sensitivity analysis for certain permutation inferences in matched observational studies summary in observational studies treatments are not randomly assigned to experimental units so that randomization tests and their associated interval estimates are not generally applicable in an effort to compensate for the lack of randomization treated and control units are often matched on the basis of observed covariates however the possibility remains of bias due to residual imbalances in unobserved covariates a general though simple method is proposed for displaying the sensitivity of permutation inferences to a range of assumptions about unobserved covariates in matched observational studies the sensitivity analysis is applicable to wilcoxon s signed rank test to the mcnemar cox test for paired binary responses and to some matching problems with a variable number of controls

case control studies assessing the effect of a confounding factor summary upper and lower bounds for the strength of the effect of a dichotomous confounding factor on the exposure disease relationship are developed for case control studies of a a problem in the design and analysis of a case control study is the identification of confounding factors controversies frequently arise about whether an exposure disease relationship is spurious i e caused by extraneous or confounding factors that were not measured or controlled as part of the study the effect of confounding factors has been discussed quantitatively by bross 1966 and schlesselman 1978 in this paper we develop upper and lower bounds for the stratum specific odds ratios which are applicable for assessing the effect of a confounding factor we restrict our attention to the simple case involving a dichotomous disease variable denoted by d if present and d if absent a dichotomous exposure variable denoted by e if present and e if absent and a single dichotomous extraneous factor f with f1 and fo denoting its two levels 2 bounds we parameterize the joint distributions of e and f in d and d as follows

lack of diamagnetism and the little parks effect when a superconducting sample is submitted to a sufficiently strong external magnetic field the superconductivity of the material is lost in this paper we prove that this effect does not in general take place at a unique value of the external magnetic field strength indeed for a sample in the shape of a narrow annulus the set of magnetic field strengths for which the sample is superconducting is not an interval this is a rigorous justification of the little parks effect we also show that the same oscillation effect can happen for disc shaped samples if the external magnetic field is non uniform in this case the oscillations can even occur repeatedly along arbitrarily large values of the ginzburg landau parameter the analysis is based on an understanding of the underlying spectral theory for a magnetic schrodinger operator it is shown that the ground state energy of such an operator is not in general a monotone function of the intensity of the field even in the limit of strong fields

recursive combination tests we present a method that extends the flexibility of adaptive designs to the number of interim analyses and to the choice of decision boundaries at each stage of the trial the design of the next stage can be determined using all of the information gathered so far additionally one can specify the next stage as the final stage or can plan a further interim analysis the method is based on a recursive application of the two stage combination tests for p values the crucial point is the appropriate definition of a p value function that combines p values from two separate stages to a single p value formally we start with a two stage combination test however the p value of the second stage can be replaced by the p value of a further combination test this applies if the experimenter decides in the first interim analysis to perform another interim analysis thereby extending the design to at least three stages obviously this can be also done in a recursive way in the following interim analyses the test

spiral waves in reaction diffusion equations we consider the reaction diffusion system begin gathered r t nabla 2 r r left 1 r 2 vec nabla theta cdot vec nabla theta right hfill r theta t r nabla 2 theta 2 vec nabla r cdot vec nabla theta qr 3 hfill end gathered this system governs the solutions of reaction diffusion systems near a hopf bifurcation point in two spatial dimensions we use formal asymptotic expansions to contruct one armed and multi armed archimedean spiral waves for small values of the parameter q we then show that the one armed spiral waves are probably stable and the multi armed ones are unstable for q small next by numerical continuation methods we construct spiral waves for all q these calculations show that the one armed spiral waves are unstable when q 1 397 cdots we also find the explicit one dimensional analogues of spiral waves for all q and show that they are unstable for q small

inversion of polynomial systems and separation of nonlinear mixtures of finite alphabet sources in this contribution multiple input multiple output mimo mixing systems are considered which are instantaneous and nonlinear but polynomial we first address the problem of invertibility searching the inverse in the class of polynomial systems it is shown that grobner bases techniques offer an attractive solution for testing the existence of an exact inverse and computing it by noticing that any nonlinear mapping can be interpolated by a polynomial on a finite set we tackle the general nonlinear case relying on a finite alphabet assumption of the input source signals theoretical results on polynomials allow us to represent nonlinear systems as linear combinations of a finite set of monomials we then generalize the first results to give a condition for the existence of an exact nonlinear inverse the proposed method allows to compute this inverse in polynomial form in the light of the previous results we go further to the blind source separation problem it is shown that for sources in a finite alphabet the nonlinear problem is tightly connected with both problems of under determination and of dependent sources we concentrate on the case of two binary sources for which an easy solution can be found by simulation this solution is compared to techniques borrowed from classification methods

sensitivity analysis for m estimates tests and confidence intervals in matched observational studies huber s m estimates use an estimating equation in which observations are permitted a controlled level of influence the family of m estimates includes least squares and maximum likelihood but typical applications give extreme observations limited weight maritz proposed methods of exact and approximate permutation inference for m tests confidence intervals and estimators which can be derived from random assignment of paired subjects to treatment or control in contrast in observational studies where treatments are not randomly assigned subjects matched for observed covariates may differ in terms of unobserved covariates so differing outcomes may not be treatment effects in observational studies a method of sensitivity analysis is developed for m tests m intervals and m estimates it shows the extent to which inferences would be altered by biases of various magnitudes due to nonrandom treatment assignment the method is developed for both matched pairs with one treated subject matched to one control and for matched sets with one treated subject matched to one or more controls the method is illustrated using two studies i a paired study of damage to dna from exposure to chromium and nickel and ii a study with one or two matched controls comparing side effects of two drug regimes to treat tuberculosis the approach yields sensitivity analyses for i m tests with huber s weight function and other robust weight functions ii the permutational t test which uses the observations directly and iii various other procedures such as the sign test noether s test and the permutation distribution of the efficient score test for a location family of distributions permutation inference with covariance adjustment is briefly discussed

nonlinear blind source separation using a radial basis function network this paper proposes a novel neural network approach to blind source separation in nonlinear mixture the approach utilizes a radial basis function rbf neural network to approximate the inverse of the nonlinear mixing mapping which is assumed to exist and able to be approximated using an rbf network a contrast function which consists of the mutual information and partial moments of the outputs of the separation system is defined to separate the nonlinear mixture the minimization of the contrast function results in the independence of the outputs with desirable moments such that the original sources are separated properly two learning algorithms for the parametric rbf network are developed by using the stochastic gradient descent method and an unsupervised clustering method by virtue of the rbf neural network this proposed approach takes advantage of high learning convergence rate of weights in the hidden layer and output layer natural unsupervised learning characteristics modular structure and universal approximation capability simulation results are presented to demonstrate the feasibility robustness and computability of the proposed method

confidence intervals for uncommon but dramatic responses to treatment a small literature discusses locally most powerful rank tests when only a fraction of treated subjects respond to treatment the ranks used in these tests are very different from conventional ranks being relatively flat for low responses and then rising steeply and the associated tests are much more powerful than conventional rank tests when indeed only a small fraction of treated subjects exhibit dramatic responses because the tests are derived from considerations of local power they do not yield a plausible family of models for effect and therefore they do not yield confidence intervals for the magnitude of effect formed by inverting the tests there is a similarity between these tests and another family of tests originally motivated by different considerations involving peak performance in small subsets exploiting this similarity a method for obtaining confidence statements is proposed in the case of observational studies sensitivity to unobserved bias from nonrandom assignment of treatments is also examined two examples are used as illustrations i a study of smoking during pregnancy and its effects on birth weight in which smokers are matched to six controls and ii a matched pair study of damage to dna among workers at aluminum production plants

blind separation of parametric nonlinear mixtures of possibly autocorrelated and non stationary sources in this paper we present a new method formulated in a maximum likelihood framework for blindly separating nonlinear mixtures of statistically independent signals our method exploits on the one hand the knowledge of the parametric model of the mixing transformation with unknown parameter values and on the other hand the possible structure of source signals i e their autocorrelation and or nonstationarity one of the main advantages of the proposed method is that it can be implemented even if the analytical expression of the inverse model is unknown the method is first addressed in a general configuration then detailed for two special cases i e a simple bijective toy model and a linear quadratic model the study of the toy model is interesting because of its simplicity and its global bijectivity which allows us to focus our efforts on parameter estimation the linear quadratic model is chosen due to its capacity to describe real world mixing phenomena simulation results using the toy model and using a subclass of the linear quadratic model i e the bilinear model show that taking into account the nonlinearity of the mixing transformations and the structure of signals considerably improves separation performance

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

some approximate evidence factors in observational studies an observational study or nonrandomized experiment has exact evidence factors if it permits several statistically independent tests of the same null hypothesis h0 of no treatment effect where these several tests depend upon different assumptions about bias from nonrandom treatment assignment in an observational study we are typically uncertain about what assumptions truly describe treatment assignment if independent tests each reject h0 and if each of these tests is valid under assumptions about treatment assignment that would invalidate the others then rejection of h0 does not depend upon the truth of any one of these assumptions although exact evidence factors do exist the requirement of exact independence may limit the class of test statistics in ways that reduce pitman efficiency and design sensitivity so one might wish to be free of these limitations a much larger class of statistics permits approximate evidence factors which are not independent but which preserve some of the important con

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

sensitivity analysis for unmeasured confounding in principal stratification settings with binary variables within causal inference principal stratification ps is a popular approach for dealing with intermediate variables that is variables affected by treatment that also potentially affect the response however when there exists unmeasured confounding in the treatment arms as can happen in observational studies causal estimands resulting from ps analyses can be biased we identify the various pathways of confounding present in ps contexts and their effects for ps inference we present model based approaches for assessing the sensitivity of complier average causal effect estimates to unmeasured confounding in the setting of binary treatments binary intermediate variables and binary outcomes these same approaches can be used to assess sensitivity to unknown direct effects of treatments on outcomes because as we show direct effects are operationally equivalent to one of the pathways of unmeasured confounding we illustrate the methodology using a randomized study with artificially introduced confounding and a sensitivity analysis for an observational study of the effects of physical activity and body mass index on cardiovascular disease

kernel based nonlinear blind source separation we propose ktdsep a kernel based algorithm for nonlinear blind source separation bss it combines complementary research fields kernel feature spaces and bss using temporal information this yields an efficient algorithm for nonlinear bss with invertible nonlinearity key assumptions are that the kernel feature space is chosen rich enough to approximate the nonlinearity and that signals of interest contain temporal information both assumptions are fulfilled for a wide set of real world applications the algorithm works as follows first the data are implicitly mapped to a high possibly infinite dimensional kernel feature space in practice however the data form a smaller submanifold in feature space even smaller than the number of training data points a fact that has already been used by for example reduced set techniques for support vector machines we propose to adapt to this effective dimension as a preprocessing step and to construct an orthonormal basis of this submanifold the latter dimension reduction step is essential for making the subsequent application of bss methods computationally and numerically tractable in the reduced space we use a bss algorithm that is based on second order temporal decorrelation finally we propose a selection procedure to obtain the original sources from the extracted nonlinear components automatically experiments demonstrate the excellent performance and efficiency of our ktdsep algorithm for several problems of nonlinear bss and for more than two sources

stability of symmetric vortices for two component ginzburg landau systems abstract we study ginzburg landau equations for a complex vector order parameter c 2 we consider the dirichlet problem in the disk in r 2 with a symmetric degree one boundary condition and study its stability in the sense of the spectrum of the second variation of the energy we find that the stability of the degree one equivariant solution depends on the ginzburg landau parameter as well as the sign of the interaction term in the energy

symmetric quantile averages and related estimators summary the average of two complementary order statistics is termed a symmetric quantile average in addition to having quite good efficiency robustness and computational properties exact nonparametric confidence intervals for location can be derived from it a related type of estimator called a combined quantile average is introduced it is slightly more difficult to compute than the symmetric quantile average but can have better efficiency and robustness properties in fact the recommended form of combined quantile average is comparable for robustness and normal efficiency with the 15 trimmed mean but in addition it leads like symmetric quantile averages to the definition of exact nonparametric confidence intervals

a fast fixed point algorithm for independent component analysis we introduce a novel fast algorithm for independent component analysis which can be used for blind source separation and feature extraction we show how a neural network learning rule can be transformed into a fixedpoint iteration which provides an algorithm that is very simple does not depend on any user defined parameters and is fast to converge to the most accurate solution allowed by the data the algorithm finds one at a time all nongaussian independent components regardless of their probability distributions the computations can be performed in either batch mode or a semiadaptive manner the convergence of the algorithm is rigorously proved and the convergence speed is shown to be cubic some comparisons to gradient based algorithms are made showing that the new algorithm is usually 10 to 100 times faster sometimes giving the solution in just a few iterations

a generic framework for blind source separation in structured nonlinear models this paper is concerned with blind source separation in nonlinear models special attention is paid to separability issues results show that separation is impossible in the general case however for specific nonlinear models the problem becomes tractable a generic set of parametric nonlinear mixtures is considered this set has the lie group structure a group structure with continuous binary operation in the parameter set a definition of a relative gradient is given and is used to design both batch and stochastic algorithms for the latter it is shown how a proper use of the relative gradient leads to equivariant adaptive algorithms

a unifying approach for confidence intervals and testing of equivalence and difference summary general families of null hypotheses are defined which refer to problems of testing equivalence and difference between treatments corresponding confidence intervals have been proposed in the literature in a different context the unifying approach demonstrates how waiving of particular one sided tests in the parameter space relates to the construction of the corresponding confidence interval

blind separation of post nonlinear mixtures using linearizing transformations and temporal decorrelation we propose two methods that reduce the post nonlinear blind source separation problem pnl bss to a linear bss problem the first method is based on the concept of maximal correlation we apply the alternating conditional expectation ace algorithm a powerful technique from non parametric statistics to approximately invert the componentwise non linear functions the second method is a gaussianizing transformation which is motivated by the fact that linearly mixed signals before nonlinear transformation are approximately gaussian distributed this heuristic but simple and efficient procedure works as good as the ace method using the framework provided by ace convergence can be proven the optimal transformations obtained by ace coincide with the sought after inverse functions of the nonlinearities after equalizing the nonlinearities temporal decorrelation separation tdsep allows us to recover the source signals numerical simulations testing ace td and gauss td on realistic examples are performed with excellent results

hodges lehmann point estimates of treatment effect in observational studies abstract a hodges lehmann point estimate of an additive treatment effect is a robust estimate derived from the randomization distribution of a rank test this article shows how to carry out a sensitivity analysis for such an estimate in an observational study where treatments are not randomly assigned two cases are discussed in detail matched pairs and the comparison of two unmatched groups the method uses a model for the distribution of treatment assignments when hidden biases may be present this model has previously been used for sensitivity analysis of significance levels and confidence intervals

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

channel dependent constrained combinatorial clustering constrained combinatorial clustering ccc is a new approach for grouping multiple features where the clustering metric depends on an unknown communication channel assignment features assigned to the same channel cannot be from the same source and conversely channels assigned to the same source must be distinct while the number of sources and their states are unknown the channels are assumed to be known except for additive noise potential clustering assignments are checked for compatibility with the constraints in a structured way that results in significant computational savings with respect to exhaustive enumeration especially when combined with a k best channel assignment algorithm that has polynomial complexity by combining two channel assignment methods exhaustive and k best with two clustering techniques ccc and greedy four new algorithms are presented to solve this novel problem along with detailed computational complexity analyses the main algorithm ccc is a top down clustering strategy based on assignment aggregation in a channel constrained environment the approaches are compared on a one dimensional simulation significant performance differences in source estimation accuracy and estimated number of sources are observed at low signal to noise ratios snrs and for low values of k some novel permutation symmetry properties arising from the study which lead to a new type of self affine set or discrete fractal are also presented

some remarks on the linearized operator about the radial solution for the ginzburg landau equation abstract we consider the linearized operators denoted l d 1 of the ginzburg landau operator u u 1 u 2 in r2 about the radial solutions ud 1 x fd r eid for all d 1 we state the correspondence between the real vector space of the bounded solutions of the equation l d 1 w 0 and the eigenvalues of the linearized operators of the equations u 1 e2u 1 u 2 0 in b 0 1 about the radial solutions ud e x fd r e eid that tend to 0 as e tends to 0

design sensitivity in observational studies summary outside the field of statistics the literature on observational studies offers advice about research designs or strategies for judging whether or not an association is causal such as multiple operationalism or a dose response relationship these useful suggestions are typically informal and qualitative a quantitative measure design sensitivity is proposed for measuring the contribution such strategies make in distinguishing causal effects from hidden biases several common strategies are then evaluated in terms of their contribution to design sensitivity a related method for computing the power of a sensitivity analysis is also developed

a characterization of optimal designs for observational studies summary an empirical investigation of the effects of a treatment is an observational study if it involves the comparison of treated and control groups that were not formed by randomization in such studies treated and control groups may differ systematically with respect to pretreatment measures or covariates and addressing these pre treatment differences is a central concern matching and subclassification are two standard methods of adjusting for observed pretreatment differences they may be used alone e g cochran 1968 or in conjunction with analytical or model based adjustments e g rubin 1973 1979 holford 1978 rosenbaum and rubin 1984 section 3 3 and rosenbaum 1987 1988a in particular rubin s simulation studies suggest that model based adjustments applied to matched or subclassified samples are more robust than model based adjustments applied to unmatched samples the purpose of this paper is to identify the structure of an optimal subclassification i e one in which the treated and control subjects in the same subclass are on average as similar as possible with respect to observed covariates it turns out that this structure is simple and intuitive while adjustments may control imbalances in observed covariates they cannot

testing one hypothesis twice in observational studies in a matched observational study of treatment effects a sensitivity analysis asks about the magnitude of the departure from random assignment that would need to be present to alter the conclusions of an analysis that assumes that matching for measured covariates removes all bias the reported degree of sensitivity to unmeasured biases depends on both the process that generated the data and the chosen methods of analysis so a poor choice of method may lead to an exaggerated report of sensitivity to bias this suggests the possibility of performing more than one analysis with a correction for multiple inference say testing one null hypothesis using two or three different tests in theory and in an example it is shown that in large samples the gains from testing twice will often be large because testing twice has the larger of the two design sensitivities of the component tests and the losses due to correcting for two tests will often be small because two tests of one hypothesis will typically be highly correlated so a correction for multiple testing that takes this into account will be small an illustration uses data from the u s national health and nutrition examination survey concerning lead in the blood of cigarette smokers copyright 2012 oxford university press

blind separation of mixture of independent sources through a quasi maximum likelihood approach we propose two methods for separating mixture of independent sources without any precise knowledge of their probability distribution they are obtained by considering a maximum likelihood ml solution corresponding to some given distributions of the sources and relaxing this assumption afterward the first method is specially adapted to temporally independent non gaussian sources and is based on the use of nonlinear separating functions the second method is specially adapted to correlated sources with distinct spectra and is based on the use of linear separating filters a theoretical analysis of the performance of the methods has been made a simple procedure for optimally choosing the separating functions is proposed further in the second method a simple implementation based on the simultaneous diagonalization of two symmetric matrices is provided finally some numerical and simulation results are given illustrating the performance of the method and the good agreement between the experiments and the theory

radial solutions for the ginzburg landau equation with applied magnetic field abstract the purpose of this work is a systematic study of symmetric vortices for the ginzburg landau model of superconductivity along a cylinder with applied magnetic field parallel to its axis the ginzburg landau constant of the material and the degree d of the vortex are fixed for any given parameters r the radius of the cylinder and h the intensity of the applied magnetic field one can find a symmetric vortex a which satisfies the boundary conditions b r e i d and curl a b r he 3 it is then shown that symmetric vortices form a family depending continuously on two real parameters and c which describe the behaviour at the center of the vortex as the boundary conditions depend smoothly on those parameters one can distinguish two main connected domains of vortices the first one defined by the boundary conditions b r e i d and ra r b r is a zone of stability where remains increasing the second one defined by the boundary conditions b r e i d and ra r b r d is a zone where some instability can occur attention is focused on the smooth branch of vortices which separates those two domains it is indexed by the parameter running from some l 0 to and the limit as decreases to l corresponds to a berger and chen type vortex

a new u statistic with superior design sensitivity in matched observational studies summary in an observational or nonrandomized study of treatment effects a sensitivity analysis indicates the magnitude of bias from unmeasured covariates that would need to be present to alter the conclusions of a naive analysis that presumes adjustments for observed covariates suffice to remove all bias the power of sensitivity analysis is the probability that it will reject a false hypothesis about treatment effects allowing for a departure from random assignment of a specified magnitude in particular if this specified magnitude is no departure then this is the same as the power of a randomization test in a randomized experiment a new family of u statistics is proposed that includes wilcoxon s signed rank statistic but also includes other statistics with substantially higher power when a sensitivity analysis is performed in an observational study wilcoxon s statistic has high power to detect small effects in large randomized experiments that is it often has good pitman efficiency but small effects are invariably sensitive to small unobserved biases members of this family of u statistics that emphasize medium to large effects can have substantially higher power in a sensitivity analysis for example in one situation with 250 pair differences that are normal with expectation 1 2 and variance 1 the power of a sensitivity analysis that uses wilcoxon s statistic is 0 08 while the power of another member of the family of u statistics is 0 66 the topic is examined by performing a sensitivity analysis in three observational studies using an asymptotic measure called the design sensitivity and by simulating power in finite samples the three examples are drawn from epidemiology clinical medicine and genetic toxicology

a general class of one sample nonparametric test statistics based on subsamples abstract a general class of nonparametric test statistics is constructed by considering the sign of the most extreme value in subsamples of size m taken from n independent observations the test statistics can be expressed as linear rank statistics and reduce to the sign test statistic for m 1 and a modified wilcoxon signed rank test statistic for m 2 asymptotic normality of properly standardized versions of our statistics is established under general conditions small sample power simulations as well as pitman and bahadur efficiencies indicate that members of our class do well in comparison with already existing test statistics

assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome this paper proposes a simple technique for assessing the range of plausible causal con clusions from observational studies with a binary outcome and an observed categorical covariate the technique assesses the sensitivity of conclusions to assumptions about an unobserved binary covariate relevant to both treatment assignment and response a medical study of coronary artery disease is used to illustrate the technique inevitably the results of clinical studies are subject to dispute in observational studies one basis for dispute is obvious since patients were not assigned to treatments at random patients at greater risk may be over represented in some treatment groups this paper proposes a method for assess ing the sensitivity of causal conclusions to an unmeasured patient characteristic relevant to both treatment assignment and response despite their limitations observational studies will continue to be a valuable source of information and therefore it is prudent to develop appropriate methods of analysis for them our sensitivity analysis consists of the estimation of the average effect of a treatment on a binary outcome variable after adjustment for observed categorical covariates and an unobserved binary covariate u under several sets of assumptions about u both cornfield et al 1959 and bross 1966 have proposed guidelines for determining whether an unmeasured binary covariate having specified properties could explain all of the apparent effect of a treatment that is whether the treatment effect after adjustment for u could be zero our method has two advantages first cornfield et al 1959 and bross 1966 adjust only for the unmeasured binary covariate u whereas we adjust for measured covariates in addition to the unmeasured covariate u second cornfield et al 1959 and bross 1966 1967 only judge whether the effect of the treatment could be zero having adjusted for u where cornfield et al 1959 employ an implicit yet extreme assumption about u in contrast we provide actual estimates of the treatment effect adjusted for both u and the observed categorical covariates under any assumption about u in principle the ith of the n patients under study has both a binary response r1i that would have resulted if he had received the new treatment and a binary response ro0 that would have resulted if he had received the control treatment in this formulation treatment effects are comparisons of r1i and roi such as r1i roi since each patient receives only one treatment either rli or ro0 is observed but not both and therefore comparisons of rli and roi imply some degree of speculation treatment effects defined as comparisons of the two potential responses r1i and roi of individual patients are implicit in fisher s 1953 randomization test of the sharp null

sensitivity analysis for equivalence and difference in an observational study of neonatal intensive care units in randomized experiments it is sometimes important to demonstrate that two treatments do not differ greatly in their effects or to demonstrate that the treatments have very different effects on one outcome but similar effects on another outcome these demonstrations may take the form of rejecting a null hypothesis of inequivalence in an equivalence test or rejecting a null hypothesis of equal and inequivalent effects on two outcomes the procedures often express a complex hypothesis in terms of component hypotheses and combine the component significance levels to test the complex hypothesis if used in a randomized trial randomization provides valid significance levels for each component test and hence also for the combined procedure in an observational study that is in a study of treatments that were not randomly assigned there is typically concern that significance levels for testing hypotheses about treatment effects may be distorted by failure to control for some unobserved pretreatment cov

markovian source separation a maximum likelihood ml approach is used to separate the instantaneous mixtures of temporally correlated independent sources with neither preliminary transformation nor a priori assumption about the probability distribution of the sources a markov model is used to represent the joint probability density of successive samples of each source the joint probability density functions are estimated from the observations using a kernel method for the special case of autoregressive models the theoretical performance of the algorithm is computed and compared with the performance of second order algorithms and i i d based separation algorithms

sensitivity analysis for instrumental variables regression with overidentifying restrictions instrumental variables regression iv regression is a method for making causal inferences about the effect of a treatment based on an observational study in which there are unmeasured confounding variables the method requires one or more valid instrumental variables ivs a valid iv is a variable that is associated with the treatment is independent of unmeasured confounding variables and has no direct effect on the outcome often there is uncertainty about the validity of the proposed ivs when a researcher proposes more than one iv the validity of these ivs can be tested through the overidentifying restrictions test although the overidentifying restrictions test does provide some information the test has no power versus certain alternatives and can have low power versus many alternatives due to its omnibus nature to fully address uncertainty about the validity of the proposed ivs we argue that a sensitivity analysis is needed a sensitivity analysis examines the impact of plausible amounts of

effect modification and design sensitivity in observational studies in an observational study of treatment effects subjects are not randomly assigned to treatment or control so differing outcomes in treated and control groups may reflect a bias from nonrandom assignment rather than a treatment effect after adjusting for measured pretreatment covariates perhaps by matching a sensitivity analysis determines the magnitude of bias from an unmeasured covariate that would need to be present to alter the conclusions of the naive analysis that presumes adjustments eliminated all bias other things being equal larger effects tend to be less sensitive to bias than smaller effects effect modification is an interaction between a treatment and a pretreatment covariate controlled by matching so that the treatment effect is larger at some values of the covariate than at others in the presence of effect modification it is possible that results are less sensitive to bias in subgroups experiencing larger effects two cases are considered i an a priori grouping into a few categ

the bias due to incomplete matching observational studies comparing groups of treated and control units are often used to estimate the effects caused by treatments matching is a method for sampling a large reservoir of potential controls to produce a control group of modest size that is ostensibly similar to the treated group in practice there is a trade off between the desires to find matches for all treated units and to obtain matched treated control pairs that are extremely similar to each other we derive expressions for the bias in the average matched pair difference due to the failure to match all treated units incomplete matching and the failure to obtain exact matches inexact matching a practical example shows that the bias due to incomplete matching can be severe and moreover can be avoided entirely by using an appropriate multivariate nearest available matching algorithm which in the example leaves only a small residual bias due to inexact matching

source separation in post nonlinear mixtures we address the problem of separation of mutually independent sources in nonlinear mixtures first we propose theoretical results and prove that in the general case it is not possible to separate the sources without nonlinear distortion therefore we focus our work on specific nonlinear mixtures known as post nonlinear mixtures these mixtures constituted by a linear instantaneous mixture linear memoryless channel followed by an unknown and invertible memoryless nonlinear distortion are realistic models in many situations and emphasize interesting properties i e in such nonlinear mixtures sources can be estimated with the same indeterminacies as in instantaneous linear mixtures the separation structure of nonlinear mixtures is a two stage system namely a nonlinear stage followed by a linear stage the parameters of which are updated to minimize an output independence criterion expressed as a mutual information criterion the minimization of this criterion requires knowledge or estimation of source densities or of their log derivatives a first algorithm based on a gram charlier expansion of densities is proposed unfortunately it fails for hard nonlinear mixtures a second algorithm based on an adaptive estimation of the log derivative of densities leads to very good performance even with hard nonlinearities experiments are proposed to illustrate these results