The performance of multistage group screening designs

This article deals with multistage group screening in which group-factors contain the same number of factors. A usual assumption of this procedure is that the directions of possible effects are known. In practice, however, this assumption i s often unreasonable. This paper examines, in the case of no errors in observations, the performance of multistage group screening when this assumption is false . This enails consideration of cancellation effects within group-factors.     

On multistage group screening designs

In this article we discuss multistage group screening in which group-factors contain differing number of factors. We describe a procedure for grouping the factors in the absence of concrete prior information, so that the relative testing cost is minimal. It Is shown that under quite general conditions, these designs will require fewer runs than the equivalent designs in which the group-factors contain same number of factors.     

Three-stage group screening with unequal group sizes and with errors in observations

In this paper three-stage group screening in which group-factors contain differing number of factors is discussed. A procedure for grouping the factors in the absence of concrete prior information is described. Formulas for the expected number of runs and the expected number of incorrect decisions have also been obtained. These formulas are used to formulate criteria for optimal designs.     

2006-2008年中国省际高技术产业效率实证研究

 采用三阶段DEA分析方法对中国2006-2008年高技术产业的30个省际面板数据进行分析,衡量和评价各省市高技术产业运营效率。结果表明,一方面各省市高技术产业运营效率与当地经济发展程度相适应,区域差异明显,东部表现最优,西部次之,中部最差;另一方面环境因素对高技术产业运营效率具有重要的影响,剔除环境和随机因素影响后各省市高技术产业运营效率值变化较大,虽然纯技术效率有所提高,但是由于规模效率下降较大导致综合技术效率普遍下降。最后,提出提高高技术产业运营效率的政策建议。     

Detection of interactions in experiments on large numbers of factors

One of the main advantages of factorial experiments is the information that they can offer on interactions. When there are many factors to be studied, some or all of this information is often sacrificed to keep the size of an experiment economically feasible. Two strategies for group screening are presented for a large number of factors, over two stages of experimentation, with particular emphasis on the detection of interactions. One approach estimates only main effects at the first stage (classical group screening), whereas the other new method (interaction group screening) estimates both main effects and key two-factor interactions at the first stage. Three criteria are used to guide the choice of screening technique, and also the size of the groups of factors for study in the first-stage experiment. The criteria seek to minimize the expected total number of observations in the experiment, the probability that the size of the experiment exceeds a prespecified target and the proportion of active individual factorial effects which are not detected. To implement these criteria, results are derived on the relationship between the grouped and individual factorial effects, and the probability distributions of the numbers of grouped factors whose main effects or interactions are declared active at the first stage. Examples are used to illustrate the methodology, and some issues and open questions for the practical implementation of the results are discussed.     

Group screening method for the statistical analysis of -optimal mixed-level supersaturated designs

In this paper, we propose the application of group screening methods for analyzing data using E(f_NOD)-optimal mixed-level supersaturated designs possessing the equal occurrence property. Supersaturated designs are a large class of factorial designs which can be used for screening out the important factors from a large set of potentially active variables. The huge advantage of these designs is that they reduce the experimental cost drastically, but their critical disadvantage is the high degree of confounding among factorial effects. Based on the idea of the group screening methods, the f factors are sub-divided into g “group-factors”. The “group-factors” are then studied using the penalized likelihood statistical analysis methods at a factorial design with orthogonal or near-orthogonal columns. All factors in groups found to have a large effect are then studied in a second stage of experiments. A comparison of the Type I and Type II error rates of various estimation methods via simulation experiments is performed. The results are presented in tables and discussion follows.     

Modified dorfman-sterrett screening (group testing) procedures and the effects of faulty inspection

Continuing previous work on effects of errors in inspection on group sampling schemes, a modification of Dorfman-Sterrett schemes is studied. The modification consists of reversion to group sampling when a specified number of decisions of nonconformance have occurred in the course of inspection of individual items.     

A comparison of random balance and two-stage group screening designs: A case study

In this paper we focus on the problem of supersaturated (fewer runs than factors) screening experiments. We consider two major types of designs which have been proposed in this situ¬ation: random balance and two-stage group screening. We discuss the relative merits and demerits of each strategy. In addition, we compare the performance of these strategies by means of a case study in which 100 factors are screened in 20,42,62, and 84 runs.     

Statistical assessment of multivalued screening tests

When the outcome of a screening test is expressed by the probabilities of k possible outcomes among individuals with a certain physiologic condition and by the corresponding probabilities among individuals without the condition, the screening usefulness of the test depends on the relative likelihood that its result may properly alter the management of a given patient. New statistical methods are introduced to apply the screening usefulness concept to the assessment of combined or multivalued tests. The method is applied to assess the usefulness of genotypes at cytochrome P450 IAI and glutathione-S-transferase-μ as biomarkers of susceptibility to developing lung cancer. The argument and methods developed should be widely applicable to the statistical assessment of screening tests for a wide range of physiologic conditions.     

Non-orthogonal designs for measuring dispersion effects in sequential factor screening experiments using search linear models

“Dispersion” effects are considered in addition to “Location” effects of factors in the inferential procedure of sequential factor screening experiments with m factors each at two levels under search linear models. Search designs in measuring "Dispersion" and "Location" effects of factors are presented for both stage one and stage two of factor screening experiments with 4 ≤ m ≤ 10.     

Application of group screening to dynamic building energy simulation models

In order to select the most influential parameters of a building thermal model, a group screening technique was conducted. This technique uses regression analysis and experimental Plackett and Burman designs. After 136 simulations, 23 factors were selected from the initial set of 390. We came to the conclusion that global output variations (obtained with all parameters) can be accurately predicted from these 23 parameters. On the other hand, the results confirmed that group screening can be employed in the case of the building energy models despite the fact that the signs of the parameter effects are unknown. For the analysed configuration, the effects were found to be strongly influenced by the exchanged heat flows. In addition, the influential parameters (with respect to the inner air temperature) were all related to the building components having the largest heat exchange with the air cell.     

On the estimation of the proportion of positives in a sequence of screening experiments

A metaanalytic estimator of the proportion of positives in a sequence of screening experiments is proposed. The distribution-free estimator is based on the empirical distribution of P-values from individual experiments, which is uniform under the global null hypotheses of no positives in the sequence of experiments performed. Under certain regularity conditions, the proportion of positives corresponds to the derivative of this distribution under the alternative hypothesis of the existence of some positives. The statistical properties of the estimator are established, including its bias, variance, and rate of convergence to normality. Optimal estimators with minimum mean squared error are also developed under specific alternative hypotheses. The application of the proposed methods is illustrated using data from a sequence of screening experiments with chemicals to determine their carcinogenic potential.     

On correlation rank screening for ultra-high dimensional competing risks data

In recent years, numerous feature screening schemes have been developed for ultra-high dimensional standard survival data with only one failure event. Nevertheless, existing literature pays little attention to related investigations for competing risks data, in which subjects suffer from multiple mutually exclusive failures. In this article, we develop a new marginal feature screening for ultra-high dimensional time-to-event data to allow for competing risks. The proposed procedure is model-free, and robust against heavy-tailed distributions and potential outliers for time to the type of failure of interest. Apart from this, it is invariant to any monotone transformation of event time of interest. Under rather mild assumptions, it is shown that the newly suggested approach possesses the ranking consistency and sure independence screening properties. Some numerical studies are conducted to evaluate the finite-sample performance of our method and make a comparison with its competitor, while an application to a real data set is provided to serve as an illustration.     

Variance ratio screening for ultrahigh dimensional discriminant analysis

This article is concerned with feature screening for the ultrahigh dimensional discriminant analysis. A variance ratio screening method is proposed and the sure screening property of this screening procedure is proved. The proposed method has some additional desirable features. First, it is model-free which does not require specific discriminant model and can be directly applied to the multi-categories situation. Second, it can effectively screen main effects and interaction effects simultaneously. Third, it is relatively inexpensive in computational cost because of the simple structure. The finite sample properties are performed through the Monte Carlo simulation studies and two real-data analyses.     

On the efficiency of two-stage and three-stage least squares estimators

This paper utilizes the results of Kruskal (1968), Zyskind (1967), and more recently Milliken and Albohali (1984) to derive a simple necessary and sufficient condition for 3SLS to be equivalent to 2SLS. This condition depends upon the inverse of the variance:covariance matrix of the disturbances, and the set of second stage regressors of each structural equation. More importantly, this condition should prove useful for econometric students and provides an easy method for checking sufficiency.     

On the efficiency of two-stage and three-stage least squares estimators

This paper utilizes the results of Kruskal (1968), Zyskind (1967), and more recently Milliken and Albohali (1984) to derive a simple necessary and sufficient condition for 3SLS to be equivalent to 2SLS. This condition depends upon the inverse of the variance:covariance matrix of the disturbances, and the set of second stage regressors of each structural equation. More importantly, this condition should prove useful for econometric students and provides an easy method for checking sufficiency.     

A review of cancer screening evaluation techniques, with some particular examples in breast cancer screening

Summary.  The instigation of mass screening for breast cancer has, over the last three decades, raised various statistical issues and led to the development of new statistical approaches. Initially, the design of screening trials was the main focus of research but, as the evidence in favour of population-based screening programmes mounts, a variety of other applications have also been identified. These include administrative and quality control tasks, for monitoring routine screening services, as well as epidemiological modelling of incidence and mortality. We review the commonly used methods of cancer screening evaluation, highlight some current issues in breast screening and, using examples from randomized trials and established screening programmes, illustrate the role that statistical science has played in the development of clinical research in this field.     

Some new factor screening designs using the search linear model

Factor screening designs for searching two and three effective factors using the search linear model are discussed. The construction of such factor screening designs involved finding a fraction with small number of treatments of a 2^m factorial experiment having the property P_2t (no 2t columns are linearly dependent) for t=2 and 3. A ‘Packing Problem’ is introduced in this connection. A complete solution of the problem in one case and partial solutions for the other cases are presented. Many practically useful new designs are listed.     

Bayesian analysis of prevalence from the results of small screening samples

Bayesian analysis is applied to the number of cases screened positive to estimate the disease prevalence and to predict the number of future cases with disease. The analysis makes use of additional experimental information about the test’s sensitivity and specificity and of prior information on the prevalence of disease. Prior and posterior probability distributions of disease prevalence are conjugate mixtures of Beta densities and can be expressed in exact algebraic form.