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

covariate imbalance and conditional size dependence on model based adjustments analysis of covariance ancova is frequently recommended to correct for covariate imbalance and to control conditional size of hypothesis tests in randomized designs such control however depends on the accuracy of the ancova model used to make the adjustments examination of residuals together with knowledge of the subject matter are important for obtaining an accurate model stratified assignment procedures lessen the dependence of proper control of conditional size on the specific model used in the adjustment procedure

nonparametric two sample comparisons of changes on ordinal responses abstract we discuss two armed clinical trials in which an ordinal response is observed on entry and at follow up in certain subject areas such data are often reduced to the counts of patients who have deteriorated remained the same or improved we develop asymptotic distribution theory to compare this approach to the use of nonparametric tests based on poststratification of the follow up responses according to the entry levels the theory for the latter approach is established by a general result for two sample u statistics based on bivariate data application to data from clinical trials and evaluation of asymptotic relative efficiencies and powers for a variety of contexts illustrate the increased sensitivity of poststratified wilcoxon tests

non parametric analysis of covariance for confirmatory randomized clinical trials to evaluate dose response relationships in confirmatory randomized clinical trials that are designed to compare multiple doses of a test treatment with a control group and with one another there are often statistical issues regarding compound hypotheses and multiple comparisons which need to be considered in most cases the analysis plan needs a clear specification for the proposed order for conducting statistical tests or for managing the overall significance level which statistical methods will be used and whether adjustment for covariates will be performed there are several benefits of specifying non parametric analysis of covariance ancova for performing the primary confirmatory analyses only minimal assumptions are needed beyond randomization in the study design whereas regression model based methods have assumptions about model fit for which departures may require modifications that are incompatible with a fully prespecified analysis plan non parametric methods provide traditionally expected results of ancova namely a typically small adjustment to the estimate for a treatment comparison so as to account for random imbalance of covariates between treatment groups and variance reduction for this estimate when covariates are strongly correlated with the response of interest the application of non parametric ancova is illustrated for two randomized clinical trials the first has a 3 x 4 factorial response surface design for the comparison of 12 treatments that is combinations of three doses of one drug and four doses of a second drug for change in blood pressure and the second example addresses the comparison of three doses of test treatment and placebo for time to disease progression this clinical trial has comparisons among treatments made for a dichotomous criterion wilcoxon rank scores and averages of cumulative survival rates in each example the non parametric covariance method provides variance reduction relative to its unadjusted counterpart

conditional permutation tests and the propensity score in observational studies abstract in observational studies the distribution of treatment assignments is unknown and therefore randomization tests are not generally applicable however permutation tests that condition on sample information about the treatment assignment mechanism can be applicable in observational studies provided treatment assignment is strongly ignorable these tests use the conditional distribution of the treatment assignments given a sufficient statistic for the unknown parameter of the propensity score several tests that are commonly used in observational studies are particular instances of this general procedure moreover conditional permutation tests and covariance adjustment are closely related in the sense that the conditional permutation distribution of the covariance adjusted difference leads to the same inferences as the conditional permutation distribution of the unadjusted difference of sample means a backtrack algorithm is developed to permit efficient calculation of the exact conditional si

another look at the regression discontinuity design the attractiveness of the regression discontinuity design rdd rests on its close similarity to a formal experimental design on the other hand it is of limited applicability since it is not often the case that units are assigned to the treatment group on the basis of an observable to the analyst pre program measure besides it only allows to identify the mean impact on a very specific sub population in this paper we show that the rdd straightforwardly generalizes to the instances in which the units eligibility is established on an observable pre program measure with eligible units allowed to freely self select into the program this set up also turns out very convenient to build a specification test on conventional non experimental estimators of the program mean impact data requirements are made explicit

inconsistent treatment estimates from mis specified logistic regression analyses of randomized trials when the difference between treatments in a clinical trial is estimated by a difference in means then it is well known that randomization ensures unbiassed estimation even if no account is taken of important baseline covariates however when the treatment effect is assessed by other summaries for example by an odds ratio if the outcome is binary then bias can arise if some covariates are omitted regardless of the use of randomization for treatment allocation or the size of the trial we present accurate closed form approximations for this asymptotic bias when important normally distributed covariates are omitted from a logistic regression we compare this approximation with ones in the literature and derive more convenient forms for some of these existing results the expressions give insight into the form of the bias which simulations show is usable for distributions other than the normal the key result applies even when there are additional binary covariates in the model

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

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

the impact of covariate adjustment at randomization and analysis for binary outcomes understanding differences between superiority and noninferiority trials the question of when to adjust for important prognostic covariates often arises in the design of clinical trials and there remain various opinions on whether to adjust during both randomization and analysis at randomization alone or at analysis alone furthermore little is known about the impact of covariate adjustment in the context of noninferiority ni designs the current simulation based research explores this issue in the ni setting as compared with the typical superiority setting by assessing the differential impact on power type i error and bias in the treatment estimate as well as its standard error in the context of logistic regression under both simple and covariate adjusted permuted block randomization algorithms in both the superiority and ni settings failure to adjust for covariates that influence outcome in the analysis phase regardless of prior adjustment at randomization results in treatment estimates that are biased toward zero with standard errors that are deflated however as no treatment difference is approached under the null hypothesis in superiority and under the alternative in ni this results in decreased power and nominal or conservative deflated type i error in the context of superiority but inflated power and type i error under ni results from the simulation study suggest that regardless of the use of the covariate in randomization it is appropriate to adjust for important prognostic covariates in analysis as this yields nearly unbiased estimates of treatment as well as nominal type i error

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

dependence on parameters for a discrete emden fowler equation abstract we investigate the dependence on parameters for the discrete boundary value problem connected with the emden fowler equation a variational method is used in order to obtain a general scheme allowing for investigating the dependence on parameters of discrete boundary value problems

code construction and decoding algorithms for semi quantitative group testing with nonuniform thresholds we analyze a new group testing scheme termed semi quantitative group testing which may be viewed as a concatenation of an adder channel and a discrete quantizer our focus is on non uniform quantizers with arbitrary thresholds for the most general semi quantitative group testing model we define three new families of sequences capturing the constraints on the code design imposed by the choice of the thresholds the sequences represent extensions and generalizations of b h and certain types of super increasing and lexicographically ordered sequences and they lead to code structures amenable for efficient recursive decoding we describe the decoding methods and provide an accompanying computational complexity and performance analysis

randomization matching and propensity scores in the design and analysis of experimental studies with measured baseline covariates in many experimental situations researchers have information on a number of covariates prior to randomization this information can be used to balance treatment assignment with respect to these covariates as well as in the analysis of the outcome data in this paper we investigate the use of propensity scores in both of these roles we also introduce a randomization procedure in which the balance of all measured covariates is approximately indexed by the variance of the empirical propensity scores and randomization is restricted to those permutations with the least variable propensity scores this procedure is compared with recently proposed methods in terms of resulting covariate balance and estimation efficiency properties of the estimators resulting from each procedure are compared with estimates which incorporate the propensity score in the analysis stage simulation results show that analytical adjustment for the propensity score yields results on par with those obtained through restricted randomization procedures and can be used in conjunction with such procedures to further improve inferential efficiency

a note on non parametric ancova for covariate adjustment in randomized clinical trials koch et al recently 1998 proposed two covariate adjusted approaches for the comparison of continuous ordinal and binary responses in a randomized clinical trial statist med 1998 17 1863 1892 the first is a randomization approach while the second assumes that the study is a sample of a population here we study the second approach and consider the simplest cases of two treatments with a continuous response and with a binary response koch s second approach will be compared with the classical ancova for a continuous response from this relationship we demonstrate that koch s method cannot preserve the probability of the type i error simulations with continuous responses as well as with binary outcomes confirm the aforementioned theoretical result on the performance of koch s method under the null hypothesis of no treatment effect however this poses only a problem for relatively small to moderate sample sizes further as specified in the original paper of koch et al the first approach does preserve the type i error for any sample size as the p values can be reported in an exact manner statist med 1998 17 1863 1892 finally we propose a correction factor for koch s test statistic that better preserves the type i error copyright c 2003 john wiley sons ltd

non parametric covariance methods for incidence density analyses of time to event data from a randomized clinical trial and their complementary roles to proportional hazards regression the principal response criteria for many clinical trials involve time to event variables usual methods of analysis for this type of response criterion include product limit estimators of cumulative survival for the treatment groups stratified logrank tests to compare treatments and proportional hazards regression models with treatment and relevant covariates when adjustment for covariates is of some importance the relative roles of these methods may be of some concern particularly for confirmatory clinical trials which must provide convincing findings to regulatory agencies unadjusted methods may have lower power but there are issues regarding adjustment for covariates that may be controversial these issues include applicability of proportional hazards assumptions whether the correct model has been specified and whether there is parallelism between treatments for relationships with covariates one way to address these issues is to use non parametric analysis of covariance strategies with extensions to log incidence density estimation the principal basis for this method is no association between covariates and treatment groups as provided by randomized assignment of patients to groups the background theory and strategies for computation are described for this method aspects of its application are illustrated for a clinical trial with two treatment groups and 722 patients the objective of analysis for this clinical trial is evaluation of treatment effects with and without adjustment for 22 a priori covariates and a stratification for three geographical regions

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

optimal probability weights for inference with constrained precision abstractprobability weights are used in many areas of research including complex survey designs missing data analysis and adjustment for confounding factors they are useful analytic tools but can lead to statistical inefficiencies when they contain outlying values this issue is frequently tackled by replacing large weights with smaller ones or by normalizing them through smoothing functions while these approaches are practical they are also prone to yield biased inferences this article introduces a method for obtaining optimal weights defined as those with smallest euclidean distance from target weights among all sets of weights that satisfy a constraint on the variance of the resulting weighted estimator the optimal weights yield minimum bias estimators among all estimators with specified precision the method is based on solving a constrained nonlinear optimization problem whose lagrange multipliers and objective function can help assess the trade off between bias and precision of the resulting

superimposed codes in r sup n the authors introduce the concept of superimposed codes in euclidean n space r sup n an asymptotic existence bound is derived for such codes the proof uses the idea of random coding in particular the asymptotic properties of long codes are studied it is shown that the derived existence bound differs only by a factor of four from a nonexistence bound obtained by a simple sphere packing argument

adjusting treatment effect estimates by post stratification in randomized experiments summary experimenters often use post stratification to adjust estimates post stratification is akin to blocking except that the number of treated units in each stratum is a random variable because stratification occurs after treatment assignment we analyse both post stratification and blocking under the neyman rubin model and compare the efficiency of these designs we derive the variances for a post stratified estimator and a simple difference in means estimator under different randomization schemes post stratification is nearly as efficient as blocking the difference in their variances is of the order of 1 n2 with a constant depending on treatment proportion post stratification is therefore a reasonable alternative to blocking when blocking is not feasible however in finite samples post stratification can increase variance if the number of strata is large and the strata are poorly chosen to examine why the estimators variances are different we extend our results by conditioning on the observed number of treated units in each stratum conditioning also provides more accurate variance estimates because it takes into account how close or far a realized random sample is from a comparable blocked experiment we then show that the practical substance of our results remains under an infinite population sampling model finally we provide an analysis of an actual experiment to illustrate our analytical results

nonlinear difference equations investigated via critical point methods abstract the multiplicity of solutions for nonlinear difference equations involving the p laplacian is investigated the approach is based on critical point theorems in the setting of finite dimensional banach spaces

comparisons of minimization and atkinson s algorithm some general points regarding efficiency in clinical trials are made reasons as to why fitting many covariates to adjust the estimate of the treatment effect may be less problematic than commonly supposed are given two methods of dynamic allocation of patients based on covariates minimization and atkinson s approach are compared and contrasted for the particular case where all covariates are binary the results of monte carlo simulations are also presented it is concluded that in the cases considered atkinson s approach is slightly more efficient than minimization although the difference is unlikely to be very important in practice both are more efficient than simple randomization although it is concluded that fitting covariates may make a more valuable and instructive contribution to inferences about treatment effects than only balancing them

superimposed codes for the multiaccess binary adder channel superimposed codes for multiple access communication in a binary adder channel are analyzed the superposition mechanism used in this correspondence is ordinary addition each user is assigned a codeword from a superimposed code it is proved that every constant weight code c of weight w and maximal correlation c corresponds to a subclass of a disjunctive code d of order m

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

ineligibles and eligible non participants as a double comparison group in regression discontinuity designs in a sharp regression discontinuity design rdd the participation status deterministically depends on whether a pre programme characteristic is above or below a specified threshold the attractiveness of such a design rests on close similarities with a formal experiment nevertheless it is of limited applicability since participation into a programme is seldom determined according to this rule besides in the presence of heterogeneous effects a sharp rdd only allows identification of mean effects for individuals around the threshold for participation two results are presented in this paper and they both partially overcome the two limitations described above we show that when individuals self select into participation conditional on some eligibility criteria a sharp rdd provides a natural framework to define a specification test for the non experimental estimation of programme effects for participants away from the threshold we also show that in this set up the regularity conditions required for the identification of the mean counterfactual outcome for participants marginally eligible for the programme are essentially the same as in a sharp rdd

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

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

poisson group testing a probabilistic model for boolean compressed sensing we introduce a novel probabilistic group testing framework termed poisson group testing in which the number of defectives follows a right truncated poisson distribution the poisson model has a number of new applications including dynamic testing with diminishing relative rates of defectives we consider both nonadaptive and semi adaptive identification methods for nonadaptive methods we derive a lower bound on the number of tests required to identify the defectives with a probability of error that asymptotically converges to zero in addition we propose test matrix constructions for which the number of tests closely matches the lower bound for semiadaptive methods we describe a lower bound on the expected number of tests required to identify the defectives with zero error probability in addition we propose a stage wise reconstruction algorithm for which the expected number of tests is only a constant factor away from the lower bound the methods rely only on an estimate of the average number of defectives rather than on the individual probabilities of subjects being defective

on efficiency of constrained longitudinal data analysis versus longitudinal analysis of covariance in randomized clinical trials measurements are often collected on each subject at a baseline visit and several post randomization time points the longitudinal analysis of covariance in which the postbaseline values form the response vector and the baseline value is treated as a covariate can be used to evaluate the treatment differences at the postbaseline time points liang and zeger 2000 sankhy the indian journal of statistics series b 62 134 148 propose a constrained longitudinal data analysis in which the baseline value is included in the response vector together with the postbaseline values and a constraint of a common baseline mean across treatment groups is imposed on the model as a result of randomization if the baseline value is subject to missingness the constrained longitudinal data analysis is shown to be more efficient for estimating the treatment differences at postbaseline time points than the longitudinal analysis of covariance the efficiency gain increases with the number of subjects missing baseline and the number of subjects missing all postbaseline values and for the pre post design decreases with the absolute correlation between baseline and postbaseline values

covariance analysis in generalized linear measurement error models we summarize some of the recent work on the errors in variables problem in generalized linear models the focus is on covariance analysis and in particular testing for and estimation of treatment effects there is a considerable difference between the randomized and non randomized models when testing for an effect in randomized studies simple techniques exist for testing for a treatment effect in some instances such as linear and multiplicative regression simple methods exist for estimating the treatment effect in other examples such as logistic regression estimating a treatment effect requires careful attention to measurement error in non randomized studies there is no recourse to understanding and modelling measurement error in particular ignoring measurement error can lead to the wrong conclusions for example the true but unobserved data may indicate a positive effect for treatment while the observed data indicate the opposite some of the possible methods are outlined and compared

a family of k 1 ary signature codes for noisy multiple access adder channel a coding scheme of k 1 ary error correcting signature codes for a noisy multiple access adder channel is proposed given a signature matrix a and a difference matrix d d d a priori a larger signature matrix is obtained by replacing each element in the hadamard matrix with a or d or d depending on the values of the elements and their locations in the hadamard matrix the set of rows in the proposed matrix gives an error correcting signature code introducing a difference matrix makes it possible to construct an error correcting signature code whose sum rate is increased with an increase in the order of the hadamard matrix either binary or non binary signature codes are constructed when the pairs of matrices a and d are given

some aspects of analysis of covariance an account from first principles is given of a number of aspects of analysis of covariance six different meanings of analysis of covariance are outlined and the history of this technique is sketched briefly the development of the key formulae from the method of least squares is described and generalizations to other distributions in the exponential family are mentioned special problems of application in randomized experiments and in observational studies are discussed finally the decomposition of regression relations is considered along with components of covariance

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

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

existence of solutions for some discrete boundary value problems with a parameter in this paper the existence and multiplicity results of solutions are obtained for the discrete nonlinear two point boundary value problem bvp email protected 2u k 1 email protected k u k email protected z 1 t u 0 email protected t where t is a positive integer z 1 t 1 2 t d is the forward difference operator defined by du k u k 1 u k and f z 1 t xr r is continuous email protected r is a parameter by using the critical point theory and morse theory we obtain that the above bvp has solutions for l being in some different intervals

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

should baseline be a covariate or dependent variable in analyses of change from baseline in clinical trials in randomized clinical trials a pre treatment measurement is often taken at baseline and post treatment effects are measured at several time points post baseline say t 1 t at the end of the trial it is of interest to assess the treatment effect based on the mean change from baseline at the last time point t we consider statistical methods for i a point estimate and 95 per cent confidence interval for the mean change from baseline at time t for each treatment group and ii a p value and 95 per cent confidence interval for the between group difference in the mean change from baseline the manner in which the baseline responses are used in the analysis influences both the accuracy and the efficiency of items i and ii in this paper we will consider the ancova approach with change from baseline as a dependent variable and compare that with a constrained longitudinal data analysis clda model proposed by liang and zeger sankhya indian j stat ser b 2000 62 134 148 in which the baseline is modeled as a dependent variable in conjunction with the constraint of a common baseline mean across the treatment groups some drawbacks of the ancova model and potential advantages of the clda approach are discussed and illustrated using numerical simulations copyright 2009 john wiley sons ltd

constructive proof for existence of nonlinear two point boundary value problems owing to the importance of differential equations in physics the existence of solutions for differential equations has been paid much attention in this paper the existence of solution are obtained for the nonlinear second order two point boundary value problem in the reproducing kernel space under certain assumptions on right hand side we propose constructive proof for the existence result and a method is presented to obtain the exact solution expressed by the form of series this paper is a extension of previous paper wei jiang minggen cui the exact solution and stability analysis for integral equation of third or first kind with singular kernel appl math comput 202 2 2008 666 674 which extends a method of solving linear problems to present method for solving nonlinear problems

moving beyond the conventional stratified analysis to estimate an overall treatment efficacy with the data from a comparative randomized clinical study for a two group comparative study a stratified inference procedure is routinely used to estimate an overall group contrast to increase the precision of the simple two sample estimator unfortunately most commonly used methods including the cochran mantel haenszel statistic for a binary outcome and the stratified cox procedure for the event time endpoint do not serve this purpose well in fact these procedures may be worse than their two sample counterparts even when the observed treatment allocations are imbalanced across strata various procedures beyond the conventional stratified methods have been proposed to increase the precision of estimation when the naive estimator is consistent in this paper we are interested in the case when the treatment allocation proportions vary markedly across strata we study the stochastic properties of the two sample naive estimator conditional on the ancillary statistics the observed treatment allocation proportions and or the stratum sizes and present a biased adjusted estimator this adjusted estimator is asymptotically equivalent to the augmentation estimators proposed under the unconditional setting moreover this consistent estimation procedure is also equivalent to a rather simple procedure which estimates the mean response of each treatment group first via a stratum size weighted average and then constructs the group contrast estimate this simple procedure is flexible and readily applicable to any target patient population by choosing appropriate stratum weights all the proposals are illustrated with the data from a cardiovascular clinical trial whose treatment allocations are imbalanced

methods for assessing difference between groups in change when initial measurement is subject to intra individual variation statistical analysis of difference between groups in change for some variable adjusting for initial value is complicated by the presence of intra individual variation in that variable we estimate here the asymptotic bias that results from calculating the adjusted between group difference by ordinary least squares ols from observed data we also present explicit formulae that use the ols estimates the difference between treatment groups in mean initial values and a measure of the intra individual variation to compute a corrected estimator and its variance alternatively we can use ols on transformed data to obtain unbiased estimates in which we replace initial observed values by conditional stein estimates of true values we illustrate the results with data from an observational study and a clinical trial

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

spreading set with error correction for multiple access adder channel the necessary and sufficient condition for constructing a spreading set with decodability is investigated it is proved that for a given delta decodable spreading set and a qtimesq square matrix h with components 1 or 1 a qdelta decodable spreading set s is obtained if and only if h is a hadamard matrix in addition a decoding rule with error correction and message data detection is provided

on the dependence on parameters for mountain pass solutions of second order discrete bvp s we investigate the continuous dependence on parameters for the mountain pass solutions of second order discrete equations with p laplacian and dirichlet type boundary conditions we show that assumptions leading to the existence of nontrivial solutions lead also to its continuous dependence on parameters we investigate also the uniqueness of solutions

a note on a partial empirical likelihood a partial profile empirical likelihood for a semiparametric mixture model zou et al 2002 is shown to originate in a conditional likelihood involving additional nuisance parameters the partial likelihood is the conditional likelihood with the nuisance parameters replaced by their estimators from the full likelihood the conditional likelihood suggests alternative estimators we demonstrate that the partial likelihood estimator is more efficient than an estimator for which the nuisance parameters are known the practical implications of this counter intuitive result are discussed

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