Point estimates and confidence regions for sequential trials involving selection

A number of authors have proposed clinical trial designs involving the comparison of several experimental treatments with a control treatment in two or more stages. At the end of the first stage, the most promising experimental treatment is selected, and all other experimental treatments are dropped from the trial. Provided it is good enough, the selected experimental treatment is then compared with the control treatment in one or more subsequent stages. The analysis of data from such a trial is problematic because of the treatment selection and the possibility of stopping at interim analyses. These aspects lead to bias in the maximum-likelihood estimate of the advantage of the selected experimental treatment over the control and to inaccurate coverage for the associated confidence interval. In this paper, we evaluate the bias of the maximum-likelihood estimate and propose a bias-adjusted estimate. We also propose an approach to the construction of a confidence region for the vector of advantages of the experimental treatments over the control based on an ordering of the sample space. These regions are shown to have accurate coverage, although they are also shown to be necessarily unbounded. Confidence intervals for the advantage of the selected treatment are obtained from the confidence regions and are shown to have more accurate coverage than the standard confidence interval based upon the maximum-likelihood estimate and its asymptotic standard error.

Sequential designs for phase III clinical trials incorporating treatment selection

Most statistical methodology for phase III clinical trials focuses on the comparison of a single experimental treatment with a control. An increasing desire to reduce the time before regulatory approval of a new drug is sought has led to development of two-stage or sequential designs for trials that combine the definitive analysis associated with phase III with the treatment selection element of a phase II study. In this paper we consider a trial in which the most promising of a number of experimental treatments is selected at the first interim analysis. This considerably reduces the computational load associated with the construction of stopping boundaries compared to the approach proposed by Follman, Proschan and Geller (Biometrics 1994; 50: 325-336). The computational requirement does not exceed that for the sequential comparison of a single experimental treatment with a control. Existing methods are extended in two ways. First, the use of the efficient score as a test statistic makes the analysis of binary, normal or failure-time data, as well as adjustment for covariates or stratification straightforward. Second, the question of trial power is also considered, enabling the determination of sample size required to give specified power. Copyright © 2003 John Wiley & Sons, Ltd.

Mutational meltdown in primary endosymbionts: selection limits Muller's ratchet

Background Primary bacterial endosymbionts of insects (p-endosymbionts) are thought to be undergoing the process of Muller's ratchet where they accrue slightly deleterious mutations due to genetic drift in small populations with negligible recombination rates. If this process were to go unchecked over time, theory predicts mutational meltdown and eventual extinction. Although genome degradation is common among p-endosymbionts, we do not observe widespread p-endosymbiont extinction, suggesting that Muller's ratchet may be slowed or even stopped over time. For example, selection may act to slow the effects of Muller's ratchet by removing slightly deleterious mutations before they go to fixation thereby causing a decrease in nucleotide substitutions rates in older p-endosymbiont lineages. Methodology/Principal Findings To determine whether selection is slowing the effects of Muller's ratchet, we determined the age of the Candidatus Riesia/sucking louse assemblage and analyzed the nucleotide substitution rates of several p-endosymbiont lineages that differ in the length of time that they have been associated with their insect hosts. We find that Riesia is the youngest p-endosymbiont known to date, and has been associated with its louse hosts for only 13–25 My. Further, it is the fastest evolving p-endosymbiont with substitution rates of 19–34% per 50 My. When comparing Riesia to other insect p-endosymbionts, we find that nucleotide substitution rates decrease dramatically as the age of endosymbiosis increases. Conclusions/Significance A decrease in nucleotide substitution rates over time suggests that selection may be limiting the effects of Muller's ratchet by removing individuals with the highest mutational loads and decreasing the rate at which new mutations become fixed. This countering effect of selection could slow the overall rate of endosymbiont extinction.

Insight overview: natural selection 150 years on

The theory of evolution by natural selection has prospered in its first 150 years and provides a consistent account of species as highly adapted and rare survivors in the struggle for existence. It now faces the challenge of finding order in the evolution of complex systems, including human society.

In vivo expression technology (IVET) selection of genes of Rhizobium leguminosarum biovar viciae A34 expressed in the rhizosphere

IVET was used to identify genes that are specifically expressed in the rhizosphere of the pea-nodulating bacterium Rhizobium leguminosarum A34. A library of R. leguminosarum A34 cloned in the integration vector pIE1, with inserts upstream of a promoter-less purN:gfp:gusA, was conjugated into purN host RU2249 and recombined into the genome. After removal of colonies that expressed the reporter genes of the vector under laboratory conditions, the library was inoculated into a nonsterile pea rhizosphere. The key result is that 29 rhizosphere-induced loci were identified. Sequence analysis of these clones showed that a wide variety of R. leguminosarum A34 genes are expressed specifically in the rhizosphere including those encoding proteins involved in environmental sensing, control of gene expression, metabolic reactions and membrane transport. These genes are likely to be important for survival and colonization of the pea rhizosphere.

Selection and sticklebacks

Over the last decade, there has been increasing circumstantial evidence for the action of natural selection in the genome, arising largely from molecular genetic surveys of large numbers of markers. In nonmodel organisms without densely mapped markers, a frequently used method is to identify loci that have unusually high or low levels of genetic differentiation, or low genetic diversity relative to other populations. The paper by Makinen et al. (2008a) in this issue of Molecular Ecology reports the results of a survey of microsatellite allele frequencies at more than 100 loci in seven populations of the three-spined stickleback (Gasterosteus aculeatus). They show that a microsatellite locus and two indel markers located within the intron of the Eda gene, known to control the number of lateral plates in the stickleback (Fig. 1), tend to be much more highly genetically differentiated than other loci, a finding that is consistent with the action of local selection. They identify a further two independent candidates for local selection, and, most intriguingly, they further suggest that up to 15% of their loci may provide evidence of balancing selection.

Estimation following selection of the largest of two normal means

This paper considers the problem of estimation when one of a number of populations, assumed normal with known common variance, is selected on the basis of it having the largest observed mean. Conditional on selection of the population, the observed mean is a biased estimate of the true mean. This problem arises in the analysis of clinical trials in which selection is made between a number of experimental treatments that are compared with each other either with or without an additional control treatment. Attempts to obtain approximately unbiased estimates in this setting have been proposed by Shen [2001. An improved method of evaluating drug effect in a multiple dose clinical trial. Statist. Medicine 20, 1913–1929] and Stallard and Todd [2005. Point estimates and confidence regions for sequential trials involving selection. J. Statist. Plann. Inference 135, 402–419]. This paper explores the problem in the simple setting in which two experimental treatments are compared in a single analysis. It is shown that in this case the estimate of Stallard and Todd is the maximum-likelihood estimate (m.l.e.), and this is compared with the estimate proposed by Shen. In particular, it is shown that the m.l.e. has infinite expectation whatever the true value of the mean being estimated. We show that there is no conditionally unbiased estimator, and propose a new family of approximately conditionally unbiased estimators, comparing these with the estimators suggested by Shen.

In vivo selection for metastasis promoting genes in the mouse

Here, we report the identification of a metastasis promoting factor by a forward genetic screen in mice. A retroviral cDNA library was introduced into the nonmetastatic cancer cell line 168FARN, which was then orthotopically transplanted into mouse mammary fat pads, followed by selection for cells that metastasize to the lung. The genes encoding the disulfide isomerase ERp5 and beta-catenin were found to promote breast cancer invasion and metastasis. Disulfide isomerases (thiol isomerases), which catalyze disulfide bond formation, reduction, and isomerization, have not previously been implicated in cancer cell signaling and tumor metastasis. Overexpression of ERp5 promotes both in vitro migration and invasion and in vivo metastasis of breast cancer cells. These effects were shown to involve activation of ErbB2 and phosphoinositicle 3-kinase (PI3K) pathways through dimerization of ErbB2. Activation of ErbB2 and PI3K subsequently stimulates RhoA and beta-catenin, which mediate the migration and invasion of tumor cells. Inhibition of ErbB2 and PI3K reverses the phenotypes induced by ERp5. Finally, ERp5 was shown to be up-regulated in human surgical samples of invasive breast cancers. These data identify a link between disulfide isomerases and tumor development, and provide a mechanism that modulates ErbB2 and PI3K signaling in the promotion of cancer progression.