SIMEX and standard error estimation in semiparametric measurement error models

Conditional score approaches to errors-in-variables competing risks data in discrete time

Analysis of competing risks data has been an important topic in survival analysis due to the need to account for the dependence among the competing events. Also, event times are often recorded on discrete time scales, rendering the models tailored for discrete-time nature useful in the practice of survival analysis. In this work, we focus on regression analysis with discrete-time competing risks data, and consider the errors-in-variables issue where the covariates are prone to measurement errors. Viewing the true covariate value as a parameter, we develop the conditional score methods for various discrete-time competing risks models, including the cause-specific and subdistribution hazards models that have been popular in competing risks data analysis. The proposed estimators can be implemented by efficient computation algorithms, and the associated large sample theories can be simply obtained. Simulation results show satisfactory finite sample performances, and the application with the competing risks data from the scleroderma lung study reveals the utility of the proposed methods.

Biomarker data with measurement error in medical research: A literature review

A biomarker is a measurable indicator of the severity or presence of a disease or medical condition in biomedical or epidemiological research. Biomarkers may help in early diagnosis and prevention of diseases. Several biomarkers have been identified for many diseases such as carbohydrate antigen 19-9 for pancreatic cancer. However, biomarkers may be measured with errors due to many reasons such as specimen collection or day-to-day within-subject variability of the biomarker, among others. Measurement error in the biomarker leads to bias in the regression parameter estimation for the association of the biomarker with disease in epidemiological studies. In addition, measurement error in the biomarkers may affect standard diagnostic measures to evaluate the performance of biomarkers such as the receiver operating characteristic (ROC) curve, area under the ROC curve, sensitivity, and specificity. Measurement error may also have an effect on how to combine multiple cancer biomarkers as a composite predictor for disease diagnosis. In follow-up studies, biomarkers are often collected intermittently at examination times, which may be sparse and typically biomarkers are not observed at the event times. Joint modeling of longitudinal and time-to-event data is a valid approach to account for measurement error in the analysis of repeatedly measured biomarkers and time-to-event outcomes. In this article, we provide a literature review on existing methods to correct for estimation in regression analysis, diagnostic measures, and joint modeling of longitudinal biomarkers and survival outcomes when the biomarkers are measured with errors. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Robust MethodsStatistical and Graphical Methods of Data Analysis > EM AlgorithmStatistical Models > Survival Models.

A SIMEX approach for meta-analysis of diagnostic accuracy studies with attention to ROC curves

Bivariate random-effects models represent an established approach for meta-analysis of accuracy measures of a diagnostic test, which are typically given by sensitivity and specificity. A recent formulation of the classical model describes the test accuracy in terms of study-specific Receiver Operating Characteristics curves. In this way, the resulting summary curve can be thought of as an average of the study-specific Receiver Operating Characteristics curves. Within this framework, the paper shows that the standard likelihood approach for inference is prone to several issues. Small sample size can give rise to unreliable conclusions and convergence problems deeply affect the analysis. The proposed alternative is a simulation-extrapolation method, called SIMEX, developed within the measurement error literature. It suits the meta-analysis framework, as the accuracy measures provided by the studies are estimates rather than true values, and thus are prone to error. The methods are compared in a series of simulation studies, covering different scenarios of interest, including deviations from normality assumptions. SIMEX reveals a satisfactory strategy, providing more accurate inferential results if compared to the likelihood approach, while avoiding convergence failure. The approaches are applied to a meta-analysis of the accuracy of the ultrasound exam for diagnosing abdominal tuberculosis in HIV-positive subjects.

Simulation extrapolation method for measurement error: A review

Measurement error is pervasive in statistics due to the non-availability of authentic data. The reasons for measurement error mainly relate to cost, convenience, and human error. Measurement error can result in non-negligible bias due to attenuated estimates, reduced power of statistical tests, and lower coverage probabilities of the coefficient estimators in a regression model. Several methods have been proposed to correct for measurement error, all of which can be grouped into two broad categories based on the underlying model-functional and structural. Functional models provide flexibility and robustness to estimators by placing minimal or no assumptions on the distribution of the mismeasured covariate or by treating them as a fixed entity, as opposed to a structural model which treats the underlying mismeasured covariates as random with a specified structure. The simulation extrapolation method is one method that is used for the partial correction of measurement error in both structural and functional models. Reviews of measurement error correction techniques are available in the literature. However, none of the previously conducted reviews has exclusively focused on simulation extrapolation and its application in continuous measurement error models, despite its widespread use and ease of application. We attempt to close this gap in the literature by highlighting its development over the past two and a half decades.

Simulation-selection-extrapolation: Estimation in high-dimensional errors-in-variables models

Errors-in-variables models in high-dimensional settings pose two challenges in application. First, the number of observed covariates is larger than the sample size, while only a small number of covariates are true predictors under an assumption of model sparsity. Second, the presence of measurement error can result in severely biased parameter estimates, and also affects the ability of penalized methods such as the lasso to recover the true sparsity pattern. A new estimation procedure called SIMulation-SELection-EXtrapolation (SIMSELEX) is proposed. This procedure makes double use of lasso methodology. First, the lasso is used to estimate sparse solutions in the simulation step, after which a group lasso is implemented to do variable selection. The SIMSELEX estimator is shown to perform well in variable selection, and has significantly lower estimation error than naive estimators that ignore measurement error. SIMSELEX can be applied in a variety of errors-in-variables settings, including linear models, generalized linear models, and Cox survival models. It is furthermore shown in the Supporting Information how SIMSELEX can be applied to spline-based regression models. A simulation study is conducted to compare the SIMSELEX estimators to existing methods in the linear and logistic model settings, and to evaluate performance compared to naive methods in the Cox and spline models. Finally, the method is used to analyze a microarray dataset that contains gene expression measurements of favorable histology Wilms tumors.

Simulation Extrapolation Method for Cox Regression Model with a Mixture of Berkson and Classical Errors in the Covariates using Calibration Data

Many biomedical or epidemiological studies often aim to assess the association between the time to an event of interest and some covariates under the Cox proportional hazards model. However, a problem is that the covariate data routinely involve measurement error, which may be of classical type, Berkson type or a combination of both types. The issue of Cox regression with error-prone covariates has been well-discussed in the statistical literature, which has focused mainly on classical error so far. This paper considers Cox regression analysis when some covariates are possibly contaminated with a mixture of Berkson and classical errors. We propose a simulation extrapolation-based method to address this problem when two replicates of the mismeasured covariates are available along with calibration data for some subjects in a subsample only. The proposed method places no assumption on the mixture percentage. Its finite-sample performance is assessed through a simulation study. It is applied to the analysis of data from an AIDS clinical trial study.

Hospital quality measures: are process indicators associated with hospital standardized mortality ratios in French acute care hospitals?

Background

Results of associations between process and mortality indicators, both used for the external assessment of hospital care quality or public reporting, differ strongly across studies. However, most of those studies were conducted in North America or United Kingdom. Providing new evidence based on French data could fuel the international debate on quality of care indicators and help inform French policy-makers. The objective of our study was to explore whether optimal care delivery in French hospitals as assessed by their Hospital Process Indicators (HPIs) is associated with low Hospital Standardized Mortality Ratios (HSMRs).

Methods

The French National Authority for Health (HAS) routinely collects for each hospital located in France, a set of mandatory HPIs. Five HPIs were selected among the process indicators collected by the HAS in 2009. They were measured using random samples of 60 to 80 medical records from inpatients admitted between January 1st, 2009 and December 31, 2009 in respect with some selection criteria. HSMRs were estimated at 30, 60 and 90 days post-admission (dpa) using administrative health data extracted from the national health insurance information system (SNIIR-AM) which covers 77% of the French population. Associations between HPIs and HSMRs were assessed by Poisson regression models corrected for measurement errors with a simulation-extrapolation (SIMEX) method.

Results

Most associations studied were not statistically significant. Only two process indicators were found associated with HSMRs. Completeness and quality of anesthetic records was negatively associated with 30 dpa HSMR (0.72 [0.52–0.99]). Early detection of nutritional disorders was negatively associated with all HSMRs: 30 dpa HSMR (0.71 [0.54–0.95]), 60 dpa HSMR (0.51 [0.39–0.67]) and 90 dpa HSMR (0.52 [0.40–0.68]).

Conclusion

In absence of gold standard of quality of care measurement, the limited number of associations suggested to drive in-depth improvements in order to better determine associations between process and mortality indicators. A smart utilization of both process and outcomes indicators is mandatory to capture aspects of the hospital quality of care complexity.

Electronic supplementary material

The online version of this article (doi:10.1186/s12913-017-2534-3) contains supplementary material, which is available to authorized users.

Inference in a survival cure model with mismeasured covariates using a simulation-extrapolation approach

In many situations in survival analysis, it may happen that a fraction of individuals will never experience the event of interest: they are considered to be cured. The promotion time cure model takes this into account. We consider the case where one or more explanatory variables in the model are subject to measurement error, which should be taken into account to avoid biased estimators. A general approach is the simulation-extrapolation algorithm, a method based on simulations which allows one to estimate the effect of measurement error on the bias of the estimators and to reduce this bias. We extend this approach to the promotion time cure model. We explain how the algorithm works, and we show that the proposed estimator is approximately consistent and asymptotically normally distributed, and that it performs well in finite samples. Finally, we analyse a database in cardiology: among the explanatory variables of interest is the ejection fraction, which is known to be measured with error.

Expected estimating equation using calibration data for generalized linear models with a mixture of Berkson and classical errors in covariates

Data collected in many epidemiological or clinical research studies are often contaminated with measurement errors that may be of classical or Berkson error type. The measurement error may also be a combination of both classical and Berkson errors and failure to account for both errors could lead to unreliable inference in many situations. We consider regression analysis in generalized linear models when some covariates are prone to a mixture of Berkson and classical errors, and calibration data are available only for some subjects in a subsample. We propose an expected estimating equation approach to accommodate both errors in generalized linear regression analyses. The proposed method can consistently estimate the classical and Berkson error variances based on the available data, without knowing the mixture percentage. We investigated its finite-sample performance numerically. Our method is illustrated by an application to real data from an HIV vaccine study.

Data Envelopment Analysis in the Presence of Measurement Error: Case Study from the National Database of Nursing Quality Indicators® (NDNQI®)

Data Envelopment Analysis (DEA) is the most commonly used approach for evaluating healthcare efficiency (Hollingsworth, 2008), but a long-standing concern is that DEA assumes that data are measured without error. This is quite unlikely, and DEA and other efficiency analysis techniques may yield biased efficiency estimates if it is not realized (Gajewski, Lee, Bott, Piamjariyakul and Taunton, 2009; Ruggiero, 2004). We propose to address measurement error systematically using a Bayesian method (Bayesian DEA). We will apply Bayesian DEA to data from the National Database of Nursing Quality Indicators® (NDNQI®) to estimate nursing units' efficiency. Several external reliability studies inform the posterior distribution of the measurement error on the DEA variables. We will discuss the case of generalizing the approach to situations where an external reliability study is not feasible.

Testing for Constant Nonparametric Effects in General Semiparametric Regression Models with Interactions

We consider the problem of testing for a constant nonparametric effect in a general semi-parametric regression model when there is the potential for interaction between the parametrically and nonparametrically modeled variables. The work was originally motivated by a unique testing problem in genetic epidemiology (Chatterjee, et al., 2006) that involved a typical generalized linear model but with an additional term reminiscent of the Tukey one-degree-of-freedom formulation, and their interest was in testing for main effects of the genetic variables, while gaining statistical power by allowing for a possible interaction between genes and the environment. Later work (Maity, et al., 2009) involved the possibility of modeling the environmental variable nonparametrically, but they focused on whether there was a parametric main effect for the genetic variables. In this paper, we consider the complementary problem, where the interest is in testing for the main effect of the nonparametrically modeled environmental variable. We derive a generalized likelihood ratio test for this hypothesis, show how to implement it, and provide evidence that our method can improve statistical power when compared to standard partially linear models with main effects only. We use the method for the primary purpose of analyzing data from a case-control study of colorectal adenoma.

Cocaine Dependence Treatment Data: Methods for Measurement Error Problems With Predictors Derived From Stationary Stochastic Processes

In a cocaine dependence treatment study, we use linear and nonlinear regression models to model posttreatment cocaine craving scores and first cocaine relapse time. A subset of the covariates are summary statistics derived from baseline daily cocaine use trajectories, such as baseline cocaine use frequency and average daily use amount. These summary statistics are subject to estimation error and can therefore cause biased estimators for the regression coefficients. Unlike classical measurement error problems, the error we encounter here is heteroscedastic with an unknown distribution, and there are no replicates for the error-prone variables or instrumental variables. We propose two robust methods to correct for the bias: a computationally efficient method-of-moments-based method for linear regression models and a subsampling extrapolation method that is generally applicable to both linear and nonlinear regression models. Simulations and an application to the cocaine dependence treatment data are used to illustrate the efficacy of the proposed methods. Asymptotic theory and variance estimation for the proposed subsampling extrapolation method and some additional simulation results are described in the online supplementary material.

Methods for estimation of radiation risk in epidemiological studies accounting for classical and Berkson errors in doses

With a binary response Y, the dose-response model under consideration is logistic in flavor with pr(Y=1 | D) = R (1+R)(-1), R = λ(0) + EAR D, where λ(0) is the baseline incidence rate and EAR is the excess absolute risk per gray. The calculated thyroid dose of a person i is expressed as Dimes=fiQi(mes)/Mi(mes). Here, Qi(mes) is the measured content of radioiodine in the thyroid gland of person i at time t(mes), Mi(mes) is the estimate of the thyroid mass, and f(i) is the normalizing multiplier. The Q(i) and M(i) are measured with multiplicative errors Vi(Q) and ViM, so that Qi(mes)=Qi(tr)Vi(Q) (this is classical measurement error model) and Mi(tr)=Mi(mes)Vi(M) (this is Berkson measurement error model). Here, Qi(tr) is the true content of radioactivity in the thyroid gland, and Mi(tr) is the true value of the thyroid mass. The error in f(i) is much smaller than the errors in ( Qi(mes), Mi(mes)) and ignored in the analysis. By means of Parametric Full Maximum Likelihood and Regression Calibration (under the assumption that the data set of true doses has lognormal distribution), Nonparametric Full Maximum Likelihood, Nonparametric Regression Calibration, and by properly tuned SIMEX method we study the influence of measurement errors in thyroid dose on the estimates of λ(0) and EAR. The simulation study is presented based on a real sample from the epidemiological studies. The doses were reconstructed in the framework of the Ukrainian-American project on the investigation of Post-Chernobyl thyroid cancers in Ukraine, and the underlying subpolulation was artificially enlarged in order to increase the statistical power. The true risk parameters were given by the values to earlier epidemiological studies, and then the binary response was simulated according to the dose-response model.

Estimation via corrected scores in general semiparametric regression models with error-prone covariates

This paper considers the problem of estimation in a general semiparametric regression model when error-prone covariates are modeled parametrically while covariates measured without error are modeled nonparametrically. To account for the effects of measurement error, we apply a correction to a criterion function. The specific form of the correction proposed allows Monte Carlo simulations in problems for which the direct calculation of a corrected criterion is difficult. Therefore, in contrast to methods that require solving integral equations of possibly multiple dimensions, as in the case of multiple error-prone covariates, we propose methodology which offers a simple implementation. The resulting methods are functional, they make no assumptions about the distribution of the mismeasured covariates. We utilize profile kernel and backfitting estimation methods and derive the asymptotic distribution of the resulting estimators. Through numerical studies we demonstrate the applicability of proposed methods to Poisson, logistic and multivariate Gaussian partially linear models. We show that the performance of our methods is similar to a computationally demanding alternative. Finally, we demonstrate the practical value of our methods when applied to Nevada Test Site (NTS) Thyroid Disease Study data.