A Multistage Procedure for Analyzing Unreplicated Factorial Experiments

A multistage procedure, which is based on the likelihood principle, is proposed to identify active effects in unreplicated factorial designs and their fractions. The proposed procedure controls the experimental error rate (EER) at any prespecified level in industrial and biomedical experiments. Extensive comparison with Lenth 's (1989) test is discussed.     

On the False Discovery Rate and Expected Type I Errors

The paper is concerned with expected type I errors of some stepwise multiple test procedures based on independent p‐values controlling the so‐called false discovery rate (FDR). We derive an asymptotic result for the supremum of the expected type I error rate(EER) when the number of hypotheses tends to infinity. Among others, it will be shown that when the original Benjamini‐Hochberg step‐up procedure controls the FDR at level α, its EER may approach a value being slightly larger than α/4 when the number of hypotheses increases. Moreover, we derive some least favourable parameter configuration results, some bounds for the FDR and the EER as well as easily computable formulae for the familywise error rate (FWER) of two FDR‐controlling procedures. Finally, we discuss some undesirable properties of the FDR concept, especially the problem of cheating.     

Evaluation of expected absolute error affecting the maximum specific growth rate for random relative error of cell concentration

Borzani's [(1994) World Journal of Microbiology and Biotechnology 10, 475–476] idea of evaluation of absolute error affecting the 'maximum specific growth rate' (ESGR), calculated on the basis of the first and the last time points of the entire experimental time period, is generalized to the real-life situations where the relative errors of cell concentration cannot be assumed to be constant during the experiment. Visualizing the entire experimental time period as to comprise of several successive, mutually exclusive and exhaustive time intervals, we compute specific growth rates (SGRs) for each of these time intervals. Defining maximum of these SGR values as MSGR in contrast to Borzani's ESGR our aim is to study the effect of the expected absolute error on SGRs of different intervals. This will reveal the discrepancy between the true and observed MSGRs. Assuming the relative error distribution on (0,1) to be rectangular and symmetric truncated normal with mean at 0.5 and suitable variance, the expected values of the absolute errors are evaluated and numerically tabulated using the software packages MATHEMATICA and S-PLUS. Our results thus hold for situations involving varying relative errors where Borzani's results cannot be applied. A discussion with a concrete numerical example on the misidentification of the MSGR interval due to the effect of the random relative measuremental errors reveals to an experimental biologist that ignorance of this fact may lead to his/her entire experiment being futile.     

6-10× pyrosequencing is a practical approach for whole prokaryote genome studies

Next generation 454 pyrosequencing technology for whole bacterial genome sequencing involves a deep sequencing strategy with at least 15-20 × in depth proposed by official protocols but usually done with over 20 × in practices. In this study, we carried out a comprehensive evaluation of quality of the de novo assemblies based on realistic pyrosequencing simulated data from 1480 prokaryote genomes and 7 runs of machine-generated data. Our results demonstrated that for most of the prokaryote genomes, 6-10 × sequencing in qualified runs with 400 bp reads could produce high quality draft assembly (> 98% genome coverage, < 100 contigs with N50 size > 100 kb, single base accuracy > 99.99, indel error rate < 0.01%, false gene loss/duplication rate < 0.5%). Our study proves the power of low depth pyrosequencing strategy, which provides a cost-effective way for sequencing whole prokaryote genomes in a short time and enables further studies in microbial population diversity and comparative genomics.     

Evaluation of the maximum specific growth rate of a yeast indicating non-linear growth trends in batch culture

The maximum specific growth rate (μ_max) of an ethanolic D-xylose-fermenting yeast, Pichia stipitis, showing non-linear growth trends in batch culture, was calculated using the rate equation μ₂ = (1/Δt) ln(x ₂/x ₁). The absolute error Δμ, affecting μ₂, was derived using an equation given by Borzani (1994). Based on the assumption of linearity of growth curves between two closest time points, the relation between the two rate formulae, μ₁ = (1/xˉ)dx _t /dt and μ₂ = (1/Δt) ln(x ₂/x ₁) was established. In a particular condition, when μ₁ = μ₂, an equation has been developed, the roots of which are the specific growth rates at different time points. This revised version was published online in July 2006 with corrections to the Cover Date.     

Challenges and regulatory experiences with non‐inferiority trial design without placebo arm

For a non‐inferiority trial without a placebo arm, the direct comparison between the test treatment and the selected positive control is in principle the only basis for statistical inference. Therefore, evaluating the test treatment relative to the non‐existent placebo presents extreme challenges and requires some kind of bridging from the past to the present with no current placebo data. For such inference based partly on an indirect bridging manipulation, fixed margin method and synthesis method are the two widely discussed methods in the recent literature. There are major differences in statistical inference paradigm between the two methods. The fixed margin method employs the historical data that assess the performances of the active control versus a placebo to guide the selection of the non‐inferiority margin. Such guidance is not part of the ultimate statistical inference in the non‐inferiority trial. In contrast, the synthesis method connects the historical data to the non‐inferiority trial data for making broader inferences relating the test treatment to the non‐existent current placebo. On the other hand, the type I error rate associated with the direct comparison between the test treatment and the active control cannot shed any light on the appropriateness of the indirect inference for faring the test treatment against the non‐existent placebo. This work explores an approach for assessing the impact of potential bias due to violation of a key statistical assumption to guide determination of the non‐inferiority margin.     

Comparison of group testing algorithms for case identification in the presence of test error

We derive and compare the operating characteristics of hierarchical and square array-based testing algorithms for case identification in the presence of testing error. The operating characteristics investigated include efficiency (i.e., expected number of tests per specimen) and error rates (i.e., sensitivity, specificity, positive and negative predictive values, per-family error rate, and per-comparison error rate). The methodology is illustrated by comparing different pooling algorithms for the detection of individuals recently infected with HIV in North Carolina and Malawi.     

Modeling the impact of periodic bottlenecks, unidirectional mutation, and observational error in experimental evolution

Antibiotic resistant bacteria are a constant threat in the battle against infectious diseases. One strategy for reducing their effect is to temporarily discontinue the use of certain antibiotics in the hope that in the absence of the antibiotic the resistant strains will be replaced by the sensitive strains. An experiment where this strategy is employed in vitro [5] produces data which showed a slow accumulation of sensitive mutants. Here we propose a mathematical model and statistical analysis to explain this data.The stochastic model elucidates the trend and error structure of the data. It provides a guide for developing future sampling strategies, and provides a framework for long term predictions of the effects of discontinuing specific antibiotics on the dynamics of resistant bacterial populations.This Research is part of the Initiative in Bioinformatics and Evolutionary Studies (IBEST) at the University of Idaho. Funding was provided by NSF EPSCoR EPS-0080935, NSF EPSCoR, EPS-0132626, and NIH NCRR grant NIH NCRR- 20RR016448. Paul Joyce is also funded by NSF DEB-0089756, and NSF DMS-0072198.     

Comparative study on the performance of textural image features for active contour segmentation

We present a computerized method for the semi-automatic detection of contours in ultrasound images.The novelty of our study is the introduction of a fast and efficient image function relating to parametric active contour models.This new function is a combination of the gray-level information and first-order statistical features,called standard deviation parameters.In a comprehensive study,the developed algorithm and the efficiency of segmentation were first tested for synthetic images.Tests were also performed on breast and liver ultrasound images.The proposed method was compared with the watershed approach to show its efficiency.The performance of the segmentation was estimated using the area error rate.Using the standard deviation textural feature and a 5×5 kernel,our curve evolution was able to produce results close to the minimal area error rate(namely 8.88% for breast images and 10.82% for liver images).The image resolution was evaluated using the contrast-to-gradient method.The experiments showed promising segmentation results.     

On the identification of mortality hotspots in linear infrastructures

One of the main tasks when dealing with the impacts of infrastructures on wildlife is to identify hotspots of high mortality so one can devise and implement mitigation measures. A common strategy to identify hotspots is to divide an infrastructure into several segments and determine when the number of collisions in a segment is above a given threshold, reflecting a desired significance level that is obtained assuming a probability distribution for the number of collisions, which is often the Poisson distribution. The problem with this approach, when applied to each segment individually, is that the probability of identifying false hotspots (Type I error) is potentially high. The way to solve this problem is to recognize that it requires multiple testing corrections or a Bayesian approach. Here, we apply three different methods that implement the required corrections to the identification of hotspots: (i) the familywise error rate correction, (ii) the false discovery rate, and (iii) a Bayesian hierarchical procedure. We illustrate the application of these methods with data on two bird species collected on a road in Brazil. The proposed methods provide practitioners with procedures that are reliable and simple to use in real situations and, in addition, can reflect a practitioner’s concerns towards identifying false positive or missing true hotspots. Although one may argue that an overly cautionary approach (reducing the probability of type I error) may be beneficial from a biological conservation perspective, it may lead to a waste of resources and, probably worse, it may raise doubts about the methodology adopted and the credibility of those suggesting it.     

An Investigation on the Allelic Chi‐Square Test Used in Genetic Association Studies

Case‐control studies are primary study designs used in genetic association studies. Sasieni (Biometrics 1997, 53, 1253–1261) pointed out that the allelic chi‐square test used in genetic association studies is invalid when Hardy‐Weinberg equilibrium (HWE) is violated in a combined population. It is important to know how much type I error rate is deviated from the nominal level under violated HWE. We examine bounds of type I error rate of the allelic chi‐square test. We also investigate power of the goodness‐of‐fit test for HWE which can be used as a guideline for selecting an appropriate test between the allelic chi‐square test and the modified allelic chi‐square test, the latter of which was proposed for cases of violated HWE. In small samples, power is not large enough to detect the Wright's inbreeding model of small values of inbreeding coefficient. Therefore, when the null hypothesis of HWE is barely accepted, the modified test should be considered as an alternative method. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Confidence limits for drug-induced response rates in carcinogenesis experiments

Animal experiments in chemical carcinogenesis are often analysed by tests for equal proportions in a 2 × 2 table. Since hereby nothing is said about the power of the tests, we propose to describe the outcome of such an experiment by an upper confidence limit of an adjusted difference between the two response rates.     

Multiple testing to establish superiority/equivalence of a new treatment compared with k standard treatments for unbalanced designs

In clinical studies, multiple superiority/equivalence testing procedures can be applied to classify a new treatment as superior, equivalent (same therapeutic effect), or inferior to each set of standard treatments. Previous stepwise approaches (Dunnett and Tamhane, 1997, Statistics in Medicine16, 2489-2506; Kwong, 2001, Journal of Statistical Planning and Inference 97, 359-366) are only appropriate for balanced designs. Unfortunately, the construction of similar tests for unbalanced designs is far more complex, with two major difficulties: (i) the ordering of test statistics for superiority may not be the same as the ordering of test statistics for equivalence; and (ii) the correlation structure of the test statistics is not equi-correlated but product-correlated. In this article, we seek to develop a two-stage testing procedure for unbalanced designs, which are very popular in clinical experiments. This procedure is a combination of step-up and single-step testing procedures, while the familywise error rate is proved to be controlled at a designated level. Furthermore, a simulation study is conducted to compare the average powers of the proposed procedure to those of the single-step procedure. In addition, a clinical example is provided to illustrate the application of the new procedure.     

Distinct error rates for reference and nonreference genotypes estimated by pedigree analysis

Errors in genotype calling can have perverse effects on genetic analyses, confounding association studies, and obscuring rare variants. Analyses now routinely incorporate error rates to control for spurious findings. However, reliable estimates of the error rate can be difficult to obtain because of their variance between studies. Most studies also report only a single estimate of the error rate even though genotypes can be miscalled in more than one way. Here, we report a method for estimating the rates at which different types of genotyping errors occur at biallelic loci using pedigree information. Our method identifies potential genotyping errors by exploiting instances where the haplotypic phase has not been faithfully transmitted. The expected frequency of inconsistent phase depends on the combination of genotypes in a pedigree and the probability of miscalling each genotype. We develop a model that uses the differences in these frequencies to estimate rates for different types of genotype error. Simulations show that our method accurately estimates these error rates in a variety of scenarios. We apply this method to a dataset from the whole-genome sequencing of owl monkeys (Aotus nancymaae) in three-generation pedigrees. We find significant differences between estimates for different types of genotyping error, with the most common being homozygous reference sites miscalled as heterozygous and vice versa. The approach we describe is applicable to any set of genotypes where haplotypic phase can reliably be called and should prove useful in helping to control for false discoveries.     

High error rates for avian molecular sex identification primer sets applied to molted feathers

ABSTRACT Molted feathers are becoming increasingly important as a source of DNA for identifying the sex of individuals, and accurate methods for molecular sex identification are needed. Three molecular sex identification primer sets have been developed for use in nearly all nonratite birds, but performance of these primer sets has not been evaluated for molted feathers. For two species of birds, the Ring‐necked Pheasant (Phasianus colchicus) and the Scarlet Macaw (Ara macao), we evaluated success and error rates among primer sets using DNA from molted feathers and assessed the percentage of times an incorrect sex would be assigned when analyses are completed in duplicate. Amplification success rates differed among the primer sets for both species, ranging from 67.5% to 89.2% (P= 0.0002 and 0.009), and error rates were high, ranging from 1.9% to 24.2%. Success rates and error rates were not consistent between species and among primer sets. To improve the accuracy of molecular sex identification tests when using molted feathers, we suggest determining acceptable confidence levels in the accuracy of sex assignment, conducting pilot tests to evaluate the performance of different primer sets, and using high‐resolution electrophoresis systems to increase detection of errors.     

Estimation of false discovery rates in multiple testing: application to gene microarray data

Testing for significance with gene expression data from DNA microarray experiments involves simultaneous comparisons of hundreds or thousands of genes. If R denotes the number of rejections (declared significant genes) and V denotes the number of false rejections, then V/R, if R > 0, is the proportion of false rejected hypotheses. This paper proposes a model for the distribution of the number of rejections and the conditional distribution of V given R, V / R. Under the independence assumption, the distribution of R is a convolution of two binomials and the distribution of V / R has a noncentral hypergeometric distribution. Under an equicorrelated model, the distributions are more complex and are also derived. Five false discovery rate probability error measures are considered: FDR = E(V/R), pFDR = E(V/R / R > 0) (positive FDR), cFDR = E(V/R / R = r) (conditional FDR), mFDR = E(V)/E(R) (marginal FDR), and eFDR = E(V)/r (empirical FDR). The pFDR, cFDR, and mFDR are shown to be equivalent under the Bayesian framework, in which the number of true null hypotheses is modeled as a random variable. We present a parametric and a bootstrap procedure to estimate the FDRs. Monte Carlo simulations were conducted to evaluate the performance of these two methods. The bootstrap procedure appears to perform reasonably well, even when the alternative hypotheses are correlated (rho = .25). An example from a toxicogenomic microarray experiment is presented for illustration.     

Paternity validation and estimation of genotyping error rate for the BovineSNP50 BeadChip

Incorrect paternity assignment in cattle can have a major effect on rates of genetic gain. Of the 576 Israeli Holstein bulls genotyped by the BovineSNP50 BeadChip, there were 204 bulls for which the father was also genotyped. The results of 38 828 valid single nucleotide polymorphisms (SNPs) were used to validate paternity, determine the genotyping error rates and determine criteria enabling deletion of defective SNPs from further analysis. Based on the criterion of >2% conflicts between the genotype of the putative sire and son, paternity was rejected for seven bulls (3.5%). The remaining bulls had fewer conflicts by one or two orders of magnitude. Excluding these seven bulls, all other discrepancies between sire and son genotypes are assumed to be caused by genotyping mistakes. The frequency of discrepancies was >0.07 for nine SNPs, and >0.025 for 81 SNPs. The overall frequency of discrepancies was reduced from 0.00017 to 0.00010 after deletion of these 81 SNPs, and the total expected fraction of genotyping errors was estimated to be 0.05%. Paternity of bulls that are genotyped for genomic selection may be verified or traced against candidate sires at virtually no additional cost.