Conditional Markov Chain Design for Accrual Clinical Trials

Randomization in a comparative experiment has, as one aim, the control of bias in the initial selection of experimental units. When the experiment is a clinical trial employing the accrual of patients, two additional aims are the control of admission bias and control of chronologic bias. This can be accomplished by using a method of randomization, such as the “biased coin design” of Efron, which sequentially forces balance. As an extension of Efron's design, this paper develops a class of conditional Markov chain designs. The detailed randomization employed utilizes the sequential imbalances in the treatment allocation as states in a Markov process. Through the use of appropriate transition probabilities, a range of possible designs can be attained. An additional objective of physical randomization is to provide a model for data analysis. Such a randomization theoretic analysis is presented for the current designs. In addition, Monte Carlo sampling results are given to support the proposed normal theory approximation to the exact randomization distribution.     

Bayesian Adaptive Randomization and Trial Monitoring with Predictive Probability for Time-to-Event Endpoint

There has been much development in Bayesian adaptive designs in clinical trials. In the Bayesian paradigm, the posterior predictive distribution characterizes the future possible outcomes given the currently observed data. Based on the interim time-to-event data, we develop a new phase II trial design by combining the strength of both Bayesian adaptive randomization and the predictive probability. By comparing the mean survival times between patients assigned to two treatment arms, more patients are assigned to the better treatment on the basis of adaptive randomization. We continuously monitor the trial using the predictive probability for early termination in the case of superiority or futility. We conduct extensive simulation studies to examine the operating characteristics of four designs: the proposed predictive probability adaptive randomization design, the predictive probability equal randomization design, the posterior probability adaptive randomization design, and the group sequential design. Adaptive randomization designs using predictive probability and posterior probability yield a longer overall median survival time than the group sequential design, but at the cost of a slightly larger sample size. The average sample size using the predictive probability method is generally smaller than that of the posterior probability design.     

Restricted randomization designs in clinical trials.

Though therapeutic clinical trials are often categorized as using either "randomization" or "historical controls" as a basis for treatment evaluation, pure random assignment of treatments is rarely employed. Instead various restricted randomization designs are used. The restrictions include the balancing of treatment assignments over time and the stratification of the assignment with regard to covariates that may affect response. Restricted randomization designs for clinical trials differ from those of other experimental areas because patients arrive sequentially and a balanced design cannot be ensured. The major restricted randomization designs and arguments concerning the proper role of stratification are reviewed here. The effect of randomization restrictions on the validity of significance tests is discussed.     

Importance of randomization in microarray experimental designs with Illumina platforms

Measurements of gene expression from microarray experiments are highly dependent on experimental design. Systematic noise can be introduced into the data at numerous steps. On Illumina BeadChips, multiple samples are assayed in an ordered series of arrays. Two experiments were performed using the same samples but different hybridization designs. An experiment confounding genotype with BeadChip and treatment with array position was compared to another experiment in which these factors were randomized to BeadChip and array position. An ordinal effect of array position on intensity values was observed in both experiments. We demonstrate that there is increased rate of false-positive results in the confounded design and that attempts to correct for confounded effects by statistical modeling reduce power of detection for true differential expression. Simple analysis models without post hoc corrections provide the best results possible for a given experimental design. Normalization improved differential expression testing in both experiments but randomization was the most important factor for establishing accurate results. We conclude that lack of randomization cannot be corrected by normalization or by analytical methods. Proper randomization is essential for successful microarray experiments.     

Allocation of patients to treatment in clinical trials.

This article is intended as a practical guide to the various methods of patient assignment in clinical trials. Topics discussed include a critical appraisal of non-randomized studies, methods of restricted randomization such as random permuted blocks and the biased coin technique, the extent to which stratification is necessary and the methods available, the possible benefits of randomization with a greater proportion of patients on a new treatment, factorial designs, crossover designs, randomized consent designs and adaptive assignment procedures. With all this diversity of approach it needs to be remembered that the effective implementation and reliability of a relatively straightforward randomization scheme may be more important than attempting theoretical optimality with more complex designs.     

Simultaneous Randomization Tests

Randomization analyses have been developed for testing main effects and interactions in standard experimental designs. However, exact multiple comparisons procedures for these randomization analyses have received little attention. This article proposes a general procedure for constructing simultaneous randomization tests that have prescribed type I error rates. An application of the procedure does provide for multiple comparisons in the randomization analyses of designed experiments. This application is made to data collected in a biopharmaceutical experiment.     

Is the concept of “control group” valid? A quantitative comparison of behavior of caged baboon groups

Behavioral comparisons between six caged baboon groups indicate that the groups have consistent and similar behavioral attributes. At the same time it is possible to distinguish between classes of animals in each group such as males versus females and high status versus low status rank. Comparable results are obtained in both ANOVA and Kruskal-Wallis one-way analysis of variance by ranks. This investigation supports the assumption that baboon groups exhibit behaviors that are both consistent and predictable where environment and group composition are controlled. Thus there appears to be a strong species-appropriate set of behaviors. Behavioral plasticity and group variability might be due largely to a combination of environmental stimuli and the particular history of that group. Differential individual histories or idiosyncracies do not invalidate experimental designs which rely on randomization to structure control groups.     

A comparison of experimental designs for selection in breeding trials with nested treatment structure

Plant breeders frequently evaluate large numbers of entries in field trials for selection. Generally, the tested entries are related by pedigree. The simplest case is a nested treatment structure, where entries fall into groups or families such that entries within groups are more closely related than between groups. We found that some plant breeders prefer to plant close relatives next to each other in the field. This contrasts with common experimental designs such as the α-design, where entries are fully randomized. A third design option is to randomize in such a way that entries of the same group are separated as much as possible. The present paper compares these design options by simulation. Another important consideration is the type of model used for analysis. Most of the common experimental designs were optimized assuming that the model used for analysis has fixed treatment effects. With many entries that are related by pedigree, analysis based on a model with random treatment effects becomes a competitive alternative. In simulations, we therefore study the properties of best linear unbiased predictions (BLUP) of genetic effects based on a nested treatment structure under these design options for a range of genetic parameters. It is concluded that BLUP provides efficient estimates of genetic effects and that resolvable incomplete block designs such as the α-design with restricted or unrestricted randomization can be recommended.     

The use of statistical tools in field testing of putative effects of genetically modified plants on nontarget organisms

To fulfill existing guidelines, applicants that aim to place their genetically modified (GM) insect‐resistant crop plants on the market are required to provide data from field experiments that address the potential impacts of the GM plants on nontarget organisms (NTO's). Such data may be based on varied experimental designs. The recent EFSA guidance document for environmental risk assessment (2010) does not provide clear and structured suggestions that address the statistics of field trials on effects on NTO's. This review examines existing practices in GM plant field testing such as the way of randomization, replication, and pseudoreplication. Emphasis is placed on the importance of design features used for the field trials in which effects on NTO's are assessed. The importance of statistical power and the positive and negative aspects of various statistical models are discussed. Equivalence and difference testing are compared, and the importance of checking the distribution of experimental data is stressed to decide on the selection of the proper statistical model. While for continuous data (e.g., pH and temperature) classical statistical approaches – for example, analysis of variance (ANOVA) – are appropriate, for discontinuous data (counts) only generalized linear models (GLM) are shown to be efficient. There is no golden rule as to which statistical test is the most appropriate for any experimental situation. In particular, in experiments in which block designs are used and covariates play a role GLMs should be used. Generic advice is offered that will help in both the setting up of field testing and the interpretation and data analysis of the data obtained in this testing. The combination of decision trees and a checklist for field trials, which are provided, will help in the interpretation of the statistical analyses of field trials and to assess whether such analyses were correctly applied.     

Genetic analysis of biological pathway data through genomic randomization

Genome Wide Association Studies (GWAS) are a standard approach for large-scale common variation characterization and for identification of single loci predisposing to disease. However, due to issues of moderate sample sizes and particularly multiple testing correction, many variants of smaller effect size are not detected within a single allele analysis framework. Thus, small main effects and potential epistatic effects are not consistently observed in GWAS using standard analytical approaches that consider only single SNP alleles. Here, we propose unique methodology that aggregates variants of interest (for example, genes in a biological pathway) using GWAS results. Multiple testing and type I error concerns are minimized using empirical genomic randomization to estimate significance. Randomization corrects for common pathway-based analysis biases, such as SNP coverage and density, linkage disequilibrium, gene size and pathway size. Pathway Analysis by Randomization Incorporating Structure (PARIS) applies this randomization and in doing so directly accounts for linkage disequilibrium effects. PARIS is independent of association analysis method and is thus applicable to GWAS datasets of all study designs. Using the KEGG database as an example, we apply PARIS to the publicly available Autism Genetic Resource Exchange GWAS dataset, revealing pathways with a significant enrichment of positive association results.     

Some floristic and ecological characteristics of association Bromo-Plantaginetum mediae Ht. (31)49 on permanent plot No. 82 (National Park Plitvice Lakes — Croatia)

Plot 82 is one of a hundred permanent plots that have been set up in Croatia for the purpose of long-term and continual investigations of ecosystems and their successions. It is located in the area of Karleuine Plase within the Plitvice Lakes National Park. Vegetation on the plot belongs to association Bromo-Plantaginetum mediae. The association develops in mountainous regions of continental Croatia within a wide altitude range, from 180–1300 m a.s.l. on shallow soil over pervious carbonate rocks. The floristic composition and phytocoenological characteristics of the association have been analyzed using the common methods of the phytocoenological school Zürich-Montpellier, on the basis of 17 phytocoenological records. In addition to floristic composition, some site characteristics have been analysed: soil moisture, calcium carbonate, phosphates, pH value, humus, cation exchange capacity and nitrogen mineralization on the site and in the laboratory. The results obtained are comparable with the data presented in the available phytocoenological and ecological literature.     

滇南热带雨林物种多样性的取样面积探讨

通过不同面积样方种数的比较、物种多样性指数等的计算和逐步扩大样地面积的调查, 本文研究了滇南热带雨林种数/面积关系、个体/种数关系、物种多样性及树种的频度分布规律, 认为滇南热带雨林群落学调查的最适取样(样方)面积是0.25 hm², 这个面积接近该类型热带雨林理论上的群落最小表现面积。 为能体现一个具体森林(群落)类型的基本的植物区系组成, 需设置4～5个这样的样方(总面积累计1 hm²以上)。从与世界不同地区热带雨林的比较亦可见,云南热带雨林有类似的树种频度分布规律,单位面积上的物种多样性比典型的东南亚低地热带雨林稍低,但比非洲的热带雨林要高。     

Significance Levels of Randomization Trend Tests in the Event of Rare Occurrences

In the statistical evaluation of data from a dose-response experiment, it is frequently of interest to test for dose-related trend: an increasing trend in response with increasing dose. The randomization trend test, a generalization of Fisher's exact test, has been recommended for animal tumorigenicity testing when the numbers of tumor occurrences are small. This paper examines the type I error of the randomization trend test, and the Cochran-Armitage and Mantel-Haenszel tests. Simulation results show that when the tumor incidence rates are less than 10%, the randomization test is conservative; the test becomes very conservative when the incidence rate is less than 5%. The Cochran-Armitage and Mantel-Haenszel tests are slightly anti-conservative (liberal) when the incidence rates are larger than 3%. Further, we propose a less conservatived method of calculating the p-value of the randomization trend test by excluding some permutations whose probabilities of occurrence are greater than the probability of the the observed outcome.     

象限法在热带山地雨林群落学调查中的应用研究

 本研究用象限法对海南岛尖峰岭地区一个山地雨林林分作了群落学调查,并将所得结果与78.5%面积取样比的记数样地法调查结果及实测结果进行比较。56个点的象限法调查所得密度、平均胸高断面积、优势度、组成种数量及组成种重要值序是令人满意的,而所花费时间最多为记数样地法的40%。但对该林分来说,样点数不能依照象限法的设计者Cottam和Curtis的结论来确定,即平均距离调查所需的点数即为群落调查所需的样点数,而要依据平均胸高断面积调查所需的点数来确定。     

On the PBB Designs for Multiresponse Experiments

We present the idea of using multiresponse incomplete block designs when not all responses can be observed in all experimental units. For a special class of such designs, in which partial designs are PBB designs, a method for estimating natural treatment contrast is given. We also consider the problem of testing the hypotheses concerning the natural and any estimable treatment contrasts. For testing this hypothesis the Wald statistics, being asymptotically chi-square distributed, is proposed.     

Use of randomization testing to detect multiple epistatic QTLs

Here, we describe a randomization testing strategy for mapping interacting quantitative trait loci (QTLs). In a forward selection strategy, non-interacting QTLs and simultaneously mapped interacting QTL pairs are added to a total genetic model. Simultaneous mapping of epistatic QTLs increases the power of the mapping strategy by allowing detection of interacting QTL pairs where none of the QTL can be detected by their marginal additive and dominance effects. Randomization testing is used to derive empirical significance thresholds for every model selection step in the procedure. A simulation study was used to evaluate the statistical properties of the proposed randomization tests and for which types of epistasis simultaneous mapping of epistatic QTLs adds power. Least squares regression was used for QTL parameter estimation but any other QTL mapping method can be used. A genetic algorithm was used to search for interacting QTL pairs, which makes the proposed strategy feasible for single processor computers. We believe that this method will facilitate the evaluation of the importance at epistatic interaction among QTLs controlling multifactorial traits and disorders.     

Conditional analysis of mixed Poisson processes with baseline counts: implications for trial design and analysis

The design of clinical trials is typically based on marginal comparisons of a primary response under two or more treatments. The considerable gains in efficiency afforded by models conditional on one or more baseline responses has been extensively studied for Gaussian models. The purpose of this article is to present methods for the design and analysis of clinical trials in which the response is a count or a point process, and a corresponding baseline count is available prior to randomization. The methods are based on a conditional negative binomial model for the response given the baseline count and can be used to examine the effect of introducing selection criteria on power and sample size requirements. We show that designs based on this approach are more efficient than those proposed by McMahon et al. (1994).     

A novel statistical test for treatment differences in clinical trials using a response-adaptive forward-looking Gittins Index Rule

The most common objective for response-adaptive clinical trials is to seek to ensure that patients within a trial have a high chance of receiving the best treatment available by altering the chance of allocation on the basis of accumulating data. Approaches that yield good patient benefit properties suffer from low power from a frequentist perspective when testing for a treatment difference at the end of the study due to the high imbalance in treatment allocations. In this work we develop an alternative pairwise test for treatment difference on the basis of allocation probabilities of the covariate-adjusted response-adaptive randomization with forward-looking Gittins Index (CARA-FLGI) Rule for binary responses. The performance of the novel test is evaluated in simulations for two-armed studies and then its applications to multiarmed studies are illustrated. The proposed test has markedly improved power over the traditional Fisher exact test when this class of nonmyopic response adaptation is used. We also find that the test's power is close to the power of a Fisher exact test under equal randomization.     

Robust and efficient design of experiments for the Monod model

In this paper the problem of designing experiments for the Monod model, which is frequently used in microbiology, is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research, pharmacokinetics, and plant physiology. The designs presented so far in the literature are local optimal designs, which depend sensitively on a preliminary guess of the unknown parameters, and are for this reason in many cases not robust with respect to their misspecification. Uniform designs and maximin optimal designs are considered as a strategy to obtain robust and efficient designs for parameter estimation. In particular, standardized maximin D- and E-optimal designs are determined and compared with uniform designs, which are usually applied in these microbiological models. It is demonstrated that maximin optimal designs are substantially more efficient than uniform designs. Parameter variances can be decreased by a factor of two by simply sampling at optimal times during the experiment. Moreover, the maximin optimal designs usually provide the possibility for the experimenter to check the model assumptions, because they have more support points than parameters in the Monod model.