Evaluation of experimental combined toxicity by use of dose-frequency curves: comparison with theoretical additivity as well as independence

Dose-frequency curves of toxic effects of a substance A were evaluated in the absence and in the presence of a fixed dose of a second substance B. Data were fitted by the curve-fitting program ALLFIT. Observed combined frequencies of A + B were compared statistically with the expected frequencies of additivity and (or) independence by the phi 2-square goodness-of-fit test. The theoretical dose-frequency curves expected for an additive response were obtained by a solely graphical procedure and the theoretical curves for independent effects were calculated from the effects of B and A at certain doses. In rotarod tests with trained mice, the combined deteriorating effect of ethanol and benzodiazepines were significantly over-additive. However, their lethal interaction appeared underadditive in mice. The lethal underadditive interaction of ethanol and phencyclidine (PCP) can be ascribed largely to independent actions of these compounds. Loss of righting reflex was additively enhanced by PCP, whereas PCP overadditively enhanced the effect of ethanol. The insecticidal action of the cholinesterase inhibitors malathion and parathion appeared additive and significantly different from independent interaction. A comparison of results from dose-response curves with isoboles showed good agreement. The method appears as an attractive alternative or as a complementary procedure to the isobolographic analysis. Combination experiments as described can be carried out and evaluated rather simply, with a minimum of expenditure and a maximum of information.     

Phase-Lifetime Spectroscopy of Photocycle Processes: Kinetic Analysis of Amplitude Dispersion Curves

Phase-lifetime spectroscopy has been recently used to obtain kinetic information on biological photocycles. A simple, general method is presented for deriving the amplitude response function for light-driven processes. These amplitude response functions may be used to analyze the experimental data obtained when driving the photosystem with a mechanically chopped, actinic light source. This analysis allows a comparison of kinetic parameters obtained from modulation methods with those obtained by flash techniques. Typically the experimental data consist of the signal amplitude measured at several chopping frequencies of the actinic light. These amplitude dispersion curves will be dependent on the harmonic sensitivity of the phase-sensitive detector used to measure the signal. This harmonic sensitivity is taken into account by performing a Fourier decomposition on the amplitude response function of the system and weighting each harmonic in a fashion appropriate for the specific amplifier under consideration. The resulting response function obtained for two commonly used amplifiers is derived. In addition to simple photocycles, the analysis of photocycle-coupled processes is also considered. This second relaxation process, which is coupled to a photocycle process, could represent the chemiosmotic coupling of a light-driven ion pump to a second ion transport protein. Conditions are established in which the kinetics of the second process can be resolved from the photocycle process.     

A Review and Comparison of Methods for Recreating Individual Patient Data from Published Kaplan-Meier Survival Curves for Economic Evaluations: A Simulation Study

Background

In general, the individual patient-level data (IPD) collected in clinical trials are not available to independent researchers to conduct economic evaluations; researchers only have access to published survival curves and summary statistics. Thus, methods that use published survival curves and summary statistics to reproduce statistics for economic evaluations are essential. Four methods have been identified: two traditional methods 1) least squares method, 2) graphical method; and two recently proposed methods by 3) Hoyle and Henley, 4) Guyot et al. The four methods were first individually reviewed and subsequently assessed regarding their abilities to estimate mean survival through a simulation study.

Methods

A number of different scenarios were developed that comprised combinations of various sample sizes, censoring rates and parametric survival distributions. One thousand simulated survival datasets were generated for each scenario, and all methods were applied to actual IPD. The uncertainty in the estimate of mean survival time was also captured.

Results

All methods provided accurate estimates of the mean survival time when the sample size was 500 and a Weibull distribution was used. When the sample size was 100 and the Weibull distribution was used, the Guyot et al. method was almost as accurate as the Hoyle and Henley method; however, more biases were identified in the traditional methods. When a lognormal distribution was used, the Guyot et al. method generated noticeably less bias and a more accurate uncertainty compared with the Hoyle and Henley method.

Conclusions

The traditional methods should not be preferred because of their remarkable overestimation. When the Weibull distribution was used for a fitted model, the Guyot et al. method was almost as accurate as the Hoyle and Henley method. However, if the lognormal distribution was used, the Guyot et al. method was less biased compared with the Hoyle and Henley method.     

Estimation of food consumption from field observations of fish feeding cycles

The available methods of estimating food consumption by fish require that experiments be performed on confined animals and that experimental results may be validly applied to free fish. A method is described by which food consumption in periodically feeding fish may be estimated without performing laboratory experiments. A relatively simple input–output model of stomach contents is fitted to the observed time trajectory of stomach fullness, and food consumption is calculated from the estimated model parameters. Feeding is considered to be restricted to a distinct feeding period, and the rate of feeding during that period can be either constant or linearly decreased with the quantity of food already present in the stomach.
The method is applied to three examples. The model appears robust, and generally provides very similar food consumption estimates to those obtained from methods requiring an independent estimate of gastric evacuation rate. However, the described method is sensitive to violation of the assumption that feeding occurs only during a discrete feeding period.     

Analysis of entrainment of circadian oscillators by skeleton photoperiods using phase transition curves

A skeleton photoperiod consists of two short pulses which are applied on the circadian oscillator at times corresponding to the beginning and to the end of a continuous light stimulus. To study several problems in entrainment of circadian rhythms by skeleton photoperiods, we develop a simple diagrammatic solution of the steady state entrainment making use of phase transition curves which are directly gotten from phase response curves. The graphical method is simple and systematic to study entrainment by light cycles with various day lengths. As the method is also intuitive, we can easily examine three problems. (1) In Drosophila the phase relation (ψ) between rhythm and light cycle is a continuous function of day length of skeleton photoperiods up to about 12 h, but a marked discontinuity (ψ-jump) sets in between 13 and 14h. By the diagrammatic method we find that ψ-jump is mathematically a bifurcation phenomenon. (2) The action of photoperiods up to about 12 h is fully simulated by two 15-min skeleton pulses. Do 3-min skeleton pulses imitate the complete photoperiods? We find that pulse width is arbitrary to some extent. (3) Why skeleton photoperiods up to about 12 h are good models of complete photoperiods? The reason is the small amplitude and the nearly symmetrical form of phase response curves in the subjective day.     

A method of DNA histogram analysis by computer and its evaluation by simultaneous combination with 3H-thymidine autoradiography

A method for determining the fractions of cells in the G1, S, and G2 + M phases of the cell life cycle, by quantifying DNA histograms derived from static fluorescence cytophotometry, was evaluated by simultaneous combination with 3H-thymidine autoradiography. DNA histograms were obtained by cytofluorometry on the Feulgen-stained autoradiographs of HeLa cells, and mouse and rat hepatocytes, after DNA labelling with 3H-thymidine. The synthetic histogram determined by "sum of discrete normal curves" technique was fitted to the experimental data according to a weighted least-squares method by a desk-top computer (HP 85F). The mean relative percent deviations of estimated cell cycle phase fractions from the actual phase fractions determined directly on an autoradiograph was 6.6 +/- 3.3%.     

Direct and Model Free Calculation of Force-Dependent Dissociation Rates from Force Spectroscopic Data

Force spectroscopy allows testing the free energy landscapes of molecular interactions. Usually, the dependency of the most probable rupture force on the force rate or the shape of the rupture force histogram is fitted with different models that contain approximations and basic assumptions. We present a simple and model free approach to extract the force-dependent dissociation rates directly from the force curve data. Simulations show that the dissociation rates at any force are given directly by the ratio of the number of detected rupture events to the time this force was acting on the bond. To calculate these total times of acting forces, all force curve data points of all curves measured are taken into account, which significantly increases the amount of information which is considered for data analysis compared to other methods. Moreover, by providing force-dependent dissociation rates this method allows direct testing and validating of any energy landscape model.     

Lung tumour induction in mice after X-rays and neutrons

Dose-response curves were determined for pulmonary adenomas and adenocarcinomas in mice after single acute doses of 200 kVp X-rays and cyclotron neutrons (E = 7.5 MeV). A serial-killing experiment established that the radiation induces the tumours and does not merely accelerate the appearance of spontanoeus cancers [corrected]. The dose versus incidence (I) of tumours in male and female mice for X-ray doses between 0.25 and 7.5 Gy is 'bell-shaped' and best fitted with a purely quadratic induction and exponential inactivation terms, i.e. I = A + BD2e-alpha D. In contrast, the tumour dose-response after 0.1-4.0 Gy of neutrons is best fitted by I = A + BDe-alpha D and is steeply linear less than or equal to 1 Gy, peaks between 1 and 3 Gy and sharply declines at 4.0 Gy. The data for the female mice less than or equal to 1 Gy neutrons are best fitted to the square root of the dose. A major objective of the experiments was to derive neutron RBE values. Because of the differences between the X-ray (quadratic) and neutron (linear) curves, the RBEn will vary inversely with decreasing X-ray dose. The RBE values at 1 Gy of X-rays derived from the B coefficients in the above equations are 7.4 +/- 3.2 (male and female); 8.6 +/- 3.6 (female) and 4.7 +/- 1.8 (male). These are high values and imply even higher values at the doses of interest to radiation protection. If, however, one restricts the analysis to the initial, induction side of the response (less than or equal to 1 Gy neutrons, less than or equal to 3 Gy X-rays) then good linear fits are obtainable for both radiations and indicate neutron RBE values of 7.4 +/- 2.3 for female mice and 4.5 +/- 1.8 for males, and these are independent of dose level.     

A comparison of methods for estimating the kinetic parameters of two simple types of transport process

Sets of experimental data, with known characteristics and error structures, have been simulated for the Michaelis-Menten equation plus a second term, either for linear transport or for competitive inhibition. The Michaelis-Menten equation plus linear term was fitted by several methods and the accuracy and the precision of the parameter estimates from the several methods were compared. The model-fitting methods were: three for least-squares non-linear regression, computer versions of two graphical methods and of two non-parametric methods. The most precise and accurate method was that of D.W. Marquardt (J. Soc. Ind. Appl. Math. 11 (1963) 431–441). The Michaelis-Menten equation with competitive inhibition was also fitted by several methods, viz., two for least-squared non-linear regression, a non-parametric method and four variants of the Preston-Schaeffer-Curran plot (Preston, R.L. et al. (1974) J. Gen. Physiol. 64, 443–467). The most precise and accurate of these was the non-linear regression method of W.W. Cleland (Adv. Enzymol. 29 (1967) 1–32). For both these models, the various graphical methods and non-parametric methods gave poor results and are not recommended.     

Analysis of the circular dichroism spectrum of proteins using the convex constraint algorithm: a practical guide.

Due to the time scale of circular dichroism (CD) measurements, it is theoretically possible to deconvolute such a spectrum if the pure CD spectra differ significantly from one another. In the last decade several methods have been published aiming at obtaining the conformational weights, or percentages (which are the coefficients for a linear combination) of the so-called typical secondary structural elements making up the three-dimensional structure of proteins. Two methods that can be used to determine the secondary structures of proteins are described here. The first method, called LINCOMB, is a simple algorithm based on a least-squares fit with a set of reference spectra representing the known secondary structures and yielding an estimation of weights attributed to alpha-helix, beta-pleated sheet (mainly antiparallel), beta-turns, unordered form, and aromatic/disulfide (or nonpeptide) contributions of the protein being analyzed. This method requires a "template" or reference curve set, which was obtained from the second method. The second method, "convex constraint analysis," is a general deconvolution method for a CD spectra set of any variety of conformational type. The algorithm, based on a set of three constraints, is able to deconvolute a set of CD curves to its common "pure"-component curves and conformational weights. To analyze a single CD spectrum with this method, the spectrum is appended to the data set used as a reference data set. As a way to determine the reliability of the algorithm and provide a guideline to its usage, some applications are presented.     

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.     

Molecular mechanisms of radiation carcinogenesis and the linear, non-threshold dose response model of radiation risk estimation

Recent research in molecular radiation carcinogenesis is reviewed with the specific aim of exploring the implications this research may have on the dose response relationship of radiation-induced cancer at low doses and low dose rates. It is concluded that the linear non-threshold dose response hypothesis may be used in radiation protection planning as a simple, convenient method to optimize procedures and regulations, but should not be mistaken as a stringent scientific conclusion directly derived from the present state of knowledge of the processes involved in radiation carcinogenesis.     

Peak drug levels in linear pharmacokinetic systems—I. Effect of rate of injection

This paper presents three theorems on the peak drug levels that result from injection into a linear pharmacokinetic system. As a preliminary, the “rate of injection” is defined in terms of time expansion or time contraction of the injection function (input). The first theorem then states that the peak drug level will not be greater when the rate of injection is slow than when it is fast, if the impulse response is unimodal. The second theorem sets limits for the time of the maximum drug level, in relation to the time of the maximum of the (unimodal) impulse response and the duration of the input. The third theorem defines conditions which assure a definitely lower peak drug level if the rate of injection is slower. A graphical method is suggested for determining the times and magnitudes of the peak drug levels that result from constant infusions of a fixed dose at different rates. An example is provided to show that if the impulse response is multimodal then the peak drug level may sometimes increase with a decrease in the injection rate. Supported in part by U.S. Public Health Service Research Grant GM 21269 from the National Institute of General Medical Sciences, and in part by Biomedical Research Support Grant S07 RR 05392 from the National Institutes of Health. A portion of this work was presented at the Annual Meeting of the Society for Mathematical Biology at the Medical School of the University of Pennsylvania, Philadelphia, August 1976.     

Dose response in neutral filter elution

In neutral filter elution a nonlinear relationship between fraction of eluted DNA and dose is usually observed, which is often interpreted as a nonlinear induction of DNA double-strand breaks (DSBs) with dose. The conclusiveness of this hypothesis is questioned here on the basis of theoretical considerations regarding the size distribution of DNA fragments. A simple hydrodynamic model is proposed which generates the typical features of the dose response of neutral filter elution: (1) the shoulder at low doses, (2) a quasilinear correlation in an intermediate dose range, (3) a saturation at high doses, and (4) a linearization of the curve in the intermediate and higher dose range in a semilogarithmic plot. These features were derived even with the assumption of a linear induction of DSBs with dose. Thus it is demonstrated that the fraction of eluted DNA could conceivably be a nonlinear function of dose even if the induction of DSBs is directly proportional to the radiation dose.     

Generalization of the variance-covariance method for microdosimetric measurements

The variance method of microdosimetric measurements and its extension, the variance-covariance method, permit the determination of an essential parameter of radiation quality, the dose mean event size,y _d. The methods have — among other advantages — the feature that they permit measurements for smaller simulated sites than the conventional single-event technique. It is, therefore, desirable to employ them also for the determination of further moments of the distribution ofy. The formulae for the first three moments are here derived both for the case of constant dose rate and of fluctuating dose rates. A second article will use the same mathematical approach to deduce formulae that remain valid even if there are slow changes of the ratio of dose rates in the two detectors for the variance-covariance method. A third article will explore — in terms of microdosimetric data — the applicability of the formulae.     

Tests for profile analysis of paired curves based on friedman ranking methods

Two nonparametric tests are proposed for the comparison of a paired sample of response curves with T congruent time points. The first procedure rank transforms each curve and tests the homogeneity of the resulting pair of averaged rank vectors. The second procedure rank transforms each pair of curves and tests the homogeneity of the related pair of averaged rank vectors. The first test detects only pure interactions; the second test checks if any difference exists between the rank curves. Both tests are presented in finite and asymptotic as well as in combined (by T singular tests) and multivariate form.     

A Markov chain model for animal estrous cycling data

Estrous cycling data contain sequences of characters (e.g., DPEMD). Each sequence represents an animal's estrous cycle, with each character indicating the daily estrous cycle stage. Changes in the estrous cycle pattern, which is determined by estrous stage lengths, can provide information on adverse events. Stage lengths are not directly observable. However interval censored lengths for all but the first and the last stages in a sequence can be extracted from the data. We propose a Markov chain model to approximate the estrous cycling process. The transition probabilities from one stage to another can be derived by conditioning on stage lengths. Assuming Weibull distribution for stage lengths, with the second Weibull parameter depending upon treatment effects and animal-specific random effects, regression models on censored stage lengths are fitted. A Bayesian approach is used for inference on dose effects. The analysis is implemented with MCMC method in WinBUGS. An estrous cycling data set from a National Toxicology Program study is analyzed as an example.     

Estimates of mean alveolar PCO2 during steady-state exercise in man: a theoretical study.

The partial pressure of carbon dioxide in arterial blood is an important operator in the control of breathing, by actions on peripheral and central chemoreceptors. In experiments on man we must often assume that lung alveolar PCO2 equals arterial PCO2 and obtain estimates of the former derived from measurements in expired gas sampled at the mouth. This paper explores the potential errors of such estimates, which are magnified during exercise. We used a published model of the cardiopulmonary system to simulate various levels of exercise up to 300 W. We tested three methods of estimating mean alveolar PCO2 (PACO2) against the true value derived from a time average of the within-breath oscillation in steady-state exercise. We used both sinusoidal and square-wave ventilatory flow wave forms. Over the range 33-133 W end-tidal PCO2 (P(et)CO2) overestimated PACO2 progressively with increasing workload, by about 4 mmHg at 133 W with normal respiratory rate for that load. PCO2 by a graphical approximation technique (PgCO2; "graphical method") underestimated PACO2 by 1-2 mmHg. PCO2 from an experimentally obtained empirical equation (PnjCO2; "empirical method") overestimated PACO2 by 0.5-1.0 mmHg. Graphical and empirical methods were insensitive to alterations in cardiac output or respiratory rate. End-tidal PCO2 was markedly affected by respiratory rate during exercise, the overestimate of PACO2 increasing if respiratory rate was slowed. An increase in anatomical dead space with exercise tends to decrease the error in P(et)CO2 and increase the error in the graphical method. Changes in the proportion of each breath taken up by inspiration make no important difference, and changes in functional residual capacity, while important in principle, are too small to have any major effect on the estimates. Changes in overall alveolar ventilation which alter steady-state PACO2 over a range of 30-50 mmHg have no important effect. At heavy work loads (200-300 W), P(et)CO2 grossly overestimates by 6-9 mmHg. The graphical method progressively underestimates, by about 5 mmHg at 300 W. A simulated CO2 response (the relation between ventilation and increasing PCO2) performed at 100 W suggests that a response slope close to the true one can be obtained by using any of the three methods. The graphical method gave results closest to the true absolute values. Either graphical or empirical methods should be satisfactory for detecting experimentally produced changes in PACO2 during steady-state exercise, to make comparisons between different steady-state exercise loads, and to assess CO2 response in exercise.(ABSTRACT TRUNCATED AT 400 WORDS)