causal analysis in the health sciences the final quarter of the twentieth century witnessed a burgeoning of formal methods for the analysis of causal effects of the methods that appeared in the health sciences most can be identified with approaches to causal analysis that originated much earlier in the century in other fields counterfactual potential outcomes models graphical models and structural equations models connections among these approaches were elucidated during the 1990s and the near future may bring a unified methodology for causal analysis this vignette briefly reviews the counterfactual approach to causal analysis in the health sciences its connections to graphical and structural equations approaches its extension to longitudinal data analysis and some areas needing further work for deeper and more extensive reviews i especially recommend sobel s 1995 discussion of the connections among causal concepts in philosophy statistics and social sciences pearl s 2000 unified approach to counterfactual graphical and structural equations models and robins s 1997 review of causal analysis for longitudinal data

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

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

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

randomization inference and sensitivity analysis for composite null hypotheses with binary outcomes in matched observational studies abstractwe present methods for conducting hypothesis testing and sensitivity analyses for composite null hypotheses in matched observational studies when outcomes are binary causal estimands discussed include the causal risk difference causal risk ratio and the effect ratio we show that inference under the assumption of no unmeasured confounding can be performed by solving an integer linear program while inference allowing for unmeasured confounding of a given strength requires solving an integer quadratic program through simulation studies and data examples we demonstrate that our formulation allows these problems to be solved in an expedient manner even for large datasets and for large strata we further exhibit that through our formulation one can assess the impact of various assumptions about the potential outcomes on the performed inference r scripts are provided that implement our methods supplementary materials for this article are available online

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

resampling based multiple testing methods with covariate adjustment application to investigation of antiretroviral drug susceptibility identifying genetic mutations that cause clinical resistance to antiretroviral drugs requires adjustment for potential confounders such as the number of active drugs in a hiv infected patient s regimen other than the one of interest motivated by this problem we investigated resampling based methods to test equal mean response across multiple groups defined by hiv genotype after adjustment for covariates we consider construction of test statistics and their null distributions under two types of model parametric and semiparametric the covariate function is explicitly specified in the parametric but not in the semiparametric approach the parametric approach is more precise when models are correctly specified but suffer from bias when they are not the semiparametric approach is more robust to model misspecification but may be less efficient to help preserve type i error while also improving power in both approaches we propose resampling approaches based on matching of observations with similar covariate values matching reduces the impact of model misspecification as well as imprecision in estimation these methods are evaluated via simulation studies and applied to a data set that combines results from a variety of clinical studies of salvage regimens our focus is on relating hiv genotype to viral susceptibility to abacavir after adjustment for the number of active antiretroviral drugs excluding abacavir in the patient s regimen

an exact distribution free test comparing two multivariate distributions based on adjacency summary a new test is proposed comparing two multivariate distributions by using distances between observations unlike earlier tests using interpoint distances the new test statistic has a known exact distribution and is exactly distribution free the interpoint distances are used to construct an optimal non bipartite matching i e a matching of the observations into disjoint pairs to minimize the total distance within pairs the cross match statistic is the number of pairs containing one observation from the first distribution and one from the second distributions that are very different will exhibit few cross matches when comparing two discrete distributions with finite support the test is consistent against all alternatives the test is applied to a study of brain activation measured by functional magnetic resonance imaging during two linguistic tasks comparing brains that are impaired by arteriovenous abnormalities with normal controls a second exact distribution free test is also discussed it ranks the pairs and sums the ranks of the cross matched pairs

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

substantial gains in bias reduction from matching with a variable number of controls summary in observational studies that match several controls to each treated subject substantially greater bias reduction is possible if the number of controls is not fixed but rather is allowed to vary from one matched set to another in certain cases matching with a fixed number of controls may remove only 50 of the bias in a covariate whereas matching with a variable number of controls may remove 90 of the bias even though both control groups have the same number of controls in total an example of matching in a study of surgical mortality is discussed in detail

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

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

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

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

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

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

confidence intervals for causal parameters consider an unbiased follow up study designed to investigate the causal effect of a dichotomous exposure on a dichotomous disease outcome under a deterministic outcome model a standard 95 per cent binomial confidence interval may fail to cover the causal parameter of interest at the nominal rate when we take the causal parameter to be a parameter associated with the observed study population regardless of whether the observed study population was sampled from a larger superpopulation i propose new interval estimators that in this setting improve upon the performance of the standard binomial confidence interval

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

combining propensity score matching with additional adjustments for prognostic covariates abstract propensity score matching refers to a class of multivariate methods used in comparative studies to construct treated and matched control samples that have similar distributions on many covariates this matching is the observational study analog of randomization in ideal experiments but is far less complete as it can only balance the distribution of observed covariates whereas randomization balances the distribution of all covariates both observed and unobserved an important feature of propensity score matching is that it can be easily combined with model based regression adjustments or with matching on a subset of special prognostic covariates or combinations of prognostic covariates that have been identified as being especially predictive of the outcome variables we extend earlier results by developing approximations for the distributions of covariates in matched samples created with linear propensity score methods for the practically important situation where matching uses both the estimat

from association to causation in observational studies the role of tests of strongly ignorable treatment assignment abstract if treatment assignment is strongly ignorable then adjustment for observed covariates is sufficient to produce consistent estimates of treatment effects in observational studies a general approach to testing this critical assumption is developed and applied to a study of the effects of nuclear fallout on the risk of childhood leukemia r a fisher s advice on the interpretation of observational studies was make your theories elaborate formally make causal theories sufficiently detailed that under the theory strongly ignorable assignment has testable consequences

matching and weighting with functions of error prone covariates for causal inference abstractmatching estimators are commonly used to estimate causal effects in nonexperimental settings covariate measurement error can be problematic for matching estimators when observational treatment groups differ on latent quantities observed only through error prone surrogates we establish necessary and sufficient conditions for matching and weighting with functions of observed covariates to yield unconfounded causal effect estimators generalizing results from the standard i e no measurement error case we establish that in common covariate measurement error settings including continuous variables with continuous measurement error discrete variables with misclassification and factor and item response theory models no single function of the observed covariates computed for all units in a study is appropriate for matching however we demonstrate that in some circumstances it is possible to create different functions of the observed covariates for treatment and control units to construct a va

efficient estimation of average treatment effects using the estimated propensity score we are interested in estimating the average effect of a binary treatment on a scalar outcome if assignment to the treatment is exogenous or unconfounded that is independent of the potential outcomes given covariates biases associated with simple treatmentcontrol average comparisons can be removed by adjusting for differences in the covariates rosenbaum and rubin 1983 show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates although adjusting for differences in the propensity score removes all the bias this can come at the expense of efficiency as shown by hahn 1998 heckman ichimura and todd 1998 and robins mark and newey 1992 we show that weighting by the inverse of a nonparametric estimate of the propensity score rather than the true propensity score leads to an efficient estimate of the average treatment effect we provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score

facilitating score and causal inference trees for large observational studies assessing treatment effects in observational studies is a multifaceted problem that not only involves heterogeneous mechanisms of how the treatment or cause is exposed to subjects known as propensity but also differential causal effects across sub populations we introduce a concept termed the facilitating score to account for both the confounding and interacting impacts of covariates on the treatment effect several approaches for estimating the facilitating score are discussed in particular we put forward a machine learning method called causal inference tree cit to provide a piecewise constant approximation of the facilitating score with interpretable rules cit splits data in such a way that both the propensity and the treatment effect become more homogeneous within each resultant partition causal inference at different levels can be made on the basis of cit together with an aggregated grouping procedure cit stratifies data into strata where causal effects can be conveniently assessed within each besides a feasible way of predicting individual causal effects ice is made available by aggregating ensemble cit models both the stratified results and the estimated ice provide an assessment of heterogeneity of causal effects and can be integrated for estimating the average causal effect ace mean square consistency of cit is also established we evaluate the performance of proposed methods with simulations and illustrate their use with the nsw data in dehejia and wahba 1999 where the objective is to assess the impact of a labor training program the national supportedwork nsw demonstration on post intervention earnings

nonparametric survival estimation using prognostic longitudinal covariates one of the primary problems facing statisticians who work with survival data is the loss of information that occurs with right censored data this research considers trying to recover some of this endpoint information through the use of a prognostic covariate which is measured on each individual we begin by defining a survival estimate which uses time dependent covariates to more precisely get at the underlying survival curves in the presence of censoring this estimate has a smaller asymptotic variance than the usual kaplan meier in the presence of censoring and reduces to the kaplan meier 1958 journal of the american statistical association 53 457 481 in situations where the covariate is not prognostic or no censoring occurs in addition this estimate remains consistent when the incorporated covariate contains information about the censoring process as well as survival information because the kaplan meier estimate is known to be biased in this situation due to informative censoring we recommend use of our estimate

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

multivariate matching methods that are monotonic imbalance bounding we introduce a new monotonic imbalance bounding mib class of matching methods for causal inference with a surprisingly large number of attractive statistical properties mib generalizes and extends in several new directions the only existing class equal percent bias reducing epbr which is designed to satisfy weaker properties and only in expectation we also offer strategies to obtain specific members of the mib class and analyze in more detail a member of this class called coarsened exact matching whose properties we analyze from this new perspective we offer a variety of analytical results and numerical simulations that demonstrate how members of the mib class can dramatically improve inferences relative to epbr based matching methods

using inverse weighting and predictive inference to estimate the effects of time varying treatments on the discrete time hazard we estimate the effects of non randomized time varying treatments on the discrete time hazard using inverse weighting we consider the special monotone pattern of treatment that develops over time as subjects permanently discontinue an initial treatment and assume that treatment selection is sequentially ignorable we use a propensity score in the hazard model to reduce the potential for finite sample bias due to inverse weighting when the number of subjects who discontinue treatment at any given time is small we impose scientific restrictions on the potentially observable discontinuation hazards to improve efficiency we use predictive inference to account for the correlation of the potential hazards when comparing outcomes under different durations of initial treatment

semiparametric regression estimation in the presence of dependent censoring summary we propose a semiparametric estimation procedure for estimating the regression of an outcome y measured at the end of a fixed follow up period on baseline explanatory variables x measured prior to start of follow up in the presence of dependent censoring given x the proposed estimators are consistent when the data are missing at random but not missing completely at random rubin 1976 and do not require full specification of the complete data likelihood specifically we assume that the probability of censoring at time t is independent of the outcome y conditional on the recorded history up to t of a vector of time dependent covariates that are correlated with y our estimators can be used to adjust for dependent censoring and nonrandom noncompliance in randomised trials studying the effect of a treatment on the mean of a response variable of interest even with independent censoring our methods allow the investigator to increase efficiency by exploiting the correlation of the outcome with a vector of time dependent covariates

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

effects attributable to treatment inference in experiments and observational studies with a discrete pivot summary in randomisation and permutation inference pivotal arguments remove the hypothesised treatment effect thereby basing inferences on the null distribution in which the treatment has no effect this is common for instance with additive treatment effects the current paper uses attributable effects to expand substantially the scope of pivotal arguments attributable effects are defined for three cases namely the 2 x 2 contingency table displacement effects and the mann whitney wilcoxon statistic and in each case removing an appropriate attributable effect restores the familiar null randomisation distribution of the associated statistic yielding exact inferences the procedure extends immediately for use in sensitivity analysis in nonrandomised observational studies

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

testing for individual and population equivalence based on the proportion of similar responses this paper focuses on the classical problem of comparison of treatment effects we show that we can base a simple and intuitive approach to comparison of two treatments on the proportion of similar responses this approach is equivalent to the standard comparison of the treatment means in the normal case with equal known variances but is quite different in other cases our approach applies under two different settings testing a null hypothesis of no treatment difference against an alternative hypothesis of a difference and testing the null hypothesis of at least a specific difference against an alternative hypothesis of equivalence we develop our approach both for parallel groups independent samples and cross over paired samples studies the two situations give rise to the known concepts of population and individual equivalence we present a graphical procedure to supplement the method

logistic regression survival analysis and the kaplan meier curve abstract we discuss the use of standard logistic regression techniques to estimate hazard rates and survival curves from censored data these techniques allow the statistician to use parametric regression modeling on censored data in a flexible way that provides both estimates and standard errors an example is given that demonstrates the increased structure that can be seen in a parametric analysis as compared with the nonparametric kaplan meier survival curves in fact the logistic regression estimates are closely related to kaplan meier curves and approach the kaplan meier estimate as the number of parameters grows large

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

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

dealing with limited overlap in estimation of average treatment effects summary estimation of average treatment effects under unconfounded or ignorable treatment assignment is often hampered by lack of overlap in the covariate distributions between treatment groups this lack of overlap can lead to imprecise estimates and can make commonly used estimators sensitive to the choice of specification in such cases researchers have often used ad hoc methods for trimming the sample we develop a systematic approach to addressing lack of overlap we characterize optimal subsamples for which the average treatment effect can be estimated most precisely under some conditions the optimal selection rules depend solely on the propensity score for a wide range of distributions a good approximation to the optimal rule is provided by the simple rule of thumb to discard all units with estimated propensity scores outside the range 0 1 0 9

totally blind channel identification by exploiting guard intervals blind identification techniques estimate the impulse response of a channel by exploiting known finite alphabet or statistical properties of the transmitted symbols alternatively oversampling the output is known to introduce dependencies also exploitable for channel identification this paper proves the feasibility of estimating the channel by relying instead on the short sequences of zeros known as guard intervals or zero padding introduced between transmitted blocks by a number of communication protocols since no property of the transmitted information symbols is assumed the method is called totally blind channel identification it is proved that totally blind channel identification requires only two received blocks to estimate the channel

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

new multivariate tests for assessing covariate balance in matched observational studies we propose new tests for assessing whether covariates in a treatment group and matched control group are balanced in observational studies the tests exhibit high power under a wide range of multivariate alternatives some of which existing tests have little power for the asymptotic permutation null distributions of the proposed tests are studied and the p values calculated through the asymptotic results work well in simulation studies facilitating the application of the test to large data sets the tests are illustrated in a study of the effect of smoking on blood lead levels the proposed tests are implemented in an r package balancecheck

new blind block synchronization for transceivers using redundant precoders this paper studies the blind block synchronization problem in block transmission systems using linear redundant precoders lrp two commonly used lrp systems namely zero padding zp and cyclic prefix cp systems are considered in this paper in particular the block synchronization problem in cp systems is a broader version of timing synchronization problem in the popular orthogonal frequency division multiplexing ofdm systems the proposed algorithms exploit the rank deficiency property of the matrix composed of received blocks when the block synchronization is perfect and use a parameter called repetition index which can be chosen as any positive integer theoretical results suggest advantages in blind block synchronization performances when using a large repetition index furthermore unlike previously reported algorithms which require a large amount of received data the proposed methods with properly chosen repetition indices guarantee correct block synchronization in absence of noise using only two received blocks in zp systems and three in cp systems computer simulations are conducted to evaluate the performances of the proposed algorithms and compare them with previously reported algorithms simulation results not only verify the capability of the proposed algorithms to work with limited received data but also show significant improvements in the block synchronization error rate performance of the proposed algorithms over previously reported algorithms

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

a two step bayesian approach for propensity score analysis simulations and case study a two step bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous bayesian propensity score approaches the corresponding variance estimators are also provided the two step bayesian propensity score is provided for three methods of implementation propensity score stratification weighting and optimal full matching three simulation studies and one case study are presented to elaborate the proposed two step bayesian propensity score approach results of the simulation studies reveal that greater precision in the propensity score equation yields better recovery of the frequentist based treatment effect a slight advantage is shown for the bayesian approach in small samples results also reveal that greater precision around the wrong treatment effect can lead to seriously distorted results however greater precision around the correct treatment effect parameter yields quite good results with slight improvement seen with greater precision in the propensity score equation a comparison of coverage rates for the conventional frequentist approach and proposed bayesian approach is also provided the case study reveals that credible intervals are wider than frequentist confidence intervals when priors are non informative

randomization inference for treatment effects on a binary outcome two methods are developed for constructing randomization based confidence sets for the average effect of a treatment on a binary outcome the methods are nonparametric and require no assumptions about random sampling from a larger population both of the resulting 1 confidence sets are exact in the sense that the probability of containing the true treatment effect is at least 1 both types of confidence sets are also guaranteed to have width no greater than one in contrast a previously proposed asymptotic confidence interval is not exact and may have width greater than one the first approach combines bonferroni adjusted prediction sets for the attributable effects in the treated and untreated the second method entails inverting a permutation test simulations are presented comparing the two randomization based confidence sets with the asymptotic interval as well as the standard wald confidence interval and a commonly used exact interval for the difference in binomial proportions results show for small to moderate sample sizes that the permutation confidence set attains the narrowest width on average among the methods that maintain nominal coverage extensions that allow for stratifying on categorical baseline covariates are also discussed

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

ml estimation of time and frequency offset in ofdm systems we present the joint maximum likelihood ml symbol time and carrier frequency offset estimator in orthogonal frequency division multiplexing ofdm systems redundant information contained within the cyclic prefix enables this estimation without additional pilots simulations show that the frequency estimator may be used in a tracking mode and the time estimator in an acquisition mode

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

robust alternatives to ancova for estimating the treatment effect via a randomized comparative study in comparing two treatments via a randomized clinical trial the analysis of covariance ancova technique is often utilized to estimate an overall treatment effect the ancova is generally perceiv

statistics and causal inference abstract problems involving causal inference have dogged at the heels of statistics since its earliest days correlation does not imply causation and yet causal conclusions drawn from a carefully designed experiment are often valid what can a statistical model say about causation this question is addressed by using a particular model for causal inference holland and rubin 1983 rubin 1974 to critique the discussions of other writers on causation and causal inference these include selected philosophers medical researchers statisticians econometricians and proponents of causal modeling

doubly robust estimation in missing data and causal inference models the goal of this article is to construct doubly robust dr estimators in ignorable missing data and causal inference models in a missing data model an estimator is dr if it remains consistent when either but not necessarily both a model for the missingness mechanism or a model for the distribution of the complete data is correctly specified because with observational data one can never be sure that either a missingness model or a complete data model is correct perhaps the best that can be hoped for is to find a dr estimator dr estimators in contrast to standard likelihood based or nonaugmented inverse probability weighted estimators give the analyst two chances instead of only one to make a valid inference in a causal inference model an estimator is dr if it remains consistent when either a model for the treatment assignment mechanism or a model for the distribution of the counterfactual data is correctly specified because with observational data one can never be sure that a model for the treatment assignment mechanism or a model for the counterfactual data is correct inference based on dr estimators should improve upon previous approaches indeed we present the results of simulation studies which demonstrate that the finite sample performance of dr estimators is as impressive as theory would predict the proposed method is applied to a cardiovascular clinical trial

improving massive experiments with threshold blocking inferences from randomized experiments can be improved by blocking assigning treatment in fixed proportions within groups of similar units however the use of the method is limited by the difficulty in deriving these groups current blocking methods are restricted to special cases or run in exponential time are not sensitive to clustering of data points and are often heuristic providing an unsatisfactory solution in many common instances we present an algorithm that implements a widely applicable class of blocking threshold blocking that solves these problems given a minimum required group size and a distance metric we study the blocking problem of minimizing the maximum distance between any two units within the same group we prove this is a nondeterministic polynomial time hard problem and derive an approximation algorithm that yields a blocking where the maximum distance is guaranteed to be at most four times the optimal value this algorithm runs in o n log n time with o n space complexity this makes it to our knowledge the first blocking method with an ensured level of performance that works in massive experiments whereas many commonly used algorithms form pairs of units our algorithm constructs the groups flexibly for any chosen minimum size this facilitates complex experiments with several treatment arms and clustered data a simulation study demonstrates the efficiency and efficacy of the algorithm tens of millions of units can be blocked using a desktop computer in a few minutes

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