Expected loss functions as additional measures to assess performance of multiple testing procedures for combination drug dose finding

There are several measures that are commonly used to assess performance of a multiple testing procedure (MTP). These measures include power, overall error rate (family‐wise error rate), and lack of power. In settings where the MTP is used to estimate a parameter, for example, the minimum effective dose, bias is of interest. In some studies, the parameter has a set‐like structure, and thus, bias is not well defined. Nevertheless, the accuracy of estimation is one of the essential features of an MTP in such a context. In this paper, we propose several measures based on the expected values of loss functions that resemble bias. These measures are constructed to be useful in combination drug dose response studies when the target is to identify all minimum efficacious drug combinations. One of the proposed measures allows for assigning different penalties for incorrectly overestimating and underestimating a true minimum efficacious combination. Several simple examples are considered to illustrate the proposed loss functions. Then, the expected values of these loss functions are used in a simulation study to identify the best procedure among several methods used to select the minimum efficacious combinations, where the measures take into account the investigator's preferences about possibly overestimating and/or underestimating a true minimum efficacious combination. The ideas presented in this paper can be generalized to construct measures that resemble bias in other settings. These measures can serve as an essential tool to assess performance of several methods for identifying set‐like parameters in terms of accuracy of estimation. Copyright © 2012 John Wiley & Sons, Ltd.     

论医院的三层次阶梯分摊法全成本核算

按照三层次分摊原则,将医院的行政后勤管理成本、医疗辅助服务成本和医疗技术服务成本分摊到医疗临床科室的医院全成本核算当中,进而对职工数分摊法、工作量分摊法和营业额分摊法的优点和弊端进行了分析。     

Bogen's Critique of Linear‐No‐Threshold Default Assumptions

In an article recently published in this journal, Bogen⁽¹⁾ concluded that an NRC committee's recommendations that default linear, nonthreshold (LNT) assumptions be applied to dose– response assessment for noncarcinogens and nonlinear mode of action carcinogens are not justified. Bogen criticized two arguments used by the committee for LNT: when any new dose adds to a background dose that explains background levels of risk (additivity to background or AB), or when there is substantial interindividual heterogeneity in susceptibility (SIH) in the exposed human population. Bogen showed by examples that SIH can be false. Herein is outlined a general proof that confirms Bogen's claim. However, it is also noted that SIH leads to a nonthreshold population distribution even if individual distributions all have thresholds, and that small changes to SIH assumptions can result in LNT. Bogen criticizes AB because it only applies when there is additivity to background, but offers no help in deciding when or how often AB holds. Bogen does not contradict the fact that AB can lead to LNT but notes that, even if low‐dose linearity results, the response at higher doses may not be useful in predicting the amount of low‐dose linearity. Although this is theoretically true, it seems reasonable to assume that generally there is some quantitative relationship between the low‐dose slope and the slope suggested at higher doses. Several incorrect or misleading statements by Bogen are noted.     

A Bayesian dose‐finding design for drug combination clinical trials based on the logistic model

In early phase dose‐finding cancer studies, the objective is to determine the maximum tolerated dose, defined as the highest dose with an acceptable dose‐limiting toxicity rate. Finding this dose for drug‐combination trials is complicated because of drug–drug interactions, and many trial designs have been proposed to address this issue. These designs rely on complicated statistical models that typically are not familiar to clinicians, and are rarely used in practice. The aim of this paper is to propose a Bayesian dose‐finding design for drug combination trials based on standard logistic regression. Under the proposed design, we continuously update the posterior estimates of the model parameters to make the decisions of dose assignment and early stopping. Simulation studies show that the proposed design is competitive and outperforms some existing designs. We also extend our design to handle delayed toxicities. Copyright © 2014 John Wiley & Sons, Ltd.     

A Simple Data Transformation for Estimating Benchmark Doses in Developmental Toxicity Experiments

Developmental anomalies induced by toxic chemicals may be identified using laboratory experiments with rats, mice or rabbits. Multinomial responses of fetuses from the same mother are often positively correlated, resulting in overdispersion relative to multinomial variation. In this article, a simple data transformation based on the concept of generalized design effects due to Rao-Scott is proposed for dose-response modeling of developmental toxicity. After scaling the original multinomial data using the average design effect, standard methods for analysis of uncorrected multinomial data can be applied. Benchmark doses derived using this approach are comparable to those obtained using generalized estimating equations with an extended Dirichlet-trinomial covariance function to describe the dispersion of the original data. This empirical agreement, coupled with a large sample theoretical justification of the Rao-Scott transformation, confirms the applicability of the statistical methods proposed in this article for developmental toxicity risk assessment.     

Estimation of Acute Toxicity by Fitting a Dose-Time-Response Surface

In acute toxicity testing, organisms are continuously exposed to progressively increasing concentrations of a chemical and deaths of test organisms are recorded at several selected times. The results of the test are traditionally summarized by a dose-response curve, and the time course of effect is usually ignored for lack of a suitable model. A model which integrates the combined effects of dose and exposure duration on response is derived from the biological mechanisms of aquatic toxicity, and a statistically efficient approach for estimating acute toxicity by fitting the proposed model is developed in this paper. The proposed procedure has been computerized as software and a typical data set is used to illustrate the theory and procedure. The new statistical technique is also tested by a data base of a variety of chemical and fish species.     

Role of the Standard Deviation in the Estimation of Benchmark Doses with Continuous Data

For continuous data, risk is defined here as the proportion of animals with values above a large percentile, e.g., the 99th percentile or below the 1st percentile, for the distribution of values among control animals. It is known that reducing the standard deviation of measurements through improved experimental techniques will result in less stringent (higher) doses for the lower confidence limit on the benchmark dose that is estimated to produce a specified risk of animals with abnormal levels for a biological effect. Thus, a somewhat larger (less stringent) lower confidence limit is obtained that may be used as a point of departure for low-dose risk assessment. It is shown in this article that it is important for the benchmark dose to be based primarily on the standard deviation among animals, s(a), apart from the standard deviation of measurement errors, s(m), within animals. If the benchmark dose is incorrectly based on the overall standard deviation among average values for animals, which includes measurement error variation, the benchmark dose will be overestimated and the risk will be underestimated. The bias increases as s(m) increases relative to s(a). The bias is relatively small if s(m) is less than one-third of s(a), a condition achieved in most experimental designs.     

On the Correlation Coefficient Between the TD50 and the MTD

The existence of correlation between the carcinogenic potency and the maximum tolerated dose has been the subject of many investigations in recent years. Several attempts have been made to quantify this correlation in different bioassay experiments. By using some distributional assumptions, Krewski et al .⁽¹⁾ derive an analytic expression for the coefficient of correlation between the carcinogenic potency TD₅₀ and the maximum tolerated dose. Here, we discuss the deviation that may result in using their analytical expression. By taking a more general approach we derive an expression for the correlation coefficient which includes the result of Krewski et al .⁽¹⁾ as a special case, and show that their expression may overestimate the correlation in some instances and yet underestimate the correlation in other instances. The proposed method is illustrated by application to a real dataset.     

Applications of Multinomial Dose-Response Models in Developmental Toxicity Risk Assessment

Reproductive and developmental anomalies induced by toxic chemicals may be identified using laboratory experiments with small mammalian species such as rats, mice, and rabbits. In this paper, dose-response models for correlated multinomial data arising in studies of developmental toxicity are discussed. These models provide a joint characterization of dose-response relationships for both embryolethality and teratogenicity. Generalized estimating equations are used for model fitting, incorporating overdispersion relative to the multinomial variation due to correlation among littermates. The fitted dose-response models are used to estimate benchmark doses in a series of experiments conducted by the U.S. National Toxicology Program. Joint analysis of prenatal death and fetal malformation using an extended Dirichlet-trinomial covariance function to characterize overdispersion appears to have statistical and computational advantages over separate analysis of these two end points. Benchmark doses based on overall toxicity are below the minimum of those for prenatal death and fetal malformation and may, thus, be preferred for risk assessment purposes.