the analysis of rates using poisson regression models models are considered in which the underlying rate at which events occur can be represented by a regression function that describes the relation between the predictor variables and the unknown parameters estimates of the parameters can be obtained by means of iteratively reweighted least squares irls when the events of interest follow the poisson distribution the irls algorithm is equivalent to using the method of scoring to obtain maximum likelihood ml estimates the general poisson regression models include log linear quasilinear and intrinsically nonlinear models the approach considered enables one to concentrate on describing the relation between the dependent variable and the predictor variables through the regression model standard statistical packages that support irls can then be used to obtain ml estimates their asymptotic covariance matrix and diagnostic measures that can be used to aid the analyst in detecting outlying responses and extreme points in the model space applications of these methods to epidemiologic follow up studies with the data organized into a life table type of format are discussed the method is illustrated by using a nonlinear model derived from the multistage theory of carcinogenesis to analyze lung cancer death rates among british physicians who were regular cigarette smokers

regression calibration with more surrogates than mismeasured variables in a recent paper weller ea milton dk eisen ea spiegelman d regression calibration for logistic regression with multiple surrogates for one exposure journal of statistical planning and inference 2007 137 449 461 the authors discussed fitting logistic regression models when a scalar main explanatory variable is measured with error by several surrogates that is a situation with more surrogates than variables measured with error they compared two methods of adjusting for measurement error using a regression calibration approximate model as if it were exact one is the standard regression calibration approach consisting of substituting an estimated conditional expectation of the true covariate given observed data in the logistic regression the other is a novel two stage approach when the logistic regression is fitted to multiple surrogates and then a linear combination of estimated slopes is formed as the estimate of interest applying estimated asymptotic variances for both methods in a single data set with some sensitivity analysis the authors asserted superiority of their two stage approach we investigate this claim in some detail a troubling aspect of the proposed two stage method is that unlike standard regression calibration and a natural form of maximum likelihood the resulting estimates are not invariant to reparameterization of nuisance parameters in the model we show however that under the regression calibration approximation the two stage method is asymptotically equivalent to a maximum likelihood formulation and is therefore in theory superior to standard regression calibration however our extensive finite sample simulations in the practically important parameter space where the regression calibration model provides a good approximation failed to uncover such superiority of the two stage method we also discuss extensions to different data structures copyright 2012 john wiley sons ltd

adjustment for non differential misclassification error in the generalized linear model it is well known that estimates of association between an outcome variable and a set of categorical covariates some of which are measured with misclassification tend to be biased upon application of the usual methods of estimation that ignore the classification error we propose a method to adjust for misclassification in covariates when one applies the generalized linear model in the case where one can observe some true covariates only through surrogates we combine a latent class analysis with the approach to incorporate multiple surrogates into the model we include discussion on the efficacy of repeated measurements which one can view as a special case of multiple surrogates with identical distribution we provide two examples to demonstrate the applicability of the method and the efficacy of multiple replicates for a covariate subject to misclassification in a regression framework

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

measurement errors in the binary instrumental variable model author s jiang z ding p abstract 2019 biometrika trust instrumental variable methods can identify causal effects even when the treatment and outcome are confounded we study the problem of imperfect measurements of the binary instrumental variable treatment and outcome we first consider nondifferential measurement errors that is the mismeasured variable does not depend on other variables given its true value we show that the measurement error of the instrumental variable does not bias the estimate that the measurement error of the treatment biases the estimate away from zero and that the measurement error of the outcome biases the estimate toward zero moreover we derive sharp bounds on the causal effects without additional assumptions these bounds are informative because they exclude zero we then consider differential measurement errors and focus on sensitivity analyses in those settings

global identifiability of linear structural equation models structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables we consider the classical case of linear relationships and additive gaussian noise terms we give a necessary and sufficient condition for global identifiability of the model in terms of a mixed graph encoding the linear structural equations and the correlation structure of the error terms global identifiability is understood to mean injectivity of the parametrization of the model and is fundamental in particular for applicability of standard statistical methodology

there is no impact of exposure measurement error on latency estimation in linear models identification of the latency period for the effect of a time varying exposure is key when assessing many environmental nutritional and behavioral risk factors a pre specified exposure metric involving an unknown latency parameter is often used in the statistical model for the exposure disease relationship likelihood based methods have been developed to estimate this latency parameter for generalized linear models but do not exist for scenarios where the exposure is measured with error as is usually the case here we explore the performance of naive estimators for both the latency parameter and the regression coefficients which ignore exposure measurement error assuming a linear measurement error model we prove that in many scenarios under this general measurement error setting the least squares estimator for the latency parameter remains consistent while the regression coefficient estimates are inconsistent as has previously been found in standard measurement error models where the primary disease model does not involve a latency parameter conditions under which this result holds are generalized to a wide class of covariance structures and mean functions the findings are illustrated in a study of body mass index in relation to physical activity in the health professionals follow up study

a new method for estimating subgroup means under misclassification summary this paper considers the estimation of the subgroup means of a response variable when the individuals in a random sample are allocated to the subgroups or classes by a fallible device a double sampling scheme under which we determine also the true classes of the individuals in a subsample is utilized a simple distributional free estimator is proposed and the associated large sample properties are also derived the proposed estimator is also demonstrated by simulation studies to be more efficient than selen s estimator 1986

on the potential of measurement error to induce differential bias on odds ratio estimates an example from radon epidemiology it is well established that odds ratios estimated by logistic regression are subject to bias if exposure is measured with error the dependence of this bias on exposure parameter values particularly for multiplicative measurement error and its implications in epidemiology are not however as fully acknowledged we have been motivated by a german west case control study on lung cancer and residential radon where restriction to a subgroup exhibiting larger mean and variance of exposure than the entire group has shown higher odds ratio estimates as compared to the full analysis by means of correction formulae and simulations we show that bias from additive classical type error depends on the exposure variance not on the exposure mean and that bias from multiplicative classical type error depends on the geometric standard deviation in other words on the coefficient of variation of exposure but not on the geometric mean of exposure bias from additive or multiplicative berkson type error is independent of exposure distribution parameters this indicates that there is a potential of differential bias between groups where these parameters vary such groups are commonly compared in epidemiology for example when the results of subgroup analyses are contrasted or meta analyses are performed for the german west radon study we show that the difference of measurement error bias between the subgroup and the entire group exhibits the same direction but not the same dimension as the observed results regarding meta analysis of five european radon studies we find that a study such as this german study will necessarily result in smaller odds ratio estimates than other studies due to the smaller exposure variance and coefficient of variation of exposure therefore disregard of measurement error can not only lead to biased estimates but also to inconsistent results and wrongly concluded effect differences between groups

semiparametric quasilikelihood and variance function estimation in measurement error models abstract we consider a quasilikelihood variance function model when a predictor x is measured with error and a surrogate w is observed when in addition to a primary data set containing y w a validation data set exists for which x w is observed we can i estimate the first and second moments of the response y given w by kernel regression ii use quasilikelihood and variance function techniques to estimate the regression parameters as well as variance structure parameters the estimators are shown to be asymptotically normally distributed with asymptotic variance depending on the size of the validation data set and not on the bandwith used in the kernel estimates a more refined analysis of the asymptotic covariance shows that the optimal bandwidth converges to zero at the rate n 1 3

on the identification of a single factor model with correlated residuals summary a necessary and sufficient condition for the identification of a single factor model with correlated residuals is derived by studying the zero elements of their concentration matrix in particular the new condition is expressed in terms of the complementary graph of the residuals this graphical condition can be simply checked by means of an efficient algorithm an example is also given showing that sometimes the single factor model with correlated residuals can be used to overcome the problem of non identification of a larger factor model

on the smoothing property of linear delay partial differential equations abstract we consider linear partial differential equations with an additional delay term which under spatial discretization lead to ordinary differential equations with fixed delay of retarded type this means that the semi discrete solution gains smoothness over time for the concept of classical mild and weak solutions we analyse whether this effect also takes place in the original system we show that some systems behave in a neutral way only as a result the smoothness of the exact solution remains unchanged instead of gaining smoothness over time

graphical identifiability criteria for causal effects in studies with an unobserved treatment response variable summary we consider the problem of using data in studies with an unobserved treatment response variable in order to evaluate average causal effects when cause effect relationships between variables can be described by a directed acyclic graph and the corresponding recursive factorization of a joint distribution the paper proposes graphical criteria to test whether average causal effects are identifiable even if a treatment response variable is unobserved if the answer is affirmative we provide further formulations for average causal effects from the observed data the graphical criteria enable us to evaluate average causal effects when it is difficult to observe a treatment response variable

using the overdispersed exponential family to estimate the distribution of usual daily intakes of people aged between 18 and 28 in taiwan assessment of usual dietary intake of a population is essential to understand the nutrition status of the population methods like 24 hour dietary recall and food records are commonly used for this task however within individual variation exists in the food record data methods considering measurement errors have been used to evaluate the association between nutrient intakes and diseases few have been devoted to estimating the distribution of usual daily intakes this paper proposes applying the formulation of the overdispersed exponential family to estimate the distribution of usual nutrient intake and applies the adjustments developed by liu to reduce the variance of the distribution the proposed method has the advantages of working on the original scale of data and implementation convenience the adjustment of the variance is carried out by dividing the variance into within individual variance and among individual variance the adjusted variance then is used to estimate the distribution of the usual daily intake sampling weights are considered in all the steps except the estimation of the ratio of within to among variance the data for this study are from the nutritional and health survey in taiwan conducted between 1993 and 1996 nahsit 1993 1996 an independent external set of data for people aged between 18 and 28 years 49 males and 20 females is used to estimate the ratio of within to among individual variance due to the availability of data in estimating the ratio of within to among individual variance 430 males and 422 females in the nahsit sample are used to estimate the distribution of usual daily intakes for people aged between 18 and 28 in taiwan the distribution also allows us to estimate the proportion of people who do not meet the recommended daily nutrient allowance rdna the results show that the intakes of calcium and vitamin e of this group of people fall far below rdna

a general approach to analyzing epidemiologic data that contain misclassification errors misclassification is a common source of bias and reduced efficiency in the analysis of discrete data several methods have been proposed to adjust for misclassification using information on error rates i gathered by resampling the study population ii gathered by sampling a separate population or iii assumed a priori we present unified methods for incorporating these types of information into analyses based on log linear models and maximum likelihood estimation general variance expressions are developed examples from epidemiologic studies are used to demonstrate the proposed methodology

multiply robust causal inference with double negative control adjustment for categorical unmeasured confounding unmeasured confounding is a threat to causal inference in observational studies in recent years the use of negative controls to mitigate unmeasured confounding has gained increasing recognition and popularity negative controls have a long standing tradition in laboratory sciences and epidemiology to rule out non causal explanations although they have been used primarily for bias detection recently miao and colleagues have described sufficient conditions under which a pair of negative control exposure and outcome variables can be used to identify non parametrically the average treatment effect ate from observational data subject to uncontrolled confounding we establish non parametric identification of the ate under weaker conditions in the case of categorical unmeasured confounding and negative control variables we also provide a general semiparametric framework for obtaining inferences about the ate while leveraging information about a possibly large number of measured covariates in particular we derive the semiparametric efficiency bound in the non parametric model and we propose multiply robust and locally efficient estimators when non parametric estimation may not be feasible we assess the finite sample performance of our methods in extensive simulation studies finally we illustrate our methods with an application to the post licensure surveillance of vaccine safety among children

bounds on direct effects in the presence of confounded intermediate variables this article considers the problem of estimating the average controlled direct effect acde of a treatment on an outcome in the presence of unmeasured confounders between an intermediate variable and the outcome such confounders render the direct effect unidentifiable even in cases where the total effect is unconfounded hence identifiable kaufman et al 2005 statistics in medicine 24 1683 1702 applied a linear programming software to find the minimum and maximum possible values of the acde for specific numerical data in this article we apply the symbolic balke pearl 1997 journal of the american statistical association 92 1171 1176 linear programming method to derive closed form formulas for the upper and lower bounds on the acde under various assumptions of monotonicity these universal bounds enable clinical experimenters to assess the direct effect of treatment from observed data with minimum computational effort and they further shed light on the sign of the direct effect and the accuracy of the assessments

bayesian small sample estimation of misclassified multinomial data bayesian small sample estimation of a multinomial distribution based on its apparent distribution and a matrix of misclassification probabilities is considered

on convergence of difference schemes for delay parabolic equations the convergence of difference schemes for the approximate solutions of the initial boundary value problem for the delay parabolic differential equation dv t dt av t b t v email protected t 0 v t g t email protected email protected 0 in an arbitrary banach space e with the unbounded linear operators a and b t in e with dense domains d a d b t is investigated theorems on convergence estimates for the solutions of the first and the second order of accuracy difference schemes in fractional spaces e a are established in practice the convergence estimates in holder norms for the solutions of difference schemes of the first and the second order of approximation in t of the approximate solutions of multi dimensional delay parabolic equations are obtained the theoretical statements for the solution of these difference schemes are supported by the numerical example

on the effect of misclassification on bias of perfectly measured covariates in regression this note clarifies under what conditions a naive analysis using a misclassified predictor will induce bias for the regression coefficients of other perfectly measured predictors in the model an apparent discrepancy between some previous results and a result for measurement error of a continuous variable in linear regression is resolved we show that similar to the linear setting misclassification even when not related to the other predictors induces bias in the coefficients of the perfectly measured predictors unless the misclassified variable and the perfectly measured predictors are independent conditional and asymptotic biases are discussed in the case of linear regression and explored numerically for an example relating birth weight to the weight and smoking status of the mother

l2 regularity for parabolic partial integrodifferential equations with delay in the highest order derivatives abstract a partial integrodifferential equation is studied in which the derivatives of highest order also contain a discrete and a distributed delay by means of abstract regularity results global existence and uniqueness of a strict solution are obtained moreover a characterization of the infinitesimal generator of the solution operator is given

expected estimating equations to accommodate covariate measurement error estimating equations which are not necessarily likelihood based score equations are becoming increasingly popular for estimating regression model parameters this paper is concerned with estimation based on general estimating equations when true covariate data are missing for all the study subjects but surrogate or mismeasured covariates are available instead the method is motivated by the covariate measurement error problem in marginal or partly conditional regression of longitudinal data we propose to base estimation on the expectation of the complete data estimating equation conditioned on available data the regression parameters and other nuisance parameters are estimated simultaneously by solving the resulting estimating equations the expected estimating equation eee estimator is equal to the maximum likelihood estimator if the complete data scores are likelihood scores and conditioning is with respect to all the available data a pseudo eee estimator which requires less computation is also investigated asymptotic distribution theory is derived small sample simulations are conducted when the error process is an order 1 autoregressive model regression calibration is extended to this setting and compared with the eee approach we demonstrate the methods on data from a longitudinal study of the relationship between childhood growth and adult obesity

measurement error in the explanatory variable of a binary regression regression calibration and integrated conditional likelihood in studies of residential radon and lung cancer in epidemiology one approach to investigating the dependence of disease risk on an explanatory variable in the presence of several confounding variables is by fitting a binary regression using a conditional likelihood thus eliminating the nuisance parameters when the explanatory variable is measured with error the estimated regression coefficient is biased usually towards zero motivated by the need to correct for this bias in analyses that combine data from a number of case control studies of lung cancer risk associated with exposure to residential radon two approaches are investigated both employ the conditional distribution of the true explanatory variable given the measured one the method of regression calibration uses the expected value of the true given measured variable as the covariate the second approach integrates the conditional likelihood numerically by sampling from the distribution of the true given measured explanatory variable the two approaches give very similar point estimates and confidence intervals not only for the motivating example but also for an artificial data set with known properties these results and some further simulations that demonstrate correct coverage for the confidence intervals suggest that for studies of residential radon and lung cancer the regression calibration approach will perform very well so that nothing more sophisticated is needed to correct for measurement error

determining the value of additional surrogate exposure data for improving the estimate of an odds ratio we consider the design of both cohort and case control studies in which an initial stage 1 sample of complete data on an error free disease indicator d a correct gold standard dichotomous exposure measurement x and an error prone exposure measurement z are available we calculate the amount of additional information on the odds ratio relating d to x that one can obtain from a second stage 2 sample of measurements only on d and z if one allows for differential measurement error in z there is often little advantage in having more than four times as much data in stage 2 data as in stage 1 with the assumption that a non differential measurement error model is reasonable larger amounts of stage 2 data can be useful simulations indicate that stage 1 samples of modest size 50 cases in case control studies and 50 failures in cohort studies yield sufficiently reliable estimates of needed parameters to assist in determining an appropriate size for the stage 2 sample these ideas apply in settings either where the amount of stage 1 data is limited and fixed by external constraints or where one has gathered stage 1 data in advance to avoid collecting superfluous stage 2 data

on a class of retarded partial differential equations on developpe des resultats recents sur des equations d evolution abstraites afin de les appliquer a un type d equations dans des espaces de banach avec un retard discret et continu ces equations peuvent etre considerees comme la version abstraite d equations integrodifferentielles partielles a retard

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

instrumental variable estimation in binary regression measurement error models abstract we describe two approaches to instrumental variable estimation in binary regression measurement error models the methods entail constructing approximate mean models for the binary response as a function of the measured predictor the instrument and any covariates in the model estimates are obtained by exploiting relationships between regression parameters just as in linear instrumental variable estimation in the course of deriving the approximate mean models we obtain an alternative characterization of instrumental variable estimation in linear measurement error models

on the identification of path analysis models with one hidden variable summary we study criteria for identifiability of path analysis models with one hidden variable we first derive sufficient criteria for identification of models in which marginalisation is carried out over the hidden variable the sufficient criteria are based on the structure of the directed acyclic graph associated with the path analysis model and can be derived from the graph we treat further the identification of models when the hidden variable is conditioned on and establish connections with the extended skew normal distribution finally it is shown that the derived conditions extend the existing graphical criteria for identification

exposure misclassification bias in category specific poisson regression coefficients in epidemiologic studies of the association between exposure and disease misclassification of exposure is common and known to induce bias in the effect estimates the nature of the bias is difficult to foretell for this purpose we present a simple method to assess the bias in poisson regression coefficients for a categorical exposure variable subject to misclassification we derive expressions for the category specific coefficients from the regression on the error prone exposure naive coefficients in terms of the coefficients from the regression on the true exposure true coefficients these expressions are similar for crude and adjusted models if we assume that the covariates are measured without error and that it is independence between the misclassification probabilities and covariate values we find that the bias in the naive coefficient for one category of the exposure variable depends on all true category specific coefficients weighted by misclassification probabilities on the other hand misclassification of an exposure variable does not induce bias in the estimates of the coefficients of the perfectly measured covariates similarities with linear regression models are pointed out for selected scenarios of true exposure disease associations and selected patterns of misclassification we illustrate the inconsistency in naive poisson regression coefficients and show that it can be difficult to intuitively characterize the nature of the bias both the magnitude and the direction of the bias may vary between categories of an exposure variable

a bayesian approach to logistic regression models having measurement error following a mixture distribution to estimate the parameters in a logistic regression model when the predictors are subject to random or systematic measurement error we take a bayesian approach and average the true logistic probability over the conditional posterior distribution of the true value of the predictor given its observed value we allow this posterior distribution to consist of a mixture when the measurement error distribution changes form with observed exposure we apply the method to study the risk of alcohol consumption on breast cancer using the nurses health study data we estimate measurement error from a small subsample where we compare true with reported consumption some of the self reported non drinkers truly do not drink the resulting risk estimates differ sharply from those computed by standard logistic regression that ignores measurement error

covariate measurement errors and parameter estimation in a failure time regression model summary estimation in cox s failure time regression model is considered when the regression vector is subject to measurement error a hazard function model is induced for the failure rate given the measured covariate and a partial likelihood function is derived for the relative risk parameters this partial likelihood function may involve the baseline hazard function as well as the regression parameter but useful inference techniques arise for testing whether the regression parameter equals zero and for more general inferences in important special cases explicit consideration is given to testing equality of survival curves when group membership is subject to misclassification and to relative risk estimation with normally distributed covariates approaches to regression estimation using the overall likelihood function and a marginal likelihood function based on failure time ranks are also indicated illustration of the possible effect of covariate errors on relative risk estimation is provided

correction of logistic regression relative risk estimates and confidence intervals for systematic within person measurement error errors in the measurement of exposure that are independent of disease status tend to bias relative risk estimates and other measures of effect in epidemiologic studies toward the null value two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random unbiased within person variation or to systematic errors for individual subjects these methods require a separate validation study to estimate the regression coefficient lambda relating the surrogate measure to true exposure in the linear approximation method the true logistic regression coefficient beta is estimated by beta lambda where beta is the observed logistic regression coefficient based on the surrogate measure in the likelihood approximation method a second order taylor series expansion is used to approximate the logistic function enabling closed form likelihood estimation of beta confidence intervals for the corrected relative risks are provided that include a component representing error in the estimation of lambda based on simulation studies both methods perform well for true odds ratios up to 3 0 for higher odds ratios the likelihood approximation method was superior with respect to both bias and coverage probability an example is provided based on data from a prospective study of dietary fat intake and risk of breast cancer and a validation study of the questionnaire used to assess dietary fat intake

inferences about exposure disease associations using probability of exposure information unconditional and conditional likelihood methods are proposed for modeling odds and odds ratios relating a binary disease variable and an exposure variable that is only known probabilistically e g via measurement of a surrogate exposure variable while adjusting appropriately for a vector of covariables assuming nondifferential errors a probabilistic structure is developed that permits analysis of the marginal relation between disease and the surrogate while maintaining important properties of the marginal relation between disease and true exposure in particular analyses conditioned on marginal totals in surrogate disease tables remove the same nuisance parameters as are removed in a conditional analysis of true exposure disease tables in addition a relation between the probability of exposure poe in the disease and disease free groups is derived permitting the use of information about exposure from populations with structure different from the study population examples are presented illustr

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

conditional independence models for epidemiological studies with covariate measurement error we construct a unifying representation of the structure of measurement error problems with particular reference to situations commonly encountered in epidemiological studies and outline how estimation of the parameters of interest can be carried out in a bayesian framework using gibbs sampling we show how this approach can be implemented for designs involving continuous measurement errors assessed through a validation substudy and discuss our results on simulated data

bayesian analysis of misclassified binary data from a matched case control study with a validation sub study bayesian methods are proposed for analysing matched case control studies in which a binary exposure variable is sometimes measured with error but whose correct values have been validated for a random sample of the matched case control sets three models are considered model 1 makes few assumptions other than randomness and independence between matched sets while models 2 and 3 are logistic models with model 3 making additional distributional assumptions about the variation between matched sets with models 1 and 2 the data are examined in two stages the first stage analyses data from the validation sample and is easy to perform the second stage analyses the main body of data and requires mcmc methods all relevant information is transferred between the stages by using the posterior distributions from the first stage as the prior distributions for the second stage with model 3 a hierarchical structure is used to model the relationship between the exposure probabilities of the matched sets which gives the potential to extract more information from the data all the methods that are proposed are generalized to studies in which there is more than one control for each case the bayesian methods and a maximum likelihood method are applied to a data set for which the exposure of every patient was measured using both an imperfect measure that is subject to misclassification and a much better measure whose classifications may be treated as correct to test methods the latter information was suppressed for all but a random sample of matched sets

conditional regression analysis of the exposure disease odds ratio using known probability of exposure values conditional inference methods are proposed for the odds ratio between binary exposure and disease variables when only the probability of exposure is known for each study subject we develop a conditional likelihood approach that removes nuisance parameters and permits inferences to be made about important parameters in log odds ratio regression models we also discuss a heuristic procedure based on estimating the unknown number of truly exposed individuals this procedure provides a simple framework for interpreting our likelihood based statistics and leads to a mantel haenszel type estimator and a goodness of fit test as an example of the use of this methodology we present an analysis of some genetic data of swift et al 1976 cancer research 36 209 215

efficient regression calibration for logistic regression in main study internal validation study designs with an imperfect reference instrument an extension to the version of the regression calibration estimator proposed by rosner et al for logistic and other generalized linear regression models is given for main study internal validation study designs this estimator combines the information about the parameter of interest contained in the internal validation study with rosner et al s regression calibration estimate using a generalized inverse variance weighted average it is shown that the validation study selection model can be ignored as long as this model is jointly independent of the outcome and the incompletely observed covariates conditional at most upon the surrogates and other completely observed covariates in an extensive simulation study designed to follow a complex multivariate setting in nutritional epidemiology it is shown that with validation study sizes of 340 or more this estimator appears to be asymptotically optimal in the sense that it is nearly unbiased and nearly as efficient as a properly specified maximum likelihood estimator a modification to the regression calibration variance estimator which replaces the standard uncorrected logistic regression coefficient variance with the sandwich estimator to account for the possible misspecification of the logistic regression fit to the surrogate covariates in the main study was also studied in this same simulation experiment in this study the alternative variance formula yielded results virtually identical to the original formula a version of the proposed estimator is also derived for the case where the reference instrument available only in the validation study is imperfect but unbiased at the individual level and contains error that is uncorrelated with other covariates and with error in the surrogate instrument replicate measures are obtained in a subset of study participants in this case it is shown that the validation study selection model can be ignored when sampling into the validation study depends at most only upon perfectly measured covariates two data sets a study of fever in relation to occupational exposure to antineoplastics among hospital pharmacists and a study of breast cancer incidence in relation to dietary intakes of alcohol and vitamin a adjusted for total energy intake from the nurses health study were analysed using these new methods in these data because the validation studies contained less than 200 observations and the events of interest were relatively rare as is typical the potential improvements offered by this new estimator were not apparent

asymptotics for the simex estimator in nonlinear measurement error models abstract cook and stefanski have described a computer intensive method the simex method for approximately consistent estimation in regression problems with additive measurement error in this article we derive the asymptotic distribution of their estimators and show how to compute estimated standard errors these standard error estimators can either be used alone or as prepivoting devices in a bootstrap analysis we also give theoretical justification to some of the phenomena observed by cook and stefanski in their simulations

estimation and inference for logistic regression with covariate misclassification and measurement error in main study validation study designs abstract in epidemiological studies continuous covariates often are measured with error and categorical covariates often are misclassified using the logistic regression model to represent the relationship between the binary outcome and the perfectly measured and classified covariates the model for the observed main study data is derived this derivation relies on the assumption that the error in the continuous covariates is multivariate normally distributed and uses a chain of logistic regression models to describe the misclassification processes these model assumptions are empirically verified in the validation study where the misclassified and mismeasured covariates are validated using perfectly measured and classified data the full data likelihood including contributions from both the main study and the validation study is maximized to obtain the maximum likelihood estimates for the parameters of the underlying logistic regression model and of the measurement error model and reclassification mo

modelling complexity applications of gibbs sampling in medicine summary we review applications of gibbs sampling in medicine involving longitudinal spatial covariate measurement and survival models applications in immunology pharmacology transplantation cancer screening industrial epidemiology and genetic epidemiology are discussed

identifying causal effects with proxy variables of an unmeasured confounder we consider a causal effect that is confounded by an unobserved variable but with observed proxy variables of the confounder we show that with at least two independent proxy variables satisfying a certain rank condition the causal effect is nonparametrically identified even if the measurement error mechanism i e the conditional distribution of the proxies given the confounder may not be identified our result generalizes the identification strategy of kuroki pearl 2014 that rests on identification of the measurement error mechanism when only one proxy for the confounder is available or the required rank condition is not met we develop a strategy to test the null hypothesis of no causal effect

adjusting for errors in classification and measurement in the analysis of partly and purely categorical data abstract this article examines a method of adjusting subgroup means when there are errors both in the allocation of elements to the subgroups and in the measurement of the response the advantages with the method are that it is simple it is also applicable when there are many subgroups and it requires no distributional assumptions for the response variable the method is compared to the maximum likelihood method for a dichotomous response and an example from the swedish level of living survey is given

estimation of linear and nonlinear errors in variables models using validation data abstract consistent estimators for linear and nonlinear regression models with measurement errors in variables in the presence of validation data are proposed the estimation procedures are based on least squares methods with regression functions replaced by wide sense conditional expectation functions the methods do not depend on distributional assumptions and are robust against the misspecification of a measurement error model they are computationally and analytically simpler than semiparametric methods based on nonparametric regression or density functions

positions of convex bodies associated to extremal problems and isotropic measures abstract we show that there are close relations between extremal problems in dual brunn minkowski theory and isotropic type properties for some borel measures on the sphere the methods we use allow us to obtain similar results in the context of firey brunn minkowski theory we also study reverse inequalities for dual mixed volumes which are related with classical positions such as l position or isotropic position

binary regression using an extended beta binomial distribution with discussion of correlation induced by covariate measurement errors abstract the beta binomial distribution is extended to allow negative correlations among binary variates within an experimental unit regression models are proposed for both the binary variate response rate and for the pairwise correlation between binary variates and corresponding likelihood estimation procedures are described binary regression problems are also considered in which measurement errors in the regression variables represent the sole source of overdispersion some corresponding response rate estimation procedures are described and illustrated

variance estimation for epidemiologic effect estimates under misclassification this paper presents basic methods for construction of variance estimators for epidemiologic effect estimates when adjusting for misclassification methods are described for differential and non differential misclassification and for external and internal estimates of classification rates the methods take account of sampling variability in both the observed data and the estimated classification rates the methods are illustrated in a case control analysis of the association of antibiotic use during pregnancy with sudden infant death syndrome

on the abstract cauchy problem of parabolic type in spaces of continuous functions on etudie l existence l unicite et les proprietes de regularite des solutions du probleme de cauchy u t au r f t o t t u o u 0 ou a d a ce e est un operateur lineaire clos dans l espace de banach e

a class of semiparametric tests of treatment effect robust to confounder measurement error when assessing the presence of an exposure causal effect on a given outcome measurement error of a confounder can inflate the type i error rate of a treatment effect in even the simplest of settings in this paper we develop a large class of semiparametric test statistics of an exposure causal effect which are completely robust to additive unbiased measurement error of a subset of confounders a unique and appealing feature of our proposed methodology is that it requires no external information such as validation data or replicates of error prone confounders we present a doubly robust form of this test that requires the exposure mean model to be linear in the mismeasured confounders and only one of two models involving error free confounders to be correctly specified for the resulting test statistic to have correct type i error rate we demonstrate validity within our class of test statistics through simulation studies we apply the methods to a multi us city time series data set to test for an effect of temperature on mortality while adjusting for atmospheric particulate matter with diameter of 2 5 micrometres or less which is known to be measured with error

regression calibration in failure time regression in this paper we study a regression calibration method for failure time regression analysis when data on some covariates are missing or mismeasured the method estimates the missing data based on the data structure estimated from a validation data set a random subsample of the study cohort in which covariates are always observed ordinary cox 1972 journal of the royal statistical society series b 34 187 220 regression is then applied to estimate the regression coefficients using the observed covariates in the validation data set and the estimated covariates in the nonvalidation data set the method can be easily implemented we present the asymptotic theory of the proposed estimator finite sample performance is examined and compared with an estimated partial likelihood estimator and other related methods via simulation studies where the proposed method performs well even though it is technically inconsistent finally we illustrate the method with a mouse leukemia data set

formulating tightest bounds on causal effects in studies with unmeasured confounders this paper considers the problem of evaluating the causal effect of an exposure on an outcome in observational studies with both measured and unmeasured confounders between the exposure and the outcome under such a situation maclehose et al epidemiology 2005 16 548 555 applied linear programming optimization software to find the minimum and maximum possible values of the causal effect for specific numerical data in this paper we apply the symbolic balke pearl linear programming method probabilistic counterfactuals semantics computation and applications ph d thesis ucla cognitive systems laboratory 1995 j amer statist assoc 1997 92 1172 1176 to derive the simple closed form expressions for the lower and upper bounds on causal effects under various assumptions of monotonicity these universal bounds enable epidemiologists and medical researchers to assess causal effects from observed data with minimum computational effort and they further shed light on the accuracy of the assessment

cost efficient study designs for binary response data with gaussian covariate measurement error summary when mismeasurement of the exposure variable is anticipated epidemiologic cohort studies may be augmented to include a validation study where a small sample of data relating the imperfect exposure measurement method to the better method is collected optimal study designs i e least expensive subject to specified power constraints are developed that give the overall sample size and proportion of the overall sample size allocated to the validation study if better exposure measurements can be collected on a sample of subjects an optimal design can be suggested that conforms to realistic budgetary constraints the properties of three designs those that include an internal validation study those where the validated subsample is derived from subjects external to the primary investigation and those that use the better method of exposure assessment on all subjects are compared the proportion of overall study resources allocated to the validation substudy increases with increasing sample disease frequency decreasing unit cost of the superior exposure measurement relative to the imperfect one increasing unit cost of outcome ascertainment increasing distance between two alternative values of the relative risk between which the study is designed to discriminate and increasing magnitude of hypothesized values this proportion also depends in a nonlinear fashion on the severity of measurement error and when the validation study is internal measurement error reaches a point after which the optimal design is the smaller fully validated one

necessary conditions for partial differential equations with delay to generate c0 semigroups on etudie l existence des solutions ou le caractere bien pose d equations aux derivees partielles a retard du type du t dt f u t ou f est un operateur d un espace de fonction 7b f r 0 y dans l espace de banach y dans lequel l equation evolue

prospective analysis of logistic case control studies abstract in a classical case control study prentice and pyke proposed to ignore the study design and instead base estimation and inference on a random sampling i e prospective formulation we generalize this prospective formulation of case control studies to include multiplicative models stratification missing data measurement error robustness and other examples the resulting estimators which ignore the case control study aspect and instead are based on a random sampling formulation are typically consistent for nonintercept parameters and are asymptotically normally distributed we derive the resulting asymptotic covariance matrix of the parameter estimates the covariance matrix obtained by ignoring the case control sampling scheme and using prospective formulas instead is shown to be at worst asymptotically conservative and asymptotically correct in a variety of problems a simple sufficient condition guaranteeing the latter is obtained

a modified estimating equation approach to correcting for measurement error in regression summary a modified estimating equation approach is proposed to correct for measurement error in regression problems we allow changing measurement error variances and covariances across units allow the regressors to be fixed allow estimation of the measurement error variances covariances and account for uncertainty arising from this estimation and explicitly model measurement error in the response multiple linear quadratic poisson and logistic regression are considered in detail and it is seen that some previously developed estimators arise as special cases from the proposed approach a small simulation study is presented for logistic regression

polynomial regression and estimating functions in the presence of multiplicative measurement error we consider the polynomial regression model in the presence of multiplicative measurement error in the predictor two general methods are considered with the methods differing in their assumptions about the distributions of the predictor and the measurement errors consistent parameter estimates and asymptotic standard errors are derived by using estimating equation theory diagnostics are presented for distinguishing additive and multiplicative measurement error data from a nutrition study are analysed by using the methods the results from a simulation study are presented and the performances of the methods are compared

covariate measurement error in generalized linear models summary the em algorithm is used to obtain estimators of regression coefficients for generalized linear models with canonical link when normally distributed covariates are masked by normally distributed measurement errors by casting the true covariates as missing data the em procedure suggests an iterative scheme in which each cycle consists of an e step requiring the computation of approximate first and second conditional moments of the true covariates given the observed data followed by an m step in which regression parameters are updated by iteratively reweighted least squares based on these approximations the proposed procedure is compared numerically with the exact maximum likelihood solution obtained by using gaussian quadrature instead of the approximations in the e step of the em algorithm and with alternative estimators for simple logistic regression with measurement error the results for the proposed procedure are encouraging a procedure is proposed in this paper for estimating regression coefficients in generalized linear models when one or more of the covariates is measured with error this work is related to the paper by carroll et al 1984 in which maximum likelihood estimates are considered for the structural logistic regression model these authors provide estimates for the computationally simpler probit regression model and suggest that the structural logistic regression can be done in principle this paper follows up on that suggestion but differs in detail from similar work by armstrong 1985 other procedures with related aims have been suggested by stefanski carroll 1985 wolter fuller 1982 and prentice 1982 for a quick introduction to the proposed method it is convenient to display the naive estimator which ignores measurement error in its standard computational form if yi is an observed response variable and xi is the observed covariate then for the model which equates the canonical parameter of the distribution of yi to xtf3 the maximum likelihood estimator of f3 can be obtained by iteratively reweighted least squares the estimate of f3 after s 1 cycles is given by

correcting for multivariate measurement error by regression calibration in meta analyses of epidemiological studies within person variability in measured values of multiple risk factors can bias their associations with disease the multivariate regression calibration rc approach can correct for such measurement error and has been applied to studies in which true values or independent repeat measurements of the risk factors are observed on a subsample we extend the multivariate rc techniques to a meta analysis framework where multiple studies provide independent repeat measurements and information on disease outcome we consider the cases where some or all studies have repeat measurements and compare study specific averaged and empirical bayes estimates of rc parameters additionally we allow for binary covariates e g smoking status and for uncertainty and time trends in the measurement error corrections our methods are illustrated using a subset of individual participant data from prospective long term studies in the fibrinogen studies collaboration to assess the relationship between usual levels of plasma fibrinogen and the risk of coronary heart disease allowing for measurement error in plasma fibrinogen and several confounders

measurement bias and effect restoration in causal inference summary this paper highlights several areas where graphical techniques can be harnessed to address the problem of measurement errors in causal inference in particular it discusses the control of unmeasured confounders in parametric and nonparametric models and the computational problem of obtaining bias free effect estimates in such models we derive new conditions under which causal effects can be restored by observing proxy variables of unmeasured confounders with without external studies

on correcting for misclassification in twin studies and other matched pair studies in twin studies and other matched pair studies of the effect of a k level risk factor on disease risk one must estimate the proportion of pairs in each of k2 possible pair categories of which k k 1 categories represent discordant pairs in particular for a binary factor one must estimate proportions within two discordant pair categories and the variances of functions of these estimates this paper shows how to do so when misclassification is present and stable estimates of the classification rates are available unlike methods that estimate only the discordance ratio one can use the methods presented here to improve estimates of epidemiologic effects

compensation and amplification of attenuation bias in causal effect estimates covariate adjusted treatment effects are commonly estimated in non randomized studies it has been shown that measurement error in covariates can bias treatment effect estimates when not appropriately accounted for so far these delineations primarily assumed a true data generating model that included just one single covariate it is however more plausible that the true model consists of more than one covariate we evaluate when a further covariate may reduce bias due to measurement error in another covariate and in which cases it is not recommended to include a further covariate we analytically derive the amount of bias related to the fallible covariate s reliability and systematically disentangle bias compensation and amplification due to an additional covariate with a fallible covariate it is not always beneficial to include an additional covariate for adjustment as the additional covariate can extensively increase the bias the mechanisms for an increased bias due to an additional covariate can be complex even in a simple setting of just two covariates a high reliability of the fallible covariate or a high correlation between the covariates cannot in general prevent from substantial bias we show distorting effects of a fallible covariate in an empirical example and discuss adjustment for latent covariates as a possible solution

semiparametric estimation in generalized linear mixed models with auxiliary covariates a pairwise likelihood approach auxiliary covariates are often encountered in biomedical research settings where the primary exposure variable is measured only for a subgroup of study subjects this article is concerned with generalized linear mixed models in the presence of auxiliary covariate information for clustered data we propose a novel semiparametric estimation method based on a pairwise likelihood function and develop an estimating equation based inference procedure by treating both the error structure and random effects as nuisance parameters this method is robust against misspecification of either error structure or random effects distribution and allows for dependence between random effects and covariates we show that the resulting estimators are consistent and asymptotically normal extensive simulation studies evaluate the finite sample performance of the proposed estimators and demonstrate their advantage over the validation set based method and the existing method we illustrate the method with two real data examples

estimating strata means in double sampling with corrections based on second phase sampling an estimator for strata means is presented for double sampling for stratification where the first phase strata estimates are corrected by second phase subsampling a variance estimator is derived for the estimated strata weights and for the adjusted strata means these are compared with two bootstrap variance estimators in a simulation study the stratum mean estimator has negligible bias and either bootstrap variance estimator is clearly better than the classical estimator in estimating the true variance the variability of the strata weights is most reliably estimated by the classical variance estimator

effects of exposure misclassification on regression analyses of epidemiologic follow up study data in epidemiologic studies subjects are often misclassified as to their level of exposure ignoring this misclassification error in the analysis introduces bias in the estimates of certain parameters and invalidates many hypothesis tests for situations in which there is misclassification of exposure in a follow up study with categorical data we have developed a model that permits consideration of any number of exposure categories and any number of multiple category covariates when used with logistic and poisson regression procedures this model helps assess the potential for bias when misclassification is ignored when reliable ancillary information is available the model can be used to correct for misclassification bias in the estimates produced by these regression procedures

an integral inequality concerning isotropic measures on the unit circle abstract we prove a trigonometric integral inequality involving isotropic measures in the plane which can be applied to characterize the solution of extremal problems of convex bodies in r 2 in terms of properties of measures the methods used include new estimates of hypergeometric functions and some cancellation lemmas

confounder adjustment in multiple hypothesis testing we consider large scale studies in which thousands of significance tests are performed simultaneously in some of these studies the multiple testing procedure can be severely biased by latent confounding factors such as batch effects and unmeasured covariates that correlate with both primary variable s of interest e g treatment variable phenotype and the outcome over the past decade many statistical methods have been proposed to adjust for the confounders in hypothesis testing we unify these methods in the same framework generalize them to include multiple primary variables and multiple nuisance variables and analyze their statistical properties in particular we provide theoretical guarantees for ruv 4 gagnon bartsch jacob and speed 2013 and leapp ann appl stat 6 2012 1664 1688 which correspond to two different identification conditions in the framework the first requires a set of negative controls that are known a priori to follow the null distribution the second requires the true nonnulls to be sparse two different estimators which are based on ruv 4 and leapp are then applied to these two scenarios we show that if the confounding factors are strong the resulting estimators can be asymptotically as powerful as the oracle estimator which observes the latent confounding factors for hypothesis testing we show the asymptotic z tests based on the estimators can control the type i error numerical experiments show that the false discovery rate is also controlled by the benjamini hochberg procedure when the sample size is reasonably large

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

log linear models for doubly sampled categorical data fitted by the em algorithm abstract double sampling experiments can be expressed as incomplete multiway contingency tables and analyzed by using techniques appropriate for fitting log linear models the framework described can be applied to experiments with any number of factors and measurement devices maximum likelihood estimation via the em algorithm leads to straightforward expressions for covariances of estimates of the parameters and functions of the parameters

identification and estimation of nonlinear models with misclassification error using instrumental variables a general solution abstract this paper provides a general solution to the problem of identification and estimation of nonlinear models with misclassification error in a general discrete explanatory variable using instrumental variables the misclassification error is allowed to be correlated with all the explanatory variables in the model it is not enough to identify the model by simply generalizing the identification in the binary case with a claim that the number of restrictions is no less than that of the unknowns such a claim requires solving a complicated nonlinear system of equations this paper introduces a matrix diagonalization technique which allows one to easily find the unique solution of the system the solution shows that the latent model can be expressed as an explicit function of directly observed distribution functions therefore the latent model is nonparametrically identifiable and directly estimable using instrumental variables the results show that certain monotonicity restrictions on the latent model may lead to its identification with virtually no restrictions on the misclassification probabilities an alternative identification condition suggests that the nonparametric identification may rely on the belief that people always have a higher probability of telling the truth than of misreporting the nonparametric identification in this paper directly leads to a n consistent semiparametric estimator the monte carlo simulation and empirical illustration show that the estimator performs well with a finite sample and real data