Choice of number of doses for maximum likelihood estimation of the ED50 for quantal dose-response data

We address the question of how to choose the number of doses when estimating the median effective dose (ED50) of a symmetric dose-response curve by the maximum likelihood method. One criterion for this choice here is the asymptotic mean squared error (determined by the asymptotic variance) of the estimated ED50 of a dose-response relationship with qualitative responses. The choice is based on an analysis of the inverse of the information matrix. We find that in many cases, assuming various symmetric dose-response curves and various design densities, choice of as many doses as possible, i.e., the allocation of one subject per dose, is optimal. The theoretical and numerical results are supported by simulations and by an example concerning choice of design in an adolescence study.     

An effective method for the estimation and comparison of the ED50 with small sample sizes

In ED50 experiments the relationship between dose and probability of response is often modelled by the probit function. Standard statistical analysis estimates the parameters of this function by the maximum likelihood principle and derives the ED50 and its fiducial limits from these parameters. Bayesian analysis is more effective in two respects: It optionally includes prior information and in all but very few instances yields confidence intervals, whereas fiducial intervals often cannot be determined. Bayesian analysis of experiments with one substance has been treated in GRIEVE (1988). In the present article the mathematically interested reader is shown how to compare two substances. The probability of higher ED50 in the one substance as well as estimates of the ratio of the ED50's are obtained. The methods are easily extended to the effective dose for any other reasonable percentage of animals, e.g. ED90 or ED25. Experiments concerning lethal doses can be analysed by these methods as well. Both types of analysis are applied in two examples which compare new batches of vaccines with an established standard. In the first example both substances are nearly equivalent, while in the second example the new batch is considerably more efficient. An interactive FORTRAN program for a personal computer is available (cf. last section of 5.). It computes the maximum likelihood and the Bayesian solution, using approximate formulas in the latter case. Due to these approximations it was possible to develop a Bayesian program which is fast enough to run on a PC. Validation procedures have been performed. The output consists of a print file and, optionally, an ASCII file containing the coordinates of the posterior probability density and distribution functions.     

Small-sample confidence limits for parameters under inequality constraints with application to quantal bioassay

A family of methods is presented for constructing confidence limits for the parameters of a collection of distributions when a simple ordering is assumed among the parameters. The methods are shown to yield confidence limits that are exact or conservative for finite samples. For discrete distributions, one of the methods produces confidence limits that are at least as tight as the limits produced by a commonly used single-sample procedure. Confidence limits are demonstrated for a binomial quantal bioassay problem assuming a nondecreasing dose-response function. Results of a simulation study show that competing asymptotic methods can produce serious discrepancies between nominal and actual coverage probabilities for binomial samples of sizes up to 30, and demonstrate that the new approach can be competitive with the asymptotic methods when the latter maintain their nominal error rates.     

An augmented probit model for missing predictable covariates in quantal bioassay with small sample size

Summary Quantal bioassay experiments relate the amount or potency of some compound; for example, poison, antibody, or drug to a binary outcome such as death or infection in animals. For infectious diseases, probit regression is commonly used for inference and a key measure of potency is given by the ID_P , the amount that results in P% of the animals being infected. In some experiments, a validation set may be used where both direct and proxy measures of the dose are available on a subset of animals with the proxy being available on all. The proxy variable can be viewed as a messy reflection of the direct variable, leading to an errors‐in‐variables problem. We develop a model for the validation set and use a constrained seemingly unrelated regression (SUR) model to obtain the distribution of the direct measure conditional on the proxy. We use the conditional distribution to derive a pseudo‐likelihood based on probit regression and use the parametric bootstrap for statistical inference. We re‐evaluate an old experiment in 21 monkeys where neutralizing antibodies (nABs) to HIV were measured using an old (proxy) assay in all monkeys and with a new (direct) assay in a validation set of 11 who had sufficient stored plasma. Using our methods, we obtain an estimate of the ID₁ for the new assay, an important target for HIV vaccine candidates. In simulations, we compare the pseudo‐likelihood estimates with regression calibration and a full joint likelihood approach.     

Likelihood-based experimental design for estimation of ED50

In selecting the best dosage choice for the estimation of ED50, it is natural to try to minimize the length of the confidence intervals. In this presentation, the dose allocation that minimizes the length of the likelihood-based confidence intervals is presented and compared with alternative allocations that have been proposed based on the length of different types of confidence intervals, such as those based on the asymptotic variance or on Fieller's Theorem. Effective strategies to deal with the parameter dependence of these allocations are explored. A series of experiments to evaluate the effect of small doses per fraction on the radiation tolerance of the rat cervical spinal cord provide the motivation and an illustration for the proposed procedures.     

On the use of historical control data to estimate dose response trends in quantal bioassay.

New tests for trend in proportions, in the presence of historical control data, are proposed. One such test is a simple score statistic based on a binomial likelihood for the "current" study and beta-binomial likelihoods for each historical control series. A closely related trend statistic based on estimating equations is also proposed. Trend statistics that allow overdispersed proportions in the current study are also developed, including a version of Tarone's (1982, Biometrics 38, 215-220) test that acknowledges sampling variation in the beta distribution parameters, and a trend statistic based on estimating equations. Each such trend test is evaluated with respect to size and power under both binomial and beta-binomial sampling conditions for the current study, and illustrations are provided.     

ED50 G Na Block Predictions for Phenyl Substituted and Unsubstituted n-Alkanols

To study the role the phenyl group plays in producing local anesthetic block, a sequence of n-alkanols and phenyl-substituted alkanols (Φ-alkanols) were characterized in their ability to block Na channels. The sequence of n-alkanols studied possess 3–5 carbons (propanol-pentanol). The action of phenol and 3-Φ-alkanols (benzyl alcohol, phenethyl alcohol, 3-phenyl-1-propanol) were also studied. Na currents (I _Na ) were recorded from single frog skeletal muscle fibers using the Vaseline-gap voltage clamp technique. I _Na s were recorded prior to, during, and following the removal of the solutes in Ringer's solution. All alkanols and phenol acted to block I _Na in a dose-dependent manner. Effective doses to produce half block (ED₅₀) of I _Na or Na conductance (G _Na ) were obtained from dose-response relations for all solutes used. The block of G _Na depended on voltage, and could be separated into voltage-dependent and -independent components. Each solute acted to shift G _Na -V relations in a depolarized direction and reduce the maximum G _Na and slope of the relation. All solutes acted to speed up I _Na kinetics and cause hyperpolarizing shifts in steady-state inactivation. The magnitude of the kinetic changes increased with dose. Size was an important variable in determining the magnitude of the changes in I _Na ; however, size alone was not sufficient to predict the changes in I _Na . ED₅₀s for G _Na and AP block could be predicted as a function of intrinsic molar volume, hydrogen bond acceptor basicity (β) and donor acidity (α), and polarity (P) of the solutes. The equivalency of ED₅₀ predictions for AP and G _Na block can be explained by the fact that AP block arises from channel block and solute-induced changes in I _Na kinetics. Φ-alkanols were more effective at blocking and inactivating Na channels than their unsubstituted counterparts. Phenyl-substituted alkanols are more likely to interact with the channel than their unsubstituted counterparts. Received: 11 August 2000/Revised: 21 December 2000     

一种改进的粉虱成虫生物测定方法

生物测定是检测害虫抗药性的一项重要技术。利用100mL插口圆底聚丙烯离心管对现在应用较多的粉虱成虫生物测定方法——琼脂保湿浸叶法进行了改进。改进后的方法不影响粉虱成虫的持续取食,具有操作简单、结果重复性好及无需对成虫麻醉等优点。同时发现茄子叶片对于B型烟粉虱Bemisia tabaci(Gennadius)B-biotype和温室白粉虱Trialeurodes vaporariorum(Westwood)成虫均是一种非常适合的生测材料。利用该方法分3次独立测定了烯啶虫胺对B型烟粉虱和温室白粉虱混合日龄成虫的毒力,结果具有很好的重复性。     

Modification of the data-processing method for the turbidimetric bioassay of nisin

The data processing method of the turbidimetric bioassay of nisin was modified to facilitate its industrial application. The influence of the initial indicator concentration was minimized by a redefined specific dose of the bacteriocin as the quotient between the titer of the added bacteriocin and the initial population density of the indicator in the suspension. It was found that d _c = 0.125 μg ml⁻¹ was the critical dose of nisin that can cause a complete inhibition of the indicator, Pediococcus acidilactici UL5, with an initial OD of 0.135. To eliminate the interference of the cell debris, an equation, , exploiting d _c, was formulated to obtain the intrinsic survival proportion. The use of the specific dose of the bacteriocin and the intrinsic survival proportion as parameters of the dose/response curve greatly enhanced its repeatability and feasibility. A dual-dosage approach was developed to further simplify the conventional standard dose/response curve method.     

Determination of ED50 values for praziquantel in praziquantel-resistant and -susceptible Schistosoma mansoni isolates

The dose of praziquantel required to kill 50% of adult worms in vivo (i.e. the ED50) was estimated for nine different isolates of Schistosoma mansoni in infected mice. Four of the isolates were selected because they had not knowingly been in contact with the drug (i.e. they were putatively praziquantel-susceptible). Five putatively praziquantel-resistant isolates were chosen because they had been selectively bred for drug-resistance in the laboratory and/or had previously been shown to be relatively resistant to praziquantel in the field. The work was performed in three laboratories in different countries using pre-agreed and comparable experimental protocols. All four praziquantel-susceptible isolates had ED50s estimated to be <100 mg/kg (mean=70+/-7 SD; median=68), while all five putatively praziquantel-resistant isolates had estimated ED50s >100 mg/kg (mean=209+/-48 SD; median=192). Thus, the five praziquantel-resistant isolates, including two that had been subjected to drug pressure during more than 20 passages in mice, had drug ED50s that were approximately three times as great as those of the praziquantel-susceptible isolates. Two of the five isolates in the putatively resistant group had previously been passaged 15 or more times in mice without administration of drug-pressure, but had ED50s consistent with the other three isolates in the group, indicating that the trait of praziquantel-resistance did not necessarily impair biological fitness during laboratory passage. The protocols used here to estimate the praziquantel ED50s of S. mansoni isolates should be useful for establishing and monitoring the drug susceptibility/resistance profiles of parasite isolates freshly obtained from endemic areas, particularly those in which increased usage of the drug is likely to occur.