Rank Tests for Complete Block Designs

In this article a general univariate K-sample rank test for complete block designs with proportional cell frequencies is derived. It is shown that the test statistic has under H₀ and for arbitrary scores asymptotically a X²-distribution with K — 1 degrees of freedom. Special cases of this test are the Kruskal-Wallis test and the Friedman test. The test is compared with the Benard-van-Elteren test, the Mack-Skillings test and a test proposed by Downton. Finally the application of the test is illustrated by two examples.     

Sharp simultaneous confidence intervals for the means of selected populations with application to microarray data analysis

Summary Simultaneous inference for a large number, N, of parameters is a challenge. In some situations, such as microarray experiments, researchers are only interested in making inference for the K parameters corresponding to the K most extreme estimates. Hence it seems important to construct simultaneous confidence intervals for these K parameters. The naïve simultaneous confidence intervals for the K means (applied directly without taking into account the selection) have low coverage probabilities. We take an empirical Bayes approach (or an approach based on the random effect model) to construct simultaneous confidence intervals with good coverage probabilities. For N= 10,000 and K= 100, typical for microarray data, our confidence intervals could be 77% shorter than the naïve K‐dimensional simultaneous intervals.     

Analysis of Triangular Diallel Table for Experiments in Block Designs

In this paper the analysis of genotypes obtained in diallel crossing system, including one set of F₁′s and parents, arranged in triangular table is given. This analysis is presented for data obtained from the experiments laid out in block designs. The analysis of variance, estimators of general and specific combining abilities as well as statistics for testing of hypotheses concerning those parameters are given.     

A new nonparametric approach for baseline covariate adjustment for two-group comparative studies

SUMMARY: We consider two-armed clinical trials in which the response and/or the covariates are observed on either a binary, ordinal, or continuous scale. A new general nonparametric (NP) approach for covariate adjustment is presented using the notion of a relative effect to describe treatment effects. The relative effect is defined by the probability of observing a higher response in the experimental than in the control arm. The notion is invariant under monotone transformations of the data and is therefore especially suitable for ordinal data. For a normal or binary distributed response the relative effect is the transformed effect size or the difference of response probability, respectively. An unbiased and consistent NP estimator for the relative effect is presented. Further, we suggest a NP procedure for correcting the relative effect for covariate imbalance and random covariate imbalance, yielding a consistent estimator for the adjusted relative effect. Asymptotic theory has been developed to derive test statistics and confidence intervals. The test statistic is based on the joint behavior of the estimated relative effect for the response and the covariates. It is shown that the test statistic can be used to evaluate the treatment effect in the presence of (random) covariate imbalance. Approximations for small sample sizes are considered as well. The sampling behavior of the estimator of the adjusted relative effect is examined. We also compare the probability of a type I error and the power of our approach to standard covariate adjustment methods by means of a simulation study. Finally, our approach is illustrated on three studies involving ordinal responses and covariates.     

A Combined Invariant Test for a Null Variance Ratio

This paper investigates the properties of a test that combines the Wald and LMPI (locally most powerful invariant) tests of variance components in unbalanced mixed models. The combined test statistic is easily computed and its null distribution may be approximated by a central F distribution with the degrees of freedom of the numerator adjusted in accordance with the degree of imbalance of the design. Numerical methods are used to show that the approximation is accurate over a wide range of conditions and that the efficiency of the combined test, relative to the power envelope, is satisfactorily high overall.     

Analysis of Diallel Table for Experiments in Block Designs

In this paper the analysis of genotypes obtained in diallel crossing system, including parents, one set of F₁s and reciprocal F₁'s, is given. This analysis is presented for data obtained from the experiments laid out in block designs. The analysis of variance, estimator of reciprocal effects, estimators of general and specific combining abilities as well as statistics for testing of hypotheses concerning those parameters are given.     

One Degree of Freedom for Interaction in a Two-Way Classification without Replications

The paper develops F-tests with single numerator degree of freedom (d.f.) for interaction in a two-way crossed classification with one observation per cell. Thus, a convenient and possibly more powerful alternative to the Johnson and Graybill (1972) test is provided.     

Approximate Confidence Intervals for Contrasts in the Balanced Three Factor Mixed Model

When conducting a statistical analysis of data from a designed experiment, an investigator is often interested in confidence intervals for contrasts of the fixed effects. If the analysis involves a mixed linear model, exact confidence intervals for contrasts of the fixed effects are not always available. In such cases, confidence intervals with approximate coverage probabilities must be used. As will be shown, this problem may be generalized to that of constructing a confidence interval for the parameter μ, where X is a normal random variable with mean μ and variance ∑ a_qθ_q, where a₁…,a_Q are known constants, U_q = n_qS/θ_q is a chi-squared random variable with n_q degrees of freedom, for each q = 1,…, Q, and X,U₁,…, U_Q are mutually independent. In this paper, we consider the case where Q = 3 and a₃ ≤0.     

Ascertainment Bias and the Pattern of Nucleotide Diversity at the Human ALDH2 Locus in a Japanese Population

Many East Asian human populations harbor a high-frequency deficiency allele for the aldehyde dehydrogenase 2 (ALDH2) enzyme, a critical protein involved in the metabolism of ethanol. Here we use resequencing and long-range SNP haplotype data from a Japanese sample to test whether patterns of nucleotide diversity and linkage disequilibrium at this locus are compatible with a standard neutral model of evolution. Examination of the pattern of polymorphism at a locus such as this, where the frequency of a common allele is known a priori, introduces an ascertainment bias that must be corrected for in analyses of the frequency spectrum of polymorphisms. We apply a flexible and generally applicable simulation approach to correct for this bias in our ALDH2 data and, also, to explore the effect of bias on the commonly used summary statistics Tajima’s D, Fu and Li’s D, and Fay and Wu’s H. Our study finds no evidence that the pattern of genetic variation at ALDH2 differs from that expected under a standard neutral model. However, our general examination of ascertainment bias indicates that a priori knowledge of segregating alleles greatly affects the expected distributions of summary statistics. Under many parameter combinations we find that ascertainment bias introduces an elevated rate of false positives when summary statistics are used to test for deviations from a standard neutral model. However, we also show that over a wide range of conditions the power of all summary statistics can be greatly increased by incorporating prior knowledge of segregating alleles. [Reviewing Editor: Dr. Martin Kreitman]     

Threshold and other departures from linear-quadratic curvature in the non-cancer mortality dose-response curve in the Japanese atomic bomb survivors

Recently released data on non-cancer mortality in Japanese atomic bomb survivors are analysed using a variety of generalised relative risk models that take account of errors in estimates of dose to assess the dose-response at low doses. If linear-threshold, quadratic-threshold or linear-quadratic-threshold relative risk models (the dose-response is assumed to be linear, quadratic or linear-quadratic above the threshold, respectively) are fitted to the non-cancer data there are no statistically significant (p>0.10) indications of threshold departures from linearity, quadratic curvature or linear-quadratic curvature. These findings are true irrespective of the assumed magnitude of dosimetric error, between 25%–45% geometric standard deviations. In general, increasing the assumed magnitude of dosimetric error had little effect on the central estimates of the threshold, but somewhat widened the associated confidence intervals. If a power of dose model is fitted, there is little evidence (p>0.10) that the power of dose in the dose-response is statistically significantly different from 1, again irrespective of the assumed magnitude of dosimetric errors in the range 25%–45%. Again, increasing the size of the errors resulted in wider confidence intervals on the power of dose, without marked effect on the central estimates. In general these findings remain true for various non-cancer disease subtypes.     

Statistical Comparison of Band Spectral Powers: An Aid in Stochastical Analysis of Brain Electrical Activity. Part 2: Construction of Confidence Intervals of Spectral Band Power and their Application in EEG-Analysis

Based on the result that the distribution of estimated spectral power in broad frequency bands can be approximated by x²-distribution the accuracy of the approximation was tested by different models of stochastical processes. Two significance tests for comparison of spectral band powers on the basis of this approximation and the estimation of confidence intervals were developed and tested by application on EEG data. By means of these test statistics, a new basis for statistical comparison between EEG maps of groups as well as between maps of groups and single maps can be suggested.     

Analysis of covariance with incomplete data via semiparametric model transformations

We propose a method for fitting semiparametric models such as the proportional hazards (PH), additive risks (AR), and proportional odds (PO) models. Each of these semiparametric models implies that some transformation of the conditional cumulative hazard function (at each t) depends linearly on the covariates. The proposed method is based on nonparametric estimation of the conditional cumulative hazard function, forming a weighted average over a range of t-values, and subsequent use of least squares to estimate the parameters suggested by each model. An approximation to the optimal weight function is given. This allows semiparametric models to be fitted even in incomplete data cases where the partial likelihood fails (e.g., left censoring, right truncation). However, the main advantage of this method rests in the fact that neither the interpretation of the parameters nor the validity of the analysis depend on the appropriateness of the PH or any of the other semiparametric models. In fact, we propose an integrated method for data analysis where the role of the various semiparametric models is to suggest the best fitting transformation. A single continuous covariate and several categorical covariates (factors) are allowed. Simulation studies indicate that the test statistics and confidence intervals have good small-sample performance. A real data set is analyzed.     

Some Simple Statistics to Test Against Ordered Alternatives in Complete Block Designs

Consider testing the hypothesis of no treatment effects against a postulated ranking of the m treatments, given data from n Complete Blocks. A suitable test statistic is the weighted average rank correlation w = σb_QiC_i where C_i is the correlation between the postulated ranking and the ranking observed within the ith block, Q_i is the rank of the ith block with respect to credibility, and the b_i's are weights such that 0 ≦ b¹ ≦ … ≦ bn. In this paper we introduce some simple statistics: the first extends the signed-rank statistic to m ≦ 3, the second uses a simple measure of correlation based on the antirank, and the third a statistic based on Spearman's footrule. Tables for critical values are provided and the normal approximation is investigated.     

Information-Theoretic Model Selection and Model Averaging for Closed-Population Capture-Recapture Studies

Specification of an appropriate model is critical to valid statistical inference. Given the “true model” for the data is unknown, the goal of model selection is to select a plausible approximating model that balances model bias and sampling variance. Model selection based on information criteria such as AIC or its variant AIC_c, or criteria like CAIC, has proven useful in a variety of contexts including the analysis of open-population capture-recapture data. These criteria have not been intensively evaluated for closed-population capture-recapture models, which are integer parameter models used to estimate population size (N), and there is concern that they will not perform well. To address this concern, we evaluated AIC, AIC_c, and CAIC model selection for closed-population capture-recapture models by empirically assessing the quality of inference for the population size parameter N. We found that AIC-, AIC_c-, and CAIC-selected models had smaller relative mean squared errors than randomly selected models, but that confidence interval coverage on N was poor unless unconditional variance estimates (which incorporate model uncertainty) were used to compute confidence intervals. Overall, AIC and AIC_c outperformed CAIC, and are preferred to CAIC for selection among the closed-population capture-recapture models we investigated. A model averaging approach to estimation, using AIC, AIC_c, or CAIC to estimate weights, was also investigated and proved superior to estimation using AIC-, AIC_c-, or CAIC-selected models. Our results suggested that, for model averaging, AIC or AIC_c should be favored over CAIC for estimating weights.     

Testing for Genetic Association in the Presence of Linkage and Gene–Covariate Interactions

In order to study family‐based association in the presence of linkage, we extend a generalized linear mixed model proposed for genetic linkage analysis (Lebrec and van Houwelingen (2007), Human Heredity 64 , 5–15) by adding a genotypic effect to the mean. The corresponding score test is a weighted family‐based association tests statistic, where the weight depends on the linkage effect and on other genetic and shared environmental effects. For testing of genetic association in the presence of gene–covariate interaction, we propose a linear regression method where the family‐specific score statistic is regressed on family‐specific covariates. Both statistics are straightforward to compute. Simulation results show that adjusting the weight for the within‐family variance structure may be a powerful approach in the presence of environmental effects. The test statistic for genetic association in the presence of gene–covariate interaction improved the power for detecting association. For illustration, we analyze the rheumatoid arthritis data from GAW15. Adjusting for smoking and anti‐cyclic citrullinated peptide increased the significance of the association with the DR locus.     

A distribution model for heritability.

A regression model to predict quantiles of narrow sense individual and family mean heritabilities is developed and used to predict confidence intervals either directly or via a generalized beta distribution model. Extensive simulations of balanced sib analysis trials in randomized complete block designs and normal distributed environmental and additive genetic effects confirmed that heritabilities follow a beta distribution even in cases with up to 10% of the data missing at random. The new model is both more accurate and more precise than commonly used alternatives based on "exact" chi 2 distributions and Satterthwaites approximations to the degrees of freedom. Estimates of the expected heritability and a Taylor approximation of the standard error of the heritability are needed as input to the quantile model. Applications of the presented models for estimating confidence intervals and as an aid in the design of experiments are provided.     

A goodness‐of‐fit test for occupancy models with correlated within‐season revisits

Occupancy modeling is important for exploring species distribution patterns and for conservation monitoring. Within this framework, explicit attention is given to species detection probabilities estimated from replicate surveys to sample units. A central assumption is that replicate surveys are independent Bernoulli trials, but this assumption becomes untenable when ecologists serially deploy remote cameras and acoustic recording devices over days and weeks to survey rare and elusive animals. Proposed solutions involve modifying the detection‐level component of the model (e.g., first‐order Markov covariate). Evaluating whether a model sufficiently accounts for correlation is imperative, but clear guidance for practitioners is lacking. Currently, an omnibus goodness‐of‐fit test using a chi‐square discrepancy measure on unique detection histories is available for occupancy models (MacKenzie and Bailey, Journal of Agricultural, Biological, and Environmental Statistics, 9, 2004, 300; hereafter, MacKenzie–Bailey test). We propose a join count summary measure adapted from spatial statistics to directly assess correlation after fitting a model. We motivate our work with a dataset of multinight bat call recordings from a pilot study for the North American Bat Monitoring Program. We found in simulations that our join count test was more reliable than the MacKenzie–Bailey test for detecting inadequacy of a model that assumed independence, particularly when serial correlation was low to moderate. A model that included a Markov‐structured detection‐level covariate produced unbiased occupancy estimates except in the presence of strong serial correlation and a revisit design consisting only of temporal replicates. When applied to two common bat species, our approach illustrates that sophisticated models do not guarantee adequate fit to real data, underscoring the importance of model assessment. Our join count test provides a widely applicable goodness‐of‐fit test and specifically evaluates occupancy model lack of fit related to correlation among detections within a sample unit. Our diagnostic tool is available for practitioners that serially deploy survey equipment as a way to achieve cost savings.     

Cumulative Damage Survival Models for the Randomized Complete Block Design

A continuous time discrete state cumulative damage process {X(t), t ≥ 0} is considered, based on a non‐homogeneous Poisson hit‐count process and discrete distribution of damage per hit, which can be negative binomial, Neyman type A, Polya‐Aeppli or Lagrangian Poisson. Intensity functions considered for the Poisson process comprise a flexible three‐parameter family. The survival function is S(t) = P(X(t) ≤ L) where L is fixed. Individual variation is accounted for within the construction for the initial damage distribution {P(X(0) = x) | x = 0, 1, …,}. This distribution has an essential cut‐off before x = L and the distribution of L – X(0) may be considered a tolerance distribution. A multivariate extension appropriate for the randomized complete block design is developed by constructing dependence in the initial damage distributions. Our multivariate model is applied (via maximum likelihood) to litter‐matched tumorigenesis data for rats. The litter effect accounts for 5.9 percent of the variance of the individual effect. Cumulative damage hazard functions are compared to nonparametric hazard functions and to hazard functions obtained from the PVF‐Weibull frailty model. The cumulative damage model has greater dimensionality for interpretation compared to other models, owing principally to the intensity function part of the model.     

Validation of a Demographic Model for Woodland Caribou

Abstract: Wildlife population models are potentially valuable for conservation planning. Validation is necessary to ensure that models are sufficiently robust for predicting management outcomes consistent with conservation objectives. Sorensen et al. (2008) produced a model of woodland caribou (Rangifer tarandus) population growth rate that was recently modified and used as a predictive tool at several scales. We computed confidence intervals and evaluated the performance of this model using novel data. Confidence intervals were wide, and results suggested that the model may have a positive bias, resulting in over-estimation of population growth rates, as well as low predictive power. Wide confidence intervals mean that current understanding of factors governing woodland caribou herd dynamics is not sufficient for wildlife managers to make reliable projections of responses to management.     

Modeling of yeast <Emphasis Type="Italic">Brettanomyces bruxellensis</Emphasis> growth at different acetic acid concentrations under aerobic and anaerobic conditions

Glucose utilization by Brettanomyces bruxellensis at different acetic acid concentrations under aerobic and anaerobic conditions was investigated. The presence of the organic acid disturbs the growth and fermentative activity of the yeast when its concentration exceeds 2 g l⁻¹. A mathematical model is proposed for the kinetic behavior analysis of yeast growing in batch culture. A Matlab algorithm was used for estimation of model parameters, whose confidence intervals were also calculated at a 0.95 probability level using a t-Student distribution for f degrees of freedom. The model successfully simulated the batch kinetics observed at different concentrations of acetic acid under both oxygen conditions.