Incorporating Prior Beliefs in Treatment Allocation for Clinical Trials

Recently Faraggi and Reiser (1991) introduced a general dynamic treatment allocation scheme which incorporates the permuted block allocation procedure and the Begg Iglewicz procedure as special cases. A drawback of previous allocation methods is that they did not allow incorporation of prior knowledge of the relative importance of the prognostic factors. In this paper we extend our allocation model to incorporate the weighting of prognostic factors. A simulation study examines the effects of this procedure and an example of its implementation is given.     

On the COLTON Model for Clinical Trials with Delayed Observations-Dichotomous Responses

In the COLTON model for clinical trials a choice is to be made between two medical treatments where there is a known patient horizon N. In an earlier paper we studied the COLTON model under the additional assumption that there is a time lag between the administration of the treatments and the availability of the responses where the responses are normally distributed. Here we extend the results of the earlier paper to the case where responses are dichotomous. The relative performance of two simple procedures for dealing with the patients who arrive during the waiting period between the end of the administration of treatment in the trial phase and observation of the final trial response is discussed within a BAYESIAN framework.     

A Problem of Equivalence in Clinical Trials

Several methods exist for testing the bioequivalence in bioavailability trials. In this article we propose a method for testing the equivalence of two drugs in clinical trials when the response variable is assumed to have a normal distribution. The null and alternative hypotheses are formulated in a nonconventional manner. Computing aspects for the power and sample size are discussed.     

Population-Based Reversible Jump Markov Chain Monte Carlo

We present an extension of population-based Markov chain MonteCarlo to the transdimensional case. A major challenge is thatof simulating from high- and transdimensional target measures.In such cases, Markov chain Monte Carlo methods may not adequatelytraverse the support of the target; the simulation results willbe unreliable. We develop population methods to deal with suchproblems, and give a result proving the uniform ergodicity ofthese population algorithms, under mild assumptions. This resultis used to demonstrate the superiority, in terms of convergencerate, of a population transition kernel over a reversible jumpsampler for a Bayesian variable selection problem. We also givean example of a population algorithm for a Bayesian multivariatemixture model with an unknown number of components. This isapplied to gene expression data of 1000 data points in six dimensionsand it is demonstrated that our algorithm outperforms some competingMarkov chain samplers. In this example, we show how to combinethe methods of parallel chains (Geyer, 1991), tempering (Geyer& Thompson, 1995), snooker algorithms (Gilks et al., 1994),constrained sampling and delayed rejection (Green & Mira,2001).     

Randomization Modelling of the Crossover Experiment for Clinical Trials

The two-period cross-over experiment for clinical trials has been examined by several writers following a Gaussian linear model approach. Some authors have expressed interest in the “derivation of the finite permutation model” and have pointed out that the randomization approach to modeling the two-period cross-over design “would highlight the importance of randomizing the subjects to the two groups as a basis for inference”. However, in the literature, there is no development of the randomization approach to this important design. In this paper, after a statement of the experimental design and formulation of the observation random variables of the finite population, two additive randomization models—one with residual effects, the other without—which are the analogues of Grizzle's Gaussian models, are derived. Statistical inference is developed for these randomization models and the results are compared with those of the corresponding Gaussian models. Also, exact inference based upon Fischer's approach is presented.     

Regression Models for Clinical Trials with Correlated Categorical Responses

Regression models for correlated categorical data are presented in which the covariance is a function of measured effects. The regression and covariance parameters are estimated by extended least square methods. A numerical example of a clinical trial comparing two antiemetic treatment regimes for patients receiving chemotherapy is given to illustrate the approach.     

An Approximation to the Bayes Optimal Multi-Stage Design in the Colton Model for Clinical Trials

A simple and operationally convenient approximation is proposed for the Bayes optimal multistage design within the Colton decision-theoretic model for the comparison of two medical treatments. The two- and three-stage designs are developed in full; the latter is found to be superior to several existing designs including some involving sequential adaptive sampling.     

Stopping Rules for Clinical Trials Implicitly Incorporating Safety Information

Clinical trials research is mainly conducted for the purpose of evaluating the relative efficacy of two or more treatments. However, a positive response due to treatment is not sufficient to put forward a new product because one must also demonstrate safety. In such cases, clinical trials which show a positive effect would need to accrue enough patients to also demonstrate that the new treatment is safe. It is our purpose to show how the efficacy and safety problems can be combined to yield a more practical clinical trial design. In this paper we propose an asymmetric stopping rule which allows the experimenter to terminate a clinical trial early for a sufficiently negative result and to continue to a specified number of patients otherwise. As it turns out, a few interim tests will have negligible effects on the overall significance level.     

A Markov Chain Model of Population Growth with an Application in Epidemiology

This paper is concerned with a class of population growth processes in discrete time; the simple epidemic process is considered as a specific example. A Markov chain model is constructed and standard Markov methods are used to study the main biological concepts. A simple and explicit formula is obtained for the transient distribution of the population size. Then, the cost of the process is defined and the joint probability generating function of its components is derived. Finally, the results are extended to the case where the inter-transition periods are bounded i.i.d. random variables.     

Estimating Variable Effective Population Sizes from Multiple Genomes: A Sequentially Markov Conditional Sampling Distribution Approach

Throughout history, the population size of modern humans has varied considerably due to changes in environment, culture, and technology. More accurate estimates of population size changes, and when they occurred, should provide a clearer picture of human colonization history and help remove confounding effects from natural selection inference. Demography influences the pattern of genetic variation in a population, and thus genomic data of multiple individuals sampled from one or more present-day populations contain valuable information about the past demographic history. Recently, Li and Durbin developed a coalescent-based hidden Markov model, called the pairwise sequentially Markovian coalescent (PSMC), for a pair of chromosomes (or one diploid individual) to estimate past population sizes. This is an efficient, useful approach, but its accuracy in the very recent past is hampered by the fact that, because of the small sample size, only few coalescence events occur in that period. Multiple genomes from the same population contain more information about the recent past, but are also more computationally challenging to study jointly in a coalescent framework. Here, we present a new coalescent-based method that can efficiently infer population size changes from multiple genomes, providing access to a new store of information about the recent past. Our work generalizes the recently developed sequentially Markov conditional sampling distribution framework, which provides an accurate approximation of the probability of observing a newly sampled haplotype given a set of previously sampled haplotypes. Simulation results demonstrate that we can accurately reconstruct the true population histories, with a significant improvement over the PSMC in the recent past. We apply our method, called diCal, to the genomes of multiple human individuals of European and African ancestry to obtain a detailed population size change history during recent times.     

Exact Markov chains versus diffusion theory for haploid random mating

Exact discrete Markov chains are applied to the Wright-Fisher model and the Moran model of haploid random mating. Selection and mutations are neglected. At each discrete value of time t there is a given number n of diploid monoecious organisms. The evolution of the population distribution is given in diffusion variables, to compare the two models of random mating with their common diffusion limit. Only the Moran model converges uniformly to the diffusion limit near the boundary. The Wright-Fisher model allows the population size to change with the generations. Diffusion theory tends to under-predict the loss of genetic information when a population enters a bottleneck.     

基于马尔科夫链的胰蛋白酶肽段蛋白酶切位点概率预测

在基于质谱技术的蛋白质鉴定过程中,数据库搜索是主要的方法。漏切位点和酶切规则决定了图谱候选肽段的范围,是数据库搜索算法的重要参数。对于常用的胰蛋白酶切来说,除了局部构象、三维结构、实验条件,以及其它偶然因素会影响赖氨酸K或者精氨酸R后的位点能否被酶切外,该位点附近的其它氨基酸也会影响蛋白水解酶的酶切效果。从质谱图谱中时常会鉴定出包含漏切位点的肽段,因此,预测蛋白质的酶切位点能够为数据库搜索算法提供更为可靠的模型,也能够为了解和分析蛋白质的酶切规律提供依据。本文提出了一种基于马尔科夫(Markov)链的预测方法,能够利用蛋白质的序列信息来预测候选酶切位点的酶切概率,在蛋白酶切过程中,预测肽段的覆盖率可以达到85%以上。     

A multistate Markov chain model for evaluating a sterilization policy

"A multistate Markov chain model corresponding to varying fertility and mortality rates at different levels of surviving children of a couple was developed. Asymptotic probabilities of having a fixed number of children have been worked out." The implied geographical focus is on India.     

Sequential Analysis of Survival Times in Clinical Trials

This paper provides a synopsis of statistical methods which can be used for the sequential analysis of possibly censored survival times in clinical trials. Especially, results on the asymptotic behaviour of the Breslow-Haug statistic and on the sequential version of the logrank statistic are presented in a standardized terminology. In addition, formulae for the explicit calculation of linear and square-root boundaries for sequential plans are given and illustrated by an example. Practical problems of applying these methods when monitoring a fixed-sample clinical trial as well as group sequential methods and calculation of P-values are also discussed.     

基于马尔可夫链的基因芯片特异性探针选择方法

对于基因表达芯片,特异性探针的选择是探针设计的重要环节,由于基因组序列数据量极大,不可能对每个候选探针都在全序列中进行特异性评价并进行取舍。对此问题,提出了一种采用马尔可夫链概率准则的探针特异性选择方法,即把基因组序列看作马尔可夫链,任何探针序列的互补序列作为它的一个子序列,都具有一定的出现概率,概率越小,越可能具有特异性。据此,选择其中概率最小的N个候选探针,能够大大减少进行特异性评价的探针数量,缩短探针设计的计算时间。对实际数据的测试结果表明,该方法选择的探针具有很高的特异性。     

Two Stage Sampling for Simultaneously Testing Main and Side Effects in Clinical Trials

In clinical trials for the comparison of two treatments it seems reasonable to stop the study if either one treatment has worked out to be markedly superior in the main effect, or one to be severely inferior with respect to an adverse side effect. Two stage sampling plans are considered for simultaneously testing a main and side effect, assumed to follow a bivariate normal distribution with known variances, but unknown correlation. The test procedure keeps the global significance level under the null hypothesis of no differences in main and side effects. The critical values are chosen under the side condition, that the probability for ending at the first or second stage with a rejection of the elementary null hypothesis for the main effect is controlled, when a particular constellation of differences in mean holds; analogously the probability of ending with a rejection of the null hypotheses for the side effect, given certain treatment differences, is controlled too. Plans “optimal” with respect to sample size are given.