對(duì)比連續(xù)端點(diǎn)基準(zhǔn)劑量計(jì)算的實(shí)驗(yàn)設(shè)計(jì)

摘要
由Crump根據(jù)劑量—反應(yīng)模型提出的BMD（基準(zhǔn)劑量）方法被用作對(duì)化學(xué)物質(zhì)進(jìn)行危險(xiǎn)度評(píng)定。考慮到數(shù)據(jù)和模型擬合的不確定性，我們把BMD評(píng)定的置信下限作為健康風(fēng)險(xiǎn)評(píng)估的起始點(diǎn)。本文中，我們將研究如何運(yùn)用BMD方法獲得連續(xù)數(shù)據(jù)的最佳實(shí)驗(yàn)設(shè)計(jì)方法。通過研究冪連續(xù)模型來實(shí)例說明我們的方法，主要目的是研究提高基準(zhǔn)劑量評(píng)定條件后，單個(gè)劑量組動(dòng)物數(shù)量減少的同時(shí)是否需要增加劑量組的數(shù)目。由于冪連續(xù)模型是非線性模型，所以最佳的設(shè)計(jì)還要根據(jù)未知參數(shù)的值來確定。這也是為什么我們認(rèn)為貝氏設(shè)計(jì)和假設(shè)參數(shù)向量有一個(gè)先驗(yàn)分布的原因。設(shè)計(jì)的最主要標(biāo)準(zhǔn)就是要盡量減小BMD評(píng)定的預(yù)計(jì)方差。文中，我們舉出了一個(gè)例子，例子講述了幾個(gè)設(shè)計(jì)中的設(shè)計(jì)標(biāo)準(zhǔn)值的計(jì)算并試圖找出劑量組、劑量組中的動(dòng)物數(shù)量和劑量的選擇是如何影響冪連續(xù)模型曲線的。從我們的計(jì)算中得到，實(shí)驗(yàn)中使用四個(gè)以上的劑量組會(huì)提高取得數(shù)據(jù)的正確性，從而避免了不利的劑量分配。從而我們也可以斷定一些關(guān)于預(yù)期的劑量—反應(yīng)曲線的其他信息，例如，從以前的研究中獲得的信息，在設(shè)計(jì)實(shí)驗(yàn)時(shí)也應(yīng)該考慮在內(nèi)，以使實(shí)驗(yàn)設(shè)計(jì)更加精準(zhǔn)。

關(guān)鍵詞：基準(zhǔn)劑量，劑量 - 反應(yīng)模型，冪連續(xù)模型，優(yōu)化設(shè)計(jì)
 

Comparing Experimental Designs for Benchmark
Dose Calculations for Continuous Endpoints
Abstract
The BMD (benchmark dose) method that is used in risk assessment of chemical compounds was introduced by Crump and is based on dose-response modeling. To take uncertainty in the data and model fitting into account, the lower confidence bound of the BMD estimate is suggested to be used as a point of departure in health risk assessments. In this article, we study how to design optimum experiments for applying the BMD method for continuous data. We exemplify our approach by considering the Power Continuous models. The main aim is to study whether an increased number of dose groups and at the same time a decreased number of animals in each dose group improves conditions for estimating the benchmark dose. Since Power Continuous models are nonlinear, the optimum design depends on the values of the unknown parameters. That is why we consider Bayesian designs and assume that the parameter vector has a prior distribution. A natural design criterion is to minimize the expected variance of the BMD estimator. We present an example where we calculate the value of the design criterion for several designs and try to find out how the number of dose groups, the number of animals in the dose groups, and the choice of doses affects this value for different Power Continuous curves. It follows from our calculations that to avoid the risk of unfavorable dose placements, it is good to use designs with more than four dose groups.We can also conclude that any additional information about the expected dose-response curve, e.g., information obtained from studies made in the past, should be taken into account when planning a study because it can improve the design.

KEYWORDS: Benchmark dose，dose-response modeling，Power Continuous models，optimum designs

目錄
1緒論 1
2方法 3
2.1冪連續(xù)模型 3
2.2貝葉斯設(shè)計(jì) 3
2.3 基準(zhǔn)劑量法的設(shè)計(jì)標(biāo)準(zhǔn) 4
2.4不同設(shè)計(jì)的比較 7
3結(jié)果與討論 9
3.1斜率參數(shù) 的冪連續(xù)模型 10
3.2斜率參數(shù) 的冪連續(xù)模型 11
3.3斜率參數(shù) 的冪連續(xù)模型 12
3.4斜率參數(shù)為 的冪連續(xù)模型 13
4一般性討論 15
5結(jié)論 16
致謝 17
參考文獻(xiàn) 18
附錄 20