too many covariates and too few cases a comparative study prior research indicates that 10 15 cases or controls whichever fewer are required per parameter to reliably estimate regression coefficients in multivariable logistic regression models this condition may be difficult to meet even in a well designed study when the number of potential confounders is large the outcome is rare and or interactions are of interest various propensity score approaches have been implemented when the exposure is binary recent work on shrinkage approaches like lasso were motivated by the critical need to develop methods for the p n situation where p is the number of parameters and n is the sample size those methods however have been less frequently used when p n and in this situation there is no guidance on choosing among regular logistic regression models propensity score methods and shrinkage approaches to fill this gap we conducted extensive simulations mimicking our motivating clinical data estimating vaccine effectiveness for preventing influenza hospitalizations in the 2011 2012 influenza season ridge regression and penalized logistic regression models that penalize all but the coefficient of the exposure may be considered in these types of studies copyright 2016 john wiley sons ltd

moving towards best practice when using inverse probability of treatment weighting iptw using the propensity score to estimate causal treatment effects in observational studies the propensity score is defined as a subject s probability of treatment selection conditional on observed baseline covariates weighting subjects by the inverse probability of treatment received creates a synthetic sample in which treatment assignment is independent of measured baseline covariates inverse probability of treatment weighting iptw using the propensity score allows one to obtain unbiased estimates of average treatment effects however these estimates are only valid if there are no residual systematic differences in observed baseline characteristics between treated and control subjects in the sample weighted by the estimated inverse probability of treatment we report on a systematic literature review in which we found that the use of iptw has increased rapidly in recent years but that in the most recent year a majority of studies did not formally examine whether weighting balanced measured covariates between treatment groups we then proceed to describe a suite of quantitative and qualitative methods that allow one to assess whether measured baseline covariates are balanced between treatment groups in the weighted sample the quantitative methods use the weighted standardized difference to compare means prevalences higher order moments and interactions the qualitative methods employ graphical methods to compare the distribution of continuous baseline covariates between treated and control subjects in the weighted sample finally we illustrate the application of these methods in an empirical case study we propose a formal set of balance diagnostics that contribute towards an evolving concept of best practice when using iptw to estimate causal treatment effects using observational data

power and sample size for observational studies of point exposure effects inverse probability of treatment weights iptws are commonly used to control for confounding when estimating causal effects of point exposures from observational data when planning a study that will be analyzed with iptws determining the required sample size for a given level of statistical power is challenging because of the effect of weighting on the variance of the estimated causal means this paper considers the utility of the design effect to quantify the effect of weighting on the precision of causal estimates the design effect is defined as the ratio of the variance of the causal mean estimator divided by the variance of a naive estimator if counter to fact no confounding had been present and weights were not needed a simple closed form approximation of the design effect is derived that is outcome invariant and can be estimated during the study design phase once the design effect is approximated for each treatment group sample size calculations are conducted as for a randomized trial but with variances inflated by the design effects to account for weighting simulations demonstrate the accuracy of the design effect approximation and practical considerations are discussed

bayesian approach for addressing differential covariate measurement error in propensity score methods propensity score methods are an important tool to help reduce confounding in non experimental studies and produce more accurate causal effect estimates most propensity score methods assume that covariates are measured without error however covariates are often measured with error recent work has shown that ignoring such error could lead to bias in treatment effect estimates in this paper we consider an additional complication that of differential measurement error across treatment groups such as can occur if a covariate is measured differently in the treatment and control groups we propose two flexible bayesian approaches for handling differential measurement error when estimating average causal effects using propensity score methods we consider three scenarios systematic i e a location shift heteroscedastic i e different variances and mixed both systematic and heteroscedastic measurement errors we also explore various prior choices i e weakly informative or point mass on the sensitivity parameters related to the differential measurement error we present results from simulation studies evaluating the performance of the proposed methods and apply these approaches to an example estimating the effect of neighborhood disadvantage on adolescent drug use disorders

a really simple approximation of smallest grammar in this paper we present a really simple linear time algorithm constructing a context free grammar of size 4 g log 3 2 n g for the input string where n is the size of the input string and g the size of the optimal grammar generating this string the algorithm works for arbitrary size alphabets but the running time is linear assuming that the alphabet of the input string can be identified with numbers from 1 n c for some constant c algorithms with such an approximation guarantee and running time are known however all of them were non trivial and their analyses were involved the here presented algorithm computes the lz77 factorisation and transforms it in phases to a grammar in each phase it maintains an lz77 like factorisation of the word with at most factors as well as additional o letters where was the size of the original lz77 factorisation in one phase in a greedy way by a left to right sweep and a help of the factorisation we choose a set of pairs of consecutive letters to be replaced with new symbols i e nonterminals of the constructed grammar we choose at least 2 3 of the letters in the word and there are o many different pairs among them hence there are o log n phases each of them introduces o nonterminals to a grammar a more precise analysis yields a bound 4 log n as g this yields the desired bound g 4 g log n g

conditioning on the propensity score can result in biased estimation of common measures of treatment effect a monte carlo study propensity score methods are increasingly being used to estimate causal treatment effects in the medical literature conditioning on the propensity score results in unbiased estimation of the expected difference in observed responses to two treatments the degree to which conditioning on the propensity score introduces bias into the estimation of the conditional odds ratio or conditional hazard ratio which are frequently used as measures of treatment effect in observational studies has not been extensively studied we conducted monte carlo simulations to determine the degree to which propensity score matching stratification on the quintiles of the propensity score and covariate adjustment using the propensity score result in biased estimation of conditional odds ratios hazard ratios and rate ratios we found that conditioning on the propensity score resulted in biased estimation of the true conditional odds ratio and the true conditional hazard ratio in all scenarios examined treatment effects were biased towards the null treatment effect however conditioning on the propensity score did not result in biased estimation of the true conditional rate ratio in contrast conventional regression methods allowed unbiased estimation of the true conditional treatment effect when all variables associated with the outcome were included in the regression model the observed bias in propensity score methods is due to the fact that regression models allow one to estimate conditional treatment effects whereas propensity score methods allow one to estimate marginal treatment effects in several settings with non linear treatment effects marginal and conditional treatment effects do not coincide

uniformly semiparametric efficient estimation of treatment effects with a continuous treatment this article studies identification estimation and inference of general unconditional treatment effects models with continuous treatment under the ignorability assumption we show identification of the parameters of interest the dose response functions under the assumption that selection to treatment is based on observables we propose a semiparametric two step estimator and consider estimation of the dose response functions through moment restriction models with generalized residual functions that are possibly nonsmooth this general formulation includes average and quantile treatment effects as special cases the asymptotic properties of the estimator are derived namely uniform consistency weak convergence and semiparametric efficiency we also develop statistical inference procedures and establish the validity of a bootstrap approach to implement these methods in practice monte carlo simulations show that the proposed methods have good finite sample properties finally we apply the proposed

a deficiency of the odds ratio as a measure of effect size the odds ratio is probably the most widely used measure of association for binary variables it has many well recognized advantages and disadvantages vis a vis the risk ratio we demonstrate that for chained or conditional probabilities odds ratios can behave paradoxically by failing to show a reinforcement effect that is expressed very clearly when risk ratios are used

the performance of different propensity score methods for estimating differences in proportions risk differences or absolute risk reductions in observational studies propensity score methods are increasingly being used to estimate the effects of treatments on health outcomes using observational data there are four methods for using the propensity score to estimate treatment effects covariate adjustment using the propensity score stratification on the propensity score propensity score matching and inverse probability of treatment weighting iptw using the propensity score when outcomes are binary the effect of treatment on the outcome can be described using odds ratios relative risks risk differences or the number needed to treat several clinical commentators suggested that risk differences and numbers needed to treat are more meaningful for clinical decision making than are odds ratios or relative risks however there is a paucity of information about the relative performance of the different propensity score methods for estimating risk differences we conducted a series of monte carlo simulations to examine this issue we examined bias variance estimation coverage of confidence intervals mean squared error mse and type i error rates a doubly robust version of iptw had superior performance compared with the other propensity score methods it resulted in unbiased estimation of risk differences treatment effects with the lowest standard errors confidence intervals with the correct coverage rates and correct type i error rates stratification matching on the propensity score and covariate adjustment using the propensity score resulted in minor to modest bias in estimating risk differences estimators based on iptw had lower mse compared with other propensity score methods differences between iptw and propensity score matching may reflect that these two methods estimate the average treatment effect and the average treatment effect for the treated respectively copyright 2010 john wiley sons ltd

the smallest grammar problem this paper addresses the smallest grammar problem what is the smallest context free grammar that generates exactly one given string spl sigma this is a natural question about a fundamental object connected to many fields such as data compression kolmogorov complexity pattern identification and addition chains due to the problem s inherent complexity our objective is to find an approximation algorithm which finds a small grammar for the input string we focus attention on the approximation ratio of the algorithm and implicitly the worst case behavior to establish provable performance guarantees and to address shortcomings in the classical measure of redundancy in the literature our first results are concern the hardness of approximating the smallest grammar problem most notably we show that every efficient algorithm for the smallest grammar problem has approximation ratio at least 8569 8568 unless p np we then bound approximation ratios for several of the best known grammar based compression algorithms including lz78 b isection sequential longest match greedy and re pair among these the best upper bound we show is o n sup 1 2 we finish by presenting two novel algorithms with exponentially better ratios of o log sup 3 n and o log n m sup where m sup is the size of the smallest grammar for that input the latter algorithm highlights a connection between grammar based compression and lz77

variance estimation when using inverse probability of treatment weighting iptw with survival analysis propensity score methods are used to reduce the effects of observed confounding when using observational data to estimate the effects of treatments or exposures a popular method of using the propensity score is inverse probability of treatment weighting iptw when using this method a weight is calculated for each subject that is equal to the inverse of the probability of receiving the treatment that was actually received these weights are then incorporated into the analyses to minimize the effects of observed confounding previous research has found that these methods result in unbiased estimation when estimating the effect of treatment on survival outcomes however conventional methods of variance estimation were shown to result in biased estimates of standard error in this study we conducted an extensive set of monte carlo simulations to examine different methods of variance estimation when using a weighted cox proportional hazards model to estimate the effect of treatment we considered three variance estimation methods i a naive model based variance estimator ii a robust sandwich type variance estimator and iii a bootstrap variance estimator we considered estimation of both the average treatment effect and the average treatment effect in the treated we found that the use of a bootstrap estimator resulted in approximately correct estimates of standard errors and confidence intervals with the correct coverage rates the other estimators resulted in biased estimates of standard errors and confidence intervals with incorrect coverage rates our simulations were informed by a case study examining the effect of statin prescribing on mortality 2016 the authors statistics in medicine published by john wiley sons ltd

flexible regression approach to propensity score analysis and its relationship with matching and weighting in propensity score analysis the frequently used regression adjustment involves regressing the outcome on the estimated propensity score and treatment indicator this approach can be highly efficient when model assumptions are valid but can lead to biased results when the assumptions are violated we extend the simple regression adjustment to a varying coefficient regression model that allows for nonlinear association between outcome and propensity score we discuss its connection with some propensity score matching and weighting methods and show that the proposed analytical framework can shed light on the intrinsic connection among some mainstream propensity score approaches stratification regression kernel matching and inverse probability weighting and handle commonly used causal estimands we derive analytic point and variance estimators that properly take into account the sampling variability in the estimated propensity score extensive simulations show that the proposed approach possesses desired finite sample properties and demonstrates competitive performance in comparison with other methods estimating the same causal estimand the proposed methodology is illustrated with a study on right heart catheterization

matched or unmatched analyses with propensity score matched data propensity score matching has been used widely in observational studies to balance confounders across treatment groups however whether matched pairs analyses should be used as a primary approach is still in debate we compared the statistical power and type 1 error rate for four commonly used methods of analyzing propensity score matched samples with continuous outcomes 1 an unadjusted mixed effects model 2 an unadjusted generalized estimating method 3 simple linear regression and 4 multiple linear regression multiple linear regression had the highest statistical power among the four competing methods we also found that the degree of intraclass correlation within matched pairs depends on the dissimilarity between the coefficient vectors of confounders in the outcome and treatment models multiple linear regression is superior to the unadjusted matched pairs analyses for propensity score matched data

the performance of different propensity score methods for estimating marginal hazard ratios propensity score methods are increasingly being used to reduce or minimize the effects of confounding when estimating the effects of treatments exposures or interventions when using observational or non randomized data under the assumption of no unmeasured confounders previous research has shown that propensity score methods allow for unbiased estimation of linear treatment effects e g differences in means or proportions however in biomedical research time to event outcomes occur frequently there is a paucity of research into the performance of different propensity score methods for estimating the effect of treatment on time to event outcomes furthermore propensity score methods allow for the estimation of marginal or population average treatment effects we conducted an extensive series of monte carlo simulations to examine the performance of propensity score matching 1 1 greedy nearest neighbor matching within propensity score calipers stratification on the propensity score inverse probability of treatment weighting iptw using the propensity score and covariate adjustment using the propensity score to estimate marginal hazard ratios we found that both propensity score matching and iptw using the propensity score allow for the estimation of marginal hazard ratios with minimal bias of these two approaches iptw using the propensity score resulted in estimates with lower mean squared error when estimating the effect of treatment in the treated stratification on the propensity score and covariate adjustment using the propensity score result in biased estimation of both marginal and conditional hazard ratios applied researchers are encouraged to use propensity score matching and iptw using the propensity score when estimating the relative effect of treatment on time to event outcomes copyright 2012 john wiley sons ltd

estimating propensity scores with missing covariate data using general location mixture models in many observational studies analysts estimate causal effects using propensity scores e g by matching sub classifying or inverse probability weighting based on the scores estimation of propensity scores is complicated when some values of the covariates are missing analysts can use multiple imputation to create completed data sets from which propensity scores can be estimated we propose a general location mixture model for imputations that assumes that the control units are a latent mixture of i units whose covariates are drawn from the same distributions as the treated units covariates and ii units whose covariates are drawn from different distributions this formulation reduces the influence of control units outside the treated units region of the covariate space on the estimation of parameters in the imputation model which can result in more plausible imputations in turn this can result in more reliable estimates of propensity scores and better balance in the true covariate distributions when matching or sub classifying we illustrate the benefits of the latent class modeling approach with simulations and with an observational study of the effect of breast feeding on children s cognitive abilities

bias associated with using the estimated propensity score as a regression covariate the use of propensity score methods to adjust for selection bias in observational studies has become increasingly popular in public health and medical research a substantial portion of studies using propensity score adjustment treat the propensity score as a conventional regression predictor through a monte carlo simulation study austin and colleagues investigated the bias associated with treatment effect estimation when the propensity score is used as a covariate in nonlinear regression models such as logistic regression and cox proportional hazards models we show that the bias exists even in a linear regression model when the estimated propensity score is used and derive the explicit form of the bias we also conduct an extensive simulation study to compare the performance of such covariate adjustment with propensity score stratification propensity score matching inverse probability of treatment weighted method and nonparametric functional estimation using splines the simulation scenarios are designed to reflect real data analysis practice instead of specifying a known parametric propensity score model we generate the data by considering various degrees of overlap of the covariate distributions between treated and control groups propensity score matching excels when the treated group is contained within a larger control pool while the model based adjustment may have an edge when treated and control groups do not have too much overlap overall adjusting for the propensity score through stratification or matching followed by regression or using splines appears to be a good practical strategy

covariate imbalance and random allocation in clinical trials a model is developed to estimate the effect of covariate imbalance on the size of a test of treatment efficacy in randomized clinical trials comparing two treatments when dispersion parameters are known it is concluded that tests of homogeneity on the covariates should not be performed that covariate imbalance is just as much a problem for large studies as for small ones in terms of effect on size and that the effect of correlation between covariates and measures of efficacy is more complex than has previously been suggested the best way to adjust for covariate imbalance is by an analysis of covariance

estimators and confidence intervals for the marginal odds ratio using logistic regression and propensity score stratification propensity score methods are widely used to estimate treatment or exposure effects in observational studies in studies with binary response the effect can be described as an odds ratio and the mantel haenszel estimator is traditionally used for stratified data although propensity score methods are designed for marginal treatment effects it has been shown that the mantel haenszel estimator stratified for propensity score is a questionable estimator for the marginal odds ratio which describes the change in odds of response if everybody versus nobody were treated we studied recently proposed alternative estimators for the marginal odds ratio one stratified for propensity score the other derived from logistic regression additionally we adapted the methodology of the logistic regression based estimator for the derivation of a marginal odds ratio estimator to covariate adjustment by the propensity score we also derived corresponding variance estimators using the delta method the estimators were illustrated and compared to the inverse probability weighted estimator and the stratified mantel haenszel estimator in a study dealing with respiratory tract infections in children in germany furthermore simulation studies that were carried out to investigate relative bias variance and coverage probability showed reasonable performance of marginal odds ratio estimators if response rates or regression based approaches were used their variances were accurately estimated in contrast the stratified mantel haenszel estimator was substantially biased in some situations due to problems of non collapsibility and thus it is generally inappropriate for a reliable estimation of the marginal odds ratio

nonparametric functional mapping of quantitative trait loci functional mapping is a useful tool for mapping quantitative trait loci qtl that control dynamic traits it incorporates mathematical aspects of biological processes into the mixture model based likelihood setting for qtl mapping thus increasing the power of qtl detection and the precision of parameter estimation however in many situations there is no obvious functional form and in such cases this strategy will not be optimal here we propose to use nonparametric function estimation typically implemented with b splines to estimate the underlying functional form of phenotypic trajectories and then construct a nonparametric test to find evidence of existing qtl using the representation of a nonparametric regression as a mixed model the final test statistic is a likelihood ratio test we consider two types of genetic maps dense maps and general maps and the power of nonparametric functional mapping is investigated through simulation studies and demonstrated by examples

model averaging in semiparametric estimation of treatment effects choosing the covariates and functional form of the propensity score is an important choice for estimating treatment effects this paper proposes a data driven way of averaging the estimators over candidate specifications to resolve the specification uncertainty in the propensity score weighting estimation of the att the proposed procedures minimize the estimated mse of the att estimator in a local asymptotic framework we formulate model averaging as a statistical decision problem in a limit experiment and derive an averaging scheme that is bayes optimal with respect to a given prior the averaging estimator outperforms selection estimators and the estimators in any of the candidate models in terms of bayes asymptotic mse our monte carlo studies illustrate the size of the mse gains we apply the averaging procedure to evaluate the effect of a labor market program

propensity score methods for estimating relative risks in cluster randomized trials with low incidence binary outcomes and selection bias despite randomization selection bias may occur in cluster randomized trials classical multivariable regression usually allows for adjusting treatment effect estimates with unbalanced covariates however for binary outcomes with low incidence such a method may fail because of separation problems this simulation study focused on the performance of propensity score ps based methods to estimate relative risks from cluster randomized trials with binary outcomes with low incidence the results suggested that among the different approaches used multivariable regression direct adjustment on ps inverse weighting on ps and stratification on ps only direct adjustment on the ps fully corrected the bias and moreover had the best statistical properties

stratification and weighting via the propensity score in estimation of causal treatment effects a comparative study estimation of treatment effects with causal interpretation from observational data is complicated because exposure to treatment may be confounded with subject characteristics the propensity score the probability of treatment exposure conditional on covariates is the basis for two approaches to adjusting for confounding methods based on stratification of observations by quantiles of estimated propensity scores and methods based on weighting observations by the inverse of estimated propensity scores we review popular versions of these approaches and related methods offering improved precision describe theoretical properties and highlight their implications for practice and present extensive comparisons of performance that provide guidance for practical use

bagged one to one matching for efficient and robust treatment effect estimation observational studies present challenges due to bias from imbalance in baseline confounders one to one matching oom a popular cohort construction technique for observational studies reduces bias and provides a compelling basis for inference but generally leads to at least some loss of efficiency due to the exclusion of potentially informative subjects we introduce the bagged one to one matching boom estimator which combines the bias reducing properties of oom with the variance reducing properties of bootstrap aggregation bagging we describe the boom algorithm in detail provide r code for its implementation and investigate its performance in simulation studies and a case study in the simulation studies under different types of model misspecification we compare the boom estimator s performance in terms of mean squared error bias variance accuracy of standard error estimation and coverage of nominal 95 confidence intervals to that of oom and to that of ordinary least squares estimation inverse probability weighting and targeted maximum likelihood estimation all on the full unmatched cohort in our simulations the boom estimator achieves as much bias reduction as the estimator based on oom while having much lower variance in all of the settings examined in the simulations the boom s mean squared error is comparable to or better than that of the comparison methods in the case study boom yields estimates similar to those from the established methods with narrower 95 confidence intervals

bayesian estimation of the average treatment effect on the treated using inverse weighting we develop a bayesian approach to estimate the average treatment effect on the treated in the presence of confounding the approach builds on developments proposed by saarela et al in the context of marginal structural models using importance sampling weights to adjust for confounding and estimate a causal effect the bayesian bootstrap is adopted to approximate posterior distributions of interest and avoid the issue of feedback that arises in bayesian causal estimation relying on a joint likelihood we present results from simulation studies to estimate the average treatment effect on the treated evaluating the impact of sample size and the strength of confounding on estimation we illustrate our approach using the classic right heart catheterization data set and find a negative causal effect of the exposure on 30 day survival in accordance with previous analyses of these data we also apply our approach to the data set of the national center for health statistics birth data and obtain a negative effect of maternal smoking during pregnancy on birth weight

metrics for covariate balance in cohort studies of causal effects inferring causation from non randomized studies of exposure requires that exposure groups can be balanced with respect to prognostic factors for the outcome although there is broad agreement in the literature that balance should be checked there is confusion regarding the appropriate metric we present a simulation study that compares several balance metrics with respect to the strength of their association with bias in estimation of the effect of a binary exposure on a binary count or continuous outcome the simulations utilize matching on the propensity score with successively decreasing calipers to produce datasets with varying covariate balance we propose the post matching c statistic as a balance metric and found that it had consistently strong associations with estimation bias even when the propensity score model was misspecified as long as the propensity score was estimated with sufficient study size this metric along with the average standardized difference and the general weighted difference outperformed all other metrics considered in association with bias including the unstandardized absolute difference kolmogorov smirnov and levy distances overlapping coefficient mahalanobis balance and l1 metrics of the best performing metrics the c statistic and general weighted difference also have the advantage that they automatically evaluate balance on all covariates simultaneously and can easily incorporate balance on interactions among covariates therefore when combined with the usual practice of comparing individual covariate means and standard deviations across exposure groups these metrics may provide useful summaries of the observed covariate imbalance

adjusted kaplan meier estimator and log rank test with inverse probability of treatment weighting for survival data estimation and group comparison of survival curves are two very common issues in survival analysis in practice the kaplan meier estimates of survival functions may be biased due to unbalanced distribution of confounders here we develop an adjusted kaplan meier estimator akme to reduce confounding effects using inverse probability of treatment weighting iptw each observation is weighted by its inverse probability of being in a certain group the akme is shown to be a consistent estimate of the survival function and the variance of the akme is derived a weighted log rank test is proposed for comparing group differences of survival functions simulation studies are used to illustrate the performance of akme and the weighted log rank test the method proposed here outperforms the kaplan meier estimate and it does better than or as well as other estimators based on stratification the akme and the weighted log rank test are applied to two real examples one is the study of times to reinfection of sexually transmitted diseases and the other is the primary biliary cirrhosis pbc study

on the propensity score weighting analysis with survival outcome estimands estimation and inference propensity score analysis is widely used in observational studies to adjust for confounding and estimate the causal effect of a treatment on the outcome when the outcome is survival time there are special considerations on the definition of the causal estimand point and variance estimation that have not been thoroughly studied in the literature we investigate propensity score analysis of survival data with a class of weighting methods we consider the following estimands in the two sample context average survival time restricted average survival time survival probability survival quantile and the marginal hazard ratio we propose a unified analytic framework to obtain the point and variance estimators the proposed methodology properly adjusts for the sampling variability in the estimated propensity scores extensive simulations show that the point and variance estimators possess desired finite sample properties and demonstrate better numerical performance than some existing weighting and matching methods commonly used in the literature the proposed methodology is illustrated with data from a breast cancer study

propensity score methods for bias reduction in the comparison of a treatment to a non randomized control group in observational studies investigators have no control over the treatment assignment the treated and non treated that is control groups may have large differences on their observed covariates and these differences can lead to biased estimates of treatment effects even traditional covariance analysis adjustments may be inadequate to eliminate this bias the propensity score defined as the conditional probability of being treated given the covariates can be used to balance the covariates in the two groups and therefore reduce this bias in order to estimate the propensity score one must model the distribution of the treatment indicator variable given the observed covariates once estimated the propensity score can be used to reduce bias through matching stratification subclassification regression adjustment or some combination of all three in this tutorial we discuss the uses of propensity score methods for bias reduction give references to the literature and illustrate the uses through applied examples

propensity scores used for analysis of cluster randomized trials with selection bias a simulation study cluster randomized trials crts are often prone to selection bias despite randomization using a simulation study we investigated the use of propensity score ps based methods in estimating treatment effects in crts with selection bias when the outcome is quantitative of four ps based methods adjustment on ps inverse weighting stratification and optimal full matching method three successfully corrected the bias as did an approach using classical multivariable regression however they showed poorer statistical efficiency than classical methods with higher standard error for the treatment effect and type i error much smaller than the 5 nominal level

arens regularity of banach algebras and the geometry of banach spaces we show that a banach algebra a such that a has the property v of a pelczynski is arens regular a strong uniqueness property of the extension of the product on a unital c algebra a to a is proved the algebraic structure of the bidual of a c algebra can be obtained through the local reflexivity principle we give examples which show that the results are sharp

point and interval estimation of exposure effects and interaction between exposures based on logistic model for observational studies point and interval estimation of exposure effects and interaction between exposures based on logistic model for observational studies

assessing the performance of the generalized propensity score for estimating the effect of quantitative or continuous exposures on binary outcomes propensity score methods are increasingly being used to estimate the effects of treatments and exposures when using observational data the propensity score was initially developed for use with binary exposures the generalized propensity score gps is an extension of the propensity score for use with quantitative or continuous exposures eg dose or quantity of medication income or years of education we used monte carlo simulations to examine the performance of different methods of using the gps to estimate the effect of continuous exposures on binary outcomes we examined covariate adjustment using the gps and weighting using weights based on the inverse of the gps we examined both the use of ordinary least squares to estimate the propensity function and the use of the covariate balancing propensity score algorithm the use of methods based on the gps was compared with the use of g computation all methods resulted in essentially unbiased estimation of the population dose response function however gps based weighting tended to result in estimates that displayed greater variability and had higher mean squared error when the magnitude of confounding was strong of the methods based on the gps covariate adjustment using the gps tended to result in estimates with lower variability and mean squared error when the magnitude of confounding was strong we illustrate the application of these methods by estimating the effect of average neighborhood income on the probability of death within 1 year of hospitalization for an acute myocardial infarction

a general approach to evaluating the bias of 2 stage instrumental variable estimators unmeasured confounding is a common concern when researchers attempt to estimate a treatment effect using observational data or randomized studies with nonperfect compliance to address this concern instrumental variable methods such as 2 stage predictor substitution 2sps and 2 stage residual inclusion 2sri have been widely adopted in many clinical studies of binary and survival outcomes 2sri has been accepted as the method of choice over 2sps but a compelling theoretical rationale has not been postulated we evaluate the bias and consistency in estimating the conditional treatment effect for both 2sps and 2sri when the outcome is binary count or time to event we demonstrate analytically that the bias in 2sps and 2sri estimators can be reframed to mirror the problem of omitted variables in nonlinear models and that there is a direct relationship with the collapsibility of effect measures in contrast to conclusions made by previous studies terza et al 2008 we demonstrate that the consistency of 2sri estimators only holds under the following conditions 1 when the null hypothesis is true 2 when the outcome model is collapsible or 3 when estimating the nonnull causal effect from cox or logistic regression models the strong and unrealistic assumption that the effect of the unmeasured covariates on the treatment is proportional to their effect on the outcome needs to hold we propose a novel dissimilarity metric to provide an intuitive explanation of the bias of 2sri estimators in noncollapsible models and demonstrate that with increasing dissimilarity between the effects of the unmeasured covariates on the treatment versus outcome the bias of 2sri increases in magnitude

a simulation study of finite sample properties of marginal structural cox proportional hazards models motivated by a previously published study of hiv treatment we simulated data subject to time varying confounding affected by prior treatment to examine some finite sample properties of marginal structural cox proportional hazards models we compared a unadjusted b regression adjusted c unstabilized and d stabilized marginal structural inverse probability of treatment ipt weighted model estimators of effect in terms of bias standard error root mean squared error mse and 95 confidence limit coverage over a range of research scenarios including relatively small sample sizes and ten study assessments in the base case scenario resembling the motivating example where the true hazard ratio was 0 5 both ipt weighted analyses were unbiased while crude and adjusted analyses showed substantial bias towards and across the null stabilized ipt weighted analyses remained unbiased across a range of scenarios including relatively small sample size however the standard error was generally smaller in crude and adjusted models in many cases unstabilized weighted analysis showed a substantial increase in standard error compared to other approaches root mse was smallest in the ipt weighted analyses for the base case scenario in situations where time varying confounding affected by prior treatment was absent ipt weighted analyses were less precise and therefore had greater root mse compared with adjusted analyses the 95 confidence limit coverage was close to nominal for all stabilized ipt weighted but poor in crude adjusted and unstabilized ipt weighted analysis under realistic scenarios marginal structural cox proportional hazards models performed according to expectations based on large sample theory and provided accurate estimates of the hazard ratio

stratification for the propensity score compared with linear regression techniques to assess the effect of treatment or exposure stratifying and matching by the propensity score are increasingly popular approaches to deal with confounding in medical studies investigating effects of a treatment or exposure a more traditional alternative technique is the direct adjustment for confounding in regression models this paper discusses fundamental differences between the two approaches with a focus on linear regression and propensity score stratification and identifies points to be considered for an adequate comparison the treatment estimators are examined for unbiasedness and efficiency this is illustrated in an application to real data and supplemented by an investigation on properties of the estimators for a range of underlying linear models we demonstrate that in specific circumstances the propensity score estimator is identical to the effect estimated from a full linear model even if it is built on coarser covariate strata than the linear model as a consequence the coarsening property of the propensity score adjustment for a one dimensional confounder instead of a high dimensional covariate may be viewed as a way to implement a pre specified richly parametrized linear model we conclude that the propensity score estimator inherits the potential for overfitting and that care should be taken to restrict covariates to those relevant for outcome

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

estimation of conditional and marginal odds ratios using the prognostic score introduced by hansen in 2008 the prognostic score pgs has been presented as the prognostic analogue of the propensity score pps pps based methods are intended to estimate marginal effects most previous studies evaluated the performance of existing pgs based methods adjustment stratification and matching using the pgs in situations in which the theoretical conditional and marginal effects are equal i e collapsible situations to support the use of pgs framework as an alternative to the pps framework applied researchers must have reliable information about the type of treatment effect estimated by each method we propose four new pgs based methods each developed to estimate a specific type of treatment effect we evaluated the ability of existing and new pgs based methods to estimate the conditional treatment effect cte the marginal average treatment effect on the whole population ate and the marginal average treatment effect on the treated population att when the odds ratio a non collapsible estimator is the measure of interest the performance of pgs based methods was assessed by monte carlo simulations and compared with pps based methods and multivariate regression analysis existing pgs based methods did not allow for estimating the ate and showed unacceptable performance when the proportion of exposed subjects was large when estimating marginal effects pps based methods were too conservative whereas the new pgs based methods performed better with low prevalence of exposure and had coverages closer to the nominal value when estimating cte the new pgs based methods performed as well as traditional multivariate regression copyright 2016 john wiley sons ltd

the robust inference for the cox proportional hazards model abstract we derive the asymptotic distribution of the maximum partial likelihood estimator for the vector of regression coefficients under a possibly misspecified cox proportional hazards model as in the parametric setting this estimator converges to a well defined constant vector in addition the random vector n 1 2 is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated the newly proposed robust covariance matrix estimator is similar to the so called sandwich variance estimators that have been extensively studied for parametric cases for many misspecified cox models the asymptotic limit or part of it can be interpreted meaningfully in those circumstances valid statistical inferences about the corresponding covariate effects can be drawn based on the aforementioned asymptotic theory of and the related results for the score statistics extensive studies demonstrate that the proposed robust tests and interval estimation procedures

characterizing the effect of matching using linear propensity score methods with normal distributions summary matched sampling is a standard technique for controlling bias in observational studies due to specific covariates since rosenbaum rubin 1983 multivariate matching methods based on estimated propensity scores have been used with increasing frequency in medical educational and sociological applications we obtain analytic expressions for the effect of matching using linear propensity score methods with normal distributions these expressions cover cases where the propensity score is either known or estimated using either discriminant analysis or logistic regression as is typically done in current practice the results show that matching using estimated propensity scores not only reduces bias along the population propensity score but also controls variation of components orthogonal to it matching on estimated rather than population propensity scores can therefore lead to relatively large variance reduction as much as a factor of two in common matching settings where close matches are possible approximations are given for the magnitude of this variance reduction which can be computed using estimates obtained from the matching pools related expressions for bias reduction are also presented which suggest that in difficult matching situations the use of population scores leads to greater bias reduction than the use of estimated scores

fully functional suffix trees and optimal text searching in bwt runs bounded space indexing highly repetitive texts such as genomic databases software repositories and versioned text collections has become an important problem since the turn of the millennium a relevant compressibility measure for repetitive texts is r the number of runs in their burrows wheeler transforms bwts one of the earliest indexes for repetitive collections the run length fm index used o r space and was able to efficiently count the number of occurrences of a pattern of length m in a text of length n in o m log log n time with current techniques however it was unable to locate the positions of those occurrences efficiently within a space bounded in terms of r in this article we close this long standing problem showing how to extend the run length fm index so that it can locate the occ occurrences efficiently in o occ log log n time within o r space by raising the space to o r log log n our index counts the occurrences in optimal time o m and locates them in optimal time as well o m occ by further raising the space by an o w log factor where is the alphabet size and w e log n is the ram machine size in bits we support count and locate in o m log w and o m log w occ time which is optimal in the packed setting and had not been obtained before in compressed space we also describe a structure using o r log n r space that replaces the text and extracts any text substring of length e in the almost optimal time o log n r e log w within that space we similarly provide access to arbitrary suffix array inverse suffix array and longest common prefix array cells in time o log n r and extend these capabilities to full suffix tree functionality typically in o log n r time per operation our experiments show that our o r space index outperforms the space competitive alternatives by 1 2 orders of magnitude in time competitive implementations of the original fm index are outperformed by 1 2 orders of magnitude in space and or 2 3 in time

arens regularity and local reflexivity principle for banach algebras on considere les proprietes des produits de arens et le produit j u en particulier la w continuite on montre qu un automorphisme un antiautomorphisme un multiplicateur de e peuvent etre etendus a e j u avec la meme propriete

terminating observation within matched pairs of subjects in a matched cohort analysis a monte carlo simulation study matched cohort analyses are becoming increasingly popular for estimating treatment effects in observational studies however in the applied biomedical literature analysts and authors are inconsistent regarding whether to terminate follow up among members of a matched set once one member is no longer under observation this paper focused on time to event outcomes and used monte carlo simulation methods to determine the optimal approach we found that the bias of the estimated treatment effect estimate was negligible under both approaches and that the percentage of censoring had no discernible effect on the magnitude of bias the mean model based standard error of the treatment estimate was consistently higher when we terminated observation within matched pairs furthermore the type 1 error rate was consistently lower when we did not terminate follow up within matched pairs in conclusion when the focus was on time to event outcomes we demonstrated that there was no advantage to terminating follow up within matched pairs continuing follow up on each subject until their observation was naturally complete was superior compared with terminating a subject s observation time once its matched pair had ceased to be under observation given the frequency with which these analyses are conducted in the applied literature our results provide important guidance to analysts and applied researchers as to the preferred analytic approach

using a monotone single index model to stabilize the propensity score in missing data problems and causal inference the augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems an important component of this method is the propensity score popular parametric models for the propensity score include the logistic probit and complementary log log models a common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables to avoid the need to choose a model we model the propensity score via a semiparametric single index model in which the score is an unknown monotonic nondecreasing function of the given single index under this new model the augmented inverse weighting estimator aiwe of the mean of the response is asymptotically linear semiparametrically efficient and more robust than existing estimators moreover we have made a surprising observation the inverse probability weighting and aiwes based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model a heuristic explanation of this phenomenon is provided a real data example is used to illustrate the proposed methods

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

document listing on repetitive collections with guaranteed performance abstract we consider document listing on string collections that is finding in which strings a given pattern appears in particular we focus on repetitive collections a collection of size n over alphabet 1 is composed of d copies of a string of size n and s edits are applied on ranges of copies we introduce the first document listing index with size o n s precisely o n lg s lg 2 n lg d bits and with useful worst case time guarantees given a pattern of length m the index reports the ndoc 0 strings where it appears in time o m lg 1 n ndoc for any constant 0 and tells in time o m lg n if ndoc 0 our technique is to augment a range data structure that is commonly used on grammar based indexes so that instead of retrieving all the pattern occurrences it computes useful summaries on them we show that the idea has independent interest we introduce the first grammar based index that on a text t 1 n with a grammar of size r uses o r lg n bits and counts the number of occurrences of a pattern p 1 m in time o m 2 m lg 2 r for any constant 0 we also give the first index using o z lg n z lg n bits where t is parsed by lempel ziv into z phrases counting occurrences in time o m lg 2 n

approximation of grammar based compression via recompression in this paper we present a simple linear time algorithm constructing a context free grammar of size o g log n g for the input string where n is the size of the input string and g the size of the optimal grammar generating this string the algorithm works for arbitrary size alphabets but the running time is linear assuming that the alphabet of the input string can be identified with numbers from 1 n c for some constant c otherwise additional cost of o n log is needed algorithms with such an approximation guarantee and running time are known the novelty of this paper is a particular simplicity of the algorithm as well as the analysis of the algorithm which uses a general technique of recompression recently introduced by the author furthermore contrary to the previous results this work does not use the lz representation of the input string in the construction nor in the analysis

on the compressibility of finite languages and formal proofs abstract we consider the minimal number of productions needed for a grammar to cover a finite language l as the grammatical complexity of l we study this measure for several types of word and tree grammars and show that it is closely connected to well known measures for the complexity of formal proofs in first order predicate logic we construct an incompressible sequence of finite word languages and transfer this and several other results about the complexity of word and tree languages to formal proofs

a comparison of regression trees logistic regression generalized additive models and multivariate adaptive regression splines for predicting ami mortality clinicians and health service researchers are frequently interested in predicting patient specific probabilities of adverse events e g death disease recurrence post operative complications hospital readmission there is an increasing interest in the use of classification and regression trees cart for predicting outcomes in clinical studies we compared the predictive accuracy of logistic regression with that of regression trees for predicting mortality after hospitalization with an acute myocardial infarction ami we also examined the predictive ability of two other types of data driven models generalized additive models gams and multivariate adaptive regression splines mars we used data on 9484 patients admitted to hospital with an ami in ontario we used repeated split sample validation the data were randomly divided into derivation and validation samples predictive models were estimated using the derivation sample and the predictive accuracy of the resultant model was assessed using the area under the receiver operating characteristic roc curve in the validation sample this process was repeated 1000 times the initial data set was randomly divided into derivation and validation samples 1000 times and the predictive accuracy of each method was assessed each time the mean roc curve area for the regression tree models in the 1000 derivation samples was 0 762 while the mean roc curve area of a simple logistic regression model was 0 845 the mean roc curve areas for the other methods ranged from a low of 0 831 to a high of 0 851 our study shows that regression trees do not perform as well as logistic regression for predicting mortality following ami however the logistic regression model had performance comparable to that of more flexible data driven models such as gams and mars

reducing bias in observational studies using subclassification on the propensity score abstract the propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates subclassification on an estimated propensity score is illustrated using observational data on treatments for coronary artery disease five subclasses defined by the estimated propensity score are constructed that balance 74 covariates and thereby provide estimates of treatment effects using direct adjustment these subclasses are applied within sub populations and model based adjustments are then used to provide estimates of treatment effects within these sub populations two appendixes address theoretical issues related to the application the effectiveness of subclassification on the propensity score in removing bias and balancing properties of propensity scores with incomplete data

the similarity metric a new class of distances appropriate for measuring similarity relations between sequences say one type of similarity per distance is studied we propose a new normalized information distance based on the noncomputable notion of kolmogorov complexity and show that it is in this class and it minorizes every computable distance in the class that is it is universal in that it discovers all computable similarities we demonstrate that it is a metric and call it the similarity metric this theory forms the foundation for a new practical tool to evidence generality and robustness we give two distinctive applications in widely divergent areas using standard compression programs like gzip and gencompress first we compare whole mitochondrial genomes and infer their evolutionary history this results in a first completely automatic computed whole mitochondrial phylogeny tree secondly we fully automatically compute the language tree of 52 different languages

approximation of smallest linear tree grammar a simple linear time algorithm for constructing a linear context free tree grammar of size o r g r g log n r g for a given input tree t of size n is presented where g is the size of a minimal linear context free tree grammar for t and r is the maximal rank of symbols in t which is a constant in many applications this is the first example of a grammar based tree compression algorithm with a good i e logarithmic in terms of the size of the input tree approximation ratio the analysis of the algorithm uses an extension of the recompression technique from strings to trees

balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity score matched samples the propensity score is a subject s probability of treatment conditional on observed baseline covariates conditional on the true propensity score treated and untreated subjects have similar distributions of observed baseline covariates propensity score matching is a popular method of using the propensity score in the medical literature using this approach matched sets of treated and untreated subjects with similar values of the propensity score are formed inferences about treatment effect made using propensity score matching are valid only if in the matched sample treated and untreated subjects have similar distributions of measured baseline covariates in this paper we discuss the following methods for assessing whether the propensity score model has been correctly specified comparing means and prevalences of baseline characteristics using standardized differences ratios comparing the variance of continuous covariates between treated and untreated subjects comparison of higher order moments and interactions five number summaries and graphical methods such as quantile quantile plots side by side boxplots and non parametric density plots for comparing the distribution of baseline covariates between treatment groups we describe methods to determine the sampling distribution of the standardized difference when the true standardized difference is equal to zero thereby allowing one to determine the range of standardized differences that are plausible with the propensity score model having been correctly specified we highlight the limitations of some previously used methods for assessing the adequacy of the specification of the propensity score model in particular methods based on comparing the distribution of the estimated propensity score between treated and untreated subjects are uninformative

bilinear mappings and trace class ideals in a recent paper 14 redheffer and volkmann investigated the norms of bilinear maps n cp n cq cr they had been motivated by previous work 12 13 on a classical result of schur concerning a special bilinear form on hilbert space the purpose of this paper is to sharpen the main results in 14 and to resolve the questions left open in 14 the new ingredients we use to tackle these problems are interpolation theory for trace class ideals nehari s theorem on hankel operators the rudin shapiro polynomials and a factorisation result of pisier

linear work suffix array construction suffix trees and suffix arrays are widely used and largely interchangeable index structures on strings and sequences practitioners prefer suffix arrays due to their simplicity and space efficiency while theoreticians use suffix trees due to linear time construction algorithms and more explicit structure we narrow this gap between theory and practice with a simple linear time construction algorithm for suffix arrays the simplicity is demonstrated with a c implementation of 50 effective lines of code the algorithm is called dc3 which stems from the central underlying concept of difference cover this view leads to a generalized algorithm dc that allows a space efficient implementation and moreover supports the choice of a space time tradeoff for any v 1 n it runs in o vn time using o n v space in addition to the input string and the suffix array we also present variants of the algorithm for several parallel and hierarchical memory models of computation the algorithms for bsp and erew pram models are asymptotically faster than all previous suffix tree or array construction algorithms

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

on variance estimate for covariate adjustment by propensity score analysis propensity score ps methods have been used extensively to adjust for confounding factors in the statistical analysis of observational data in comparative effectiveness research there are four major ps based adjustment approaches ps matching ps stratification covariate adjustment by ps and ps based inverse probability weighting though covariate adjustment by ps is one of the most frequently used ps based methods in clinical research the conventional variance estimation of the treatment effects estimate under covariate adjustment by ps is biased as stampf et al have shown this bias in variance estimation is likely to lead to invalid statistical inference and could result in erroneous public health conclusions e g food and drug safety and adverse events surveillance to address this issue we propose a two stage analytic procedure to develop a valid variance estimator for the covariate adjustment by ps analysis strategy we also carry out a simple empirical bootstrap resampling scheme both proposed procedures are implemented in an r function for public use extensive simulation results demonstrate the bias in the conventional variance estimator and show that both proposed variance estimators offer valid estimates for the true variance and they are robust to complex confounding structures the proposed methods are illustrated for a post surgery pain study copyright 2016 john wiley sons ltd

should a propensity score model be super the utility of ensemble procedures for causal adjustment in investigations of the effect of treatment on outcome the propensity score is a tool to eliminate imbalance in the distribution of confounding variables between treatment groups recent work has suggested that super learner an ensemble method outperforms logistic regression in nonlinear settings however experience with real data analyses tends to show overfitting of the propensity score model using this approach we investigated a wide range of simulated settings of varying complexities including simulations based on real data to compare the performances of logistic regression generalized boosted models and super learner in providing balance and for estimating the average treatment effect via propensity score regression propensity score matching and inverse probability of treatment weighting we found that super learner and logistic regression are comparable in terms of covariate balance bias and mean squared error mse however super learner is computationally very expensive thus leaving no clear advantage to the more complex approach propensity scores estimated by generalized boosted models were inferior to the other two estimation approaches we also found that propensity score regression adjustment was superior to either matching or inverse weighting when the form of the dependence on the treatment on the outcome is correctly specified

adjusted restricted mean survival times in observational studies in observational studies with censored data exposure outcome associations are commonly measured with adjusted hazard ratios from multivariable cox proportional hazards models the difference in restricted mean survival times rmsts up to a pre specified time point is an alternative measure that offers a clinically meaningful interpretation several regression based methods exist to estimate an adjusted difference in rmsts but they digress from the model free method of taking the area under the survival function we derive the adjusted rmst by integrating an adjusted kaplan meier estimator with inverse probability weighting ipw the adjusted difference in rmsts is the area between the two ipw adjusted survival functions in a monte carlo type simulation study we demonstrate that the proposed estimator performs as well as two regression based approaches the ancova type method of tian et al and the pseudo observation method of andersen et al we illustrate the methods by reexamining the association between total cholesterol and the 10 year risk of coronary heart disease in the framingham heart study

two step estimation of semiparametric censored regression models root n consistent estimators of the regression coecients in the linear censored regression model under conditional quantile restrictions on the error terms were pro posed by powell journal of econometrics 25 1984 303 325 32 1986a 143 155 while those estimators have desirable asymptotic properties under weak regularity conditions simulation studies have shown these estimators to exhibit a small sam ple bias in the opposite direction of the least squares bias for censored data this paper introduces two step estimators for these models which minimize convex objec tive functions and are designed to overcome thisnite sample bias the paper gives regularity conditions under which the proposed two step estimators are consistent and asymptotically normal a monte carlo study compares thenite sample behavior of the proposed methods with their one step counterparts 2001 elsevier science s a all rights reserved

effects and non effects of paired identical observations in comparing proportions with binary matched pairs data binary matched pairs data occur commonly in longitudinal studies such as in cross over experiments many analyses for comparing the matched probabilities of a particular outcome do not utilize pairs having the same outcome for each observation an example is mcnemar s test some methodologists find this to be counterintuitive we review this issue in the context of subject specific and population averaged models for binary data with various link functions for standard models and inferential methods pairs with identical outcomes may affect the estimated size of the effect and its standard error but they have negligible if any effect on significance we also discuss extension of this result to matched sets

matching and semi parametric iv estimation a distance based measure of migration and the wages of young men abstract our paper estimates the effect of us internal migration on wage growth for young men between their first and second job our analysis of migration extends previous research by i exploiting the distance based measures of migration in the national longitudinal surveys of youth 1979 nlsy79 ii allowing the effect of migration to differ by schooling level and iii using propensity score matching to estimate the average treatment effect on the treated atet for movers and iv using local average treatment effect late estimators with covariates to estimate the average treatment effect ate and atet for compliers we believe the conditional independence assumption cia is reasonable for our matching estimators since the nlsy79 provides a relatively rich array of variables on which to match our matching methods are based on local linear local cubic and local linear ridge regressions local linear and local ridge regression matching produce relatively similar point estimates and standard errors while local cubic regression matching badly over fits the data and provides very noisy estimates we use the bootstrap to calculate standard errors since the validity of the bootstrap has not been investigated for the matching estimators we use and has been shown to be invalid for nearest neighbor matching estimators we conduct a monte carlo study on the appropriateness of using the bootstrap to calculate standard errors for local linear regression matching the data generating processes in our monte carlo study are relatively rich and calibrated to match our empirical models or to test the sensitivity of our results to the choice of parameter values the estimated standard errors from the bootstrap are very close to those from the monte carlo experiments which lends support to our using the bootstrap to calculate standard errors in our setting from the matching estimators we find a significant positive effect of migration on the wage growth of college graduates and a marginally significant negative effect for high school dropouts we do not find any significant effects for other educational groups or for the overall sample our results are generally robust to changes in the model specification and changes in our distance based measure of migration we find that better data matters if we use a measure of migration based on moving across county lines we overstate the number of moves while if we use a measure based on moving across state lines we understate the number of moves further using either the county or state measures leads to much less precise estimates we also consider semi parametric late estimators with covariates frolich 2007 using two sets of instrumental variables we precisely estimate the proportion of compliers in our data but because we have a small number of compliers we cannot obtain precise late estimates

recompression a simple and powerful technique for word equations in this article we present an application of a simple technique of local recompression previously developed by the author in the context algorithms for compressed strings jez 2014a 2015b 2015a to word equations the technique is based on local modification of variables replacing x by ax or xa and iterative replacement of pairs of letters occurring in the equation by a fresh letter which can be seen as a bottom up compression of the solution of the given word equation or to be more specific building a straight line programme for the solution of the word equation using this technique we give new independent and self contained proofs of many known results for word equations to be more specific the presented nondeterministic algorithm runs in o n log n space and in time polynomial in n and log n where n is the size of the input equation and n the size of the length minimal solution of the word equation furthermore for o 1 variables the bound on the space consumption is in fact linear that is o m where m is the size of the space used by the input this yields that for each k the set of satisfiable word equations with k variables is context sensitive the presented algorithm can be easily generalised to a generator of all solutions of the given word equation without increasing the space usage furthermore a further analysis of the algorithm yields an independent proof of doubly exponential upper bound on the size of the length minimal solution the presented algorithm does not use exponential bound on the exponent of periodicity conversely the analysis of the algorithm yields an independent proof of the exponential bound on exponent of periodicity

inference in linear regression models with many covariates and heteroskedasticity the linear regression model is widely used in empirical work in economics statistics and many other disciplines researchers often include many covariates in their linear model specification in a

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size

comparison of drug dissolution profiles a proposal based on tolerance limits meaningful comparison of the dissolution profiles between the reference and test formulations of a drug is critical for assessing similarity between the two formulations and for quality control purposes such a dissolution profile comparison is required by regulatory authorities and the criteria used for this include the widely used difference factor f1 and a similarity factor f2 recommended by the food and drug administration in spite of their extensive use in practice the two factors have been heavily criticized on various grounds the criticisms include ignoring sampling variability and ignoring the correlations across time points while using the criteria in practice the goal of this article is to put f1 and f2 on a firm statistical footing by developing tolerance limits for the distributions of f1 and f2 so that both the sampling variability and the correlations over time points are taken into account because f1 and f2 are defined in terms of sample mean dissolution profiles they are not appropriate for comparing individual dissolution profiles for the latter we have considered similar criteria and have derived tolerance limits both parametric and nonparametric approaches are explored and a bootstrap calibration is used to improve accuracy of the tolerance limits simulated coverage probabilities show that the method leads to accurate tolerance limits two examples are used to illustrate the methodology copyright 2016 john wiley sons ltd

affinely invariant matching methods with discriminant mixtures of proportional ellipsoidally symmetric distributions in observational studies designed to estimate the effects of interventions or exposures such as cigarette smoking it is desirable to try to control background differences between the treated group e g current smokers and the control group e g never smokers on covariates x e g age education matched sampling attempts to effect this control by selecting subsets of the treated and control groups with similar distributions of such covariates this paper examines the consequences of matching using affinely invariant methods when the covariate distributions are discriminant mixtures of proportional ellipsoidally symmetric dmpes distributions a class herein defined which generalizes the ellipsoidal symmetry class of rubin and thomas ann statist 20 1992 1079 1093 the resulting generalized results help indicate why earlier results hold quite well even when the simple assumption of ellipsoidal symmetry is not met e g biometrics 52 1996 249 264 extensions to conditionally affinely invariant matching with conditionally dmpes distributions are also discussed

control of confounding through secondary samples the control of confounding is essential in many statistical problems especially in those that attempt to estimate exposure effects in some cases in addition to the primary sample there is another secondary sample which though having no direct information about the exposure effect contains information about the confounding factors the purpose of this article is to study the influence of the secondary sample on likelihood inference for the exposure effect in particular we investigate the interplay between the efficiency improvement and the possible bias introduced by the secondary sample as a function of the degree of confounding in the primary sample and the sizes of the primary and secondary samples in the case of weak confounding the secondary sample can only little improve estimation of the exposure effect whereas with strong confounding the secondary sample can be much more useful on the other hand it will be more important to consider possible biasing effects in the latter case for illustration we use a formal example of a generalized linear model and a real example with sparse data from a case control study of the association between gastric cancer and hm cap band 120