混合Poisson分布及其应用：疾病的统计分布（五）

本文讨论了混合Ｐｏｉｓｓｏｎ分布的性质、应用条件、参数的估计及混合Ｐｏｉｓｓｏｎ分布阶数的确定，指出混合Ｐｏｉｓｓｏｎ分布可用于混合样本的判别归类，并用Ｂａｙｅｓ的思想导出其判别归类方法。模拟试验结果表明：当混合Ｐｏｉｓｓｏｎ分布中各部分的比例相差不大，而各部分的均值相差较大时，抽样效果和拟合效果越好，所得到的估计值越接近理论值；反之效果越差。     

PP分布、PB分布及其应用──疾病的统计分布(三)

本文介绍并讨论了两种复合分布及其性质，即Ｐｏｉｓｓｏｎ－Ｐｏａｉｓｓｏｎ分布（ＰＰＤ）和Ｐｏｉｓｓｏｎ－二项分布（ＰＢＤ）。这两个分布的关系类似于Ｐｏｉｓｓｏｎ分布与二项分布的关系，所不同的是，二项分布属有限二项概型，而ＰＰＤ与ＰＢＤ均属无限二项概型。两者的应用条件同负二项分布，但不能相互替代．     

PP分布,PB分布及其应用

本文介绍并讨论了两种复合分布及其性质，即Ｐｏｉｓｓｏｎ－Ｐｏａｉｓｓｏｎ分布（ＰＰＤ）和Ｐｏｉｓｓｏｎ－二项分布（ＰＢＤ）。这两个分布的关系，所不同的是，二项分布属有限二项概型，而ＰＰＤ与ＰＢＤ均属无限二项概型。两者的应用条件同负二项分布，但不能相互替代。     

Poisson回归在职业队列研究中的应用

本文介绍Ｐｏｉｓｓｏｎ回归模型及其计算方法，运用这一方法对某职业人群队列研究死亡资料作了Ｐｏｉｓｓｏｎ回归分析。研究结果提示该厂可能有某些职业危害因素存在，影响了职工寿命。     

585例痰涂片阳性肺结核病例空间聚集性分布探讨

本文应用Ｐｏｉｓｓｏｎ分布和负二项分布拟合法，对蓬溪县利用世界银行贷款结核病控制项目，１９９２年登记的５８５例谈涂片阳性结核病例进行拟合分析，并作拟合优度Ｘ２检验。结果不符从Ｐｏｉｓｓｏｎ分布（Ｐ＜０．００１），而与负二项分布非常满意的配合（Ｐ＜０．９０）。表明结核病这种慢性传染病在疫点内仍具有传染性疾病聚集性分布的特征。其防治工作的重点应放在痰涂片阳性的村、家庭中。     

出生缺陷监测中O／E法的误差探讨

Ｏ／Ｅ法是出生缺陷监测中最常用的统计方法。长期以来，人们忽略了出生缺陷分布的多样性。本文讨论了Ｏ／Ｅ法的误差，结果表明：二项分布和Ｐｏｉｓｏｎ分布的误差可以忽略，但负二项分布和Ｐｉｓｏｎ分布的误差值得重视。     

Poisson模型与队列研究—原理及应用

Ｐｏｉｓｏｎ模型与队列研究——原理及应用上海医科大学李克俞顺章Ｐｏｉｓｏｎ回归模型主要用于队列研究资料的分析〔１－４〕，属于分析流行病学的范畴，鉴于它调整协变量的强大能力〔５〕，常用来研究多因素对疾病率的影响及暴露与疾病间的剂量反应关系，尤其适用于罕...     

应用非线性Poisson回归模型估计病因分配份额

在应用Ｐｏｉｓｓｏｎ回归模型描述和解释发病率或死亡率与病因因素的关系、进而估计病因因素分配份额的过程中 ,率与病因因素间关系通常采用乘法模型或加法模型、一般危险度模型或幂转换模型。在多个因素存在且其致病作用的关系较为复杂时 ,有时一般的乘法模型难以描述其内在的致病关系。另一种方法是根据致癌或致病的数学理论构造疾病率的非线性Ｐｏｉｓｓｏｎ回归模型 ,以解释致病因子与研究疾病间的关系[1,2 ] 。本研究通过对镍精炼工人职业暴露与肺癌关系的非线性Ｐｏｉｓｓｏｎ回归模型分析 ,反映职业暴露与肺癌间的剂量效应关系 ,进…     

累计和法的原理及其在出生缺陷监测中的应用

本文从序贯概率比检验的理论出发，介绍了累计和法的原理，并将其推广于非Ｐｏｉｓｓｏｎ分布资料，并通过实例说明了在出生缺陷监测中的具体应用。     

论负二项分布的应用条件

本文从复合分布的角度导出负二项分布的演绎过程，说明负二项分布即是Ｐｏｉｓｓｏｎ分布中参数λ服从Γ分布所得的复合分布，从而阐明了其生物学意义及其应用条件，更正了对负二项分布的一些误解和误用，指出复合分布有着广阔的应用前景。     

不同方差比双正态ROC参数估计样本量确定方法准确性探讨

目的 探讨不同方差比双正态参数估计时样本量确定方法的准确性,对最常用样本量估计方法--双正态法所估计样本量的准确性进行评价与修正.方法 采用Monte Carlo模拟试验,分别利用参数法和非参数法计算获得曲线下面积的参数估计值,获得实际所需样本量,对Obuchowski和Mcclish给出的不同方差比双正态ROC参数估计所需样本量的准确性进行评价,依据试验数据采用曲线拟合方法给出修正公式.结果 Obuchowski和Mcclish给出的方法是假定患病组诊断变量XA和非患病组诊断变量XN服从正态分布,样本量计算公式是以ROC曲线下面积估计值服从正态分布为前提导出的,但事实上随ROC曲线实际面积θ逐渐增大,样本估计量偏离正态,导致样本量估计结果不够准确,与实际样本需要量有一定差距.在其他条件相同的情况下,患病组与非患病组诊断变量方差比越大实际所需样本量越多,在患病组与非患病组诊断变量方差比分别为2∶1及3∶1的情况下,用Obuchowski和Mcclish方法计算出的样本量与实际所需样本量相差不是很大.根据Monte Carlo模拟试验的结果,给出了Obuchowski和Mcclish方法计算样本量的修正公式,该修正公式可有效地应用于实际.结论 Obuchowski和Mcclish方法计算的样本量进行ROC参数估计时需要调整,采用Monte Carlo方法估计的样本量,可以有效地进行双正态ROC参数估计,达到诊断试验评价要求.     

Robust Bayesian sample size determination in clinical trials

This article deals with determination of a sample size that guarantees the success of a trial. We follow a Bayesian approach and we say an experiment is successful if it yields a large posterior probability that an unknown parameter of interest (an unknown treatment effect or an effects-difference) is greater than a chosen threshold. In this context, a straightforward sample size criterion is to select the minimal number of observations so that the predictive probability of a successful trial is sufficiently large. In the paper we address the most typical criticism to Bayesian methods-their sensitivity to prior assumptions-by proposing a robust version of this sample size criterion. Specifically, instead of a single distribution, we consider a class of plausible priors for the parameter of interest. Robust sample sizes are then selected by looking at the predictive distribution of the lower bound of the posterior probability that the unknown parameter is greater than a chosen threshold. For their flexibility and mathematical tractability, we consider classes of epsilon-contamination priors. As specific applications we consider sample size determination for a Phase III trial.     

Seamless phase 2/3 oncology trial design with flexible sample size determination

Conventional seamless phase 2/3 design with fixed sample size determination (SSD) has gained its popularity in oncology drug development due to attractive features such as significantly shortening the development timeline, minimizing sample size, as well as early decision making. However, this design is not immune to inaccurate treatment effect assumption when only limited efficacy data are available at study design stage. We propose an innovative seamless phase 2/3 study design with flexible SSD for oncology trials, in which the trial is designed under a distribution of treatment effect instead of one single assumption due to huge uncertainty of treatment effect at design stage and the sample size for end of phase 3 analysis is not predetermined at design stage, but rather dynamically determined based on observed treatment effect at phase 2 portion. Some practical sample size determination rules for end of phase 3 analysis will be discussed. The proposed design can lead to reduced sample size or/and improved power compared with conventional seamless phase 2/3 design with fixed SSD. This innovative study design can be especially useful for programs with aggressive development strategy to expedite the process in delivering efficacious treatment to patients.     

Determination of free silica in dust particles: effect of particle size for the X-ray diffraction and phosphoric acid methods

The X-ray diffraction method and the phosphoric acid method are widely used to determine the fraction of free silica (mainly quartz and other silica polymorphs) in respirable dust sampled in working environments in Japan. In this study, we clarified the size effect of quartz dust for the X-ray diffraction method and the phosphoric acid method using size controlled quartz samples. The quartz samples were classified into 6 fractions with different size ranges: 1 microm and smaller, 1 to 3 microm, 3 to 5 microm, 5 to 7 microm, 7 to 10 microm and 10 microm and larger. Both of the determination methods were affected by the particle size, and especially particles smaller than 3 microm fairly dissolved in hot phosphoric acid and reduced X-ray diffraction intensity remarkably. If the content of these fine particles in the standard quartz sample is lower than that of the test samples, the fraction of free silica may be underestimated by these methods. For this reason, the standard quartz sample should have a representative size distribution of the field samples. The dust samples containing quartz were collected at a foundry and dissolved by phosphoric acid to remove non-quartz materials. The size fractions of dissolved samples were 50% for 5-10 microm, 25% for 3-5 microm, 20% for 1-3 microm and 5% for 1 microm and smaller. As the size distribution is similar to the present standard sample widely used in Japan, we concluded that the standard sample is suitable for these determination methods.     

A comparison of methods for adaptive sample size adjustment.

In fixed sample size designs, precise knowledge about the magnitude of the outcome variable's variance in the planning phase of a clinical trial is mandatory for an adequate sample size determination. Wittes and Brittain introduced the internal pilot study design that allows recalculation of the sample size during an ongoing trial using the estimated variance obtained from an interim analysis. However, this procedure requires the unblinding of the treatment code. Since unblinding of an ongoing trial should be avoided whenever possible, there should be some benefit of this design compared with blinded sample size recalculation procedures to justify the unveiling of the treatment code. In this paper, we compare several sample size recalculation procedures with and without unblinding. The simulation results indicate that the procedures behave similarly. In particular, breaking of the blind is not required for an efficient sample size adjustment. We also compare these pure sample size adaptation procedures with study designs which additionally allow for early stopping. Evaluation of the cumulative distribution function of the resulting sample sizes shows that the option for early stopping may lead to lower expectation but generally to a higher variability. The procedures are illustrated by an example of a trial in the treatment of depression.     

Multicomponent error model for mass measurement based size fractionating aerosol samplers

A mass based size fractionating aerosol sampling device such as an impactor has a number of experimental measurement errors that can affect the size distribution determination. These errors are not necessarily additive, such as weighing errors, multiplicative such as airflow errors, or a power function such as bounce. In general, the cumulative errors are a combination of different relational scales and they are likely to have different functional forms across the full range of measurements. A complete theory of errors must consider a diverse set of functional relationships between mass, flow, size distribution, and other non-linear parameters such as entry losses and bounce to estimate the error bounds for a measured size distribution and aerosol concentration. In addition, aerosol exposure measurements are single sample events. The theoretical multi-compartment error model is an extension of the Rocke and Lorenzato model of measurement errors in analytical chemistry and it includes generalized parameters for all empirically meaningful transformations. Although the general theory is complicated, heuristic reductions can be made to reduce the estimation process to a manageable size. The numerical examples of error analysis of a hypothetical impactor show that the measured distribution related error bound estimation process is not difficult to perform.     

Sample size determination in step‐up testing procedures for multiple comparisons with a control

Step‐up procedures have been shown to be powerful testing methods in clinical trials for comparisons of several treatments with a control. In this paper, a determination of the optimal sample size for a step‐up procedure that allows a pre‐specified power level to be attained is discussed. Various definitions of power, such as all‐pairs power, any‐pair power, per‐pair power and average power, in one‐ and two‐sided tests are considered. An extensive numerical study confirms that square root allocation of sample size among treatments provides a better approximation of the optimal sample size relative to equal allocation. Based on square root allocation, tables are constructed, and users can conveniently obtain the approximate required sample size for the selected configurations of parameters and power. For clinical studies with difficulties in recruiting patients or when additional subjects lead to a significant increase in cost, a more precise computation of the required sample size is recommended. In such circumstances, our proposed procedure may be adopted to obtain the optimal sample size. It is also found that, contrary to conventional belief, the optimal allocation may considerably reduce the total sample size requirement in certain cases. The determination of the required sample sizes using both allocation rules are illustrated with two examples in clinical studies. Copyright © 2010 John Wiley & Sons, Ltd.     

诊断试验ROC参数估计双正态样本量估计方法探讨

目的 探讨ROC双正态样本量估计方法的准确性。方法 通过Monte Carlo方法对ROC双正态样本量估计法进行评价与修正。结果 根据模拟试验结果得到双正态样本量估计法的校正公式及修正曲线。结论 采用文中给出的样本量调整方法。可以有效地进行样本量估计。达到诊断试验评价的要求。     

Sample size planning for survival prediction with focus on high‐dimensional data

Sample size planning should reflect the primary objective of a trial. If the primary objective is prediction, the sample size determination should focus on prediction accuracy instead of power. We present formulas for the determination of training set sample size for survival prediction. Sample size is chosen to control the difference between optimal and expected prediction error. Prediction is carried out by Cox proportional hazards models. The general approach considers censoring as well as low‐dimensional and high‐dimensional explanatory variables. For dimension reduction in the high‐dimensional setting, a variable selection step is inserted. If not all informative variables are included in the final model, the effect estimates are biased towards zero. The bias affects the prediction error, and its magnitude is influenced by the sample size. For variable selection, we consider two approaches: least absolute shrinkage and selection operator (LASCO) and univariable selection. For univariable selection, we can calculate input parameters for the sample size formula. For the LASCO, supportive simulations are necessary to appropriately choose the input parameters. We investigate the performance of the proposed formulas with the use of simulations. Simulation results support the validity of the sample size formulas. An application of a real data example illustrates the practical implementation of the method. Copyright © 2012 John Wiley & Sons, Ltd.     

Estimation and sample size considerations for clustered binary responses

Although there is much literature on sample size determination for clinical trials or experiments with independent responses, there is a lack of methodology to obtain sample sizes for dependent outcomes. This paper presents a simple way to calculate sample size for estimating treatment effects and diagnostic accuracy in the case of correlated binary outcomes. The proposed weighted procedure also has use in estimation, whose advantages we demonstrate through simulation. Recommendations are made for practical application.