a two ellipsoid overlap test for on line failure detection the problem of failure detection in dynamic systems is addressed the approach is based on modelling and estimation methods and uses some known statistical tools as well as geometric arguments a test decision is derived which is based on the overlap between the confidence regions associated with two estimates one obtained using online measurements and the other based on a priori information the algorithm proposed here is suitable for on line detection of abrupt changes and failures in the applications where fast on line decisions are of importance the implementation of a necessary and sufficient condition is shown to result in a scalar test which does not call for any optimization procedure and so offers the advantage of low computational expenditure

homotopy series solutions of perturbed pdes via approximate symmetry method we give a general result about the relation between approximate symmetry and approximate homotopy symmetry for perturbed pdes we show that the two couple equations derived by approximate symmetry method and approximate homotopy symmetry method are connected by a transformation consequently acting the transformation on the known solutions constructed by approximate symmetry method we directly obtain approximate homotopy series solutions whose accuracy can be controlled by adjusting the convergence control parameter applications to the cahn hilliard equation illustrate the effectiveness of the transformation

equivalence test and confidence interval for the difference in proportions for the paired sample design summary this paper considers a model for the di erence of two proportions in a paired or matched design of clinical trials case control studies and also sensitivity comparison studies of two laboratory tests this model includes a parameter indicating both interpatient variability of response probabilities and their correlation under the proposed model we derive a one sided test for equivalence based upon the e cient score equivalence is defined here as not more than 100 per cent inferior mcnemar s test for significance is shown to be a special case of the proposed test further a score based confidence interval for the di erence of two proportions is derived one of the features of these methods is applicability to the 2 2 table with o diagonal zero cells all the mcnemar type tests and confidence intervals published so far cannot apply to such data a monte carlo simulation study shows that the proposed test has empirical significance levels closer to the nominal a level than the other tests recently proposed and further that the proposed confidence interval has better empirical coverage probability than those of the four published methods 1998 john wiley sons ltd

lie symmetry classification analysis for nonlinear coupled diffusion the group properties of the 1 1 dimensional matrix diffusion equation of the form with respect to point symmetries are given it is shown that in particular cases the group properties of this equation are similar to those of the corresponding scalar equation namely the lie algebra is extended for power and exponential functions with additional extensions when powers of and 2 exist however a specific form of is shown to exist for cases admitting both infinite and finite groups the result obtained is used to construct new group invariant solutions for impulsive boundary inputs using two similarity variables a reduction is applied to the coupled diffusion of temperature and volumetric moisture content in porous media under periodic boundary conditions a perturbation method is employed to obtain an explicit solution for the case when can be expressed exponentially in terms of the similarity variables

approximate nonlinear self adjointness and approximate conservation laws in this paper approximate nonlinear self adjointness for perturbed pdes is introduced and its properties are studied consequently approximate conservation laws which cannot be obtained by the approximate noether theorem are constructed by means of the method as an application a class of perturbed nonlinear wave equations is considered to illustrate the effectiveness

efficient interval estimation of a ratio of marginal probabilities in matched pair data non iterative method matched pair designs have been commonly employed in diagnostic epidemiologic and laboratory studies for estimation of a ratio of two marginal probabilities in matched pair data a wald type logarithmic method is computationally simple but an actual coverage rate is known to be smaller than a nominal one and a length of the confidence interval is shorter than it should be the fieller type method based on constrained maximum likelihood cml estimators possesses asymptotically optimum statistical properties and a coverage rate is close to a nominal one however hitherto the limits have been obtained by numerical iterations in this paper we derive the efficient confidence limits based on cml as analytical solutions of a quartic equation and present the confidence limits in a closed form

comments on an algorithm for real time failure detection in kalman filters in the above mentioned paper by zolghadri ibid vol 41 1996 the commenter objects to claims made of providing simpler implementation complexity or computational burden without an explicit mechanization for obtaining a solution ever actually being offered and operations counts being tallied

sample size for testing differences in proportions for the paired sample design miettinen 1968 biometrics 24 339 352 presented an approximation for power and sample size for testing the differences between proportions in the matched pair case duffy 1984 biometrics 40 1005 1015 gave the exact power for this case and showed that miettinen s approximation tends to slightly overestimate the power or underestimate the sample size necessary for the design power a simple alternative approximation that is more conservative is presented here in many cases the sample size for the independent sample case provides a conservative approximation for the matched pair design

two approaches to the calculation of approximate symmetry exemplified using a system of advection diffusion equations two algorithms used to evaluate the approximate symmetries of nonlinear systems are compared from a theoretical view point the two quite distinct algorithms are cast into a form where one method can clearly be seen to be more general than the second the circumstances for the equivalence of the two methods are presented and for these cases it is shown how the approximate symmetries found by one method may easily be calculated for the second these ideas are exemplified by calculating new approximate symmetry reductions for a systems of advection diffusion equations that describe the simultaneous transport of heat moisture and solute in porous media and which contain unknown shape functions

assessing screening tests extensions of mcnemar s test we address the problem of comparing a new screening test to a currently available screening test in the absence of a gold standard when both tests are given to each participant in a clinical trial the usual analytical approach is to apply mcnemar s test for equality of the off diagonal probabilities with rejection of the null hypothesis implying that the tests differ for assessing equivalence however we consider a compound null hypothesis that the new test gives either fewer or more positive results than the standard if both parts of this hypothesis are rejected we assert equivalence in the rate of positive responses we propose an extension of mcnemar s test for this situation a companion step is to construct a confidence interval for the ratio of the marginal probabilities and assert equivalence if the interval is sufficiently small it is also important that the tests agree a large proportion of the time this can be verified with a complementary two tailed binomial test another situation arises when there is a gold standard for disease diagnosis and we wish to compare the sensitivity and specificity of two screening tests we show that a 2 degrees of freedom chi square test based on two mcnemar like tables is an appropriate test

an algorithm for real time failure detection in kalman filters an algorithm is presented for solving the problem of real time failure detection in dynamic systems using kalman filters we give a geometric solution to derive a test decision based on the overlap between the confidence regions associated with two estimates one obtained using on line measurements and the other based on a priori information the implementation of a necessary and sufficient condition is shown to result in a scalar test the advantage compared to standard techniques is a significantly lower computational burden

comparison of approximate symmetry and approximate homotopy symmetry to the cahn hilliard equation complete infinite order approximate symmetry and approximate homotopy symmetry classifications of the cahn hilliard equation are performed and the reductions are constructed by an optimal system of one dimensional subalgebras zero order similarity reduced equations are nonlinear ordinary differential equations while higher order similarity solutions can be obtained by solving linear variable coefficient ordinary differential equations the relationship between two methods for different order are studied and the results show that the approximate homotopy symmetry method is more effective to control the convergence of series solutions than the approximate symmetry one

confidence intervals for a ratio of binomial proportions based on paired data four interval estimation methods for the ratio of marginal binomial proportions are compared in terms of expected interval width and exact coverage probability two new methods are proposed that are based on combining two wilson score intervals the new methods are easy to compute and perform as well or better than the method recently proposed by nam and blackwelder two sample size formulas are proposed to approximate the sample size required to achieve an interval estimate with desired confidence level and width

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

recommended tests and confidence intervals for paired binomial proportions we describe evaluate and recommend statistical methods for the analysis of paired binomial proportions a total of 24 methods are considered the best tests for association include the asymptotic mcnemar test and the mcnemar mid p test for the difference between proportions we recommend two simple confidence intervals with closed form expressions and the asymptotic score interval the asymptotic score interval is also recommended for the ratio of proportions as is an interval with closed form expression based on combining two wilson score intervals for the single proportion for the odds ratio we recommend a transformation of the wilson score interval and a transformation of the clopper pearson mid p interval we illustrate the practical application of the methods using data from a recently published study of airway reactivity in children before and after stem cell transplantation and a matched case control study of the association between floppy eyelid syndrome and obstructive sleep apnea hypopnea syndrome

false alarm and correct detection probabilities over a time interval for restricted classes of failure detection algorithms the statistical analysis of failure detection decisions in terms of the instantaneous probabilities of false alarm and correct detection for a specified failure magnitude at each check time have previously been performed for several different failure detection techniques that utilize a kalman filter by performing a discrete time specialization of a result of gallager and helstrom on a tightened upper bound for continuous time level crossing probabilities upper bounds on the probabilities of false alarm and correct detection over a time interval have been obtained for the specific technique of cr2 tailnre detection to allow an accounting for the effect of time correlations of the filter estimates when these upper bounds are optimized to be as tight as possible to the desired probabilities the resulting optimization problem for discrete time is a collection of quadratic programming qp problems which may easily be solved exactly without recourse to approximate solutions as were resorted to in the continuous time formulation this technique for evaluating tightened upper bounds on the false alarm and correct detection probabilities may be of general interest since it can be applied to any failure detection technique or signal detection technique that can relate an exceeding of the deterministic decision threshold by the test statistic directly to a deterministic level being exceeded by a scalar gaussian random process

a comparative study of approximate symmetry and approximate homotopy symmetry to a class of perturbed nonlinear wave equations abstract a comparative study of approximate symmetry and approximate homotopy symmetry to a class of perturbed nonlinear wave equations is performed first complete infinite order approximate symmetry classification of the equation is obtained by means of the method originated by fushchich and shtelen an optimal system of one dimensional subalgebras is derived and used to construct general formulas of approximate symmetry reductions and similarity solutions second we study approximate homotopy symmetry of the equation and construct connections between the two symmetry methods for the first order and higher order cases respectively the series solutions derived by the two methods are compared

comparing diagnostic tests a simple graphic using likelihood ratios the diagnostic abilities of two or more diagnostic tests are traditionally compared by their respective sensitivities and specificities either separately or using a summary of them such as youden s index several authors have argued that the likelihood ratios provide a more appropriate if in practice a less intuitive comparison we present a simple graphic which incorporates all these measures and admits easily interpreted comparison of two or more diagnostic tests we show using likelihood ratios and this graphic that a test can be superior to a competitor in terms of predictive values while having either sensitivity or specificity smaller a decision theoretic basis for the interpretation of the graph is given by relating it to the tent graph of hilden and glasziou statistics in medicine 1996 finally a brief example comparing two serodiagnostic tests for lyme disease is presented published in 2000 by john wiley sons ltd

classification and approximate solutions to perturbed diffusion convection equations abstract approximate symmetries of the perturbed nonlinear diffusion convection equations are completely classified by the method originated with fushchich and shtelen moreover for some interesting cases symmetry reductions and approximate solutions are discussed in detail

regret graphs diagnostic uncertainty and youden s index regret is the difference in outcome between the action we took and the best action we could in retrospect have taken tent graphs representing decision problems under uncertainty in terms of expected regret offer an instructive geometric supplement to standard formulae allow instant calculations and suggest as we shall illustrate novel algebraic properties for instance the problem of finding the pre test probability range in which it is worthwhile doing a diagnostic test becomes trivial even when test costs depend on the unknown disease status we take the opportunity to explore the non trivial algebraic properties of this problem the graphs also provide a simple way to illustrate and read off the expected value of information and expected value of perfect information this property is used to derive a clinical interpretation of youden s index sensitivity specificity 1 namely it is the maximum proportional reduction in expected regret achieved by the test finally we examine the relationship between youden s index and the area under an roc curve

on approximate symmetry and approximate solutions of the nonlinear wave equation with a small parameter the concept of approximate symmetry is introduced the authors describe all nonlinearities f u with which the nonlinear wave equation square operator u lambda u3 epsilon f u 0 with a small parameter epsilon is approximately scale and conformally invariant some approximate solutions of wave equations in question are obtained using the approximate symmetry

on the non inferiority of a diagnostic test based on paired observations non inferiority of a diagnostic test to the standard or the optimum test is a common issue in medical research often we want to determine if a new diagnostic test is as good as the standard reference test sometimes we are interested in an inexpensive test that may have an acceptably inferior sensitivity or specificity while hypothesis testing procedures and sample size formulae for the equivalence of sensitivity or specificity alone have been proposed very few studies have discussed simultaneous comparisons of both parameters in this paper we present three different testing procedures and sample size formulae for simultaneous comparison of sensitivity and specificity based on paired observations and with known disease status these statistical procedures are then used to compare two classification rules that identify women for future osteoporotic fracture simulation experiments demonstrate that the new tests and sample size formulae give the appropriate type i and ii error rates differences between our approach and the approach of lui and cumberland are discussed

establishing equivalence of two treatments and sample size requirements in matched pairs design statistical methods for testing the null hypothesis of a nonzero difference between two treatments and the sample size determination for matched pairs studies are investigated a wald type test proposed by lu and bean 1995 statistics in medicine 14 1831 1839 is anticonservative i e its false positive error rate is greater than specified score method and normal deviate based on a restricted maximum likelihood estimation are presented these two test statistics are shown to be algebraically equal their actual type i error probabilities are satisfactorily close to a nominal level numerical examinations demonstrate that the sample size formulas using these alternative methods are reasonable while that by lu and bean is not the efficiency of matching in equivalence studies is positively related to intercorrelation or the kappa coefficient of agreements we recommend the score or ml methods to establish equivalence of two treatments for individually matched samples

improved confidence intervals for the difference between binomial proportions based on paired data by robert g newcombe statistics in medicine 17 2635 2650 1998

approximate similarity reduction for singularly perturbed boussinesq equation via symmetry perturbation and direct method we investigate the singularly perturbed boussinesq equation in terms of the approximate symmetry perturbation method and the approximate direct method the similarity reduction solutions and similarity reduction equations of different orders display formal coincidence for both methods series reduction solutions are consequently derived for the approximate symmetry perturbation method similarity reduction equations of the zero order are equivalent to the painleve iv painleve i and weierstrass elliptic equations for the approximate direct method similarity reduction equations of the zero order are equivalent to the painleve iv painleve ii painleve i or weierstrass elliptic equations the approximate direct method yields more general approximate similarity reductions than the approximate symmetry perturbation method

comments on confidence intervals for a ratio of binomial proportions based on paired data by d g bonett and r m price statistics in medicine 2006 25 3039 3047

analysis of the ratio of marginal probabilities in a matched pair setting statistical methods for testing and interval estimation of the ratio of marginal probabilities in the matched pair setting are considered in this paper we are especially interested in the situation where the null value is not one as in one sided equivalence trials we propose a fieller type statistic based on constrained maximum likelihood cml estimation of nuisance parameters for a series of examples the significance level of the cml test is satisfactorily close to the nominal level while a wald type test is anticonservative for reasonable sample sizes we present formulae for approximate power and sample size for the cml and wald tests the matched design is seen to have a clear advantage over the unmatched design in terms of asymptotic efficiency when the two responses of the pair are highly positively correlated we recommend the cml method over the wald method especially for small or moderate sample sizes

sample size requirements for stratified prospective studies with null hypothesis of non unity relative risk using the score test the standard test of the null hypothesis of unity of the relative risk seeks to determine if two treatments differ it does not apply when the requirement is either to establish the equivalence of two treatments or to determine whether the relative risk is less than a specified value other than one this paper presents the asymptotic power function of the score test for the null hypothesis of a specified value of a common relative risk for stratified prospective studies and proposes an approximate formula for the sample size required for a specific power of the test one can obtain a sample size formula for stratified studies with the standard null hypothesis of unity relative risk as a special case of this formula

a simple approximation for calculating sample sizes for detecting linear trend in proportions a simple approximate formula for sample sizes for detecting a linear trend in proportions is derived the formulas for both the uncorrected and corrected cochran armitage test are given for two binomial proportions these reduce to those given by casagrande pike and smith 1978 biometrics 34 483 486 some numerical results of a power study for small sample sizes show that the nominal power corresponding to the approximate sample size is a reasonably good approximation to the actual power

tests for equivalence or non inferiority for paired binary data assessment of therapeutic equivalence or non inferiority between two medical diagnostic procedures often involves comparisons of the response rates between paired binary endpoints the commonly used and accepted approach to assessing equivalence is by comparing the asymptotic confidence interval on the difference of two response rates with some clinical meaningful equivalence limits this paper investigates two asymptotic test statistics a wald type sample based test statistic and a restricted maximum likelihood estimation rmle based test statistic to assess equivalence or non inferiority based on paired binary endpoints the sample size and power functions of the two tests are derived the actual type i error and power of the two tests are computed by enumerating the exact probabilities in the rejection region the results show that the rmle based test controls type i error better than the sample based test to establish an equivalence between two treatments with a symmetric equivalence limit of 0 15 a minimal sample size of 120 is needed the rmle based test without the continuity correction performs well at the boundary point 0 a numerical example illustrates the proposed procedures

approximate homotopy symmetry and infinite series solutions to the perturbed mkdv equation abstract we devise a homotopy model for the perturbed mkdv equation with weak fourth order dispersion and weak dissipation and demonstrate that the related approximate equations lead to similarity reduction equations and similarity reduction solutions of different orders which are formally coincident respectively series reduction solutions for the perturbed mkdv equation are thus derived painleve ii type equations or hyperbolic secant function solutions are obtained for zero order similarity reduction equations higher order similarity reduction equations are linear variable coefficients ordinary differential equations

test statistics and sample size formulae for comparative binomial trials with null hypothesis of non zero risk difference or non unity relative risk when it is required to establish a materially significant difference between two treatments or alternatively to show that two treatments are equivalent standard test statistics and sample size formulae based on a null hypothesis of no difference no longer apply this paper reviews some of the test statistics and sample size formulae proposed for comparative binomial trials when the null hypothesis is of a specified non zero difference or non unity relative risk methods based on restricted maximum likelihood estimation are recommended and applied to studies of pertussis vaccine

reducing cost in sequential testing a limit of indifference approach in noninferiority studies a limit of indifference is used to express a tolerance in results such that the clinician would regard such results as being acceptable or not worse we applied this concept to a measure of accuracy the receiver operating characteristic roc curve for a sequence of tests we expressed a limit of indifference for the range of acceptable sensitivity values and examined the associated cost of testing within this range in doing so we generated the minimum cost maximum roc mcmroc curve which reflects the reduced sensitivity and cost of testing we compared the mcmroc and its associated cost curve between limits of indifference set to 0 999 a 0 1 reduction in true positive rate tpr 0 95 a 5 reduction in tpr and 1 no reduction in tpr the limit of indifference tended to have less of an effect on the mcmroc curves than on the associated cost curves that were greatly affected cost was reduced at high false positive rates fprs at higher limit of indifference 0 999 and at small fprs as the limit of indifference decreased 0 95 these patterns were also observed as applied to sequential strategies used to diagnose diabetes in the pima indians copyright 2013 john wiley sons ltd

the 2 x 2 matched pairs trial exact unconditional design and analysis an exact unconditional method for the design and analysis of the 2 x 2 matched pairs trial is presented unlike the exact conditional method which is based on only the number of discordant pairs the exact unconditional method uses the total number n of sampled pairs this unconditional test based on a simple z statistic yields sample sizes that are generally smaller than those produced by the exact conditional test for the cases tabulated herein namely one sided alpha 01 025 and 05 along with 80 and 90 power moreover it is found to be uniformly more powerful than the latter for all the combinations of parameters considered in this paper namely alpha 01 025 and 05 and n 10 1 200 the method is illustrated by assessing various design options of an in vitro study of the effectiveness of antimicrobial agents some numerical examples of matching efficiency are also given

on the sample size for one sided equivalence of sensitivities based upon mcnemar s test in this paper we formalize the problem of testing the one sided equivalence in the sensitivities of two medical diagnostic tests under a matched pair study design we derive conditional and unconditional sample size formulae which are decreasing functions of the probability of being diagnosed by both tests we calculate upper boundary and midpoint sample sizes results of a monte carlo simulation study that compares the proposed sample size formulae with that of lachenbruch suggest that our midpoint conditional sample size is the best choice to obtain the desired power for the type of equivalence studies discussed in the paper