A Moment‐Adjusted Imputation Method for Measurement Error Models

Studies of clinical characteristics frequently measure covariates with a single observation. This may be a mismeasured version of the "true" phenomenon due to sources of variability like biological fluctuations and device error. Descriptive analyses and outcome models that are based on mismeasured data generally will not reflect the corresponding analyses based on the "true" covariate. Many statistical methods are available to adjust for measurement error. Imputation methods like regression calibration and moment reconstruction are easily implemented but are not always adequate. Sophisticated methods have been proposed for specific applications like density estimation, logistic regression, and survival analysis. However, it is frequently infeasible for an analyst to adjust each analysis separately, especially in preliminary studies where resources are limited. We propose an imputation approach called moment-adjusted imputation that is flexible and relatively automatic. Like other imputation methods, it can be used to adjust a variety of analyses quickly, and it performs well under a broad range of circumstances. We illustrate the method via simulation and apply it to a study of systolic blood pressure and health outcomes in patients hospitalized with acute heart failure.

[1]  Raymond J. Carroll,et al.  Approximate Quasi-likelihood Estimation in Models with Surrogate Predictors , 1990 .

[2]  Raymond J. Carroll,et al.  Measurement error in nonlinear models: a modern perspective , 2006 .

[3]  Marie Davidian,et al.  The Nonlinear Mixed Effects Model with a Smooth Random Effects Density , 1993 .

[4]  J. Freudenheim,et al.  The problem of profound mismeasurement and the power of epidemiological studies of diet and cancer. , 1988, Nutrition and cancer.

[5]  M Davidian,et al.  Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data , 2001, Biometrics.

[6]  B Rosner,et al.  Correction of logistic regression relative risk estimates and confidence intervals for systematic within-person measurement error. , 2006, Statistics in medicine.

[7]  A. Gallant,et al.  Semi-nonparametric Maximum Likelihood Estimation , 1987 .

[8]  Anastasios A. Tsiatis,et al.  A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error , 2001 .

[9]  Raymond J. Carroll,et al.  Covariate Measurement Error in Logistic Regression , 1985 .

[10]  Marie Davidian,et al.  Latent-model robustness in structural measurement error models , 2006 .

[11]  T. Louis,et al.  Triple‐goal estimates in two‐stage hierarchical models , 1998 .

[12]  D. Hall.  Measurement Error in Nonlinear Models: A Modern Perspective , 2008 .

[13]  Sudhir Gupta,et al.  Statistical Regression With Measurement Error , 1999, Technometrics.

[14]  Wayne A. Fuller,et al.  Statistical analysis of measurement error models and applications : proceedings of the AMS-IMS-SIAM Joint Summer Research conference held June 10-16, 1989, with support from the National Science Foundation and the U.S. Army Research Office , 1990 .

[15]  Daniel W. Jones,et al.  Recommendations for blood pressure measurement in humans and experimental animals: Part 1: blood pressure measurement in humans: a statement for professionals from the Subcommittee of Professional and Public Education of the American Heart Association Council on High Blood Pressure Research. , 2005, Hypertension.

[16]  Raymond J. Carroll,et al.  Conditional scores and optimal scores for generalized linear measurement-error models , 1987 .

[17]  Nancy M Albert,et al.  Systolic blood pressure at admission, clinical characteristics, and outcomes in patients hospitalized with acute heart failure. , 2006, JAMA.

[18]  L. Stefanski,et al.  The Calculus of M-Estimation , 2002 .

[19]  Frantisek Stulajter,et al.  Nonlinear estimators of polynomials in mean values of a Gaussian stochastic process , 1978, Kybernetika.

[20]  Raymond J Carroll,et al.  A New Method for Dealing with Measurement Error in Explanatory Variables of Regression Models , 2004, Biometrics.

[21]  H. Schneeweiß,et al.  Polynomial regression with errors in the variables , 1998 .

[22]  J. Sanz,et al.  How Many Self-Measured Blood Pressure Readings Are Needed to Estimate Hypertensive Patients' “True” Blood Pressure? , 1999, Journal of Behavioral Medicine.

[23]  Steven J. Novick,et al.  Estimating a nonlinear function of a normal mean , 2005 .

[24]  T. Louis.  Estimating a population of parameter values using Bayes and empirical Bayes methods , 1984 .

[25]  H. Schouten,et al.  Is a series of blood pressure measurements by the general practitioner or the patient a reliable alternative to ambulatory blood pressure measurement? A study in general practice with reference to short-term and long-term between-visit variability. , 1997, American journal of hypertension.

[26]  A. Dyer,et al.  Statistical methods to assess and minimize the role of intra-individual variability in obscuring the relationship between dietary lipids and serum cholesterol. , 1978, Journal of chronic diseases.

[27]  L. Stefanski.  Unbiased estimation of a nonlinear function a normal mean with application to measurement err oorf models , 1989 .

[28]  Marie Davidian,et al.  Conditional Estimation for Generalized Linear Models When Covariates Are Subject‐Specific Parameters in a Mixed Model for Longitudinal Measurements , 2004, Biometrics.

[29]  Stefan Rolewicz,et al.  On a problem of moments , 1968 .

[30]  Marie Davidian,et al.  Smooth nonparametric maximum likelihood estimation for population pharmacokinetics, with application to quinidine , 1992, Journal of Pharmacokinetics and Biopharmaceutics.

[31]  Raymond J Carroll,et al.  A comparison of regression calibration, moment reconstruction and imputation for adjusting for covariate measurement error in regression , 2008, Statistics in medicine.

[32]  C Y Wang,et al.  Regression Analysis When Covariates Are Regression Parameters of a Random Effects Model for Observed Longitudinal Measurements , 2000, Biometrics.

[33]  A. Eddington,et al.  The correction of statistics for accidental error , 1940 .

[34]  T. Marshall,et al.  Blood pressure variability: the challenge of variation. , 2008, American journal of hypertension.