutron exposure, had no influence on the estimation of RBEm.     

Robust benchmark dose estimation using an infinite family of response functions

Researchers usually estimate benchmark dose (BMD) for dichotomous experimental data using a binomial model with a single response function. Several forms of response function have been proposed to fit dose–response models to estimate the BMD and the corresponding benchmark dose lower bound (BMDL). However, if the assumed response function is not correct, then the estimated BMD and BMDL from the fitted model may not be accurate. To account for model uncertainty, model averaging (MA) methods are proposed to estimate BMD averaging over a model space containing a finite number of standard models. Usual model averaging focuses on a pre-specified list of parametric models leading to pitfalls when none of the models in the list is the correct model. Here, an alternative which augments an initial list of parametric models with an infinite number of additional models having varying response functions has been proposed to estimate BMD for dichotomous response data. In addition, different methods for estimating BMDL based on the family of response functions are derived. The proposed approach is compared with MA in a simulation study and applied to a real dataset. Simulation studies are also conducted to compare the four methods of estimating BMDL.     

Flexible parametric measurement error models

Inferences in measurement error models can be sensitive to modeling assumptions. Specifically, if the model is incorrect, the estimates can be inconsistent. To reduce sensitivity to modeling assumptions and yet still retain the efficiency of parametric inference, we propose using flexible parametric models that can accommodate departures from standard parametric models. We use mixtures of normals for this purpose. We study two cases in detail: a linear errors-in-variables model and a change-point Berkson model.     

A two-stage stepwise estimation procedure

Summary .   This article proposes a two-stage simultaneous confidence procedure for the comparisons of k pairs of population means, without using multiplicity adjustment of more than two populations. The proposed procedure can be broadly applied to parametric or nonparametric models. It is robust and versatile because its derivation only utilizes a partitioning approach in conjunction with a bivariate adjustment, without any assumption on the underlying distribution. To elucidate the application, the proposed procedure is intertwined with the estimation of the therapeutic window of a drug. It provides confidence limits for the efficacy and the toxicity of the effective doses, highest ineffective dose, safe doses, and lowest unsafe dose, simultaneously. Such estimation information facilitates follow-up studies in clinical trials. As an illustrative example, the new procedure is applied to analyze a data set on molecular cancer therapeutics regarding the apoptotic killing effects of different chemical compounds on two leukemia cell lines.     

A Simulation-Assessment Modeling Approach for Analyzing Environmental Risks of Groundwater Contamination at Waste Landfill Sites

An integrated simulation-assessment modeling approach for analyzing environmental risks of groundwater contamination is proposed in this paper. It incorporates an analytical groundwater solute transport model, an exposure dose model, and a fuzzy risk assessment model within a general framework. The transport model is used for predicting contaminant concentrations in subsurface, and the exposure dose model is used for calculating contaminant ingestion during the exposure period under given exposure pathways. Both models are solved through the Monte Carlo simulation technique to reflect the associated uncertainties. Based on consideration of fuzzy relationships between exposure doses and cancer risks, risk levels of different exposure doses for each contaminant can be calculated to form a fuzzy relation matrix. The overall risks can then be quantified through further fuzzy synthesizing operations. Thus, probabilistic quantification of different risk levels (possibilities) can be realized. Results of the case study indicate that environmental risks at the waste landfill site can be effectively analyzed through the developed methodology. They are useful for supporting the related risk-management and remediation decisions.     

Effect of dexamethasone on human osteoblasts in culture: involvement of β1 integrin and integrin-linked kinase

Adhesive interactions play a critical role in cell biology, influencing vital processes from proliferation to cell death. Integrins regulate cell-ECM (extracellular matrix) adhesion and must associate with phosphorylating proteins such as ILK (integrin-linked kinase). Dysregulation of ILK expression is associated with anchorage-independent growth, cell survival and inhibition of apoptosis. Glucocorticoids influence differentiation and adhesion of osteoblasts and can affect bone protein synthesis. The objective of this study was to analyse the effect of DEX (dexamethasone) on the biology of osteoblasts, together with its influence on the expression of ILK and β1 integrin. For this, primary cultures of human osteoblasts were exposed to DEX at 10-9 M (physiological dose) and 10-6 M (pharmacological dose) for 24 and 48 h. Cell viability, apoptosis and cell adhesion were analysed, as well as protein expression of β1 integrin and ILK. It was observed that cell viability and adhesion were reduced in the cultures evaluated. In comparison with the control cultures, there was slightly less apoptosis in the cultures exposed to the physiological dose and considerably more apoptosis in those exposed to the pharmacological dose. In all treated cultures, protein expression of ILK was slightly higher than in the control cultures, whereas that of β1 integrin was significantly lower. Both proteins under study were co-localized at the cell periphery in all cultures. Our results suggest that DEX causes osteoblast anoikis, probably due to decreased β1 integrin expression, which might have had a direct influence upon ILK, reducing its activation and preventing it from playing its characteristic anti-apoptotic role.     

A semiparametric response surface model for assessing drug interaction

Summary .   When multiple drugs are administered simultaneously, investigators are often interested in assessing whether the drug combinations are synergistic, additive, or antagonistic. Existing response surface models are not adequate to capture the complex patterns of drug interactions. We propose a two-component semiparametric response surface model with a parametric function to describe the additive effect of a combination dose and a nonparametric function to capture the departure from the additive effect. The nonparametric function is estimated using the technique developed in thin plate splines, and the pointwise bootstrap confidence interval for this function is constructed. The proposed semiparametric model offers an effective way of formulating the additive effect while allowing the flexibility of modeling a departure from additivity. Example and simulations are given to illustrate that the proposed model provides an excellent estimation for different patterns of interactions between two drugs.