the control of confounding by intermediate variables in epidemiologic studies of the effect of an exposure on disease the crude association of exposure with disease may fail to reflect a causal association due to confounding by one or more covariates most previous discussions of confounding in the epidemiologic literature have considered only point exposure studies that is studies that measure exposure and covariate status only once at start of follow up in this paper we offer definitions of confounding suitable for longitudinal studies that obtain data on exposure covariate and vital status at several points in time an important difference between longitudinal studies and point exposure studies is that in longitudinal studies a time dependent covariate can be simultaneously a confounder and an intermediate variable on the causal pathway from exposure to disease in this paper i propose an estimator the extended standardized risk difference that provides control for confounding by a covariate that is simultaneously a confounder and an intermediate variable

two stage least squares estimation of average causal effects in models with variable treatment intensity abstract two stage least squares tsls is widely used in econometrics to estimate parameters in systems of linear simultaneous equations and to solve problems of omitted variables bias in single equation estimation we show here that tsls can also be used to estimate the average causal effect of variable treatments such as drug dosage hours of exam preparation cigarette smoking and years of schooling the average causal effect in which we are interested is a conditional expectation of the difference between the outcomes of the treated and what these outcomes would have been in the absence of treatment given mild regularity assumptions the probability limit of tsls is a weighted average of per unit average causal effects along the length of an appropriately defined causal response function the weighting function is illustrated in an empirical example based on the relationship between schooling and earnings

the foundations of confounding in epidemiology abstract a statistically coherent view of confounding motivated by the over controversy over the proper control of confounding in the presence of prior knowledge is presented confounding by a covariate c in the presence of data on c is distinguished from confounding in the absence of data on c a covariate c is defined to be a nonconfounder in the absence of data on c if the population parameter of interest can be unbiasedly estimated asymptotically absent data on c under this definition c may be a confounder for some parameters of interest and a nonconfounder for others if c is a confounder for a parameter of interest that has a causal interpretation we call c a causal confounder when data on c are available c is defined to be a nonconfounder for a particular parameter of interest if and only if inference on the parameter of interest does not depend on the data through c bayesians frequentists and pure likelihoodists will in general agree on the prior knowledge necessary to render c a non confounder in particular c will in general be a nonconfounder precisely when the crude data ignoring c are s sufficient for the parameter of interest the intuitive view held by many practicing epidemiologists that confounding by c represents a bias of the unadjusted crude estimator is in a sense correct provided inference is performed conditional on approximate ancillary statistics that measure the degree to which associations in the data differ due to sampling variability from those population associations known a priori

three dimensional instabilities in steady and unsteady non parallel boundary layers including effects of tollmien schlichting disturbances and cross flow three dimensional 3d linear stability properties are considered for steady and unsteady 2d or 3d boundary layers with significant non parallelism present two main examples of such non parallel flows whose stability is of interest are firstly steady motion over roughness elements in cross flow or in large scale separation and secondly unsteady 2d tollmien schlichting ts motion with its associated question of secondary instabilities a high frequency stability analysis is presented here it is found that for 2dts or steady boundary layers there is a swing in the direction of maximum ts spatial growth rate from 0 for parallel flow towards 64 68 away from the free stream direction as the nonparallel flow effects increase these effects then depend principally on and indeed are proportional to the local slope of the boundary layer displacement cross flow can also have a profound impact on ts instabilities further implications for higher amplitude and or fasterscale disturbances their secondary instability and nonlinear interactions are also discussed

a forward regridding method with minimal oversampling for accurate and efficient iterative tomographic algorithms reconstruction of underconstrained tomographic data sets remains a major challenge standard analytical techniques frequently lead to unsatisfactory results due to insufficient information several iterative algorithms which can easily integrate a priori knowledge have been developed to tackle this problem during the last few decades most of these iterative algorithms are based on an implementation of the radon transform that acts as forward projector this operator and its adjoint the backprojector are typically called few times per iteration and represent the computational bottleneck of the reconstruction process here we present a fourier based forward projector founded on the regridding method with minimal oversampling we show that this implementation of the radon transform significantly outperforms in efficiency other state of the art operators with o n2log2n complexity despite its reduced computational cost this regridding method provides comparable accuracy to more sophisticated projectors and can therefore be exploited in iterative algorithms to substantially decrease the time required for the reconstruction of underconstrained tomographic data sets without loss in the quality of the results

sample size formulae for two stage randomized trials with survival outcomes two stage randomized trials are growing in importance in developing adaptive treatment strategies i e treatment policies or dynamic treatment regimes usually the first stage involves randomization to one of the several initial treatments the second stage of treatment begins when an early nonresponse criterion or response criterion is met in the second stage nonresponding subjects are re randomized among second stage treatments sample size calculations for planning these two stage randomized trials with failure time outcomes are challenging because the variances of common test statistics depend in a complex manner on the joint distribution of time to the early nonresponse criterion or response criterion and the primary failure time outcome we produce simple albeit conservative sample size formulae by using upper bounds on the variances the resulting formulae only require the working assumptions needed to size a standard single stage randomized trial and in common settings are only mildly conservative these sample size formulae are based on either a weighted kaplan meier estimator of survival probabilities at a fixed time point or a weighted version of the log rank test

structural nested mean models for assessing time varying effect moderation this article considers the problem of assessing causal effect moderation in longitudinal settings in which treatment or exposure is time varying and so are the covariates said to moderate its effect intermediate causal effects that describe time varying causal effects of treatment conditional on past covariate history are introduced and considered as part of robins structural nested mean model two estimators of the intermediate causal effects and their standard errors are presented and discussed the first is a proposed two stage regression estimator the second is robins g estimator the results of a small simulation study that begins to shed light on the small versus large sample performance of the estimators and on the bias variance trade off between the two estimators are presented the methodology is illustrated using longitudinal data from a depression study

estimation of controlled direct effects in time varying treatments using structural nested mean models application to a primary prevention trial for coronary events with pravastatin for the estimation of controlled direct effects i e direct effects controlling intermediates that are set at a fixed level for all members of the population without bias two fundamental assumptions must hold the absence of unmeasured confounding factors for treatment and outcome and for intermediate variables and outcome even if these assumptions hold one would nonetheless fail to estimate direct effects using standard methods for example stratification or regression modeling when the treatment influences confounding factors for such situations the sequential g estimation method for structural nested mean models has been developed for estimating controlled direct effects in point treatment situations in this study we demonstrate that this method can be applied to longitudinal data with time varying treatments and repeatedly measured intermediate variables we sequentially estimate the parameters in two structural nested mean models one for a repeatedly measured intermediate and the other one for direct effects of a time varying treatment the method was applied to data from a large primary prevention trial for coronary events in which pravastatin was used to lower the cholesterol levels in patients with moderate hypercholesterolemia

analyzing sequentially randomized trials based on causal effect models for realistic individualized treatment rules in this paper we argue that causal effect models for realistic individualized treatment rules represent an attractive tool for analyzing sequentially randomized trials unlike a number of methods proposed previously this approach does not rely on the assumption that intermediate outcomes are discrete or that models for the distributions of these intermediate outcomes given the observed past are correctly specified in addition it generalizes the methodology for performing pairwise comparisons between individualized treatment rules by allowing the user to posit a marginal structural model for all candidate treatment rules simultaneously this is particularly useful if the number of such rules is large in which case an approach based on individual pairwise comparisons would be likely to suffer from too much sampling variability to provide an informative answer in addition such causal effect models represent an interesting alternative to methods previously proposed for selecting an optimal individualized treatment rule in that they immediately give the user a sense of how the optimal outcome is estimated to change in the neighborhood of the identified optimum we discuss an inverse probability of treatment weighted iptw estimator for these causal effect models which is straightforward to implement using standard statistical software and develop an approach for constructing valid asymptotic confidence intervals based on the influence curve of this estimator the methodology is illustrated in two simulation studies that are intended to mimic an hiv aids trial

estimation of the causal effect of a time varying exposure on the marginal mean of a repeated binary outcome abstract we provide sufficient conditions for estimating from longitudinal data the causal effect of a time dependent exposure or treatment on the marginal probability of response for a dichotomous outcome we then show how one can estimate this effect under these conditions using the g computation algorithm of robins we also derive the conditions under which some current approaches to the analysis of longitudinal data such as the generalized estimating equations gee approach of zeger and liang the feedback model techniques of liang and zeger and within subject conditional methods can provide valid tests and estimates of causal effects we use our methods to estimate the causal effect of maternal stress on the marginal probability of a child s illness from the mothers stress and children s morbidity data and compare our results with those previously obtained by zeger and liang using a gee approach

traveltime tomography a comparison of popular methods noisy or inconsistent traveltime data yielded tomographic images that contain geologically unrealistic fluctuations in addition to diverting attention away from structural patterns these high wavenumber fluctuations can generate shadow zones and caustics that destabilize iterative solution schemes requiring ray tracing we evaluated the performance of a number of popular methods that have been designed to reduce this effect using synthetic crosswell data containing gaussian noise quantitative comparisons between tomography methods were based on the misfit with the true model solution stability under different sets of noise of the same level and resolution covariance relationships other important factors included versatility and simplicity versatility is the ability to treat data with a wide range of noise levels as well as data generated by different structures simplicity is characterized by the number of adjustable inputs such as smoother shape starting model and damping or regularization para

fast simultaneous seismic source separation using stolt migration and demigration operators abstractstolt migration is a fourier domain imaging operator that assumes a constant velocity media we have developed a multivelocity version of the stolt migration and demigration operators to derive a transform that can decompose seismic data into a sparse collection of coefficients in the image space this stolt based transform is similar to the apex shifted hyperbolic radon transform ashrt however the stolt based transform is considerably faster than the classical ashrt because it uses two fast operators forward and inverse fast fourier transforms to estimate the data coefficients in the image space we used this stolt based transform as a tool for simultaneous seismic source separation by removing erratic interference noise in common receiver gathers estimating the coefficients of interference free seismic data using the stolt based transform was posed as an inverse problem the solution of this inverse problem was found by minimizing a cost function that included a sparsity promoting regular

empirical and counterfactual conditions for sufficient cause interactions summary sufficient component causes are discussed within the deterministic potential outcomes framework so as to formalize notions of sufficient causes synergism and sufficient cause in teractions doing so allows for the derivation of counterfactual and empirical conditions for detecting the presence of sufficient cause interactions the conditions are novel in that unlike other conditions in the literature they make no assumption about monotonicity the conditions can also be generalized and the conditions for three way sufficient cause interactions are given explicitly the statistical tests derived for sufficient cause interactions are compared with and contrasted to interaction terms in standard statistical models

estimating exposure effects by modelling the expectation of exposure conditional on confounders in order to estimate the causal effects of one or more exposures or treatments on an outcome of interest one has to account for the effect of confounding factors which both covary with the exposures or treatments and are independent predictors of the outcome in this paper we present regression methods which in contrast to standard methods adjust for the confounding effect of multiple continuous or discrete covariates by modelling the conditional expectation of the exposures or treatments given the confounders in the special case of a univariate dichotomous exposure or treatment this conditional expectation is identical to what rosenbaum and rubin have called the propensity score they have also proposed methods to estimate causal effects by modelling the propensity score our methods generalize those of rosenbaum and rubin in several ways first our approach straightforwardly allows for multivariate exposures or treatments each of which may be continuous ordinal or discrete second even in the case of a single dichotomous exposure our approach does not require subclassification or matching on the propensity score so that the potential for residual confounding i e bias due to incomplete matching is avoided third our approach allows a rather general formalization of the idea that it is better to use the estimated propensity score than the true propensity score even when the true score is known the additional power of our approach derives from the fact that we assume the causal effects of the exposures or treatments can be described by the parametric component of a semiparametric regression model to illustrate our methods we reanalyze the effect of current cigarette smoking on the level of forced expiratory volume in one second in a cohort of 2 713 adult white males we compare the results with those obtained using standard methods

obtaining smooth solutions to large linear inverse problems it is not uncommon now for geophysical inverse problems to be parameterized by 10 4 to 10 5 unknowns associated with upwards of 10 6 to 10 7 data con straints the matrix problem defining the linearization of such a system e g m b is usually solved with a least squares criterion m t t b the size of the matrix however discourages the direct solution of the system and researchers often tum to iterative techniques such as the method of conjugate gradients to obtain an estimate of the least squares solution these iterative methods take advantage of the sparse ness of which often has as few as 2 3 percent of its elements nonzero and do not require the calculation or storage of the matrix t although there are usually many more data constraints than unknowns these problems are in general underdetermined and therefore require some sort of regularization to obtain a solution when the regularization is simple damping the conjugate gradients method tends to converge in relatively few iterations however when derivative type regularization is applied first derivative constraints to obtain the flattest model that fits the data second deriv ative to obtain the smoothest the convergence of parts ofthe solution may be drastically inhibited in a series of i d examples and a synthetic 2 d crosshole tomography example we demonstrate this problem and also suggest a method of accelerating the convergence through the preconditioning of the conjugate gradient search direc tions we derive a i d preconditioning operator for the case of first derivative regularization using a wkbj approximation we have found that preconditioning can reduce the number of iterations necessary to obtain satisfactory convergence by up to an order of magnitude the conclusions we present are also relevant to baye sian inversion where a smoothness constraint is im posed through an a priori covariance of the model

seismic data interpolation by greedy local radon transform we propose a greedy inversion method for a spatially localized high resolution radon transform the kernel of the method is based on a conventional iterative algorithm conjugate gradient cg but is utilized adaptively in amplitude prioritized local model spaces the adaptive inversion introduces a coherence oriented mechanism to enhance focusing of significant model parameters and hence increases the model resolution and convergence rate we adopt the idea in a time space domain local linear radon transform for data interpolation we find that the local radon transform involves iteratively applying spatially localized forward and adjoint radon operators to fit the input data optimal local radon panels can be found via a subspace algorithm which promotes sparsity in the model and the missing data can be predicted using the resulting local radon panels the subspacing strategy greatly reduces the cost of computing local radon coefficients thereby reducing the total cost for inversion the method can handle irregular and regular geometries and significant spatial aliasing we compare the performance of our method using three simple synthetic data sets with a popular interpolation method known as minimum weighted norm fourier interpolation and show the advantage of the new algorithm in interpolating spatially aliased data we also test the algorithm on the 2d synthetic data and a field data set both tests show that the algorithm is a robust antialiasing tool although it cannot completely recover missing strongly curved events

conditioning likelihood and coherence a review of some foundational concepts 2000 conditioning likelihood and coherence a review of some foundational concepts journal of the american statistical association vol 95 no 452 pp 1340 1346

signed directed acyclic graphs for causal inference formal rules governing signed edges on causal directed acyclic graphs are described in this paper and it is shown how these rules can be useful in reasoning about causality specifically the notions of a monotonic effect a weak monotonic effect and a signed edge are introduced results are developed relating these monotonic effects and signed edges to the sign of the causal effect of an intervention in the presence of intermediate variables the incorporation of signed edges into the directed acyclic graph causal framework furthermore allows for the development of rules governing the relationship between monotonic effects and the sign of the covariance between two variables it is shown that when certain assumptions about monotonic effects can be made then these results can be used to draw conclusions about the presence of causal effects even when data is missing on confounding variables

accounting for covariates observed post randomization for discrete and continuous repeated measures data adjusting for covariates observed post randomization is a difficult issue in randomized clinical trials one approach is to enter these covariates as time dependent covariates in a general linear model however this approach fails to account for interactions between the primary end point and confounding variable as they evolve over time in this paper we adopt the view that since the confounder is observed following randomization it should be treated as an outcome and analysed accordingly we consider the repeated measures design where both the primary end point and the confounding measure are observed repeatedly over patient follow up a generalized estimating equation model is applied to allow each set of repeated measures to be modelled in terms of important explanatory variables seemingly unrelated regression combines the two models into an overall framework for analysis inference is then performed by imposing restrictions on the confounder regression parameters to reflect the behaviour profile of interest estimation and identification procedures are described and the methodology is illustrated with an example

fast l p solution of large sparse linear systems application to seismic travel time tomography least squares inversion tends to be sensitive to small changes in the assumptions in the statistical lexicon it is not robust least squares solutions of noisy ill conditioned systems often exhibit unphysical high frequency oscillations which have to be damped or smoothed in some fashion the iteratively reweighted least squares irls algorithm provides a means of computing approximate lp solutions 1 p we will show that irls can be combined with the preconditioned conjugate gradient algorithm in order to solve large sparse rectangular systems of linear algebraic equations very efficiently further for p 1 the resulting algorithm is extremely stable it seems to give reasonably smooth solutions without minute adjustment of the parameters and does not become unstable if an overly optimistic error estimate is used it also has the ability to reject or at least significantly diminish the influence of outliers in the data and does not require the use of damping in addition we will show how to efficiently include diagonal weighting of the observations and parameters in order to incorporate a priori information into the inversion this combined inversion algorithm has wide applicability in real world inverse theory parameter estimation filtering etc where data are noisy and not uniformly reliable numerical examples of the l1 inversion of noisy seismic travel time data will be shown

d alembert s paradox since classical inviscid theory leads to the patently absurd conclusion that the resistance experienced by a rigid body moving through a fluid with uniform velocity is zero great efforts have been made during the last hundred or so years to propose alternate theories and to explain how a vanishingly small frictional force in the fluid can nevertheless have a significant effect on the flow properties the methods used are a combination of experimental observation computation often on a very large scale and analysis of the structure of the asymptotic form of the solution as the friction tends to zero this three pronged attack has achieved considerable success especially during the last ten years so that now the paradox may be regarded as largely resolved the lecture will review these achievements in subsonic and supersonic flow for bluff bodies for trailing edge flows and for internal flows most of the work has been on steady two dimensional problems but the special difficulties in unsteady and th

improved estimation of controlled direct effects in the presence of unmeasured confounding of intermediate variables adjusting for a causal intermediate is a common analytic strategy for estimating an average causal direct effect acde the acde is the component of the total exposure effect that is not relayed through the specified intermediate even if the total effect is unconfounded the usual acde estimate may be biased when an unmeasured variable affects the intermediate and outcome variables using linear programming optimization to compute non parametric bounds we develop new acde estimators for binary measured variables in this causal structure and use root mean square confounding bias rmsb to compare their performance with the usual stratified estimator in simulated distributions of target populations comprised of the 64 possible potential response types as well as distributions of target populations restricted to subsets of 18 or 12 potential response types defined by monotonicity or no interactions assumptions of unit level causal effects we also consider target population distributions conditioned on fixed outcome risk among the unexposed or fixed true acde in one stratum of the intermediate results show that a midpoint estimator constructed from the optimization bounds has consistently lower rmsb than the usual stratified estimator both unconditionally and conditioned on any risk in the unexposed when conditioning on true acde this midpoint estimator performs more poorly only when conditioned on an extreme true acde in one stratum of the intermediate yet outperforms the stratified estimator in the other stratum when interaction is permitted an alternate limit modified crude estimator can never perform less favourably than the stratified estimator and often has lower rmsb

transition of free disturbances in inflectional flow over an isolated surface roughness three dimensional nonlinear initial value problems are derived on the onset of transition in inflectional flow over a surface roughness buried within a boundary layer and in related configurations this start on the basic transition physics is for the free evolution of general disturbances rather than forced fixed frequency or fixed wavelength evolutions an integral criterion of earlier nonlinear work holds at leading order the nonlinear amplitude evolution equation then obtained at the next order is for fairly general initial conditions of the disturbance not just wave packets three or four such initial value problems are developed along with analytical and computational solution properties which include nonlinear bounded behaviour leading to persistent vortex effects as time increases or quasi linear decay or nonlinear finite time blowups of the disturbance amplitude the discussion includes the connections between the different cases present and the links with roughness transition experiments

testing for imbalance of covariates in controlled experiments results of a controlled experiment are often adjusted for covariates found by a preliminary test to differ significantly between the treatment and control groups the resulting test s true significance level is lower than the nominal level greater power can be achieved by always adjusting for a covariate that is highly correlated with the response regardless of its distribution between groups

robust iterative inversion for the one dimensional acoustic wave equation seismic inversion can be formulated by considering a linearized integral relation which is deduced from the wave equation this born inversion approach is equivalent to linear least squares inversion for a particular parameterization of the medium the least squares solution is a member of a family of generalized lp norm solutions which are deduced from a maximum likelihood formulation this formulation allows design of various statistical inversion solutions we present two iterative solutions to the one dimensional 1 d seismic inverse problem the iterative least squares ils and the iterative reweighted least squares irls methods the ils method involves solving a distorted background velocity problem after the initial least squares solution is obtained the irls method is used as a robust regression technique which is better suited for dealing with certain types of noise and is computationally faster than ils several numerical examples demonstrate that the irls method accurately estimates impeda

traveling waves in two dimensional plane poiseuille flow the asymptotic structure of laminar modulated traveling waves in two dimensional high reynolds number plane poiseuille flow is investigated on the upper energy branch a finite set of independent slowly varying parameters are identified which parameterize the solution of the navier stokes equations in this subset of the phase space our parameterization of the weakly stable modes describes an attracting manifold of maximum entropy configurations the complementary modes which have been neglected in this parameterization are strongly damped in order to seek a closure a countably infinite number of modulation equations are derived on the long viscous time scale a single equation for averaged kinetic energy and momentum and the remaining equations for averaged powers of vorticity only a finite number of these vorticity modulation equations are required to determine the finite number of unknowns the new results show that the evolution of the slowly varying amplitude parameters is determined by the vo

a forward model and conjugate gradient inversion technique for low frequency ultrasonic imaging emerging methods of hyperthermia cancer treatment require noninvasive temperature monitoring and ultrasonic techniques show promise in this regard various tomographic algorithms are available that reconstruct sound speed or contrast profiles which can be related to temperature distribution the requirement of a high enough frequency for adequate spatial resolution and a low enough frequency for adequate tissue penetration is a difficult compromise in this study the feasibility of using low frequency ultrasound for imaging and temperature monitoring was investigated the transient probing wave field had a bandwidth spanning the frequency range 2 5 320 5 khz the results from a forward model which computed the propagation and scattering of low frequency acoustic pressure and velocity wave fields were used to compare three imaging methods formulated within the born approximation representing two main types of reconstruction the first uses fourier techniques to reconstruct sound speed profiles from projection or radon data based on optical ray theory seen as an asymptotical limit for comparison the second uses backpropagation and conjugate gradient inversion methods based on acoustical wave theory the results show that the accuracy in localization was 2 5 mm or better when using low frequencies and the conjugate gradient inversion scheme which could be used for temperature monitoring

tomography of joint p wave traveltime and polarization data a simple approach for media with low to moderate velocity gradients an elastic wave tomography method utilizing joint traveltime and polarization data is proposed that is computationally simpler than the existing methods hu and menke geophys j int 110 63 1992 farra and begat geophys j int 121 371 1995 in the linearization problem for the use of polarization data we start with ray perturbation theory and assume that the medium is weakly inhomogeneous then the problem formulation for polarization data is approximately expressed as a linear integral of the gradient of the medium slowness perturbation along a reference ray we call this a quasi linear approximation which ignores the effect of the perturbation of the ray position on the first order perturbation of the ray slowness vector to efficiently obtain the solution for multi data sets a quadratic objective functional is constructed by including the data misfit terms and a model constraint term then a new conjugate gradient type of iterative reconstruction algorithm is developed to solve this minimization problem this algorithm is also an extension of the conjugate gradient approach for standard least squares problems the feasibility and capability of the proposed tomography method is illustrated by conducting both noise free and noisy synthetic experiments in a cross hole geometry the numerical results demonstrate that the additional use of polarization data not only improves the image quality but also has a stabilizing effect on the iterative tomography solution however the limitation of the method is that it becomes inaccurate if the velocity variations in the medium change rapidly with position

geometrical theory of asymptotic ancillarity and conditional inference summary differential geometry is applied to the problems of defining higher order asymptotic ancillarity and of obtaining the asymptotic conditional distribution of an efficient estimator in multiparameter curved exponential families it is shown that a fundamental role is played in the asymptotic theory of estimation by a one parameter family of affine connexions and curvatures of subspaces asymptotic ancillary statistics of higher order are explicitly constructed with the help of the geometry the conditional distribution of an estimator is given in terms of the exponential curvature of the model and the mixture curvature of the ancillary subspaces associated with the estimator

on the development of large sized short scaled disturbances in boundary layers for high reynolds numbers the planar nonlinear stability properties of boundary layers as governed first by the triple deck interaction are discussed theoretically when a disturbance of relatively high frequency is introduced or as the distance downstream increases in the blasius case the characteristic length scale shortens an account is given of the possible progress of such a disturbance from an initially small tollmien schlichting state through a weakly nonlinear first stage that does not interrupt the amplitude growth and thence into a fully nonlinear second stage where the benjamin ono equation comes into force still higher frequencies point to the full euler equations holding although significant non parallel flow effects then emerge in the euler stage however and in the previous second stage bursts of vorticity from the viscous sublayer closest to the solid surface are almost certain to occur the relations with other basic flow problems and with turbulence modelling are noted as well as the need to consider three dimensional motion finally an appendix deals with certain issues of practical importance arising with respect to non parallel flow effects for example in breakaway separations or flow over surface mounted obstacles and points out that the slope of the local displacement in the basic flow is then a dominant controlling feature of the short scale instabilities

on the definition of a confounder the causal inference literature has provided a clear formal definition of confounding expressed in terms of counterfactual independence the causal inference literature has not however produced a clear formal definition of a confounder as it has given priority to the concept of confounding over that of a confounder we consider a number of candidate definitions arising from various more informal statements made in the literature we consider the properties satisfied by each candidate definition principally focusing on i whether under the candidate definition control for all confounders suffices to control for confounding and ii whether each confounder in some context helps eliminate or reduce confounding bias several of the candidate definitions do not have these two properties only one candidate definition of those considered satisfies both properties we propose that a confounder be defined as a pre exposure covariate c for which there exists a set of other covariates x such that effect of the exposure on the outcome is unconfounded conditional on x c but such that for no proper subset of x c is the effect of the exposure on the outcome unconfounded given the subset a variable that helps reduce bias but not eliminate bias we propose referring to as a surrogate confounder

a powerful and robust test statistic for randomization inference in group randomized trials with matched pairs of groups summary for group randomized trials randomization inference based on rank statistics provides robust exact inference against nonnormal distributions however in a matched pair design the currently available rank based statistics lose significant power compared to normal linear mixed model lmm test statistics when the lmm is true in this article we investigate and develop an optimal test statistic over all statistics in the form of the weighted sum of signed mann whitney wilcoxon statistics under certain assumptions this test is almost as powerful as the lmm even when the lmm is true but it is much more powerful for heavy tailed distributions a simulation study is conducted to examine the power

the effects of suction on the nonlinear stability of the three dimensional boundary layer above a rotating disc there exist two types of stationary instability of the flow over a rotating disc corresponding to the upper branch inviscid mode and the lower branch mode which has a triple deck structure of the neutral stability curve a theoretical investigation of the linear problem and an account of the weakly nonlinear properties of the lower branch modes have been undertaken by p hall and s mackerrell respectively motivated by recent reports of experimental sightings of the lower branch mode and an examination of the role of suction on the linear stability properties of the flow here we investigate the effects of suction on the nonlinear disturbance described by s mackerrell the additional analysis required to incorporate suction is relatively straightforward and enables us to derive an amplitude equation which describes the evolution of the mode for each value of the suction a threshold value of the disturbance amplitude is obtained modes of size greater than this threshold grow without limit as they develop away from the point of neutral stability

love wave waveform inversion in time domain for shallow shear wave velocity abstracthigh frequency surface wave techniques are widely used to estimate s wave velocity of near surface materials surface wave methods based on inversions of dispersion curves are only suitable to laterally homogeneous or smoothly laterally varying heterogeneous earth models due to the layered model assumption during calculation of dispersion curves waveform inversion directly fits the waveform of observed data and it can be applied to any kinds of earth models we have used the love wave waveform inversion in the time domain to estimate near surface s wave velocity we used the finite difference method as the forward modeling method the source effect was removed by the deconvolution technique which made our method independent of the source wavelet we defined the difference between the deconvolved observed and calculated waveform as the misfit function we divided the model into different sizes of blocks depending on the resolution of the love waves and we updated the s wave velocity of each blo

time varying effect moderation using the structural nested mean model estimation using inverse weighted regression with residuals this article considers the problem of examining time varying causal effect moderation using observational longitudinal data in which treatment candidate moderators and possible confounders are time varying the structural nested mean model snmm is used to specify the moderated time varying causal effects of interest in a conditional mean model for a continuous response given time varying treatments and moderators we present an easy to use estimator of the snmm that combines an existing regression with residuals rr approach with an inverse probability of treatment weighting iptw strategy the rr approach has been shown to identify the moderated time varying causal effects if the time varying moderators are also the sole time varying confounders the proposed iptw rr approach provides estimators of the moderated time varying causal effects in the snmm in the presence of an additional auxiliary set of known and measured time varying confounders we use a small simulation experiment to compare iptw rr versus the traditional regression approach and to compare small and large sample properties of asymptotic versus bootstrap estimators of the standard errors for the iptw rr approach this article clarifies the distinction between time varying moderators and time varying confounders we illustrate the methodology in a case study to assess if time varying substance use moderates treatment effects on future substance use

resolving seismic anisotropy sparse matrix methods for geophysical inverse problems two techniques for the singular value decomposition svd of large sparse matrices are directly applicable to geophysical inverse problems subspace iteration and the lanczos method both methods require very little in core storage and efficiently compute a set of singular values and singular vectors a comparison of the singular value and vector estimates of these iterative approaches with the results of a conventional in core svd algorithm demonstrates their accuracy hence it is possible to conduct an assessment of inversion results for larger sparse inverse problems such as those arising in seismic tomography as an example we examine the resolution matrix associated with a crosswell seismic inversion of first arrival times for lateral variations in anisotropy the application to a set of first arrival times from a crosswell survey at the grimsel laboratory emphasizes the utility of including anisotropy in a traveltime inversion the isotropic component of the estimated velocity structure appears to be well constrained even when anisotropy is included in the inversion in the case of the grimsel experiment we are able to resolve a fracture zone in agreement with borehole fracture intersections elements of the resolution matrix reveal moderate averaging among anisotropy coefficients as well as between anisotropy coefficients and source receiver static terms the information on anisotropy such as the directions of maximum velocity appears sensitive to lateral variations in velocity and must be interpreted with some caution

nonlinear waveform inversion of plane wave seismograms in stratified elastic media we present a method for determining the elastic parameters of a horizontally stratified medium from its plane wave reflectivity the nonlinear inverse problem is iteratively solved by using a generalized least squares formalism the proposed method uses the relatively fast convergence properties of the conjugate gradient algorithm and achieves computational efficiency through analytical solutions for calculating the reference and perturbational wavefields the solution method is implemented in the frequency wave slowness domain and can be readily adapted to various source receiver configurations the behavior of the algorithm conforms to the predictions of generalized least squares inverse the ory the inversion scheme yields satisfactory results as long as the correct velocity trends are introduced in the starting model in practice the inversion algorithm should be applied first in the precritical region because of the strong nonlinear behavior of postcritical data with respect to velocity perturbations the suggested inversion strategy consists of first inverting for the density and p wave velocity or p wave impedance by considering plane waves in the low slowness region near normal angles of incidence then in optimizing for the s wave velocity by progressively including contributions from the high slowness region steep angles of incidence numerical experiments performed with noise free synthetic data prove that the proposed inversion method satisfactorally reconstructs the elastic properties of a stratified medium from a limited set of plane wave components at a reasonable computing cost

row action methods for huge and sparse systems and their applications this paper brings together and discusses theory and applications of methods identified and labelled as row action methods for linear feasibility problems find x in bf r n such that ax leqq b linearly constrained optimization problems minimize f x subject to ax leqq b and some interval convex programming problems minimize f x subject to c leqq ax leqq b the main feature of row action methods is that they are iterative procedures which without making any changes to the original matrix a use the rows of a one row at a time such methods are important and have demonstrated effectiveness for problems with large or huge matrices which do not enjoy any detectable or usable structural pattern apart from a high degree of sparaseness fields of application where row action methods are used in various ways include image reconstruction from projection operations research and game theory learning theory pattern recognition and transportation theory a row action method for the

impact of mis specification of the treatment model on estimates from a marginal structural model inverse probability of treatment weighted iptw estimation for marginal structural models msms requires the specification of a nuisance model describing the conditional relationship between treatment allocation and confounders however there is still limited information on the best strategy for building these treatment models in practice we developed a series of simulations to systematically determine the effect of including different types of candidate variables in such models we explored the performance of iptw estimators across several scenarios of increasing complexity including one designed to mimic the complexity typically seen in large pharmacoepidemiologic studies our results show that including pure predictors of treatment i e not confounders in treatment models can lead to estimators that are biased and highly variable particularly in the context of small samples the bias and mean squared error of the msm based iptw estimator increase as the complexity of the problem increases the performance of the estimator is improved by either increasing the sample size or using only variables related to the outcome to develop the treatment model estimates of treatment effect based on the true model for the probability of treatment are asymptotically unbiased we recommend including only pure risk factors and confounders in the treatment model when developing an iptw based msm

semiparametric two sample tests in clinical trials with a post randomisation response indicator in many clinical trials involving survival endpoints one has additional data on some binary indicator of response such as initial tumour shrinkage in cancer trials this paper studies the case of randomised clinical trials where the response indicator is available shortly after randomisation and where one can assume that within each stratum defined by the response indicator a two treatment group proportional hazards model holds the same model may also describe some incompletely randomised or observational studies asymptotic relative efficiencies for kaplan meier based estimators versus maximum partial likelihood estimators are examined under this model for estimating either the difference in survival probabilities at a specified time or the parameter estimated by the logrank numerator it is shown that the efficiency gains using the model are more promising when estimating the difference in survival probabilities an example is given comparing the long term survival experience of two groups of patients with advanced hodgkin s disease

semiparametric efficient estimation of a conditional density with missing or mismeasured covariates summary pepe and fleming and carroll and wand have recently proposed estimators in a parametric model for the density of a random variable y conditional on a vector of covariates x v when data on one of the regressors x is missing for some study subjects we propose a new class of estimators that remains consistent and asymptotically normal even when the probability that x is missing depends on the observed v and y includes an estimator whose asymptotic variance attains the semiparametric variance bound for the model and when the data are missing completely at random includes an estimator that is asymptotically equivalent to the inefficient estimators proposed by pepe and fleming and by carroll and wand the optimal estimator in our class depends on the unknown probability law generating the data when the vector v of non missing regressors has at most two continuous components we propose an adaptive semiparametric efficient estimator and compare the performance of the proposed semiparametric efficient estimator with the estimators proposed by pepe and fleming and carroll and wand in a small simulation study when v has many continuous components we propose an alternative class of adaptive estimators that should have high efficiency

tomographic inversion via the conjugate gradient method tomographic inversion of seismic traveltime residuals is now an established and widely used technique for imaging the earth s interior this inversion procedure results in large but sparse rectangular systems of linear algebraic equations in practice there may be tens or even hundreds of thousands of simultaneous equations this paper applies the classic conjugate gradient algorithm of hestenes and stiefel to the least squares solution of large sparse systems of traveltime equations the conjugate gradient method is fast accurate and easily adapted to take advantage of the sparsity of the matrix the techniques necessary for manipulating sparse matrices are outlined in the appendix in addition the results of the conjugate gradient algorithm are compared to results from two of the more widely used tomographic inversion algorithms

criteria for confounders in epidemiological studies the paper addresses a formal definition of a confounder based on the qualitative definition that is commonly used in standard epidemiology text books to derive the criterion for a factor to be a confounder given by miettinen and cook and to clarify inconsistency between various criteria for a confounder we introduce the concepts of an irrelevant factor an occasional confounder and a uniformly irrelevant factor we discuss criteria for checking these and show that miettinen and cook s criterion can also be applied to occasional confounders moreover we consider situations with multiple potential confounders and we obtain two necessary conditions that are satisfied by each confounder set none of the definitions and results presented in this paper require the ignorability and sufficient control confounding assumptions which are commonly employed in observational and epidemiological studies

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

estimation of the time dependent accelerated failure time model in the presence of confounding factors summary cox oakes 1984 p 66 introduced the strong version of the accelerated failure time model with time dependent exposures we provide conditions under which this model could be used to estimate from observational data the causal effect of a time varying exposure or treatment on time to an event of interest in the presence of time dependent confounding variables we propose a class of semiparametric tests and estimators for the model parameters this class contains an estimator that is semipara metric efficient in the sense of begun et al 1983 the purpose of this paper is first to provide conditions under which it would be possible to estimate from observational data the causal effect of a time dependent treatment or exposure on time to an event of interest in the presence of time dependent confounding covariates and then to construct estimators for the treatment effect under these condi tions our approach will be based on the semiparametric estimation of the parameters of the strong version of the accelerated failure time model with time dependent exposures or treatments introduced by cox oakes 1984 p 66 the usual approach to the estimation of the effect of a time varying treatment on survival is to model the hazard of failure at t as a function of past treatment history using a time dependent proportional hazards model we show that the usual approach may be biased whether or not one further adjusts for past confounder history in the analysis when a there exists a time dependent risk factor for or predictor of the event of interest that also predicts subsequent treatment and b past treatment history predicts subsequent risk factor level the following four examples demonstrate conditions a and b will often be true in an observational study in which there is treatment by indication the drug zidovudine formerly azt used in the treatment of the acquired immunodeficiency syndrome is a direct red blood cell toxin that is contra indicated in anaemic subjects i e subjects with depressed red cell counts since the toxic effects of zidovudine can worsen the anaemia further anaemic patients are at increased risk of death thus in an observational study of the effect of zidovudine on survival of patients with the acquired immunodeficiency syndrome anaemia is both a risk factor for death

zones of influence in a two dimensional unsteady hypersonic boundary layer an asymptotic structure is developed for a linear high frequency unsteady disturbance superimposed upon a steady possibly separated nonlinear flow the unsteady viscous sublayer is found to split into a two region structure the leading order flowfield is driven primarily by the upper region which coincides with the region of non parallel flow in the original steady viscous sublayer it is found that introducing a viscous inviscid interaction into the unsteady problem drastically alters the domain of dependence of the unsteady flow throughout the entire viscous sublayer the determination of the correct domain of dependence is found to involve a subtle interplay between the convective terms the pressure displacement interaction and the non parallel base flow preliminary extensions to fully nonlinear unsteady interactive boundary layers are noted