dose response signal detection under model uncertainty we investigate likelihood ratio contrast tests for dose response signal detection under model uncertainty when several competing regression models are available to describe the dose response relationship the proposed approach uses the complete structure of the regression models but does not require knowledge of the parameters of the competing models standard likelihood ratio test theory is applicable in linear models as well as in nonlinear regression models with identifiable parameters however for many commonly used nonlinear dose response models the regression parameters are not identifiable under the null hypothesis of no dose response and standard arguments cannot be used to obtain critical values we thus derive the asymptotic distribution of likelihood ratio contrast tests in regression models with a lack of identifiability and use this result to simulate the quantiles based on gaussian processes the new method is illustrated with a real data example and compared to existing procedures using theoretical investigations as well as simulations

order statistics correlation coefficient as a novel association measurement with applications to biosignal analysis in this paper we propose a novel correlation coefficient based on order statistics and rearrangement inequality the proposed coefficient represents a compromise between the pearson s linear coefficient and the two rank based coefficients namely spearman s rho and kendall s tau theoretical derivations show that our coefficient possesses the same basic properties as the three classical coefficients experimental studies based on four models and six biosignals show that our coefficient performs better than the two rank based coefficients when measuring linear associations whereas it is well able to detect monotone nonlinear associations like the two rank based coefficients extensive statistical analyses also suggest that our new coefficient has superior anti noise robustness small biasedness high sensitivity to changes in association accurate time delay detection ability fast computational speed and robustness under monotone nonlinear transformations

asymptotic properties of order statistics correlation coefficient in the normal cases we have previously proposed a novel order statistics correlation coefficient oscc which possesses some desirable advantages when measuring linear and monotone nonlinear associations between two signals however the understanding of this new coefficient is far from complete a lot of theoretical questions such as the expressions of its distribution and moments remain to be addressed motivated by this unsatisfactory situation in this paper we prove that for samples drawn from bivariate normal populations the distribution of oscc is asymptotically equivalent to that of the pearson s product moment correlation coefficient ppmcc we also reveal its close relationships with the other two coefficients namely gini correlation gc and spearman s rho sr monte carlo simulation results agree with the theoretical findings

two stage plans for estimating the inverse of a monotone function this study investigates two stage plans based on nonparametric procedures for estimating an inverse regression function at a given point specifically isotonic regression is used at stage one to obtain an initial estimate followed by another round of isotonic regression in the vicinity of this estimate at stage two it is shown that such two stage plans accelerate the convergence rate of one stage procedures and are superior to existing two stage procedures that use local parametric approximations at stage two when the available budget is moderate and or the regression function is ill behaved both wald and likelihood ratio type confidence intervals for the threshold value of interest are investigated and the latter are recommended in applications due to their simplicity and robustness the developed plans are illustrated through a comprehensive simulation study and an application to car fuel efficiency data

kernel and probit estimates in quantal bioassay abstract a kernel method for the estimation of quantal dose response curves is considered in contrast to parametric modeling this local smoothing method does not require any assumptions beyond smoothness of the dose response curve and in this sense is nonparametric in finite sample situations the kernel estimate of the dose response curve is not necessarily monotone and therefore if the additional assumption of monotonicity of the dose response curve is made a monotonized version is discussed bias variance asymptotic normality and uniform consistency including rates of convergence of kernel estimates are derived and applied to establish consistency and limiting distribution of kernel estimates of the ed here ed is the effective dose at level that is the dose where 100 of the subjects show a response the properties of the kernel estimated ed are compared with the corresponding properties of the maximum likelihood estimator assuming the probit model practical application of the k

small sample ld50 confidence intervals using saddlepoint approximations confidence intervals for the median lethal dose ld50 and other dose percentiles in logistic regression models are developed using a generalization of the fieller theorem for exponential families and saddlepoint approximations simulation results show that in terms of one tailed and two tailed coverage the proposed methodology generally outperforms competing confidence intervals obtained from the classical fieller likelihood ratio and score methods in terms of two tailed coverage the proposed method is comparable to the bartlett corrected likelihood ratio method but generally outperforms it in terms of one tailed coverage an extension to the competing risk setting is presented that allows binary response adjustments to be made using observed censoring times supplementary materials for this article are available online at http pubs amstat org

optimal designs for dose finding studies with an active control summary dose finding studies often compare several doses of a new compound with a marketed standard treatment as an active control in the past however research has focused mostly on experimental designs for placebo controlled dose finding studies to the best of our knowledge optimal designs for dose finding studies with an active control have not been considered so far as the statistical analysis for an active controlled dose finding study can be formulated in terms of a mixture of two regression models the related design problem is different from what has been investigated before in the literature we present a rigorous approach to the problem of determining optimal designs for estimating the smallest dose achieving the same treatment effect as the active control we determine explicitly the locally optimal designs for a broad class of models employed in such studies we also discuss robust design strategies and determine related bayesian and standardized minimax optimal designs we illustrate the results by investigating alternative designs for a clinical trial which has recently appeared in a consulting project of one of the authors

bandwidth choice for nonparametric regression this paper is concerned with the problem of choosing a bandwidth parameter for nonparametric regression we analyze a tapered fourier series estimate and discuss the relationship of this estimate to a kernel estimate we first consider a method based on an unbiased estimate of mean square error and show that the bandwidth thus chosen is asymptotically optimal other methods are examined as well and are shown to be asymptotically equivalent a small simulation shows however that for small or moderate sample size the methods perform quite differently

a discussion on the conventional estimator of sensitivity and specificity in multiple tests both the variation of positive responses negative responses among individuals and the internal correlation among responses for the same individual affect the precision of the estimate of sensitivity specificity to estimate the sensitivity specificity of a medical diagnostic test this paper proposes a bayesian approach with a simple markov model to evaluate the performance of the conventional estimator under different situations on the basis of the assumed model we derive a general formula for the variance of the conventional estimator regarding multiple tests and present a quantitative discussion on the limitations of this estimator

kernels for nonparametric curve estimation summary the choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error imse the present proof of the optimality of the latter kernels is restricted up to order k 5 these kernels are also of interest for the nonparametric estimation of probability densities and spectral densities a finite sample study indicates that higher order kernels asymptotically improving the rate of convergence may become attractive for realistic finite sample size suitably modified kernels are considered for estimating at the extremities of the data in a way which allows to retain the order of the bias found for interior points

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

an interval estimate for the interclass correlation in beta binomial sampling the beta binomial distribution has been frequently applied to model intraclass correlation among dichotomous responses in cluster sampling to avoid using sophisticated numerical procedures to calculate maximum likelihood estimates many authors have proposed different moment estimators most of them focused their discussion however on point estimation only in this paper we have developed a closed form interval estimate for the intraclass correlation and have shown it has asymptotically correct coverage we have further used a monte carlo simulation to evaluate the performance of the proposed interval estimation in a variety of situations we have found that when the number of clusters is moderate 50 the proposed interval estimation performs reasonably well except for the situation where the intraclass correlation is large and the underlying mean response probability is small even when the number of clusters is as small as 20 the proposed interval estimation may still be useful in the situation where the intraclass correlation is small we have also extended the proposed interval estimate to accommodate stratified sampling in which each stratum has a different mean response probability but has a common intraclass correlation

rapidly detecting disorder in rhythmic biological signals a spectral entropy measure to identify cardiac arrhythmias we consider the use of a running measure of power spectrum disorder to distinguish between the normal sinus rhythm of the heart and two forms of cardiac arrhythmia atrial fibrillation and atrial flutter this spectral entropy measure is motivated by characteristic differences in the power spectra of beat timings during the three rhythms we plot patient data derived from ten beat windows on a disorder map and identify rhythm defining ranges in the level and variance of spectral entropy values employing the spectral entropy within an automatic arrhythmia detection algorithm enables the classification of periods of atrial fibrillation from the time series of patients beats when the algorithm is set to identify abnormal rhythms within 6 s it agrees with 85 7 of the annotations of professional rhythm assessors for a response time of 30 s this becomes 89 5 and with 60 s it is 90 3 the algorithm provides a rapid way to detect atrial fibrillation demonstrating usable response times as low as 6 s measures of disorder in the frequency domain have practical significance in a range of biological signals the techniques described in this paper have potential application for the rapid identification of disorder in other rhythmic signals

a note on the effect of the intraclass correlation in the multiple reading procedure with a unanimity rule the use of multiple reading procedures to improve the performance of a diagnostic test occurs often in practice evaluation of the utility of multiple reading procedures however usually ignores the effect of the intraclass correlation this paper provides a quantitative assessment of this effect in the multiple reading procedure with a unanimity rule with respect to sensitivity specificity positive and negative predictive values we have found that when the disease prevalence is rare or moderate less than or equal to 0 20 use of the multiple reading procedure with a unanimity rule is effective in increasing the positive predictive value of a single reading procedure for the situation in which the variation of responses among different subjects and the intraclass correlation among repeated tests are small this is however not true for the situation in which the disease is rare and the variation of responses among different subjects is large even when the intraclass correlation is small or 0 furthermore when the disease is rare and the variation of responses among subjects is small a small or moderate intraclass correlation can substantially decrease the positive predictive value that one calculates under the assumption that the intraclass correlation is equal to 0 in general when the disease is rare or moderate less than or equal to 0 20 the intraclass correlation between repeated tests and the variation of responses among subjects have little effect on the negative predictive value

the analysis of binary longitudinal data with time independent covariates summary this paper considers extensions of logistic regression to the case where the binary outcome variable is observed repeatedly for each subject we propose two working models that lead to consistent estimates of the regression parameters and of their variances under mild assumptions about the time dependence within each subject s data the efficiency of the proposed estimators is examined an analysis of stress in mothers with infants is presented to illustrate the proposed method

multiple reading procedures the performance of diagnostic tests this paper examines the effects on sensitivity and specificity of various multiple reading procedures multiple reading procedures entail the performance of a diagnostic test several times and consequent assignment of the subject to an affected or unaffected group a unanimity rule that is all tests must be positive leads to the largest predictive value positive but may have unacceptably low sensitivity the rule which classifies the subject as positive based on the majority of the tests increases both the sensitivity and specificity of the individual test variability of subjects sensitivity and specificity that is case of correct diagnosis on a test affects the performance of these rules we also study alternative procedures in which the final test is a better but more expensive test

sigmoidally constrained maximum likelihood estimation in quantal bioassay abstract in quantal bioassay doses x 1 xk of a test substance are administered to n 1 nk animal subjects let ii x denote the probability that an arbitrary subject responds in a specified way to a dose x in this article we consider maximum likelihood estimation of ii x 1 ii xk subject to the constraint that ii is sigmoid of particular interest is the nature of ii at very small x upper confidence bounds for ii x x x 1 are discussed these confidence bounds depend on an inequality that holds when ii is convex on 0 x 1 a test of concavity against the alternative under sigmoidicity and related tests are discussed rejecting concavity requires evidence that ii is convex on 0 x 1

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

asymptotic mean and variance of gini correlation for bivariate normal samples this paper derives the asymptotic analytical forms of the mean and variance of the gini correlation gc with respect to samples drawn from bivariate normal populations the asymptotic relative efficiency are of the gini correlation to pearson s product moment correlation coefficient ppmcc is investigated under the normal assumptions to gain further insight into gc we also compare the gini correlation to other two closely related correlation coefficients namely the order statistics correlation coefficient oscc and spearman s rho sr theoretical and simulation results suggest that the performance of gc lies in between those of oscc and sr when estimating the correlation coefficient of the bivariate normal population the newly found theoretical results along with other desirable properties enable gc to be a useful alternative to the existing coefficients especially when one wants to make a trade off between the efficiency and robustness to monotone nonlinearity

bayesian monotone regression using gaussian process projection shape constrained regression analysis has applications in dose response modelling environmental risk assessment disease screening and many other areas incorporating the shape constraints can improve estimation efficiency and avoid implausible results we propose a novel method focusing on monotone curve and surface estimation which uses gaussian process projections our inference is based on projecting posterior samples from the gaussian process we develop theory on continuity of the projection and rates of contraction our approach leads to simple computation with good performance in finite samples the proposed projection method can also be applied to other constrained function estimation problems including those in multivariate settings

a note on nonparametric estimation of the effective dose in quantal bioassay for the common binary response model we propose a direct method for the nonparametric estimation of the effective dose level the estimator is obtained by the composition of a nonparametric estimate of the quantile response curve and a classical density estimate the new method yields a simple and reliable monotone estimate of the effective dose level curve ed and is appealing to users of conventional smoothing methods as kernel estimators local polynomials series estimators or smoothing splines moreover it is computationally very efficient because it does not require a numerical inversion of a monotonized estimate of the quantile dose response curve we prove asymptotic normality of the new estimate and compare it with an available alternative estimate based on a monotonized nonparametric estimate of the dose response curve and calculation of the inverse function by means of a simulation study

assessment of long range correlation in time series how to avoid pitfalls due to the ubiquity of time series with long range correlation in many areas of science and engineering analysis and modeling of such data is an important problem while the field seems to be mature three major issues have not been satisfactorily resolved i many methods have been proposed to assess long range correlation in time series under what circumstances do they yield consistent results ii the mathematical theory of long range correlation concerns the behavior of the correlation of the time series for very large times a measured time series is finite however how can we relate the fractal scaling break at a specific time scale to important parameters of the data iii an important technique in assessing long range correlation in a time series is to construct a random walk process from the data under the assumption that the data are like a stationary noise process due to the difficulty in determining whether a time series is stationary or not however one cannot be 100 sure whether the data should be treated as a noise or a random walk process is there any penalty if the data are interpreted as a noise process while in fact they are a random walk process and vice versa in this paper we seek to gain important insights into these issues by examining three model systems the autoregressive process of order 1 on off intermittency and l evy motions and considering an important engineering problem target detection within sea clutter radar returns we also provide a few rules of thumb to safeguard against misinterpretations of long range correlation in a time series and discuss relevance of this study to pattern recognition