regularized outcome weighted subgroup identification for differential treatment effects summary to facilitate comparative treatment selection when there is substantial heterogeneity of treatment effectiveness it is important to identify subgroups that exhibit differential treatment effects existing approaches model outcomes directly and then define subgroups according to interactions between treatment and covariates because outcomes are affected by both the covariate treatment interactions and covariate main effects direct modeling outcomes can be hard due to model misspecification especially in presence of many covariates alternatively one can directly work with differential treatment effect estimation we propose such a method that approximates a target function whose value directly reflects correct treatment assignment for patients the function uses patient outcomes as weights rather than modeling targets consequently our method can deal with binary continuous time to event and possibly contaminated outcomes in the same fashion we first focus on identifying only directional estimates from linear rules that characterize important subgroups we further consider estimation of comparative treatment effects for identified subgroups we demonstrate the advantages of our method in simulation studies and in analyses of two real data sets

numerical discretization of a darcy forchheimer model we solve a steady darcy forchheimer flow in a bounded region by means of piecewise constant velocities and nonconforming piecewise mathbb p 1 pressures for the computation we solve the nonlinearity by an alternating directions algorithm and we decouple the computation of the velocity from that of the pressure by a gradient algorithm we prove a priori error estimates of the scheme and convergence of the alternating directions algorithm

cell centered finite difference method for parabolic equation abstract we develop two cell centered finite difference schemes for parabolic problems on quadrilateral grids one scheme is backward euler scheme with first order accuracy in time increment while the other is crank nicolson scheme with second order accuracy in time increment the method is based on the lowest order brezzi douglas marini bdm mixed finite element method a quadrature rule gives a block diagonal mass matrix and allows for local velocity elimination which leads to a symmetric and positive definite cell centered system for the pressures theoretical results indicate first order convergence in spacial meshsize both for pressures and for subedge flues numerical experiments using the schemes show that the convergence rates are in agreement with the theoretical analysis

supremum weighted log rank test and sample size for comparing two stage adaptive treatment strategies summary in two stage adaptive treatment strategies patients receive an induction treatment followed by a maintenance therapy given that the patient responded to the induction treatment they received to test for a difference in the effects of different induction and maintenance treatment combinations a modified supremum weighted log rank test is proposed the test is applied to a dataset from a two stage randomized trial and the results are compared to those obtained using a standard weighted log rank test a sample size formula is proposed based on the limiting distribution of the supremum weighted log rank statistic the sample size formula reduces to eng and kosorok s sample size formula for a two sample supremum log rank test when there is no second randomization monte carlo studies show that the proposed test provides sample sizes that are close to those obtained by standard weighted log rank test under a proportional hazards alternative however the proposed test is more powerful than the standard weighted log rank test under non proportional hazards alternatives

a multipoint flux mixed finite element method we develop a mixed finite element method for single phase flow in porous media that reduces to cell centered finite differences on quadrilateral and simplicial grids and performs well for discontinuous full tensor coefficients motivated by the multipoint flux approximation method where subedge fluxes are introduced we consider the lowest order brezzi douglas marini bdm mixed finite element method a special quadrature rule is employed that allows for local velocity elimination and leads to a symmetric and positive definite cell centered system for the pressures theoretical and numerical results indicate second order convergence for pressures at the cell centers and first order convergence for subedge fluxes second order convergence for edge fluxes is also observed computationally if the grids are sufficiently regular

a bayesian machine learning approach for optimizing dynamic treatment regimes medical therapy often consists of multiple stages with a treatment chosen by the physician at each stage based on the patient s history of treatments and clinical outcomes these decisions can be formalized as a dynamic treatment regime this paper describes a new approach for optimizing dynamic treatment regimes that bridges the gap between bayesian inference and existing approaches like q learning the proposed approach fits a series of bayesian regression models one for each stage in reverse sequential order each model uses as a response variable the remaining payoff assuming optimal actions are taken at subsequent stages and as covariates the current history and relevant actions at that stage the key difficulty is that the optimal decision rules at subsequent stages are unknown and even if these decision rules were known the relevant response variables may be counterfactual however posterior distributions can be derived from the previously fitted regression models for the optimal decision rules and the counterfactual response variables under a particular set of rules the proposed approach averages over these posterior distributions when fitting each regression model an efficient sampling algorithm for estimation is presented along with simulation studies that compare the proposed approach with q learning

on convergence of block centered finite differences for elliptic problems we consider linear selfadjoint elliptic problems with neumann boundary conditions in rectangular domains we demonstrate that with sufficiently smooth data the discrete l 2 norm errors for tensor product block centered finite differences in both the approximate solution and its first derivatives are second order for all nonuniform grids extensions to nonselfadjoint and parabolic problems are discussed

model free monte carlo like policy evaluation we propose an algorithm for estimating the finite horizon expected return of a closed loop control policy from an a priori given off policy sample of one step transitions it averages cumulated rewards along a set of broken trajectories made of one step transitions selected from the sample on the basis of the control policy under some lipschitz continuity assumptions on the system dynamics reward function and control policy we provide bounds on the bias and variance of the estimator that depend only on the lipschitz constants on the number of broken trajectories used in the estimator and on the sparsity of the sample of one step transitions

comparison of adaptive treatment strategies based on longitudinal outcomes in sequential multiple assignment randomized trials in sequential multiple assignment randomized trials longitudinal outcomes may be the most important outcomes of interest because this type of trials is usually conducted in areas of chronic diseases or conditions we propose to use a weighted generalized estimating equation gee approach to analyzing data from such type of trials for comparing two adaptive treatment strategies based on generalized linear models although the randomization probabilities are known we consider estimated weights in which the randomization probabilities are replaced by their empirical estimates and prove that the resulting weighted gee estimator is more efficient than the estimators with true weights the variance of the weighted gee estimator is estimated by an empirical sandwich estimator the time variable in the model can be linear piecewise linear or more complicated forms this provides more flexibility that is important because in the adaptive treatment setting the treatment changes over time and hence a single linear trend over the whole period of study may not be practical simulation results show that the weighted gee estimators of regression coefficients are consistent regardless of the specification of the correlation structure of the longitudinal outcomes the weighted gee method is then applied in analyzing data from the clinical antipsychotic trials of intervention effectiveness copyright 2016 john wiley sons ltd

interpretable dynamic treatment regimes abstractprecision medicine is currently a topic of great interest in clinical and intervention science a key component of precision medicine is that it is evidence based i e data driven and consequently there has been tremendous interest in estimation of precision medicine strategies using observational or randomized study data one way to formalize precision medicine is through a treatment regime which is a sequence of decision rules one per stage of clinical intervention that map up to date patient information to a recommended treatment an optimal treatment regime is defined as maximizing the mean of some cumulative clinical outcome if applied to a population of interest it is well known that even under simple generative models an optimal treatment regime can be a highly nonlinear function of patient information consequently a focal point of recent methodological research has been the development of flexible models for estimating optimal treatment regimes however in many settings estimati

stochastic modeling of macrodispersion in heterogeneous porous media a method for the prediction of dispersion processes of inert solutes occurring in heterogeneous porous media is presented its main features are as follows 1 the velocity field is assumed to be a space random function its moments are expressed through the physical parameters of the log transmissivity and head random fields by linearizing the flow equation the random velocity being a linear function of the head and log transmissivity which are assumed to be jointly multivariate normal mvn is thus also mvn its pdf is completely defined by its first two moments 2 the statistics of the dispersion process are obtained by the particle tracking method through monte carlo simulations which are based on gaussian conditioning the method is applied to the borden natural gradient tracer test freyberg 1986 showing favorable results

three dimensional stochastic analysis of macrodispersion in aquifers the dispersive mixing resulting from complex flow in three dimensionally heterogeneous porous media is analyzed using stochastic continuum theory stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three dimensional statistically anisotropic input covariance describing the hydraulic conductivity with a statistically isotropic input covariance the longitudinal macrodispersivity is convectively controlled but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term with an arbitrarily oriented anisotropic conductivity covariance all components of the macrodispersivity tensor are convectively controlled and the ratio of transverse to longitudinal dispersivity is of the order of 10 1 in this case the off diagonal components of the dispersivity tensor are significant being numerically larger than the diagonal transverse terms and the transverse dispersion process can be highly anisotropic dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and monte carlo simulations the theory which treats the asymptotic condition of large displacement indicates that a classical gradient transport fickian relationship is valid for large scale displacements

stochastic modeling of large scale flow in heterogeneous unsaturated soils a simulation experiment is used to test the stochastic theory of unsaturated flow proposed by mantoglou and gelhar 1987a b c tension means and variances derived from this theory are compared to tension distributions obtained from a detailed three dimensional model developed by ababou 1988 the synthetically generated unsaturated hydraulic conductivity functions used in the detailed model vary significantly over relatively small distances results from a simulated infiltration event indicate that the stochastic theory s predictions reproduce the overall trend of the heterogeneous tension distribution deviations from the predicted mean generally lie within confidence intervals derived from the predicted variance the stochastic theory predicts less vertical moisture movement and somewhat more horizontal spreading than a comparable deterministic analysis this reflects the fact that the effective hydraulic conductivity function used in the stochastic approach is anisotropic the magnitude of this anisotropy increases with increasing tension

causal inference for complex longitudinal data the continuous case we extend robins theory of causal inference for complex longitudinal data to the case of continuously varying as opposed to discrete covariates and treatments in particular we establish versions of the key results of the discrete theory the g computation formula and a collection of powerful characterizations of the g null hypothesis of no treatment eect this is accomplished under natural continuity hypotheses concerning the conditional distributions of the outcome variable and of the covariates given the past we also show that our assumptions concerning counterfactual variables place no restriction on the joint distribution of the observed variables thus in a precise sense these assumptions are for free or if you prefer harmless

breaking the curse of nonregularity with subagging inference of the mean outcome under optimal treatment regimes precision medicine is an emerging medical approach that allows physicians to select the treatment options based on individual patient information the goal of precision medicine is to identify the optimal treatment regime otr that yields the most favorable clinical outcome prior to adopting any otr in clinical practice it is crucial to know the impact of implementing such a policy although considerable research has been devoted to estimating the otr in the literature less attention has been paid to statistical inference of the otr challenges arise in the nonregular cases where the otr is not uniquely defined to deal with nonregularity we develop a novel inference method for the mean outcome under an otr the optimal value function based on subsample aggregating subagging the proposed method can be applied to multi stage studies where treatments are sequentially assigned over time bootstrap aggregating bagging and subagging have been recognized as effective variance reduction techniques to improve unstable estimators or classifiers buhlmann and yu 2002 however it remains unknown whether these approaches can yield valid inference results we show the proposed confidence interval ci for the optimal value function achieves nominal coverage in addition due to the variance reduction effect of subagging our method enjoys certain statistical optimality specifically we show that the mean squared error of the proposed value estimator is strictly smaller than that based on the simple sample splitting estimator in the nonregular cases moreover under certain conditions the length of our proposed ci is shown to be on average shorter than cis constructed based on the existing state of the art method luedtke and van der laan 2016 and the oracle method which works as well as if an otr were known extensive numerical studies are conducted to back up our theoretical findings

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

enhanced cell centered finite differences for elliptic equations on general geometry we present an expanded mixed finite element method for solving second order elliptic partial differential equations on geometrically general domains for the lowest order raviart thomas approximating spaces we use quadrature rules to reduce the method to cell centered finite differences possibly enhanced with some face centered pressures this substantially reduces the computational complexity of the problem to a symmetric positive definite system for essentially only as many unknowns as elements our new method handles general shape elements triangles quadrilaterals and hexahedra and full tensor coefficients while the standard mixed formulation reduces to finite differences only in special cases with rectangular elements as in other mixed methods we maintain the local approximation of the divergence i e local mass conservation in contrast galerkin finite element methods facilitate general element shapes at the cost of achieving only global mass conservation our method is shown to be as accurate as the standard mixed method for a large class of smooth meshes on nonsmooth meshes or with nonsmooth coefficients one can add lagrange multiplier pressure unknowns on certain element edges or faces this enhanced cell centered procedure recovers full accuracy with little additional cost if the coefficients or mesh geometry are piecewise smooth theoretical error estimates and numerical examples are given illustrating the accuracy and efficiency of the methods

mixed finite elements for elliptic problems with tensor coefficients as cell centered finite differences we present an expanded mixed finite element approximation of second order elliptic problems containing a tensor coefficient the mixed method is expanded in the sense that three variables are explicitly approximated namely the scalar unknown the negative of its gradient and its flux the tensor coefficient times the negative gradient the resulting linear system is a saddle point problem in the case of the lowest order raviart thomas elements on rectangular parallelepipeds we approximate this expanded mixed method by incorporating certain quadrature rules this enables us to write the system as a simple cell centered finite difference method requiring the solution of a sparse positive semidefinite linear system for the scalar unknown for a general tensor coefficient the sparsity pattern for the scalar unknown is a 9 point stencil in two dimensions and 19 points in three dimensions existing theory shows that the expanded mixed method gives optimal order approximations in the l 2 and h s norms and superconvergence is obtained between the l 2 projection of the scalar variable and its approximation we show that these rates of convergence are retained for the finite difference method if h denotes the maximal mesh spacing then the optimal rate is o h the superconvergence rate o h 2 is obtained for the scalar unknown and rate o h 3 2 for its gradient and flux in certain discrete norms moreover the full o h 2 is obtained in the strict interior of the domain computational results illustrate these theoretical results

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

causal interaction in factorial experiments application to conjoint analysis we study causal interaction in factorial experiments in which several factors each with multiple levels are randomized to form a large number of possible treatment combinations examples of such

on estimating functional average breakthrough curve using time warping technique and perturbation approach 1 simulated contaminant breakthrough curves btc are often used to predict mass arrival at compliance boundaries at waste storage sites in numerical simulations that involve uncertainties on input parameters such as randomly heterogeneous rock properties monte carlo simulations are commonly utilized and the mean breakthrough curve is often calculated from the arithmetic average of all realizations the arithmetic mean breakthrough curve in general overestimates the mass flow rate at early and late time but underestimates the peak mass flow rate the averaged breakthrough curve usually does not resemble any of individual breakthrough curves the reason is that btcs vary not only on amplitude but also on dynamics time and therefore it is not appropriate to take the arithmetic average directly in this study we consider each btc as a random curve and use time warping techniques to align all curves in a time warped space compute the sample mean of the curves in the time warped space and transform the means back to the original time space we show that all btcs are aligned based on the percentile of mass reaching the compliance boundary and the functional average is the percentile average of all btcs the confidence interval of the sample mean curve is estimated using the perturbation approach the functional average provides an additional metric that can be used to characterize the breakthrough behavior in addition to more traditional median and arithmetic average curves the method is illustrated using transport simulations at the material disposal area g los alamos national laboratory lanl in new mexico

characteristics and controlling factors of dispersion in bounded heterogeneous porous media 1 in this study we present first order in terms of the log conductivity variance analytical solutions to displacement covariances xij and macrodispersion coefficients dij for transport of conservative solutes in two dimensional bounded heterogeneous porous media these solutions are presented as infinity series and are explicit functions of the statistics of the log hydraulic conductivity using numerical examples the convergence of these solutions in terms of the number of terms in truncated finite summations is first investigated and the accuracy of these solutions is examined by comparing them with results from monte carlo simulations and the semianalytical solutions of osnes 1998 through several examples the general features of time dependent xij and dij are discussed unlike in unbounded domains the longitudinal macrodispersivity d11 for bounded domains does not approach an asymptotic value at large dimensionless time but instead increases quickly near the downstream constant head boundary in addition d11 for bounded domains is always larger than that in unbounded domains and accordingly the transverse macrodispersivity d22 in bounded domains is smaller than that in unbounded domains these differences stem from the lateral no flow boundaries in our bounded domain models we also investigated the effect of domain sizes on xij and dij our study shows that both xij and dij depend not only on the dimensionless size of the domain but also on its aspect ratio the dependence of xij and dij on the particles initial location has also been investigated at detail our results indicate that while this dependence is very small for x11 and d11 the release location has a significant impact on both x22 and d22 our solutions to both displacement covariances and macrodispersivity are compared against those derived from tracer test data at the borden site the comparison shows that our solutions are quite close to observed data indicating that they may be applicable to predict solute transport at the field scale

stochastic analysis of unsaturated flow in heterogeneous soils 1 statistically isotropic media steady unsaturated flow with vertical mean infiltration through unbounded heterogeneous porous media is analyzed using a perturbation approximation of the stochastic flow equation which is solved by spectral representation techniques the hydraulic conductivity k is related to the capillary pressure head by k ks exp where ks is the saturated conductivity and is a soil parameter a general formulation is presented for the case with ks and represented as statistically homogeneous spatial random fields in part 1 solutions are developed assuming is constant and representing ks variability by one dimensional and three dimensional isotropic random fields results are obtained for head variances and covariance functions effective hydraulic conductivities variances of the unsaturated hydraulic conductivity flux variances and variance of pressure gradient when the parameter is relatively large corresponding to coarse textured soils the head variance decreases and all of the results demonstrate a trend toward gravitationally dominated one dimensional vertical flow the effective conductivity is dependent on the correlation scale of ln ks and the mean hydraulic gradient

estimation and evaluation of linear individualized treatment rules to guarantee performance summary in clinical practice an informative and practically useful treatment rule should be simple and transparent however because simple rules are likely to be far from optimal effective methods to construct such rules must guarantee performance in terms of yielding the best clinical outcome highest reward among the class of simple rules under consideration furthermore it is important to evaluate the benefit of the derived rules on the whole sample and in pre specified subgroups e g vulnerable patients to achieve both goals we propose a robust machine learning method to estimate a linear treatment rule that is guaranteed to achieve optimal reward among the class of all linear rules we then develop a diagnostic measure and inference procedure to evaluate the benefit of the obtained rule and compare it with the rules estimated by other methods we provide theoretical justification for the proposed method and its inference procedure and we demonstrate via simulations its superior performance when compared to existing methods lastly we apply the method to the sequenced treatment alternatives to relieve depression star d trial on major depressive disorder and show that the estimated optimal linear rule provides a large benefit for mildly depressed and severely depressed patients but manifests a lack of fit for moderately depressed patients

concordance assisted learning for estimating optimal individualized treatment regimes in this article we propose a new concordance assisted learning for estimating optimal individualized treatment regimes we first introduce a type of concordance function for prescribing treatment and propose a robust rank regression method for estimating the concordance function we then find treatment regimes up to a threshold to maximize the concordance function named prescriptive index finally within the class of treatment regimes that maximize the concordance function we find the optimal threshold to maximize the value function we establish the convergence rate and asymptotic normality of the proposed estimator for parameters in the prescriptive index an induced smoothing method is developed to estimate the asymptotic variance of the proposed estimator we also establish the n1 3 consistency of the estimated optimal threshold and its limiting distribution in addition a doubly robust estimator of parameters in the prescriptive index is developed under a class of monotonic index models the practical use and effectiveness of the proposed methodology are demonstrated by simulation studies and an application to an aids data

the computational complexity of probabilistic inference using bayesian belief networks research note abstract bayesian belief networks provide a natural efficient method for representing probabilistic dependencies among a set of variables for these reasons numerous researchers are exploring the use of belief networks as a knowledge representation in artificial intelligence algorithms have been developed previously for efficient probabilistic inference using special classes of belief networks more general classes of belief networks however have eluded efforts to develop efficient inference algorithms we show that probabilistic inference using belief networks is np hard therefore it seems unlikely that an exact algorithm can be developed to perform probabilistic inference efficiently over all classes of belief networks this result suggests that research should be directed away from the search for a general efficient probabilistic inference algorithm and toward the design of efficient special case average case and approximation algorithms

a note on the variance of doubly robust g estimators summary a recursive variance calculation is derived for doubly robust g estimators for dynamic treatment regimes in a multi interval setting treatment decision parameters are not assumed to be shared across treatment intervals this independence of parameters permits sequential estimation of the g estimators variance when g estimation is performed in a sequential fashion the recursive variance calculation is both natural and computationally feasible this development can easily be adapted to other complex estimating procedures that require nuisance parameter estimation

dynamic treatment effects this paper develops robust models for estimating and interpreting treatment effects arising from both ordered and unordered multi stage decision problems identification is secured through instrumental variables and or conditional independence matching assumptions we decompose treatment effects into direct effects and continuation values associated with moving to the next stage of a decision problem using our framework we decompose the iv estimator showing that iv generally does not estimate economically interpretable or policy relevant parameters in prototypical dynamic discrete choice models unless policy variables are instruments continuation values are an empirically important component of estimated total treatment effects of education we use our analysis to estimate the components of what late estimates in a dynamic discrete choice model

on estimation of optimal treatment regimes for maximizing t year survival probability a treatment regime is a deterministic function that dictates personalized treatment based on patients individual prognostic information there is increasing interest in finding optimal treatment regimes which determine treatment at one or more treatment decision points so as to maximize expected long term clinical outcome where larger outcomes are preferred for chronic diseases such as cancer or hiv infection survival time is often the outcome of interest and the goal is to select treatment to maximize survival probability we propose two nonparametric estimators for the survival function of patients following a given treatment regime involving one or more decisions i e the so called value based on data from a clinical or observational study we estimate an optimal regime by maximizing these estimators for the value over a prespecified class of regimes because the value function is very jagged we introduce kernel smoothing within the estimator to improve performance asymptotic properties of the proposed estimators of value functions are established under suitable regularity conditions and simulations studies evaluate the finite sample performance of the proposed regime estimators the methods are illustrated by application to data from an aids clinical trial

min max generalization for deterministic batch mode reinforcement learning relaxation schemes we study the min max optimization problem introduced in fonteneau et al towards min max reinforcement learning icaart 2010 springer heidelberg 2011 pp 61 77 for computing policies for batch mode reinforcement learning in a deterministic setting with fixed finite time horizon first we show that the min part of this problem is np hard we then provide two relaxation schemes the first relaxation scheme works by dropping some constraints in order to obtain a problem that is solvable in polynomial time the second relaxation scheme based on a lagrangian relaxation where all constraints are dualized can also be solved in polynomial time we also theoretically prove and empirically illustrate that both relaxation schemes provide better results than those given in fonteneau et al 2011 as cited above

a perturbation expansion for diffusion in a random velocity field we present a formal perturbation expansion for the large scale effective drift velocity and diffusion matrix of a medium with stationary random velocity v x and constant nonrandom diffusion matrix a on a small scale if mu denotes the mean of v x and we express v x as mu varepsilon u x then the expansion is in powers of varepsilon with mu u and a fixed we obtain explicit expressions up to second order in varepsilon which generalize the standard formulae to the case a ne 0

residual weighted learning for estimating individualized treatment rules abstractpersonalized medicine has received increasing attention among statisticians computer scientists and clinical practitioners a major component of personalized medicine is the estimation of individualized treatment rules itrs recently zhao et al proposed outcome weighted learning owl to construct itrs that directly optimize the clinical outcome although owl opens the door to introducing machine learning techniques to optimal treatment regimes it still has some problems in performance 1 the estimated itr of owl is affected by a simple shift of the outcome 2 the rule from owl tries to keep treatment assignments that subjects actually received 3 there is no variable selection mechanism with owl all of them weaken the finite sample performance of owl in this article we propose a general framework called residual weighted learning rwl to alleviate these problems and hence to improve finite sample performance unlike owl which weights misclassification errors by clinical outcom

mixed effects gaussian process functional regression models with application to dose response curve prediction we propose a new semiparametric model for functional regression analysis combining a parametric mixed effects model with a nonparametric gaussian process regression model namely a mixed effects gaussian process functional regression model the parametric component can provide explanatory information between the response and the covariates whereas the nonparametric component can add nonlinearity we can model the mean and covariance structures simultaneously combining the information borrowed from other subjects with the information collected from each individual subject we apply the model to dose response curves that describe changes in the responses of subjects for differing levels of the dose of a drug or agent and have a wide application in many areas we illustrate the method for the management of renal anaemia an individual dose response curve is improved when more information is included by this mechanism from the subject patient over time enabling a patient specific treatment regime

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

correlation model of transport in random fields this paper is an investigation of the correlation model for transport of nonreactive solutes in media with random porosity and permeability the method of perturbation is used to obtain a second order approximate nonlocal integrodifferential equation for mean concentration an approximate method of localization is used to convert to with the same order of approximation differential equations of transport exact averaged equations for one dimensional transport are examined and the question of the consistency and asymptotic behavior for approximate average equations is discussed a detailed investigation of transport in a stratified system has been carried out the second moment of concentration is examined the variance of the concentration is computed and cross correlation moments are obtained for fields of porosity and velocity including solute concentration 24 refs 4 figs

mixed finite element methods for quasilinear second order elliptic problems a mixed finite element method is developed to approximate the solution of a quasilinear second order elliptic partial differential equation the existence and uniqueness of the approximation are demonstrated and optimal rate error estimates are derived

high dimensional a learning for optimal dynamic treatment regimes precision medicine is a medical paradigm that focuses on finding the most effective treatment decision based on individual patient information for many complex diseases such as cancer treatment decisions need to be tailored over time according to patients responses to previous treatments such an adaptive strategy is referred as a dynamic treatment regime a major challenge in deriving an optimal dynamic treatment regime arises when an extraordinary large number of prognostic factors such as patient s genetic information demographic characteristics medical history and clinical measurements over time are available but not all of them are necessary for making treatment decision this makes variable selection an emerging need in precision medicine in this paper we propose a penalized multi stage a learning for deriving the optimal dynamic treatment regime when the number of covariates is of the non polynomial np order of the sample size to preserve the double robustness property of the a learning method we adopt the dantzig selector which directly penalizes the a leaning estimating equations oracle inequalities of the proposed estimators for the parameters in the optimal dynamic treatment regime and error bounds on the difference between the value functions of the estimated optimal dynamic treatment regime and the true optimal dynamic treatment regime are established empirical performance of the proposed approach is evaluated by simulations and illustrated with an application to data from the star d study

nonstationary flow and nonergodic transport in random porous media 1 transport processes taking place in natural formations are often characterized by the spatial nonstationarity of flow field and the nonergodic condition of solute spreading the former may originate from statistical inhomogeneity of porous media properties or from the influence of boundary conditions as well as from conditioning procedures on measured data while the latter is generally due to the finite size of the solute source in real world applications these aspects sometimes dominate the transport phenomena and known literature results based on statistical homogeneity and ergodicity assumptions cannot be properly applied in this paper a method is proposed to handle different and concurrent causes of the flow field nonstationarity and to describe nonergodic transport of inert solutes by spatial moments in a domain of finite size the goal is reached by expanding the steady state flow equation in taylor series limited to the first order and by the recursive application of finite element fe method the unknowns are the piezometric head mean values and its derivatives in respect to the fluctuating porous media hydraulic conductivity from the latter the velocity statistics are derived on the basis of darcy s law according to the first order approximation by neglecting the pore scale dispersion the spatial moments of a solute plume are a posteriori obtained by a consistent lagrangian analysis starting from the knowledge of the velocity field covariance matrices without any restriction regarding the statistical homogeneity of flow and or ergodicity conditions the proposed method is here applied to investigate the influence of boundary conditions on the solute transport developing in a limited domain the results obtained from different test cases give a velocity field behavior in agreement with literature findings and allow us to define the nonergodic transport in bounded domains the comparison of the results with some ad hoc developed monte carlo simulations ensures the applicability of the proposed approach at least to the small heterogeneity cases here considered

greedy outcome weighted tree learning of optimal personalized treatment rules summary we propose a subgroup identification approach for inferring optimal and interpretable personalized treatment rules with high dimensional covariates our approach is based on a two step greedy tree algorithm to pursue signals in a high dimensional space in the first step we transform the treatment selection problem into a weighted classification problem that can utilize tree based methods in the second step we adopt a newly proposed tree based method known as reinforcement learning trees to detect features involved in the optimal treatment rules and to construct binary splitting rules the method is further extended to right censored survival data by using the accelerated failure time model and introducing double weighting to the classification trees the performance of the proposed method is demonstrated via simulation studies as well as analyses of the cancer cell line encyclopedia ccle data and the tamoxifen breast cancer data

using pilot data to size a two arm randomized trial to find a nearly optimal personalized treatment strategy a personalized treatment strategy formalizes evidence based treatment selection by mapping patient information to a recommended treatment personalized treatment strategies can produce better patient outcomes while reducing cost and treatment burden thus among clinical and intervention scientists there is a growing interest in conducting randomized clinical trials when one of the primary aims is estimation of a personalized treatment strategy however at present there are no appropriate sample size formulae to assist in the design of such a trial furthermore because the sampling distribution of the estimated outcome under an estimated optimal treatment strategy can be highly sensitive to small perturbations in the underlying generative model sample size calculations based on standard uncorrected asymptotic approximations or computer simulations may not be reliable we offer a simple and robust method for powering a single stage two armed randomized clinical trial when the primary aim is estimating the optimal single stage personalized treatment strategy the proposed method is based on inverting a plugin projection confidence interval and is thereby regular and robust to small perturbations of the underlying generative model the proposed method requires elicitation of two clinically meaningful parameters from clinical scientists and uses data from a small pilot study to estimate nuisance parameters which are not easily elicited the method performs well in simulated experiments and is illustrated using data from a pilot study of time to conception and fertility awareness

constructing dynamic treatment regimes over indefinite time horizons summaryexisting methods for estimating optimal dynamic treatment regimes are limited to cases where a utility function is optimized over a fixed time period we develop an estimation procedure for the optimal dynamic treatment regime over an indefinite time period and derive associated large sample results the proposed method can be used to estimate the optimal dynamic treatment regime in chronic disease settings we illustrate this by simulating a dataset corresponding to a cohort of patients with diabetes that mimics the third wave of the national health and nutrition examination survey and examining the performance of the proposed method in controlling the level of haemoglobin a1c

geometric multigrid methods for darcy forchheimer flow in fractured porous media in this paper we present a monolithic multigrid method for the efficient solution of flow problems in fractured porous media specifically we consider a mixed dimensional model which couples darcy flow in the porous matrix with forchheimer flow within the fractures a suitable finite volume discretization permits to reduce the coupled problem to a system of nonlinear equations with a saddle point structure in order to solve this system we propose a full approximation scheme fas multigrid solver that appropriately deals with the mixed dimensional nature of the problem by using mixed dimensional smoothing and inter grid transfer operators numerical experiments show that the proposed multigrid method is robust with respect to the fracture permeability the forchheimer coefficient and the mesh size the case of several possibly intersecting fractures in a heterogeneous porous medium is also discussed

maximin projection learning for optimal treatment decision with heterogeneous individualized treatment effects a saline feature of data from clinical trials and medical studies is inhomogeneity patients not only differ in baseline characteristics but also the way they respond to treatment optimal individualized treatment regimes are developed to select effective treatments based on patient s heterogeneity however the optimal treatment regime might also vary for patients across different subgroups in this paper we mainly consider patient s heterogeneity caused by groupwise individualized treatment effects assuming the same marginal treatment effects for all groups we propose a new maximin projection learning for estimating a single treatment decision rule that works reliably for a group of future patients from a possibly new subpopulation based on estimated optimal treatment regimes for all subgroups the proposed maximin treatment regime is obtained by solving a quadratically constrained linear programming qclp problem which can be efficiently computed by interior point methods consistency and asymptotic normality of the estimator is established numerical examples show the reliability of the proposed methodology

stochastic analysis of steady state unsaturated flow in heterogeneous media comparison of the brooks corey and gardner russo models existing stochastic models of unsaturated flow and transport are usually developed using the simple gardner russo constitutive relationship though it is generally accepted that the more complex van genuchten and brooks corey relationships may perform better in describing experimental data in this paper we develop first order stochastic models for gravity dominated flow in second order stationary media with both the brooks corey and the gardner russo constitutive relationships these models also account for the spatial variability in effective water content while the spatial variability is generally neglected in most existing stochastic models analytical solutions are obtained for the case of one dimensional gravity dominated flow on the basis of the solutions we illustrate the differences between results from these two constitutive models through some one dimensional examples it is found that the impacts of the constitutive models on the statistical moments of suction head effective water content unsaturated hydraulic conductivity and velocity depend on the saturation ranges for example the mean head and the mean effective water content for the brooks corey model differ in a great manner with their counterparts for the gardner russo model near the dry and wet limits while the differences are small at the intermediate range of saturation this finding is confirmed with some two dimensional examples it is also found that the brook corey model has certain advantages over the gardner russo model in analyzing unsaturated flow in heterogeneous media for example the stochastic model developed based on the brooks corey function requires the coefficient of variation of head and soil parameter bc to be small 1 whereas that based on the gardner russo function assumes the one point cross covariance of head and olgr to be small 1 illustrative examples reveal that the latter condition may be violated because the one point covariance is found to increase rapidly to beyond unity as the soil becomes dry whereas the former may be readily satisfied

eulerian lagrangian analysis of transport conditioned on hydraulic data 1 analytical numerical approach recently a unified eulerian lagrangian theory has been developed by one of us for nonreactive solute transport in space time nonstationary velocity fields we describe a combined analytical numerical method of solution based on this theory for the special case of steady state flow in a mildly fluctuating statistically homogeneous lognormal hydraulic conductivity field we take the unconditional mean velocity to be uniform but allow conditioning on measurements of log hydraulic conductivity or transmissivity and or hydraulic head this renders the velocity field nonstationary we solve the conditional transport problem analytically at early time and express it in pseudo fickian form at later time the deterministic pseudo fickian equations involve a conditional space time dependent dispersion tensor which we evaluate numerically along mean particle trajectories these equations lend themselves to accurate solution by standard galerkin finite elements on a relatively coarse grid the final step is an explicit numerical computation of lower bounds on conditional concentration prediction variance covariance and coefficient of variation travel time distribution cumulative mass release across a compliance surface the associated error and plume spatial moments our method also allows quantification of the uncertainty in the original source location of any solute particle located anywhere in the field at any time this paper describes the methodology and presents some unconditional results conditioning and more advanced computations are presented in the subsequent papers

interactive model building for q learning evidence based rules for optimal treatment allocation are key components in the quest for efficient effective health care delivery q learning an approximate dynamic programming algorithm is a popular method for estimating optimal sequential decision rules from data q learning requires the modeling of nonsmooth nonmonotone transformations of the data complicating the search for adequately expressive yet parsimonious statistical models the default q learning working model is multiple linear regression which is not only provably misspecified under most data generating models but also results in nonregular regression estimators complicating inference we propose an alternative strategy for estimating optimal sequential decision rules for which the requisite statistical modeling does not depend on nonsmooth nonmonotone transformed data does not result in nonregular regression estimators is consistent under a broader array of data generation models than q learning results in estimated sequential decision rules that have better sampling properties and is amenable to established statistical approaches for exploratory data analysis model building and validation we derive the new method iq learning via an interchange in the order of certain steps in q learning in simulated experiments iq learning improves on q learning in terms of integrated mean squared error and power the method is illustrated using data from a study of major depressive disorder

estimation of the effect of interventions that modify the received treatment motivated by a study of surgical operating time and post operative outcomes for lung cancer we consider the estimation of causal effects of continuous point exposure treatments to investigate causality the standard paradigm postulates a series of treatment specific counterfactual outcomes and establishes conditions under which we may learn about them from observational study data while many choices are possible causal effects are typically defined in terms of variation of the mean of counterfactual outcomes in hypothetical worlds in which specific treatment strategies are applied to all individuals for example one might compare two worlds one where each individual receives some specific dose and a second where each individual receives some other dose for our motivating study defining causal effects in this way corresponds to hypothetical interventions that could not conceivably be implemented in the real world in this work we consider an alternative complimentary framework that investigates variation in the mean of counterfactual outcomes under hypothetical treatment strategies where each individual receives a treatment dose corresponding to that actually received but modified in some pre specified way quantification of this variation is defined in terms of contrasts for specific interventions as well as in terms of the parameters of a new class of marginal structural mean models within this framework we propose three estimators an outcome regression estimator an inverse probability of treatment weighted estimator and a doubly robust estimator we illustrate the methods with an analysis of the motivating data copyright 2013 john wiley sons ltd

impossibility results for nondierentiable functionals we examine challenges to estimation and inference when the objects of interest are nondifferentiable functionals of the underlying data distribution this situation arises in a number of applications of bounds analysis and moment inequality models and in recent work on estimating optimal dynamic treatment regimes drawing on earlier work relating dierentiability to the existence of unbiased and regular estimators we show that if the target object is not continuously dierentiable in the parameters of the data distribution there exist no locally asymptotically unbiased estimators and no regular estimators this places strong limits on estimators bias correction methods and inference procedures

q learning with censored data we develop methodology for a multistage decision problem with flexible number of stages in which the rewards are survival times that are subject to censoring we present a novel q learning algorithm that is adjusted for censored data and allows a flexible number of stages we provide finite sample bounds on the generalization error of the policy learned by the algorithm and show that when the optimal q function belongs to the approximation space the expected survival time for policies obtained by the algorithm converges to that of the optimal policy we simulate a multistage clinical trial with flexible number of stages and apply the proposed censored q learning algorithm to find individualized treatment regimens the methodology presented in this paper has implications in the design of personalized medicine trials in cancer and in other life threatening diseases

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

determining soil hydraulic properties by parameter estimation on the selection of a model for the hydraulic properties parameter estimation procedures involving solution of the inverse flow problem pertinent to a transient experiment constitute a powerful method of determining the soil hydraulic properties one of the problems associated with these procedures is the selection of an appropriate model to describe the soil hydraulic properties three different models were considered those of van genuchten vg and brooks and corey bc model and the exponential model of gardner for the hydraulic conductivity soil water pressure relationships coupled with a new expression for the soil water content soil water pressure relationship gr model for a given model the soil hydraulic properties were determined from simulated and measured outflow experiments supplemented with water content at a soil water pressure head of 15 000 cm h2o using the parameter estimation procedure of kool et al 1985a and data from two soils a hypothetical sandy loam soil assumed to be described by the vg model and a silt loam soil model validation tests were performed and the most appropriate model was selected from the candidate models by discrimination tests using the akaike information criterion aic in the case of the hypothetical sandy loam the vg model was found to be the most accurate and most consistent with the data the performance of both the bc and the gr models in terms of the aic was less good but very similar to each other in the case of the silt loam soil the vg model with additional parameter m which accounts for the correlation between pores and for the flow path tortuosity m 2 02 rather than a constant m 0 5 was found to be most accurate and most consistent with the data the performance of the bc and the gr models was similar when m was considered as an unknown parameter instead of a constant

finite sample variance estimation for optimal dynamic treatment regimes of survival outcomes deriving valid confidence intervals for complex estimators is a challenging task in practice estimators of dynamic weighted survival modeling dwsurv a method to estimate an optimal dynamic treatment regime of censored outcomes are asymptotically normal and consistent for their target parameters when at least a subset of the nuisance models is correctly specified however their behavior in finite samples and the impact of model misspecification on inferences remain unclear in addition the estimators nonregularity may negatively affect the inferences under some specific data generating mechanisms our objective was to compare five methods two asymptotic variance formulas adjusting or not for the estimation of nuisance parameters to three bootstrap approaches to construct confidence intervals for the dwsurv parameters in finite samples via simulations we considered practical scenarios for example when some nuisance models are misspecified or when nonregularity is problematic we also compared the five methods in an application about the treatment of rheumatoid arthritis we found that the bootstrap approaches performed consistently well at the cost of longer computational times the asymptotic variance with adjustments generally yielded conservative confidence intervals the asymptotic variance without adjustments yielded nominal coverages for large sample sizes we recommend using the asymptotic variance with adjustments in small samples and the bootstrap if computationally feasible caution should be taken when nonregularity may be an issue

stochastic analysis of the velocity covariance and the displacement covariance tensors in partially saturated heterogeneous anisotropic porous formations considering steady state unsaturated flow in an unbounded domain of heterogeneous formation with three dimensional anisotropic structure first order approximations of the principal and off diagonal components of the velocity covariance tensor were derived for the general case in which the separation vector is inclined to the mean gradient vector j at arbitrary angles taking into account the texture of the soil materials constituting the heterogeneous formation the derived velocity covariance tensors were employed for modeling transport in the vadose zone for the general case in which j is inclined to the principal axes of the formation heterogeneity at arbitrary angles by the use of a lagrangian formulation results of this study suggest that under unsaturated flow for given statistics of the formation properties and given water saturation macrodispersion will diminish in formations of coarser texture when j does not coincide with the principal axes of the heterogeneous formation in this case and in formations of coarser texture the principal axes associated with the principal components of the dimensionless macrodispersion tensor d ij may be deflected in a direction opposite to that of j relative to the principal axes of the formation heterogeneity coarser texture may compensate for the enhanced lateral dispersion and the enhanced deflection of the principal axes of the principal components of d ij due to an increase in the statistical anisotropy of the heterogeneous formation for a formation of given statistics and texture and for a given the longitudinal component of d ij decreases while its transverse components increase when j is more inclined to the longitudinal axis of the formation heterogeneity the latter situation is pertinent to periods of redistribution between successive water applications in which increasing capillary pressure gradients combined with spatial heterogeneity in the formation properties may increase the transverse components of j

statistical analysis of spatial variability in unsaturated flow parameters core scale estimates of soil parameters of the gardner russo and van gemachten models of the hydraulic conductivity and water retention functions were obtained for 417 undisturbed soil cores taken from a wall of a trench 20 m long 2 5 m deep using a procedure based on inverse problem methodology these estimates were used to evaluate the first two statistical moments of the underlying random space functions rsfs using the restricted maximum likelihood estimation procedure coupled with the weighted least squares procedure to estimate parameters of models of the covariance and the drift functions of the pertinent rsfs the fitted models were used to evaluate the mean and covariance functions of the hydraulic conductivity and water rentention functions for given water saturations covariance functions of log saturated conductivity log ks and the shape parameters of the gardner russo and van genuchten models exhibited statistical anisotropy characterized by aspect ratios that vary between 3 to 4 correlation scales of log ks were larger than those of the shape parameters consequently the product of the variance of log unsaturated conductivity and its correlation scale remained essentially invariant for a considerable range of water saturation the implications of these results regarding stochastic modeling of transport in heterogeneous porous formations and possible applications of the results of this study are discussed briefly

a multipoint flux mixed finite element method for the compressible darcy forchheimer models abstract we develop a multipoint flux mixed finite element method for the compressible darcy forchheimer models this method is motivated by the multipoint flux approximation method based on the lowest order brezzi douglas marini mixed finite element method and combined with a special quadrature rule that allows for local velocity elimination and leads to a cell centered system for the pressures we develop two approximation methods for the problems the semi discrete method and fully discrete method where the fully discrete method includes the backward euler scheme and the crank nicolson scheme theoretical results show the convergences for both pressure and velocity the numerical experiments show that the convergence rates of the method are in agreement with the theoretical analysis

a constrained single index regression for estimating interactions between a treatment and covariates we consider a single index regression model uniquely constrained to estimate interactions between a set of pretreatment covariates and a treatment variable on their effects on a response variable in the context of analyzing data from randomized clinical trials we represent interaction effect terms of the model through a set of treatment specific flexible link functions on a linear combination of the covariates a single index subject to the constraint that the expected value given the covariates equals 0 while leaving the main effects of the covariates unspecified we show that the proposed semiparametric estimator is consistent for the interaction term of the model and that the efficiency of the estimator can be improved with an augmentation procedure the proposed single index regression provides a flexible and interpretable modeling approach to optimizing individualized treatment rules based on patients data measured at baseline as illustrated by simulation examples and an application to data from a depression clinical trial

stochastic analysis of flow in a heterogeneous unsaturated saturated system 1 in this study we develop a stochastic model for transient unsaturated saturated flow in randomly heterogeneous media with the method of moment equations we first derive partial differential equations governing the statistical moments of the flow quantities by perturbation expansions and then implement these equations under general conditions with the method of finite differences the stochastic model developed is applicable to the entire domain of a bounded multidimensional unsaturated saturated system in the presence of random or deterministic recharge and sink source and in the presence of multiscale nonstationary medium features the unsaturated and saturated zones are coupled through the water table whose position is random in randomly heterogeneous porous media the presence of the water table renders the flow moments strongly nonstationary even in the absence of medium nonstationary features this finding is confirmed with monte carlo simulations the resulting first two moments of flow may be used to approximate confidence intervals for the flow quantities in addition the integrated stochastic flow model provides the prerequisite quantities for realistically studying contaminant transport in unsaturated saturated systems with a stochastic approach

change plane analysis for subgroup detection and sample size calculation abstractwe propose a systematic method for testing and identifying a subgroup with an enhanced treatment effect we adopts a change plane technique to first test the existence of a subgroup and then identify the subgroup if the null hypothesis on nonexistence of such a subgroup is rejected a semiparametric model is considered for the response with an unspecified baseline function and an interaction between a subgroup indicator and treatment a doubly robust test statistic is constructed based on this model and asymptotic distributions of the test statistic under both null and local alternative hypotheses are derived moreover a sample size calculation method for subgroup detection is developed based on the proposed statistic the finite sample performance of the proposed test is evaluated via simulations finally the proposed methods for subgroup identification and sample size calculation are applied to a data from an aids study

interactive q learning for quantiles abstracta dynamic treatment regime is a sequence of decision rules each of which recommends treatment based on features of patient medical history such as past treatments and outcomes existing methods for estimating optimal dynamic treatment regimes from data optimize the mean of a response variable however the mean may not always be the most appropriate summary of performance we derive estimators of decision rules for optimizing probabilities and quantiles computed with respect to the response distribution for two stage binary treatment settings this enables estimation of dynamic treatment regimes that optimize the cumulative distribution function of the response at a prespecified point or a prespecified quantile of the response distribution such as the median the proposed methods perform favorably in simulation experiments we illustrate our approach with data from a sequentially randomized trial where the primary outcome is remission of depression symptoms supplementary materials for this arti

solute spreading in nonstationary flows in bounded heterogeneous unsaturated saturated media 1 it is commonly assumed in stochastic solute advective transport models that either the velocity field is stationary statistically homogeneous or the mean flow is unidirectional in this study using a lagrangian approach we develop a general stochastic model for transport in variably saturated flow in randomly heterogeneous porous media the mean flow in the model is multidirectional and the velocity field can be nonstationary with location dependent statistics the nonstationarity of the velocity field may be caused by statistical nonhomogeneity of medium properties or complex boundary configurations the particle s mean position is determined using the mean lagrangian velocity particle spreading the displacement covariances is expressed in terms of the state transition matrix that satisfies a time varying dynamic equation whose coefficient matrix is the derivative of the mean lagrangian velocity field in the special cases of stationary velocity fields the transition matrix becomes the identical matrix and our model reduces to the well known model of dagan 1984 for nonstationary but unidirectional flow fields our model reduces to that of butera and tanda 1999 and sun and zhang 2000 the validity of the transport model is examined by comparisons with monte carlo simulations for the following three cases transport in a mean gravity dominated flow in an unsaturated flow with a water table boundary and in a saturated unsaturated flow an excellent agreement is found between our model results and those from monte carlo simulations

doubly robust learning for estimating individualized treatment with censored data individualized treatment rules recommend treatments based on individual patient characteristics in order to maximize clinical benefit when the clinical outcome of interest is survival time estimation is often complicated by censoring we develop nonparametric methods for estimating an optimal individualized treatment rule in the presence of censored data to adjust for censoring we propose a doubly robust estimator which requires correct specification of either the censoring model or survival model but not both the method is shown to be fisher consistent when either model is correct furthermore we establish the convergence rate of the expected survival under the estimated optimal individualized treatment rule to the expected survival under the optimal individualized treatment rule we illustrate the proposed methods using simulation study and data from a phase iii clinical trial on non small cell lung cancer

bayesian nonparametric estimation for dynamic treatment regimes with sequential transition times abstractwe analyze a dataset arising from a clinical trial involving multi stage chemotherapy regimes for acute leukemia the trial design was a 2 2 factorial for frontline therapies only motivated by the idea that subsequent salvage treatments affect survival time we model therapy as a dynamic treatment regime dtr that is an alternating sequence of adaptive treatments or other actions and transition times between disease states these sequences may vary substantially between patients depending on how the regime plays out to evaluate the regimes mean overall survival time is expressed as a weighted average of the means of all possible sums of successive transitions times we assume a bayesian nonparametric survival regression model for each transition time with a dependent dirichlet process prior and gaussian process base measure ddp gp posterior simulation is implemented by markov chain monte carlo mcmc sampling we provide general guidelines for constructing a prior using empirical baye

conditional stochastic analysis of solute transport in heterogeneous variably saturated soils a method is developed for the conditional monte carlo simulation of steady stateflow and transient transport from point sources in variably saturated porous media it combines the geostatistical method a linearized approximation of the soil water tension perturbation solution and afinite element numerical model the method is used to investigate the usefulness of conditional simulation for predicting solute transport under a variety of sampling network designs applied to a number of hypothetical soils saturated hydraulic conductivity data yield the largest reduction of conditional uncertainty in relatively wet soils with mild heterogeneities in highly heterogeneous soils or under dry conditions soil water tension data by themselves taken at a sampling density of one to two correlation scales along the expected mean travel path can greatly reduce prediction uncertainty about solute concentration parameter uncertainty about statistical properties of the independent random variables becomes less important as the number of conditioning data increases however even with a very high number of sampling data uncertainty of predicted concentration levels remains significant

stochastic theory of field scale fickian dispersion in anisotropic porous media a three dimensional theory is described for field scale fickian dispersion in anisotropic porous media due to the spatial variability of hydraulic conductivities the study relies partly on earlier work by the authors the attributes of which are briefly reviewed it leads to results which differ in important ways from earlier theoretical conclusions about dispersion in anisotropic media we express the dispersion tensor d as the sum of a local component d and a field scale component the local component is assumed to be independent of velocity which is most appropriate if it represents molecular diffusion and its principal terms are taken to act parallel and normal to the mean velocity vector the field scale component is written as where is a dispersivity tensor and we show that at large peclet numbers p the dispersivity tensor reduces to a single principal component parallel to the mean velocity regardless of how is oriented this result valid for arbitrary covariance functions of log hydraulic conductivity differs from that of l w gelhar and c l axness 1983 according to whom the asymptotic dispersivity tensor may possess more than one nonzero eigen value they calculate the direction of the largest principal dispersivity to be offset from the mean velocity toward the direction of least spatial correlation or away from the stratification in typical layered media we show that this principal dispersivity is offset in the opposite direction at small and intermediate peclet numbers but rotates toward the mean velocity as p increases the largest eigen value is constant and dominated by field scale velocity fluctuations at large p values the other two eigen values diminish asymptotically in proportion to p 1 and are controlled by d as well as by field scale differential convection the range of small peclet numbers has not been previously investigated under anisotropic conditions yet is of much importance for transport in low permeability rocks or soils we show that at low p values all three principal dispersivities are proportional to p and thus is proportional to 2 a phenomenon reminiscent of taylor diffusion when the mean velocity is inclined to the axes of anisotropy the eigen values of are neither parallel nor normal to however since d is dominated by d at small peclet numbers the principal dispersion coefficients are asymptotically as p 0 parallel and normal to the mean velocity just like when p is large their maximum deviation from these directions occurs at intermediate p values

decision analysis by augmented probability simulation we provide a generic monte carlo method to find the alternative of maximum expected utility in a decision analysis we define an artificial distribution on the product space of alternatives and states and show that the optimal alternative is the mode of the implied marginal distribution on the alternatives after drawing a sample from the artificial distribution we may use exploratory data analysis tools to approximately identify the optimal alternative we illustrate our method for some important types of influence diagrams

a general statistical framework for subgroup identification and comparative treatment scoring summary many statistical methods have recently been developed for identifying subgroups of patients who may benefit from different available treatments compared with the traditional outcome modeling approaches these methods focus on modeling interactions between the treatments and covariates while by pass or minimize modeling the main effects of covariates because the subgroup identification only depends on the sign of the interaction however these methods are scattered and often narrow in scope in this article we propose a general framework by weighting and a learning for subgroup identification in both randomized clinical trials and observational studies our framework involves minimum modeling for the relationship between the outcome and covariates pertinent to the subgroup identification under the proposed framework we may also estimate the magnitude of the interaction which leads to the construction of scoring system measuring the individualized treatment effect the proposed methods are quite flexible and include many recently proposed estimators as special cases as a result some estimators originally proposed for randomized clinical trials can be extended to observational studies and procedures based on the weighting method can be converted to an a learning method and vice versa our approaches also allow straightforward incorporation of regularization methods for high dimensional data as well as possible efficiency augmentation and generalization to multiple treatments we examine the empirical performance of several procedures belonging to the proposed framework through extensive numerical studies

a mixed finite element method for a strongly nonlinear second order elliptic problem the approximation of the solution of the first boundary value problem for a strongly nonlinear second order elliptic problem in divergence form by the mixed finite element method is considered existence and uniqueness of the approximation are proved and optimal error estimates in l 2 are established for both the scalar and vector functions approximated by the method error estimates are also derived in l q 2 q

optimal dynamic treatment regimes summary a dynamic treatment regime is a list of decision rules one per time interval for how the level of treatment will be tailored through time to an individual s changing status the goal of this paper is to use experimental or observational data to estimate decision regimes that result in a maximal mean response to explicate our objective and to state the assumptions we use the potential outcomes model the method proposed makes smooth parametric assumptions only on quantities that are directly relevant to the goal of estimating the optimal rules we illustrate the methodology proposed via a small simulation