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Binary spatial observations arise in environmental and ecological studies, where Markov random field (MRF) models are often applied. Despite the prevalence and the long history of MRF models for spatial binary data, appropriate model diagnostics have remained an unresolved issue in practice. A complicating factor is that such models involve neighborhood specifications, which are difficult to assess for binary data. To address this, we propose a formal goodness-of-fit (GOF) test for diagnosing an MRF model for spatial binary values. The test statistic involves a type of conditional Moran's I based on the fitted conditional probabilities, which can detect departures in model form, including neighborhood structure. Numerical studies show that the GOF test can perform well in detecting deviations from a null model, with a focus on neighborhoods as a difficult issue. We illustrate the spatial test with an application to Besag's historical endive data as well as the breeding pattern of grasshopper sparrows across Iowa. [ABSTRACT FROM AUTHOR]

We propose a mu ltiple c ohort e xpansion (MUCE) approach as a design or analysis method for phase 1b multiple expansion cohort trials, which are novel first-in-human studies conducted following phase 1a dose escalation. In a phase 1b expansion cohort trial, one or more doses of a new investigational drug identified from phase 1a are tested for initial antitumour activities in patients with different indications (cancer types and/or biomarker status). Each dose–indication combination defines an arm, and patients are enrolled in parallel cohorts to all the arms. The MUCE design is based on a class of Bayesian hierarchical models that adaptively borrow information across arms. Specifically, we employ a latent probit model that allows for different degrees of borrowing across doses and indications. Statistical inference is directly based on the posterior probability of each arm being efficacious, facilitating the decision making that decides which arm to select for further testing. The MUCE design also incorporates interim looks, based on which the nonpromising arms will be stopped early due to futility. Through simulation studies, we show that MUCE exhibits superior operating characteristics. We also compare the performance of MUCE with that of Simon's two-stage design and some existing Bayesian designs for multiarm trials. To our knowledge, MUCE is the first Bayesian method for phase 1b expansion cohort trials with multiple doses and indications. [ABSTRACT FROM AUTHOR]

Concerns have been expressed over standards of statistical interpretation. Results with P <0.05 are often referred to as 'significant' which, in plain English, implies important. This leads some people directly into the misconception that this provides proof that associations are clinically relevant. There are calls for statistics educators to respond to these concerns. This article provides novel plain English interpretations that are designed to deepen understanding. Experience teaching postgraduates at Imperial College is discussed. A key issue with focusing on 'significance' is the common inappropriate practice of implying no association exists, simply because P >0.05. Referring to strengths of association in 'study participants' gives them gravitas, which may help to avoid this. This contrasts with the common practice of focusing on imprecision, by referring to the 'sample' and to 'point estimates'. Unlike formal statistical definitions, interpretations developed and presented here are rooted in the application of statistics. They are based on one set of study participants (not many random samples). Precision of strengths of association are based on using strengths in study participants to estimate strengths of association in the population (from which participants were selected by probability random sampling). Reference to 'compatibility with study data, dependent on statistical modelling assumptions' reminds us of the importance of data quality and modelling assumptions. A straightforward graph shows the relationship between P-values and test statistics. This figure and associated interpretations were developed to illuminate the continuous nature of P-values. This is designed to discourage focus on whether P <0.05, and encourage interpretation of exact P-values. [ABSTRACT FROM AUTHOR]

Summary: Estimation of tree height given diameter is an important part of the forest inventory analysis of the US Forest Service. Existing methods use parametric models to estimate the curve. We propose a semiparametric model in which log (height) is a smooth, increasing and concave function of diameter, with a random‐plot component and fixed effect covariates. Large sample properties and inference methods that work well in practice are derived. Proposed inference methods use approximate normal distributions for the fixed effects and a likelihood ratio test for the significance of the random effect. A closed form approximate prediction method is provided and overall it outperformed competitors for both a simulation and a real data application. The methods are implemented by the cgamm routine in the R package cgam and can be used for a wide range of mixed model applications. [ABSTRACT FROM AUTHOR]

Summary: The paper novelly transforms lack‐of‐fit tests for parametric quantile regression models into checking the equality of two conditional distributions of covariates. Accordingly, by applying some successful two‐sample test statistics in the literature, two tests are constructed to check the lack of fit for low and high dimensional quantile regression models. The low dimensional test works well when the number of covariates is moderate, whereas the high dimensional test can maintain the power when the number of covariates exceeds the sample size. The null distribution of the high dimensional test has an explicit form, and the p‐values or critical values can then be calculated directly. The finite sample performance of the tests proposed is examined by simulation studies, and their usefulness is further illustrated by two real examples. [ABSTRACT FROM AUTHOR]

Summary: This article describes a polynomial growth curve quantile regression model that provides a comprehensive assessment about the treatment effects on the changes of the distribution of outcomes over time. The proposed model has the flexibility, as it allows the degree of a polynomial to vary across quantiles. A high degree polynomial model fits the data adequately, yet it is not desirable due to the complexity of the model. We propose the model selection criterion based on an empirical loglikelihood that consistently identifies the optimal degree of a polynomial at each quantile. After the parsimonious model is fitted to the data, the hypothesis test is further developed to evaluate the treatment effects by comparing the growth curves. It is shown that the proposed empirical loglikelihood ratio test statistic follows a chi‐square distribution asymptotically under the null hypothesis. Various simulation studies confirm that the proposed test successfully detects the difference between the curves across quantiles. When the empirical loglikelihood is employed, we incorporate the within‐subject correlation commonly existing in longitudinal data and gain estimation efficiency of the quantile regression parameters in the growth curve model. The proposed process is illustrated through the analysis of randomized controlled longitudinal depression data. [ABSTRACT FROM AUTHOR]

In U.S. law, the Batson decision and subsequent decisions forbids the use of peremptory challenges for jury selection in ways that disproportionately eliminate cognizable classes: by race, sex, ethnicity, etc. The court designed a three-stage process: a prima facie case requires a timely objection, the identification of a cognizable class, and facts sufficient to raise an inference of discrimination. If a prima facie case is found, the side using the peremptory challenge has the opportunity of explaining its decisions, and then the court decides whether discrimination has occurred. This article addresses how statistics can be used to address the strength of evidence provided by the history of the use of peremptory challenges in a case. It contrasts two different procedures used by judges in the exercise of peremptory challenges. Frequentist and Bayesian analyses are given for both procedures, using data from a recent cases. [ABSTRACT FROM AUTHOR]

Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation coefficient is effective for capturing linear dependence, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns. We introduce a new measure, G-squared, to test whether two univariate random variables are independent and to measure the strength of their relationship. The G-squared statistic is almost identical to the square of the Pearson correlation coefficient, R-squared, for linear relationships with constant error variance, and has the intuitive meaning of the piecewise R-squared between the variables. It is particularly effective in handling nonlinearity and heteroscedastic errors. We propose two estimators of G-squared and show their consistency. Simulations demonstrate that G-squared estimators are among the most powerful test statistics compared with several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

When reading an article published in a medicaljournal, statistical tests are mentioned and the results are often supported bya P value. What are these tests? What is a P value and what is its meaning? P values are used to interpret the result of a statistical test. Both are intrinsic parts of hypothesis testing, which is a decision-making tool based on probability. Most medical and epidemiological studies are designed using a hypothesis test so understanding the key principles of a hypothesis test are crucial to interpreting results of a study. From null and alternative hypotheses to the issue of multiple tests, this paper introduces concepts related to hypothesis testing that are crucial to its implementation and interpretation. [ABSTRACT FROM AUTHOR]

We investigate the properties of a simple bootstrap method for testing the equality of mean functions or of covariance operators in functional data. Theoretical size and power results are derived for certain test statistics, whose limiting distributions depend on unknown infinite-dimensional parameters. Simulations demonstrate good size and power of the bootstrap-based functional tests. [ABSTRACT FROM AUTHOR]

Causal mediation modeling has become a popular approach for studying the effect of an exposure on an outcome through a mediator. However, current methods are not applicable to the setting with a large number of mediators. We propose a testing procedure for mediation effects of high-dimensional continuous mediators. We characterize the marginal mediation effect, the multivariate component-wise mediation effects, and the [ABSTRACT FROM AUTHOR]

In this paper, we propose constructing a confidence set for the date of a one-time structural change using a point optimal test. Following Elliott and Müller (2007, Journal of Econometrics 141, 1196-1218), we first construct a test for the break date that maximizes the weighted average of the power function. The confidence set is then obtained by inverting the test statistic. We carefully choose the weights and show by Monte Carlo simulations that the confidence set based on our method has a relatively accurate coverage rate, while the length of our confidence set is significantly shorter than the lengths proposed in the literature. [ABSTRACT FROM AUTHOR]

The problem of testing smooth components of an extended generalized additive model for equality to zero is considered. Confidence intervals for such components exhibit good across-the-function coverage probabilities if based on the approximate result , where f is the vector of evaluated values for the smooth component of interest and V f is the covariance matrix for f according to the Bayesian view of the smoothing process. Based on this result, a Wald-type test of f=0 is proposed. It is shown that care must be taken in selecting the rank used in the test statistic. The method complements previous work by extending applicability beyond the Gaussian case, while considering tests of zero effect rather than testing the parametric hypothesis given by the null space of the component’s smoothing penalty. The proposed p-values are routine and efficient to compute from a fitted model, without requiring extra model fits or null distribution simulation. [ABSTRACT FROM PUBLISHER]

We propose and develop mean-variance-ratio (MVR) statistics for comparing the performance of prospects (e.g., investment portfolios, assets, etc.) after the effect of the background risk has been mitigated. We investigate the performance of the statistics in large and small samples and show that in the non-asymptotic framework, the MVR statistic produces a uniformly most powerful unbiased (UMPU) test. We discuss the applicability of the MVR test in the case of large samples and illustrate its superiority in the case of small samples by analyzing Korea and Singapore stock returns after the impact of the American stock returns (which we view as the background risk) has been deducted. We find, in particular, that when samples are small, the MVR statistic can detect differences in asset performances while the Sharpe ratio test, which is the mean-standard-deviation-ratio statistic, may not be able to do so. [ABSTRACT FROM AUTHOR]

Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not clear whether such priors have full support so that any true data-generating model can be accurately approximated. This article develops a new class of density regression models that incorporate stochastic-ordering constraints which are natural when a response tends to increase or decrease monotonely with a predictor. Theory is developed showing large support. Methods are developed for hypothesis testing, with posterior computation relying on a simple Gibbs sampler. Frequentist properties are illustrated in a simulation study, and an epidemiology application is considered. [ABSTRACT FROM PUBLISHER]

An integrated likelihood depends only on the parameter of interest and the data, so it can be used as a standard likelihood function for likelihood-based inference. In this paper, the higher-order asymptotic properties of the signed integrated likelihood ratio statistic for a scalar parameter of interest are considered. These results are used to construct a modified integrated likelihood ratio statistic and to suggest a class of prior densities to use in forming the integrated likelihood. The properties of the integrated likelihood ratio statistic are compared to those of the standard likelihood ratio statistic. Several examples show that the integrated likelihood ratio statistic can be a useful alternative to the standard likelihood ratio statistic. [ABSTRACT FROM PUBLISHER]

In the evaluation of efficacy of a vaccine to protect against disease caused by a genetically diverse infectious pathogen, it is often important to assess whether vaccine protection depends on variations of the exposing pathogen. This problem can be viewed within the framework of a K-competing risks model where the endpoint event is pathogen-specific infection and the cause of failure is the strain type determined after the infection is diagnosed. The Cox model with time-dependent coefficients is used to relate the cause-specific outcomes to explanatory variables to allow for time-varying treatment effects. The strain-specific vaccine efficacy can be defined in terms of one minus the cause-specific hazard ratios. We develop inferential methods for testing whether the vaccine affords some protection against at least one pathogen strain, and for testing equal vaccine protection against the strains, adjusting for covariate effects. We also consider estimation of covariate-adjusted time-varying strain-specific vaccine efficacy. The methods are applied to a dataset from an oral cholera vaccine trial and the performances of the proposed tests are studied through simulations. These techniques apply more generally for testing and estimation of time-varying cause-specific hazard ratios. [ABSTRACT FROM AUTHOR]

The primary goal of a randomized clinical trial is to make comparisons among two or more treatments. For example, in a two-arm trial with continuous response, the focus may be on the difference in treatment means; with more than two treatments, the comparison may be based on pairwise differences. With binary outcomes, pairwise odds ratios or log odds ratios may be used. In general, comparisons may be based on meaningful parameters in a relevant statistical model. Standard analyses for estimation and testing in this context typically are based on the data collected on response and treatment assignment only. In many trials, auxiliary baseline covariate information may also be available, and it is of interest to exploit these data to improve the efficiency of inferences. Taking a semiparametric theory perspective, we propose a broadly applicable approach to adjustment for auxiliary covariates to achieve more efficient estimators and tests for treatment parameters in the analysis of randomized clinical trials. Simulations and applications demonstrate the performance of the methods. [ABSTRACT FROM AUTHOR]

Hypothesis tests, which aim to minimize type I errors (false positive results), are standard procedures in scientific research, but they are often inappropriate in Endangered Species Act (ESA) reviews, where the primary objective is to prevent type II errors (false negative results). Recognizing this disparity is particularly important when the best data available are sparse and therefore lack statistical power, because hypothesis tests that use data sets with law statistical power are likely to commit type II errors, thereby denying necessary protection to threatened and endangered species. Equivalence tests can alleviate this problem, and ensure that imperiled species receive the benefit of the doubt, by switching the null and alternative hypotheses. These points are illustrated by critiquing a recent review of ESA requirements for endangered fishes in Upper Klamath Lake (southern Oregon). [ABSTRACT FROM AUTHOR]

If a problem in functional data analysis is low dimensional then the methodology for its solution can often be reduced to relatively conventional techniques in multivariate analysis. Hence, there is intrinsic interest in assessing the finite dimensionality of functional data. We show that this problem has several unique features. From some viewpoints the problem is trivial, in the sense that continuously distributed functional data which are exactly finite dimensional are immediately recognizable as such, if the sample size is sufficiently large. However, in practice, functional data are almost always observed with noise, for example, resulting from rounding or experimental error. Then the problem is almost insolubly difficult. In such cases a part of the average noise variance is confounded with the true signal and is not identifiable. However, it is possible to define the unconfounded part of the noise variance. This represents the best possible lower bound to all potential values of average noise variance and is estimable in low noise settings. Moreover, bootstrap methods can be used to describe the reliability of estimates of unconfounded noise variance, under the assumption that the signal is finite dimensional. Motivated by these ideas, we suggest techniques for assessing the finiteness of dimensionality. In particular, we show how to construct a critical point such that, if the distribution of our functional data has fewer than q−1 degrees of freedom, then we should be willing to assume that the average variance of the added noise is at least . If this level seems too high then we must conclude that the dimension is at least q−1. We show that simpler, more conventional techniques, based on hypothesis testing, are generally not effective. [ABSTRACT FROM AUTHOR]

The objective of this article is to develop a hypothesis-testing procedure to determine whether a common source outbreak has ended. We consider the case when neither the calendar date of exposure to the pathogen nor the exact incubation period distribution is known. The hypothesis-testing procedure is based on the spacings between ordered calendar dates of disease onset of the cases. A simulation study was performed to evaluate the robustness of the methods to various models for the incubation period of infectious diseases. We investigated the impact of multiple testing on the overall outbreak-wise type I error probability. We derive expressions for the outbreak-wise type I error probability and show that multiple testing has minimal effect on inflating that error probability. The results are discussed in the context of the 2001 U.S. anthrax outbreak. [ABSTRACT FROM AUTHOR]

Several tests of molecular phylogenies have been proposed over the last decades, but most of them lead to strikingly different P -values. I propose that such discrepancies are principally due to different forms of null hypotheses. To support this hypothesis, two new tests are described. Both consider the composite null hypothesis that all the topologies are equidistant from the true but unknown topology. This composite hypothesis can either be reduced to the simple hypothesis at the least favorable distribution (frequentist significance test [FST]) or to the maximum likelihood topology (frequentist hypothesis test [FHT]). In both cases, the reduced null hypothesis is tested against each topology included in the analysis. The tests proposed have an information-theoretic justification, and the distribution of their test statistic is estimated by a nonparametric bootstrap, adjusting P -values for multiple comparisons. I applied the new tests to the reanalysis of two chloroplast genes, psaA and psbB , and compared the results with those of previously described tests. As expected, the FST and the FHT behaved approximately like the Shimodaira-Hasegawa test and the bootstrap, respectively. Although the tests give overconfidence in a wrong tree when an overly simple nucleotide substitution model is assumed, more complex models incorporating heterogeneity among codon positions resolve some conflicts. To further investigate the influence of the null hypothesis, a power study was conducted. Simulations showed that FST and the Shimodaira-Hasegawa test are the least powerful and FHT is the most powerful across the parameter space. Although the size of all the tests is affected by misspecification, the two new tests appear more robust against misspecification of the model of evolution and consistently supported the hypothesis that the Gnetales are nested within gymnosperms. [ABSTRACT FROM AUTHOR]

The results of Davies (1977, 1987) are extended to a linear model situation with unknown residual variance. [ABSTRACT FROM PUBLISHER]

Motivated by applications in high‐dimensional settings, we suggest a test of the hypothesis H0 that two sampled distributions are identical. It is assumed that two independent datasets are drawn from the respective populations, which may be very general. In particular, the distributions may be multivariate or infinite‐dimensional, in the latter case representing, for example, the distributions of random functions from one Euclidean space to another. Our test uses a measure of distance between data. This measure should be symmetric but need not satisfy the triangle inequality, so it is not essential that it be a metric. The test is based on ranking the pooled dataset, with respect to the distance and relative to any fixed data value, and repeating this operation for each fixed datum. A permutation argument enables a critical point to be chosen such that the test has concisely known significance level, conditional on the set of all pairwise distances. [ABSTRACT FROM PUBLISHER]

The relationship between spawning stock and recruitment in penaeid shrimp fisheries has been questioned because they exhibit unique characteristics with respect to population dynamics and fisheries. This study used meta-analyses to test the null hypothesis that recruitment is a series of random, independent events based on the penaeid shrimp stocks found in published sources. Both the derivative hypothesis test and Granger causality test rejected the null hypothesis. Thus, recruitment is related to spawner abundance. Shrimp populations should be managed so as to maintain sufficient spawning stock abundance to yield high recruitment. [ABSTRACT FROM PUBLISHER]