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.     

Comparison of planned and measured rectal dose in-vivo during high dose rate Cobalt-60 brachytherapy of cervical cancer

Cobalt-60 (Co-60) is a relatively new source for the application of high-dose rate (HDR) brachytherapy. Radiation dose to the rectum is often a limiting factor in achieving the full prescribed dose to the target during brachytherapy of cervical cancer. The aim of this study was to measure radiation doses to the rectum in-vivo during HDR Co-60 brachytherapy. A total of eleven HDR brachytherapy treatments of cervical cancer were recruited in this study. A series of diodes incorporated in a rectal probe was inserted into the patient's rectum during each brachytherapy procedure. Real-time measured rectal doses were compared to calculated doses by the treatment planning system (TPS). The differences between calculated and measured dose ranged from 8.5% to 41.2%. This corresponds to absolute dose differences ranging from 0.3 Gy to 1.5 Gy. A linear relationship was observed between calculated and measured doses with linear regression R² value of 0.88, indicating close association between the measured and calculated doses. In general, absorbed doses for the rectum as calculated by TPS were observed to be higher than the doses measured using the diode probe. In-vivo dosimetry is an important quality assurance method for HDR brachytherapy of cervical cancer. It provides information that can contribute to the reduction of errors and discrepancies in dose delivery. Our study has shown that in-vivo dosimetry is feasible and can be performed to estimate the dose to the rectum during HDR brachytherapy using Co-60.     

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.     

Designs for phase I clinical trials with multiple courses of subjects at different doses

Summary .   The goal of this article is to provide a new design framework and its corresponding estimation for phase I trials. Existing phase I designs assign each subject to one dose level based on responses from previous subjects. Yet it is possible that subjects with neither toxicity nor efficacy responses can be treated at higher dose levels, and their subsequent responses to higher doses will provide more information. In addition, for some trials, it might be possible to obtain multiple responses (repeated measures) from a subject at different dose levels. In this article, a nonparametric estimation method is developed for such studies. We also explore how the designs of multiple doses per subject can be implemented to improve design efficiency. The gain of efficiency from "single dose per subject" to "multiple doses per subject" is evaluated for several scenarios. Our numerical study shows that using "multiple doses per subject" and the proposed estimation method together increases the efficiency substantially.     

A comparison of the predicted risks of developing osteosarcoma for dogs exposed to 238PuO2 based on average bone dose or endosteal cell dose.

Dose-response relationships observed in laboratory animals can be used to identify possible human risk factors and may also be used in a quantitative manner when human data are not available. This paper presents an analysis of the dose dependency of osteosarcoma incidence in beagle dogs given a single inhalation exposure to a monodisperse aerosol of 238PuO2. We were particularly interested in comparing the predicted risks that were based on average bone dose with those based on endosteal cell dose and in evaluating the advantages of using a more biologically relevant cell-specific dose in risk estimation. The endosteal cell dose was calculated using the method of Marshall et al. (Health Phys. 35, 91-101, 1978), as extended to account for exposure by inhalation. The relationship between dose and time to tumor was analyzed by the proportional hazards regression model. The probability of developing osteosarcoma was strongly dependent on dose for dogs receiving low doses, but this was not true for dogs receiving high doses. The predicted risk based on endosteal cell dose was not consistently higher or lower than the risk based on average bone dose at various times after exposure, because the relationship between these two doses was not linear with respect to time. Also, as a result of the nonlinear relationship between these two doses, the risk estimated based on endosteal cell dose would not be a fixed factor of that based on the average dose. Random errors in the measured initial lung burden had a relatively large impact on the predicted risk based on endosteal cell dose, and the difference between the estimated risk of developing osteosarcoma based on endosteal cell dose and that based on average bone dose is likely to be within the error margins of the estimated risks.     

Cancer risk estimates from the combined Japanese A-bomb and Hodgkin cohorts for doses relevant to radiotherapy

Most information on the dose–response of radiation-induced cancer is derived from data on the A-bomb survivors who were exposed to γ-rays and neutrons. Since, for radiation protection purposes, the dose span of main interest is between 0 and 1 Gy, the analysis of the A-bomb survivors is usually focused on this range. However, estimates of cancer risk for doses above 1 Gy are becoming more important for radiotherapy patients and for long-term manned missions in space research. Therefore in this work, emphasis is placed on doses relevant for radiotherapy with respect to radiation-induced solid cancer. The analysis of the A-bomb survivor’s data was extended by including two extra high-dose categories (4–6 Sv and 6–13 Sv) and by an attempted combination with cancer data on patients receiving radiotherapy for Hodgkin’s disease. In addition, since there are some recent indications for a high neutron dose contribution, the data were fitted separately for three different values for the relative biological effectiveness (RBE) of the neutrons (10, 35 and 100) and a variable RBE as a function of dose. The data were fitted using a linear, a linear-exponential and a plateau-dose–response relationship. Best agreement was found for the plateau model with a dose-varying RBE. It can be concluded that for doses above 1 Gy there is a tendency for a nonlinear dose–response curve. In addition, there is evidence of a neutron RBE greater than 10 for the A-bomb survivor data. Many problems and uncertainties are involved in combing these two datasets. However, since very little is currently known about the shape of dose–response relationships for radiation-induced cancer in the radiotherapy dose range, this approach could be regarded as a first attempt to acquire more information on this area. The work presented here also provides the first direct evidence that the bending over of the solid cancer excess risk dose response curve for the A-bomb survivors, generally observed above 2 Gy, is due to cell killing effects.     

Radiation Sterilization: Microbiological Findings from Subprocess Dose Treatment of Disposable Plastic Syringes

S ummary : Disposable plastic hypodermic syringes were taken weekly from commercial production, immediately prior to radiation sterilization, at each of 3 firms. They were irradiated at doses less than that used for sterilization, either with electrons or gamma rays, and tested for sterility. The relationship between the dose applied and the resulting proportion of syringes positive was similar for each firm. Amongst the organisms surviving subnormal process doses was a yeast of unusually high radiation resistance. The possibility of establishing a microbiological quality control procedure based on the routine use of a subprocess dose technique is discussed.     

Intracellular calcium fluxes in human platelets

Fluorescence changes and secretory responses have been measured on addition of various excitatory agonists to platelets loaded with the cytosolic Ca2+ probe, Quin 2 or with chlortetracycline as a probe for membrane-associated Ca2+. When extracellular [Ca2+] is decreased to less than 0.1 microM by addition of EGTA a linear correlation is observed between the extent of increase in cytosolic [Ca2+] and the extent of mobilisation of membrane-associated Ca2+ on stimulation by maximal doses of five excitatory agonists. A similar linear correlation between the increase in cytosolic [Ca2+] and the extent of ATP secretion is observed over the thrombin dose/response curve. Similar EC50 values are observed for ATP secretion, the increase in cytosolic [Ca2+] and the decrease in chlortetracycline fluorescence induced by thrombin. However, the decrease in chlortetracycline fluorescence shows a sigmoidal relationship with the increase in cytosolic [Ca2+] and a hyperbolic relationship with ATP secretion over this dose/response curve. Addition of prostaglandin D2 prior to thrombin causes parallel inhibition of the increase in cytosolic [Ca2+] and the decrease in chlortetracycline fluorescence induced by this agonist. However, addition of prostaglandin D2 after thrombin reverses the increase in cytosolic [Ca2+] induced by this agonist but fails to cause a similar reversal of the decrease in chlortetracycline fluorescence. The data provide further evidence supporting the proposal that chlortatracycline can be used as a probe to monitor mobilisation of membrane-associated Ca2+ but suggest that, in platelets stimulated in the effective absence of extracellular Ca2+, both Ca2+ mobilisation and Ca2+ removal can under some conditions involve sites which are not monitored by this probe.     

Testing strategy in phase 3 trials with multiple doses

In this paper, we consider multiplicity testing approaches mainly for phase 3 trials with two doses. We review a few available approaches and propose some new ones. The doses selected for phase 3 usually have the same or a similar efficacy profile, so they have some degree of consistency in efficacy. We review the Hochberg procedure, the Bonferroni procedure, and a few consistency‐adjusted procedures, and suggest new ones by applying the available procedures to the pooled dose and the high dose, the dose that is thought to be more efficacious between two doses. The reason behind the idea is that the pooled dose and the high dose are more consistent than the original two doses if the high dose is more efficacious than the low dose. We compare all approaches via simulations and recommend using a procedure combining 4A and the pooling approach. We also discuss briefly the testing strategy for trials with more than two doses.     

Bioactivity of adrenomedullin and proadrenomedullin N-terminal 20 peptide in man.

Although the biological effects of adrenomedullin (AM) and PAMP have been reported extensively in animal studies and from in-vitro experiments, relatively little information is available on responses to the hormone administered to man. This review summarizes data from the few studies carried out in man. In healthy volunteers, i.v. infusion of AM reduces arterial pressure, probably at a lower rate of administration than is required to elicit other responses. AM stimulates heart rate, cardiac output, plasma levels of cAMP, prolactin, norepinephrine and renin whilst inhibiting any concomitant response in plasma aldosterone. Little or no increase in urine volume or sodium excretion has been observed. Patients with essential hypertension differ only in showing a greater fall in arterial pressure and in the development of facial flushing and headache. In patients with heart failure or chronic renal failure, i.v. AM has similar effects to those seen in normal subjects but also induces a diuresis and natriuresis, depending on the dose administered. Infusion of AM into the brachial artery results in a dose-related increase in forearm and skin blood flow, more prominent and more dependent on endogenous nitric oxide in healthy volunteers than in patients with cardiac failure. When infused into a dorsal hand vein, AM partially reversed the venoconstrictor action of norepinephrine. Although much more information is required to clarify the role of AM under physiological and pathophysiological circumstances, it is clear that it has prominent hemodynamic and neurohormonal effects, though generally lesser urinary effects when administered short-term in doses sufficient to raise its levels in plasma to those seen in a number of clinical disorders. The only study of PAMP in man showed that its skeletal muscle vasodilator potency, when infused into the brachial artery of healthy volunteers, was less than one hundredth that of AM, and it was without effect on skin blood flow.     

Ramp work tests with three different beta-blockers in normal human subjects

The effects of beta-blockade on the responses of oxygen uptake (VO2), heart rate (HR) and blood lactate (La-) were examined during ramp cycle ergometer tests (50 W.min-1 ramp slope) in 8 healthy male volunteers. Each subject took placebo, or one of four different doses of three different beta-blockers (propranolol, metoprolol or oxprenolol) 2 h prior to each test for a total of 15 exercise tests. VO2 was measured breath-by-breath, HR was sampled once per breath, and La- was obtained every minute. Linear regression analysis was applied to VO2 and HR data to obtain the kinetic parameter total lag time (TLT) and a slope value. La- was analyzed by a continuous exponential model with the lactate slope index (LSI) being derived from the individual response curves. Submaximal exercise HR was significantly depressed at the baseline as well as during the ramp tests by beta-blockade. TLT for HR was significantly affected by beta-blockade, with a dose dependent shift from a placebo value of 16 to 26 s with placebo to a value of -40 to -60 s at the highest dose. Slope of HR was significantly depressed relative to placebo. VO2 kinetics assessed by TLT were not significantly affected by beta-blockade. This slope of the VO2 vs work rate relationship was significantly less than placebo only at the highest dose of beta-blocker. The LSI was not significantly affected by beta-blockade. In contrast with the clear impairment of HR response to exercise during beta-blockade, both the VO2 and La- responses appear to be relatively unaffected by beta-blockade during ramp exercise tests.(ABSTRACT TRUNCATED AT 250 WORDS)     

BMA‐Mod: A Bayesian model averaging strategy for determining dose‐response relationships in the presence of model uncertainty

Successful pharmaceutical drug development requires finding correct doses. The issues that conventional dose‐response analyses consider, namely whether responses are related to doses, which doses have responses differing from a control dose response, the functional form of a dose‐response relationship, and the dose(s) to carry forward, do not need to be addressed simultaneously. Determining if a dose‐response relationship exists, regardless of its functional form, and then identifying a range of doses to study further may be a more efficient strategy. This article describes a novel estimation‐focused Bayesian approach (BMA‐Mod) for carrying out the analyses when the actual dose‐response function is unknown. Realizations from Bayesian analyses of linear, generalized linear, and nonlinear regression models that may include random effects and covariates other than dose are optimally combined to produce distributions of important secondary quantities, including test‐control differences, predictive distributions of possible outcomes from future trials, and ranges of doses corresponding to target outcomes. The objective is similar to the objective of the hypothesis‐testing based MCP‐Mod approach, but provides more model and distributional flexibility and does not require testing hypotheses or adjusting for multiple comparisons. A number of examples illustrate the application of the method.     

Adaptive response for chromosomal inversions in pKZ1 mouse prostate induced by low doses of X radiation delivered after a high dose

Adaptive responses are induced by stress such as X radiation and result in a lower than expected biological response. Two-dose adaptive response experiments typically involve a low priming dose followed by a subsequent high radiation dose. Here, we used a sensitive in vivo chromosomal inversion assay to demonstrate for the first time an adaptive response when a low dose (0.01-1 mGy) was given several hours after a high 1000-mGy radiation dose. The adaptive responses in this study were of similar magnitude to the two-dose adaptive responses previously observed in this test system when the low dose was given first. A chromosomal inversion adaptive response was also induced by two 1000-mGy doses and when a 1-mGy dose was preceded or followed by a dose of 0.01 mGy, but not by two 4000-mGy doses. This is also the first example of an adaptive response when both doses are low. Our data agree with previous reports of an on-off mechanism of adaptive response. The induction of an adaptive response by a low dose after a high damaging dose provides evidence that the mechanisms underlying radiation adaptive responses are not due to prevention of damage induced by the high dose but to modulation of the cellular response to this damage.     

Dynamics of Cellular Responses to Radiation

Understanding the consequences of exposure to low dose ionizing radiation is an important public health concern. While the risk of low dose radiation has been estimated by extrapolation from data at higher doses according to the linear non-threshold model, it has become clear that cellular responses can be very different at low compared to high radiation doses. Important phenomena in this respect include radioadaptive responses as well as low-dose hyper-radiosensitivity (HRS) and increased radioresistance (IRR). With radioadaptive responses, low dose exposure can protect against subsequent challenges, and two mechanisms have been suggested: an intracellular mechanism, inducing cellular changes as a result of the priming radiation, and induction of a protected state by inter-cellular communication. We use mathematical models to examine the effect of these mechanisms on cellular responses to low dose radiation. We find that the intracellular mechanism can account for the occurrence of radioadaptive responses. Interestingly, the same mechanism can also explain the existence of the HRS and IRR phenomena, and successfully describe experimentally observed dose-response relationships for a variety of cell types. This indicates that different, seemingly unrelated, low dose phenomena might be connected and driven by common core processes. With respect to the inter-cellular communication mechanism, we find that it can also account for the occurrence of radioadaptive responses, indicating redundancy in this respect. The model, however, also suggests that the communication mechanism can be vital for the long term survival of cell populations that are continuously exposed to relatively low levels of radiation, which cannot be achieved with the intracellular mechanism in our model. Experimental tests to address our model predictions are proposed.     

A Bayesian decision-theoretic approach to incorporate preclinical information into phase I oncology trials

Leveraging preclinical animal data for a phase I oncology trial is appealing yet challenging. In this paper, we use animal data to improve decision-making in a model-based dose-escalation procedure. We make a proposal for how to measure and address a prior-data conflict in a sequential study with a small sample size. Animal data are incorporated via a robust two-component mixture prior for the parameters of the human dose–toxicity relationship. The weights placed on each component of the prior are chosen empirically and updated dynamically as the trial progresses and more data accrue. After completion of each cohort, we use a Bayesian decision-theoretic approach to evaluate the predictive utility of the animal data for the observed human toxicity outcomes, reflecting the degree of agreement between dose–toxicity relationships in animals and humans. The proposed methodology is illustrated through several data examples and an extensive simulation study.     

Effects of angiotensin II on pressor responses to norepinephrine in humans

In previous studies in the conscious rabbit and in isolated artery preparations, low doses of angiotensin II synergistically amplified the pressor effects of the sympathetic neurotransmitter, norepinephrine (NE). To determine whether these observations could be replicated in humans, 9 normal adult male volunteers (mean age: 34) each were given 3 i.v. doses of NE (25, 50 and 100 micrograms.kg-1.min-1) during consecutive 10 min infusion periods. On a second study day, the procedure was repeated during infusion of angiotensin II in a subpressor dose (1.25 ng.kg-1.min-1). The angiotensin II didn't alter the BP responses to NE, but it attenuated the heart rate (HR) decreases associated with the NE infusions by 80% (P less than 0.05), 42% (P less than 0.05) and 42% (P less than 0.1). The two study days were then repeated following 2 weeks of oral treatment with the angiotensin converting enzyme inhibitor captopril (which, despite significantly decreasing baseline BP, also tended to decrease HR). In the presence of captopril, the pressor responses to the NE challenges were reduced by 50% (P less than 0.05), 33% (P less than 0.05) and 13% (P less than 0.1) compared with the pre-captopril responses. Thus, angiotensin II in subpressor doses appears to enhance NE pressor effects by attenuating the compensatory HR responses, whereas inhibition of endogenous angiotensin II mechanisms weakens the BP-raising actions of NE. These findings in humans are consistent with earlier observations that the renin-angiotensin system can directly amplify sympathetic pressor effects in two separate ways: by modifying baroreceptor sensitivity and by enhancing the actions of norepinephrine on vascular smooth muscle.     

Simplified Bayesian method: application in cytogenetic biological dosimetry of mixed n + γ radiation fields

This article describes the application of a simplified Bayesian method for estimation of doses from a mixed field using cytogenetic biological dosimetry, taking as an example neutron and gamma radiation emitted from the MARIA nuclear research reactor in Poland. The Bayesian approach is a good alternative to the commonly used iterative method, which allows separate dose estimation. In the present paper, a computer program, which uses the iterative and simplified Bayesian methods to calculate mixed radiation doses, is introduced.

     

Retention pharmacokinetic and pharmacodynamic parameter relationships of antihistamine drugs using biopartitioning micellar chromatography

Antihistamines are drugs which act by competitive inhibition of the H₁ or H₂ histamine receptors. Little has been known about their clinical pharmacokinetics and biological responses until the last few years. In this paper, we propose quantitative retention–activity relationship, QRAR, models based on the retention data of antihistamines in a biopartitioning micellar chromatography (BMC) system using a Brij35 mobile phase for describing pharmacokinetic parameters such as half-life and volume of distribution, or the pharmacodynamic parameters, therapeutic plasma levels, lethal doses and drug-receptor dissociation constant. The predictive ability of these models is statistically validated. These results are compared to traditional quantitative structure–activity relationship, QSAR, models using lipophilicity data. The adequacy of QRAR models can be explained taking into account the fact that the retention of compounds in BMC depends on their hydrophobic, electronic and steric characteristics which are of great importance in pharmacokinetic and pharmacodynamic behavior.     

Errors-in-variables in joint population pharmacokinetic/pharmacodynamic modeling

Pharmacokinetic (PK) models describe the relationship between the administered dose and the concentration of drug (and/or metabolite) in the blood as a function of time. Pharmacodynamic (PD) models describe the relationship between the concentration in the blood (or the dose) and the biologic response. Population PK/PD studies aim to determine the sources of variability in the observed concentrations/responses across groups of individuals. In this article, we consider the joint modeling of PK/PD data. The natural approach is to specify a joint model in which the concentration and response data are simultaneously modeled. Unfortunately, this approach may not be optimal if, due to sparsity of concentration data, an overly simple PK model is specified. As an alternative, we propose an errors-in-variables approach in which the observed-concentration data are assumed to be measured with error without reference to a specific PK model. We give an example of an analysis of PK/PD data obtained following administration of an anticoagulant drug. The study was originally carried out in order to make dosage recommendations. The prior for the distribution of the true concentrations, which may incorporate an individual's covariate information, is derived as a predictive distribution from an earlier study. The errors-in-variables approach is compared with the joint modeling approach and more naive methods in which the observed concentrations, or the separately modeled concentrations, are substituted into the response model. Throughout, a Bayesian approach is taken with implementation via Markov chain Monte Carlo methods.     

Genotoxicity of neutrons in Drosophila melanogaster. Somatic mutation and recombination induced by reactor neutrons

This paper describes the observation of a direct relationship between the absorbed doses of neutrons and the frequencies of somatic mutation and recombination using the wing somatic mutation and recombination test (SMART) of Drosophila melanogaster. This test was used for evaluating the biological effects induced by neutrons from the Triga Mark III reactor of Mexico. Two different reactor power levels were used, 300 and 1000 kW, and two absorbed doses were tested for each power level: 1.6 and 3.2 Gy for 300 kW and 0.84 and 1.7 Gy for 1000 kW. A linear relationship was observed between the absorbed dose and the somatic mutation and recombination frequencies. Furthermore, these frequencies were dependent on larval age: In 96-h-old larvae, the frequencies were increased considerably but the sizes of the spots were smaller than in 72-h-old larvae. The analysis of the balancer-heterozygous progeny showed a linear absorbed dose- response relationship, although the responses were clearly lower than found in the marker-trans-heterozygous flies. Approximately 65% of the genotoxicity observed is due to recombinational events. The results of the study indicate that thermal and fast neutrons are both mutagenic and recombinagenic in the D. melanogaster wing SMART, and that the frequencies are dependent on neutron dose, reactor power, and the age of the treated larvae.