Designing Studies for Dose Response
Designing Studies for Dose Response
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设计剂量反应研究
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发表时间：
1996
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通讯作者：
P. Lachenbruch
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作者：
W. Wong;P. Lachenbruch
《医学统计学》第一卷15,343-359(1996)加州大学洛杉矶分校生物统计系生物统计学设计研究教程。洛杉矶，CA 90024-1772，U.S.A.和Peter A.LACHENBRUCH FDAICBERIOELPS HFM-215,1401 Rockville Pike，Rockuille，MD 20852，U.S.A.我们回顾了一些剂量响应设计的选择，并比较了可能在实践中使用的各种设计。我们从两组设计开始。接下来，我们介绍了简单线性回归和二次回归的基本最优近似设计理论，说明了不同的最优准则及其对剂量水平分配的影响。然后，我们得到了这些最优近似设计的效率，以及一些具有直观吸引力的简单设计(对称性、等间距处理、减少最高剂量和最低剂量下的观察次数)。1.引言对刺激的反应的回归可用图形表示为曲线[如图11所示。当刺激的形式为‘剂量’(例如，药物，或可能的外加力或某些其他来源)时，这可称为‘剂量反应曲线’。(Kotz and Johnson‘)。在其最简单的形式中，剂量-反应曲线是简单的线性或多项式回归。更复杂的“剂量-反应”曲线可能涉及，例如，超越函数。其他的可能涉及到回归中剂量的变化。例如，剂量-反应模型通常使用剂量的对数。剂量的这个函数称为剂量计量仪。在某些情况下，反应是Quanta1(是/否)，剂量反应技术是概率分析或Logit分析。图1显示了线性和二次模型的剂量-反应曲线。阈值剂量的确定也是一个剂量-反应问题(见图1)。这里的反应是A低于一个剂量xo，B高于那个点。也就是说，模型是E(Yix)=A，当x<；xo时，E(Yix)=B，当x=2xo时，E(Yix)=B，其中E(Yix)是给定X=x的反应Y的期望值。该模型要求我们估计x0，A和B的值。在本教程中，我们将考虑反应和剂量连续且回归函数为简单线性或二次模型的剂量-反应情况，即E(Ylx)=A+Bx或E(Y(X)=A+Bx+Cx‘。我们还假设在整个过程中x被编码，使得John Wiley&Sons，Ltd.的0<；x CCC0277-6715/96/040343-17 01996。
STATISTICS IN MEDICINE, VOL. 15, 343-359 (1996) TUTORIAL IN BIOSTATISTICS DESIGNING STUDIES FOR DOSE RESPONSE WENG KEE WONG UCLA Department of Biostatistics. Los Angeles, CA 90024-1 772, U.S.A. AND PETER A. LACHENBRUCH FDAICBERIOELPS HFM-215, 1401 Rockville Pike, Rockuille, M D 20852, U.S.A. SUMMARY ‘Dose response’ refers to the regression of a response on a stimulus. We review a number of options for doseresponse designs, and compare various designs which may be used in practice. We start with two group designs. Next, we introduce basic optimal approximate design theory for simple linear and quadratic regression illustrating different criteria of optimality and their effect on the allocation of the levels of the dose. Then we obtain the efficiencies of these optimal approximate designs and some simple designs which have intuitive appeal (symmetry, equal spacing of treatments, reduced numbers of observations at the highest and lowest doses). 1. INTRODUCTION The regression of response on stimulus may be represented graphically as a curve [as in Figure 11. When the stimulus is in the form of a ‘dose’(e.g., of a drug, or possibly of an applied force or some other source), this may be called a ‘dose response curve’. (Kotz and Johnson’). In its simplest form, a dose-response curve is a simple linear or polynomial regression. More complex ‘dose-response’ curves may involve, for example, a transcendental function. Others may involve transformations of the dose in the regressions. For example, dose-response models often use the logarithm of dose. This function of the dose is called the dose metameter. In some cases, the response is quanta1 (yes/no) and the dose-response technique is a probit analysis or logit analysis. Figure 1 shows dose-response curves for linear and quadratic models. The determination of a threshold dose is also a dose-response problem (see Figure 1). Here the response is A below a dose xo and B above that point. That is, the model is E( Y Ix) = A if x < xo and E( Y Ix) = B if x 2 xo where E( Y Ix) is the expected value of the response Y given X = x. The model requires that we estimate the value of xo, A and B. In this tutorial paper we will consider the dose-response cases in which response and the dose are continuous and the regression functions are either simple linear or quadratic models, that is E(Ylx) = A + Bx or E ( Y ( x )= A + BX + CX’. We also assume throughout that x is coded so that 0 < x CCC 0277-6715/96/040343-17 0 1996 by John Wiley & Sons, Ltd.