响应服从泊松分布试验的最优区组设计
Optimal block designs for experiments with responses drawn from a Poisson distribution
摘要：
加性模型的最优区组设计通过将实验单元划分为相对均匀的区组并将处理平均分配给区组来实现其效率。然而，在许多现代实验中，响应是从诸如单参数和双参数指数族的分布中得出的，例如，来自负二项分布的RNA序列计数。这些违反了可加性。然而，通过假设可加性产生的设计继续被使用，因为没有更好的方法，因为这些问题没有得到广泛的认可。我们解决这个问题的单因素实验中的治疗，只采取分类值，安排在块和响应来自泊松分布。我们推导出两个目标函数的表达式，基于D_A-和C-最优性，有效地估计的线性对比的固定效应参数的Poisson广义线性混合模型（GLMM）的目标。这些目标函数被证明是计算效率高，不需要矩阵求逆。使用模拟退火生成泊松GLMM为基础的局部最优设计，我们表明，在这些设计中的治疗的重复数是成反比的治疗的预期计数的相对幅度。重要的是，对于不可忽略的处理效应大小，基于泊松GLMM的最优设计可能比其经典最优设计更有效。
英文摘要：
Optimal block designs for additive models achieve their efficiency by dividing experimental units among relatively homogenous blocks and allocating treatments equally to blocks. Responses in many modern experiments, however, are drawn from distributions such as the one- and two-parameter exponential families, e.g., RNA sequence counts from a negative binomial distribution. These violate additivity. Yet, designs generated by assuming additivity continue to be used, because better approaches are not available, and because the issues are not widely recognised. We solve this problem for single-factor experiments in which treatments, taking categorical values only, are arranged in blocks and responses drawn from a Poisson distribution. We derive expressions for two objective functions, based on D_A- and C-optimality, with efficient estimation of linear contrasts of the fixed effects parameters in a Poisson generalised linear mixed model (GLMM) being the objective. These objective functions are shown to be computational efficient, requiring no matrix inversion. Using simulated annealing to generate Poisson GLMM-based locally optimal designs, we show that the replication numbers of treatments in these designs are inversely proportional to the relative magnitudes of the treatments' expected counts. Importantly, for non-negligible treatment effect sizes, Poisson GLMM-based optimal designs may be substantially more efficient than their classically optimal counterparts.
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