a modified wilcoxon rank sum test for paired data summary a function of the wilcoxon rank sum statistic is proposed for testing the equality of the marginal distributions when sampling from a bivariate population the test statistic is asymptotically nonparametric a comparison is made between the test statistic and several parametric and nonparametric tests in terms of their pitman relative efficiency and small sample performance the test statistic has power comparable to the paired t test when sampling from the bivariate normal distribution and greater power in several important cases

optimal matching with minimal deviation from fine balance in a study of obesity and surgical outcomes in multivariate matching fine balance constrains the marginal distributions of a nominal variable in treated and matched control groups to be identical without constraining who is matched to whom in this way a fine balance constraint can balance a nominal variable with many levels while focusing efforts on other more important variables when pairing individuals to minimize the total covariate distance within pairs fine balance is not always possible that is it is a constraint on an optimization problem but the constraint is not always feasible we propose a new algorithm which returns a minimum distance finely balanced match when one is feasible and otherwise minimizes the total distance among all matched samples that minimize the deviation from fine balance perhaps we can come very close to fine balance when fine balance is not attainable moreover in any event because our algorithm is guaranteed to come as close as possible to fine balance the investigator may perform one match and on that basis judge whether the best attainable balance is adequate or not we also show how to incorporate an additional constraint the algorithm is implemented in two similar ways first as an optimal assignment problem with an augmented distance matrix second as a minimum cost flow problem in a network the case of knee surgery in the obesity and surgical outcomes study motivated the development of this algorithm and is used as an illustration in that example two of 47 hospitals had too few nonobese patients to permit fine balance for the nominal variable with 47 levels representing the hospital but our new algorithm came very close to fine balance moreover in that example there was a shortage of nonobese diabetic patients and incorporation of an additional constraint forced the match to include all of these nonobese diabetic patients thereby coming as close as possible to balance for this important but recalcitrant covariate

stable weights that balance covariates for estimation with incomplete outcome data weighting methods that adjust for observed covariates such as inverse probability weighting are widely used for causal inference and estimation with incomplete outcome data part of the appeal of such methods is that one set of weights can be used to estimate a range of treatment effects based on different outcomes or a variety of population means for several variables however this appeal can be diminished in practice by the instability of the estimated weights and by the difficulty of adequately adjusting for observed covariates in some settings to address these limitations this article presents a new weighting method that finds the weights of minimum variance that adjust or balance the empirical distribution of the observed covariates up to levels prespecified by the researcher this method allows the researcher to balance very precisely the means of the observed covariates and other features of their marginal and joint distributions such as variances and correlations and also for example the

permutation tests using estimated distribution functions abstract in this article we develop permutation tests for estimated distribution functions the tests are formed by averaging a functional of estimated distribution functions that are calculated from independent sampling units where the units may be a single response a set of repeated responses or a censored response we study primarily two functionals the difference in means functional and the mann whitney functional and two types of responses repeated conditionally independent responses and censored responses for repeated responses the permutation test using the difference in means functional produces a permutation form of the corresponding mixed effects test a new permutation test is developed when we apply the mann whitney functional to the repeated responses this is a case in which the rank transform method does not work on the other hand for right censored or interval censored data we obtain permutation forms of standard rank tests using the mann whitney functional or weighted forms of t

on the riemann hilbert problem for the one dimensional schrodinger equation a matrix riemann hilbert problem associated with the one dimensional schrodinger equation is considered and the existence and uniqueness of its solutions are studied the solution of this riemann hilbert problem yields the solution of the inverse scattering problem for a larger class of potentials than the usual faddeev class some examples of explicit solutions of the riemann hilbert problem are given and the connection with ambiguities in the inverse scattering problem is established

testing equality of survival functions based on both paired and unpaired censored data summary we introduce two test procedures for comparing two survival distributions on the basis of randomly right censored data consisting of both paired and unpaired observations our procedures are based on generalizations of a pooled rank test statistic previously proposed for uncensored data one generalization adapts the prentice wilcoxon score while the other adapts the akritas score the use of these particular scoring systems in pooled rank tests with randomly right censored paired data has been advocated by several researchers our test procedures utilize the permutation distributions of the test statistics based on a novel manner of permuting the scores permutation versions of tests for right censored paired data and for two independent right censored samples that use the proposed scoring systems are obtained as special cases of our test procedures simulation results show that our test procedures have high power for detecting scale and location shifts in exponential and log logistic distributions for the survival times we also demonstrate the advantages of our test procedures in terms of utilizing randomly occurring unpaired observations that are discarded in test procedures for paired data the tests are applied to skin graft data previously reported elsewhere

rank tests for association with right censored data summary rank tests for association between a time variable and a continuous covariate and between two time variables are given in the presence of censoring in the first case these tests are related to the semiparametric tests of cox 1972 and prentice 1978 but differ in that the covariate is replaced by a score computed from its rank in the second case the test statistic is again a simple inner product which in the proportional hazards model reduces to the correlation between the two vectors of log rank scores the loss of efficiency arising from incorrect score functions is also explored when there is no censoring in this paper we consider a general model for association between pairs of observations in which either variable or both variables may be right censored the aim is to develop tests based on the generalized ranks of both variables which have maximal power at alternatives which are near to the null hypothesis of independence attention will be concentrated on two special cases of interest in survival analysis tests for association between a censored survival time and a possibly censored continuous covariate and tests for association between the times to different events beginning with cox 1972 the first situation has been studied extensively in a semiparametric set up in which information based on ranks is used for the time variable but exact values are used for the covariate procedures which use only the ranks of both variables have been developed by brown hollander korwar 1974 and more recently by o brien 1978 however neither of these procedures have been developed with a particular model in mind and one of the achievements of the present paper is to derive rank tests with good local power when a particular model such as the proportional hazards model holds in the case of a proportional hazards model with a continuous covariate the present development may be preferable to the semiparametric methods when the functional form of the relation ship between the hazard and the covariate is not known in advance or when errors or outliers may exist in the observed covariate values thus significance levels may be obtained which are not inflated by multiple regroupings or transformations of the covariate data although it would be expected that parametric model building with variables found to be associated with survival would often be carried out in further analyses

signed rank tests for censored matched pairs abstract i consider the problem of testing bivariate symmetry in matched pair experiments where the observations are subject to univariate censoring thus the observable random variables are given by y 1 y 2 and 1 2 where y j min x j c and j i x j c j 1 2 here x 1 x 2 is a random pair of partially observable lifetimes and c is a fixed or random censoring variable the hypothesis to be tested is that x 1 x 2 and x 2 x 1 have the same distribution following woolson and lachenbruch 1980 i consider censored data generalizations of signed rank tests such as the sign signed wilcoxon and signed normal scores tests i derive the asymptotic distribution of these test statistics under fixed and contiguous alternatives the efficiencies of the signed rank tests are considered in a log linear model and compared with efficiencies of the paired prentice wilcoxon and log rank tests

second order theta functions and vector bundles over jacobi varieties we consider the picard vector bundles defined over jacobi varieties the rank g 1 picard bundle imbeds in the rank 29 clifford bundle so the second order theta functions viewed appropriately span the dual of the picard bundle over each fiber we prove a result on the minimum number of such second order theta functions required to span the whole bundle at each point we give an application of using these functions to describe subvarieties of the jacobian there follow comments on which functions we could use and generalizations to higher order theta functions

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

a new nuisance parameter elimination method with application to the unordered homologous chromosome pairs problem motivated by applications of the case control model or exponential tilting model in the unordered homologous chromosome pairs problem in genetic studies and in the interim analysis in double blinded clinical trials we develop a new nuisance parameter elimination method based on the empirical shannon s mutual information the asymptotic behaviors of the maximum empirical shannon s mutual information estimation and the empirical shannon s mutual information test are similar to those of the maximum likelihood estimation and the likelihood ratio test respectively interestingly we have found a connection between the empirical shannon s mutual information and the profile empirical likelihood owen 1988 under some constraints in the test of the null hypothesis that the unordered pairs come from the same distribution the maximum shannon s mutual information estimation has a degenerate information matrix as a result we have to expand the empirical shannon s mutual information test statistic up to the four

using mixed integer programming for matching in an observational study of kidney failure after surgery this article presents a new method for optimal matching in observational studies based on mixed integer programming unlike widely used matching methods based on network algorithms which attempt to achieve covariate balance by minimizing the total sum of distances between treated units and matched controls this new method achieves covariate balance directly either by minimizing both the total sum of distances and a weighted sum of specific measures of covariate imbalance or by minimizing the total sum of distances while constraining the measures of imbalance to be less than or equal to certain tolerances the inclusion of these extra terms in the objective function or the use of these additional constraints explicitly optimizes or constrains the criteria that will be used to evaluate the quality of the match for example the method minimizes or constrains differences in univariate moments such as means variances and skewness differences in multivariate moments such as correlations between covari

a paired prentice wilcoxon test for censored paired data prentice 1978 biometrika 65 167 179 has provided a censored data generalization of classical linear rank statistics this paper investigates a method to generalize the prentice statistics to the analysis of censored paired data particular emphasis is given to the paired data version of the prentice wilcoxon statistic with discussion of the reasons for preferring prentice over the gehan scores the paired prentice wilcoxon ppw statistic makes use of interblock information and can be viewed as a censored data generalization of the conover iman 1981 the american statistician 35 124 129 paired t test on the ranks or of the lam longnecker 1983 biometrika 70 510 513 modified wilcoxon rank sum statistic in simulations comparing the ppw sign and generalized signed rank gsr statistics the ppw is most powerful against all but the exponential scale alternative furthermore the small advantage of the gsr over the ppw in that alternative is lost if outlier pairs are introduced when compared to the two sample prentice wilcoxon statistic the ppw is nearly as powerful in uncorrelated data and its power becomes superior as correlation between paired members increases

minimum distance matched sampling with fine balance in an observational study of treatment for ovarian cancer in observational studies of treatment effects matched samples have traditionally been constructed using two tools namely close matches on one or two key covariates and close matches on the propensity score to stochastically balance large numbers of covariates here we propose a third tool fine balance obtained using the assignment algorithm in a new way we use all three tools to construct a matched sample for an ongoing study of provider specialty in the treatment of ovarian cancer fine balance refers to exact balance of a nominal covariate often one with many categories but it does not require individually matched treated and control subjects for this variable in the example the nominal variable has 72 9 8 categories formed from 9 possible years of diagnosis and 8 geographic locations or seer sites we obtain exact balance on the 72 categories and close individual matches on clinical stage grade year of diagnosis and other variables using a distance and stochastically balance a total of

strong control of the familywise error rate in observational studies that discover effect modification by exploratory methods an effect modifier is a pretreatment covariate that affects the magnitude of the treatment effect or its stability when there is effect modification an overall test that ignores an effect modifier may be more sensitive to unmeasured bias than a test that combines results from subgroups defined by the effect modifier if there is effect modification one would like to identify specific subgroups for which there is evidence of effect that is insensitive to small or moderate biases in this paper we propose an exploratory method for discovering effect modification and combine it with a confirmatory method of simultaneous inference that strongly controls the familywise error rate in a sensitivity analysis despite the fact that the groups being compared are defined empirically a new form of matching strength k matching permits a search through more than k covariates for effect modifiers in such a way that no pairs are lost provided that at most k covariates are selected to group the pairs in a strength k match each set of k covariates is exactly balanced although a set of more than k covariates may exhibit imbalance we apply the proposed method to study the effects of the earthquake that struck chile in 2010

balanced risk set matching a new form of matching optimal balanced risk set matching is applied in an observational study of a treatment cystoscopy and hydrodistention given in response to the symptoms of the chronic nonlethal disease interstitial cystitis when a patient receives the treatment at time t that patient is matched to another patient with a similar history of symptoms up to time t who has not received the treatment up to time t this is risk set matching by using a penalty function in integer programming in a new way we force the marginal distributions of symptoms to be balanced in the matched treated and control groups among all balanced matchings we pick the one that is optimal in the sense of minimizing the multivariate pretreatment covariate distance within matched pairs under a simple model for the treatment assignment mechanism we study the sensitivity of the findings to hidden biases in particular we show that a simple conventional sensitivity analysis is appropriate with risk set matching when the

optimal multilevel matching in clustered observational studies a case study of the effectiveness of private schools under a large scale voucher system abstracta distinctive feature of a clustered observational study is its multilevel or nested data structure arising from the assignment of treatment in a nonrandom manner to groups or clusters of units or individuals examples are ubiquitous in the health and social sciences including patients in hospitals employees in firms and students in schools what is the optimal matching strategy in a clustered observational study at first thought one might start by matching clusters of individuals and then within matched clusters continue by matching individuals but as we discuss in this article the optimal strategy is the opposite in typical applications where the intracluster correlation is not one it is best to first match individuals and once all possible combinations of matched individuals are known then match clusters in this article we use dynamic and integer programming to implement this strategy and extend optimal matching methods to hierarchical and multilevel settings among other match

matching on the fly sequential allocation with higher power and efficiency we propose a dynamic allocation procedure that increases power and efficiency when measuring an average treatment effect in fixed sample randomized trials with sequential allocation subjects arrive iteratively and are either randomized or paired via a matching criterion to a previously randomized subject and administered the alternate treatment we develop estimators for the average treatment effect that combine information from both the matched pairs and unmatched subjects as well as an exact test simulations illustrate the method s higher efficiency and power over several competing allocation procedures in both simulations and in data from a clinical trial

a concordance test for independence in the presence of censoring an extension of the definition of kendall s coefficient of concordance is proposed for testing independence in bivariate censored survival times the test statistic counts the number of known concordances minus the number of known discordances the variance of the statistic is calculated for an random censorship model which however does not require independence of the components of the censoring distribution two examples are given

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

a cautionary note on applying scores in stratified data when rank tests are used to analyze stratified data three methods for assigning scores to the observations have been proposed s independently within each stratum see lehmann 1975 nonparametrics statistical methods based on ranks san francisco holden day a after aligning the observations within each stratum and then pooling the aligned observations hodges and lehmann 1962 annals of mathematical statistics 33 482 497 and p after pooling the observations across all strata that is without alignment mantel 1963 journal of the american statistical association 58 690 700 mantel and ciminera 1979 cancer research 39 4308 4315 test statistics are formed for each method by combining the stratum specific linear rank tests using the assigned scores we show that method p is sensitive to the score function used in the case of two moderately sized strata in general we recommend methods s and a for use with moderate to large sized strata

inverse scattering with partial information on the potential the one dimensional schrodinger equation is considered when the potential is real valued and integrable and has a finite first moment the recovery of such a potential is analyzed in terms of the scattering data consisting of a reflection coefficient all the bound state energies knowledge of the potential on a finite interval and all of the bound state norming constants except one it is shown that a missing norming constant in the data can cause at most a double nonuniqueness in the recovery in the particular case when the missing norming constant in the data corresponds to the lowest energy bound state the necessary and sufficient conditions are obtained for the nonuniqueness and the two norming constants and the corresponding potentials are determined some explicit examples are provided to illustrate the nonuniqueness

reconstruction of a potential on the line that is a priori known on the half line in this paper the authors study the inverse schrodinger scattering on the real line a method is given that allows unique reconstruction of a potential that is a priori known on the half line from the knowledge of the reflection coefficient and the bound state energies in particular no information on the forming constants is required the method is based on an appropriate trace formula and on the solution of the nonlinear ordinary differential equation that is obtained when the potential is replaced by its trace formula in the schrodinger equation the deift trubowitz approach to inverse scattering is followed the main new point is the way in which bound states are treated in addition to its mathematical interest the case when the potential is a priori known on the half line is particularly interesting in many applications one can consider for example a potential that has compact support or that it is zero on a half line

inverse schro dinger scattering on the line with partial knowledge of the potential the one dimensional schrodinger equation is considered when the potential and its first moment are absolutely integrable the potential is uniquely constructed in terms of the scattering data consisting of the reflection coefficient from the right left and the knowledge of the potential on the right left half line of the real axis hence neither the bound state energies nor the bound state norming constants are needed to determine the potential and in fact these are uniquely determined by the scattering data an explicit example is provided also considered are two inverse scattering problems for a generalized schrodinger equation with two potentials when the potential to be recovered is partially known

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

a powerful approach to the study of moderate effect modification in observational studies effect modification means the magnitude or stability of a treatment effect varies as a function of an observed covariate generally larger and more stable treatment effects are insensitive to larger biases from unmeasured covariates so a causal conclusion may be considerably firmer if this pattern is noted if it occurs we propose a new strategy called the submax method that combines exploratory and confirmatory efforts to determine whether there is stronger evidence of causality that is greater insensitivity to unmeasured confounding in some subgroups of individuals it uses the joint distribution of test statistics that split the data in various ways based on certain observed covariates for l binary covariates the method splits the population l times into two subpopulations perhaps first men and women perhaps then smokers and nonsmokers computing a test statistic from each subpopulation and appends the test statistic for the whole population making 2 l 1 test statistics in total although l binary covariates define 2 l interaction groups only 2 l 1 tests are performed and at least l 1 of these tests use at least half of the data the submax method achieves the highest design sensitivity and the highest bahadur efficiency of its component tests moreover the form of the test is sufficiently tractable that its large sample power may be studied analytically the simulation suggests that the submax method exhibits superior performance in comparison with an approach using cart when there is effect modification of moderate size using data from the nhanes i epidemiologic follow up survey an observational study of the effects of physical activity on survival is used to illustrate the method the method is implemented in the r package submax which contains the nhanes example an online appendix provides simulation results and further analysis of the example

inversion of abelian integrals on small genus curves let m be a smooth projective curve of genus g 0 let j be the jacobian of m and let m be the i th symmetric product fix a base point p e m and define a map bi m j by oi d d ip mattuck 6 7 has shown that if i 2g 1 then 0i is a ipi g bundle the most interesting case occurs when i 2g 1 since in 1 the bundles for larger i are determined by this one the inversion of abelian integrals problem asks what is an explicit description of the transition functions of the bundle 0 for an excellent introduction to the problem see kempf s article 5 until now the only complete answer was given in genus 1 by the abel inversion theorem the riemann roch theorem and riemann s approach through theta functions even without the transition functions gunning 1 2 and kempf 3 4 were able to extract a great deal of information about m from the bundles 0 in this paper we present a solution to the inversion of abelian integrals problem in the cases i curves of genus 2 ii non hyperelliptic curves o f genus 3 the techniques we use are very geometric but essentially elementary we strongly emphasize the role played by effective divisors and by the riemann roch theorem to build sections we use the commutative diagram

phaseless inverse scattering and the phase problem in optics two related problems are considered i the inverse scattering problem for a potential v x supported on the half line x 0 when the given data is r k the amplitude of the reflection coefficient and ii determination of a function g t supported on the half line t 0 when the given data is g k the amplitude of the fourier transform of g under certain conditions on v or g uniqueness theorems are proved and computational methods are developed a numerical example of recovery of v x from r k is given

inverse scattering problems where the potential is not absolutely continuous on the known interior subinterval the inverse scattering problem for the schrodinger operators on the line is considered when the potential is real valued and integrable and has a finite first moment it is shown that the potential on the line is uniquely determined by the left or right reflection coefficient alone provided that the potential is known on a finite interval and it is not absolutely continuous almost everywhere on this known interval

a class of rank test procedures for censored survival data summary a class of linear rank statistics is proposed for the k sample problem with rightcensored survival data the class contains as special cases the log rank test mantel 1966 cox 1972 and a test essentially equivalent to peto peto s 1972 generalization of the wilcoxon test martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered and to derive expressions for asymptotic relative efficiencies under contiguous sequences of alternative hypotheses a class of distributions is presented which corresponds to the class of rank statistics in the sense that for each distribution there is a statistic with some optimal properties for detecting location alternatives from that distribution some monte carlo results are displayed which present small sample behaviour

sample size formula for clustered survival data using weighted log rank statistics summary we present a simple sample size formula for weighted log rank statistics applied to clustered survival data with variable cluster sizes and arbitrary treatment assignments within clusters this formula is based on the asymptotic normality of weighted log rank statistics under certain local alternatives in the clustered data context we also provide consistent variance estimators the derived sample size formula reduces to schoenfeld s 1983 formula for cases of no clustering or independence within clusters simulation results verify control of the type i error and accuracy of the sample size formula use of the sample size formula in an event driven clinical trial design is illustrated using data from the early treatment diabetic retinopathy study

large sample properties of matching estimators for average treatment effects matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases the absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data in this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results we focus on matching with replacement with a fixed number of matches first we show that matching estimators are not n 1 2 consistent in general and describe conditions under which matching estimators do attain n 1 2 consistency second we show that even in settings where matching estimators are n 1 2 consistent simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound third we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions software for implementing these methods is available in matlab stata and r

robust rank procedures for the behrens fisher problem abstract the problem of testing for equality of the medians of two populations is considered the standard distribution free tests for this problem require that the two populations have the same shape to maintain their nominal significance level under the null hypothesis a method is given to modify many of these tests so they can be used to test for equality of the medians with fewer assumptions on the shapes of the two populations the method is demonstrated using the mann whitney wilcoxon statistic

a hybrid particle swarm optimizer with sine cosine acceleration coefficients abstract particle swarm optimization pso has been widely used to solve complex global optimization tasks due to its implementation simplicity and inexpensive computational overhead however pso has premature convergence is easily trapped in the local optimum solution and is ineffective in balancing exploration and exploitation especially in complex multi peak search functions to overcome the shortcomings of pso a hybrid particle swarm optimizer with sine cosine acceleration coefficients h pso scac is proposed to solve these problems it is verified by the application of twelve numerical optimization problems in h pso scac we make the following improvements first we introduce sine cosine acceleration coefficients scac to efficiently control the local search and convergence to the global optimum solution second opposition based learning obl is adopted to initialize the population additionally we utilize a sine map to adjust the inertia weight finally we propose a modified position update formula experimental results show that in the majority of cases the h pso scac approach is capable of efficiently solving numerical optimization tasks and outperforms the existing similar population based algorithms and pso variants proposed in recent years therefore the h pso scac algorithm is successfully employed as a novel optimization strategy

using weighted kaplan meier statistics in nonparametric comparisons of paired censored survival outcomes this research introduces methods for nonparametric testing of weighted integrated survival differences in the context of paired censored survival designs the current work extends work done by pepe and fleming 1989 biometrics 45 497 507 which considered similar test statistics directed toward independent treatment group comparisons an asymptotic closed form distribution of the proposed family of tests is presented along with variance estimates constructed under null and alternative hypotheses using nonparametric maximum likelihood estimates of the closed form quantities the described method allows for additional information from individuals with no corresponding matched pair member to be incorporated into the test statistic in sampling scenarios where singletons are not prone to selection bias simulations presented over a range of potential dependence in the paired censored survival data demonstrate substantial power gains associated with taking into account the dependence structure consequences of ignoring the paired nature of the data include overly conservative tests in terms of power and size in fact simulation results using tests for independent samples in the presence of positive correlation consistently undershot both size and power targets that would have been attained in the absence of correlation this additional worrisome effect on operating characteristics highlights the need for accounting for dependence in this popular family of tests

testing causal effects in observational survival data using propensity score matching design time to event data are very common in observational studies unlike randomized experiments observational studies suffer from both observed and unobserved confounding biases to adjust for observed confounding in survival analysis the commonly used methods are the cox proportional hazards ph model the weighted logrank test and the inverse probability of treatment weighted cox ph model these methods do not rely on fully parametric models but their practical performances are highly influenced by the validity of the ph assumption also there are few methods addressing the hidden bias in causal survival analysis we propose a strategy to test for survival function differences based on the matching design and explore sensitivity of the p values to assumptions about unmeasured confounding specifically we apply the paired prentice wilcoxon ppw test or the modified ppw test to the propensity score matched data simulation studies show that the ppw type test has higher power in situations when the ph assumption fails for potential hidden bias we develop a sensitivity analysis based on the matched pairs to assess the robustness of our finding following rosenbaum s idea for nonsurvival data for a real data illustration we apply our method to an observational cohort of chronic liver disease patients from a mayo clinic study the ppw test based on observed data initially shows evidence of a significant treatment effect but this finding is not robust as the sensitivity analysis reveals that the p value becomes nonsignificant if there exists an unmeasured confounder with a small impact

evaluation of subset matching methods and forms of covariate balance this paper conducts a monte carlo simulation study to evaluate the performance of multivariate matching methods that select a subset of treatment and control observations the matching methods studied are the widely used nearest neighbor matching with propensity score calipers and the more recently proposed methods optimal matching of an optimally chosen subset and optimal cardinality matching the main findings are i covariate balance as measured by differences in means variance ratios kolmogorov smirnov distances and cross match test statistics is better with cardinality matching because by construction it satisfies balance requirements ii for given levels of covariate balance the matched samples are larger with cardinality matching than with the other methods iii in terms of covariate distances optimal subset matching performs best iv treatment effect estimates from cardinality matching have lower root mean square errors provided strong requirements for balance specifically fine balance or strength k balance plus close mean balance in standard practice a matched sample is considered to be balanced if the absolute differences in means of the covariates across treatment groups are smaller than 0 1 standard deviations however the simulation results suggest that stronger forms of balance should be pursued in order to remove systematic biases due to observed covariates when a difference in means treatment effect estimator is used in particular if the true outcome model is additive then marginal distributions should be balanced and if the true outcome model is additive with interactions then low dimensional joints should be balanced copyright 2016 john wiley sons ltd

connections between permutation and t tests relevance to adaptive methods a permutation test assigns a p value by conditioning on the data and treating the different possible treatment assignments as random the fact that the conditional type i error rate given the data is controlled at level ensures validity of the test even if certain adaptations are made we show the connection between permutation and t tests and use this connection to explain why certain adaptations are valid in a t test setting as well we illustrate this with an example of blinded sample size re calculation

discrete optimization for interpretable study populations and randomization inference in an observational study of severe sepsis mortality abstractmotivated by an observational study of the effect of hospital ward versus intensive care unit admission on severe sepsis mortality we develop methods to address two common problems in observational studies 1 when there is a lack of covariate overlap between the treated and control groups how to define an interpretable study population wherein inference can be conducted without extrapolating with respect to important variables and 2 how to use randomization inference to form confidence intervals for the average treatment effect with binary outcomes our solution to problem 1 incorporates existing suggestions in the literature while yielding a study population that is easily understood in terms of the covariates themselves and can be solved using an efficient branch and bound algorithm we address problem 2 by solving a linear integer program to use the worst case variance of the average treatment effect among values for unobserved potential outcomes that are compatible with the null hy

a simple nonparametric estimator of the bivariate survival function under univariate censoring summary in the presence of univariate censoring the bivariate survival function of paired failure times can be expressed as the ratio of the bivariate at risk probability to the survival function of the censoring time the use of this natural representation yields a very simple nonparametric estimator for the bivariate survival curve the estimator is strongly consistent and upon proper normalization converges weakly to a zero mean gaussian process with an easily estimated covariance function numerical studies demonstrate that both the survival curve estimator and its covariance function estimator perform markedly well for practical sample sizes applications to the correlation problem and to the interval estimation of the difference in median survival times are also studied

combined rank tests for the two sample problem with randomly censored data abstract in the two sample problem under random censorship we consider the uncensored observations and the censored ones as two separate groups for each group a suitable rank statistic is obtained and these two are then combined to a final one this idea which was first employed in akritas 1983 is shown here to produce tests that a closely resemble the ordinary rank tests for the uncensored case and do not require the calculation of the kaplan meier estimator b are comparatively easy to apply and to understand and c allow results on asymptotic normality to follow simply from standard results for the uncensored case it is shown that the loss due to using two separate rankings rather than one complete ranking is asymptotically negligible the optimal score function for each of the two separate rank statistics is seen to depend on the censoring distribution whereas in akritas 1983 no assumption on the form of the censoring distribution was made unrestricted adaptation here we pursue rest

nonparametric rank based statistics and significance tests for fuzzy data nonparametric rank based statistics depending only on linear orderings of the observations are extended to fuzzy data the approach relies on the definition of a fuzzy partial order based on the necessity index of strict dominance between fuzzy numbers which is shown to contain in a well defined sense all the ordinal information present in the original data a concept of fuzzy set of linear extensions of a fuzzy partial order is introduced allowing the approximate computation of fuzzy statistics alpha cutwise using a markov chain monte carlo simulation approach the usual notions underlying significance tests are also extended leading to the concepts of fuzzy p value and graded rejection of the null hypothesis quantified by a degree of possibility and a degree of necessity at a given significance level this general approach is demonstrated in two special cases kendall s rank correlation coefficient and wilcoxon s two sample rank sum statistic

bound states and inverse scattering for the schrodinger equation in one dimension the one dimensional schrodinger equation is considered when the potential and its first moment are absolutely integrable when the potential has support contained on the left right half line it is uniquely constructed by using only the reflection coefficient from the right left the bound state norming constants determine whether the potential has support contained on a half line or on the full line the bound state energies and the unique set of norming constants yielding the potential with support contained on the left right half line are completely determined by the reflection coefficient from the right left an explicit example is provided

optimal matching for observational studies abstract matching is a common method of adjustment in observational studies currently matched samples are constructed using greedy heuristics or stepwise procedures that produce in general suboptimal matchings with respect to a particular criterion a matched sample is suboptimal if it could be improved by changing the controls assigned to specific treated units that is if it could be improved with the data at hand here optimal matched samples are obtained using network flow theory in addition to providing optimal matched pair samples this approach yields optimal constructions for several statistical matching problems that have not been studied previously including the construction of matched samples with multiple controls with a variable number of controls and the construction of balanced matched samples that combine features of pair matching and frequency matching computational efficiency is discussed extensive use is made of ideas from two essentially disjoint literatures namely st

combined rank tests for randomly censored paired data abstract many authors have dealt with the problem of extending ordinary two sample rank tests to cases where censoring occurs albers and akritas 1987 proposed simple tests for this purpose based on the idea of making separate rankings for uncensored and censored observations and subsequently combining the resulting two rank statistics similarly some papers appeared that studied the problem of censoring for the paired data case rather than the two sample case this article indicates how the approach of albers and akritas can be adapted to the paired data case the tests involved are not based on the ranks of the differences but the differences of the ranks in the pooled sample in this way use is made of interblock information the asymptotic distribution of the new statistic is obtained under the null hypothesis and contiguous location alternatives by way of example wilcoxon and savage type scores are introduced that are optimal for logistic location and exponential scale alternatives respecti

full matching in an observational study of coaching for the sat among matching techniques for observational studies full matching is in principle the best in the sense that its alignment of comparable treated and control subjects is as good as that of any alternate method and potentially much better this article evaluates the practical performance of full matching for the first time modifying it in order to minimize variance as well as bias and then using it to compare coached and uncoached takers of the sat in this new version with restrictions on the ratio of treated subjects to controls within matched sets full matching makes use of many more observations than does pair matching but achieves far closer matches than does matching with k 2 controls prior to matching the coached and uncoached groups are separated on the propensity score by 1 1 sds full matching reduces this separation to 1 or 2 of an sd in older literature comparing matching and regression cochran expressed doubts that any method of adjustment could substantially reduce observed bias

simultaneous group sequential analysis of rank based and weighted kaplan meier tests for paired censored survival data this research sequentially monitors paired survival differences using a new class of nonparametric tests based on functionals of standardized paired weighted log rank pwlr and standardized paired weighted kaplan meier pwkm tests during a trial these tests may alternately assume the role of the more extreme statistic by monitoring pemax the maximum between the absolute values of the standardized pwlr and pwkm one combines advantages of rank based rb and non rb paired testing paradigms simulations show that monitoring treatment differences using pemax maintains type i error and is nearly as powerful as using the more advantageous of the two tests in proportional hazards ph as well as non ph situations hence pemax preserves power more robustly than individually monitored pwlr and pwkm while maintaining a reasonably simple approach to design and analysis of results an example from the early treatment diabetic retinopathy study etdrs is given

an extension on statistical comparisons of classifiers over multiple data sets for all pairwise comparisons in a recently published paper in jmlr dem sar 2006 recommends a set of non parametric statistical tests and procedures which can be safely used for comparing the performance of classifiers over multiple data sets after studying the paper we realize that the paper correctly introduces the basic procedures and some of the most advanced ones when comparing a control method however it does not deal with some advanced topics in depth regarding these topics we focus on more powerful proposals of statistical procedures for comparing n n classifiers moreover we illustrate an easy way of obtaining adjusted and comparable p values in multiple comparison procedures

nonparametric tests of population differences and estimation of the probability of misidentification with unidentified paired data summary a modified mann whitney statistic is used to construct a permutation test for comparing samples of paired data from two populations when the population identities of each pair are uncertain an estimator of the probability of population misidentification within a pair is also proposed this is based on the lehmann family of distributions simulation results show the new methods are generally as or more effective than existing normal theory methods unless there is strong correlation within pairs

a comparison of several tests for censored paired data this paper reviews several tests for censored paired data and uses monte carlo methods to evaluate their sizes and powers each of the tests maintains its size the akritas test and the paired prentice wilcoxon test are somewhat more powerful than the gehan statistic or the generalized signed rank test for most of the distributions studied if the survival times follow an exponential distribution then the gehan and the generalized signed rank tests are more powerful against a location shift alternative

mutual information based matching for causal inference with observational data this paper presents an information theory driven matching methodology for making causal inference from observational data the paper adopts a potential outcomes framework view on evaluating the strength of cause effect relationships the population wide average effects of binary treatments are estimated by comparing two groups of units the treated and untreated control to reduce the bias in such treatment effect estimation one has to compose a control group in such a way that across the compared groups of units treatment is independent of the units covariates this requirement gives rise to a subset selection matching problem this paper presents the models and algorithms that solve the matching problem by minimizing the mutual information mi between the covariates and the treatment variable such a formulation becomes tractable thanks to the derived optimality conditions that tackle the non linearity of the sample based mi function computational experiments with mixed integer programming formulations and four matching algorithms demonstrate the utility of mi based matching for causal inference studies the algorithmic developments culminate in a matching heuristic that allows for balancing the compared groups in polynomial close to linear time thus allowing for treatment effect estimation with large data sets

on the determination of potentials without bound state data abstract we investigate the feasibility of recovering a compactly supported potential from the s matrix for general potentials this is known to be insufficient information on the bound states being essential we prove uniqueness results and derive reconstruction algorithms for potential recovery using several different combinations of s matrix data the basic device is the transformation of the scattering data into boundary conditions for a related hyperbolic boundary value problem some generalizations to the case of step like potentials are proved

a novel approach to statistical comparison of meta heuristic stochastic optimization algorithms using deep statistics abstract in this paper a novel approach for making a statistical comparison of meta heuristic stochastic optimization algorithms over multiple single objective problems is introduced where a new ranking scheme is proposed to obtain data for multiple problems the main contribution of this approach is that the ranking scheme is based on the whole distribution instead of using only one statistic to describe the distribution such as average or median averages are sensitive to outliers i e the poor runs of the stochastic optimization algorithms and consequently medians are sometimes used however using the common approach with either averages or medians the results can be affected by the ranking scheme that is used by some standard statistical tests this happens when the differences between the averages or medians are in some neighborhood and the algorithms obtain different ranks though they should be ranked equally given the small differences that exist between them the experimental results obtained on black box benchmarking 2015 show that our approach gives more robust results compared to the common approach in cases when the results are affected by outliers or by a misleading ranking scheme

the prognostic analogue of the propensity score summary the propensity score collapses the covariates of an observational study into a single measure summarizing their joint association with treatment conditions prognostic scores summarize covariates association with potential responses as with propensity scores stratification on prognostic scores brings to uncontrolled studies a concrete and desirable form of balance a balance that is more familiar as an objective of experimental control like propensity scores prognostic scores can reduce the dimension of the covariate yet causal inferences conditional on them are as valid as are inferences conditional only on the unreduced covariate as a method of adjustment unto itself prognostic scoring has limitations not shared with propensity scoring but it holds promise as a complement to the propensity score particularly in certain designs for which unassisted propensity adjustment is difficult or infeasible