Abstract
The aim of this chapter is to review and examine different methods in order to display correct and efficient statistical techniques based on complete/incomplete data subject to different sorts of measurement error (ME) problems. Instrument inaccuracies, biological variations, and/or errors in questionnaire-based self-report data can lead to significant MEs in various clinical experiments. Ignoring MEs can cause bias or inconsistency of statistical inferences. The biostatistical literature well addresses two categories of MEs: errors related to additive models and errors caused by the limit of detection (LOD). Several statistical approaches have been developed to analyze data affected by MEs, including the parametric/nonparametric likelihood methodologies, Bayesian methods, the single and multiple imputation techniques, and the repeated measurement design of experiment. We present a novel hybrid pooled–unpooled design as one of the strategies to provide correct statistical inferences when data is subject to MEs. This hybrid design and the classical techniques are compared to show the advantages and disadvantages of the considered methods.
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References
Carroll RJ, Spiegelman C, Lan KK, Bailey KT, Abbott RD (1984) On errors-in-variables for binary regression models. Biometrika 71:19–26
Perkins NJ, Schisterman EF, Vexler A (2011) ROC curve inference for best linear combination of two biomarkers subject to limits of detection. Biom J 53:464–476
Fuller WA (1987) Measurement error models. Wiley, New York
Malinovsky Y, Albert P, Schisterman EF (2012) Pooling designs for outcomes under a Gaussian random effects model. Biometrics 68:45–52
Faraggi D, Reiser B, Schisterman EF (2003) ROC curve analysis for biomarkers based on pooled assessments. Stat Med 22:2515–2527
Vexler A, Tsai WM, Malinovsky Y (2011) Estimation and testing based on data subject to measurement errors: from parametric to nonparametric likelihood methods. Stat Med 31:2498–2512
Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM (2006) Measurement error in nonlinear models. Chapman & Hall, New York
Schimid CH, Rosner B (1993) A Bayesian approach to logistic regression models having measurement error following a mixture distribution. Stat Med 12:1141–1153
Kass RE (1993) Bayes factors in practice. J Roy Stat Soc 42:551–560
Schisterman EF, Vexler A, Ye A, Perkins NJ (2011) A combined efficient design for biomarker data subject to a limit of detection due to measuring instrument sensitivity. Ann Appl Stat 5(4):2651–2667
Vexler A, Jihnhee Y, Hutson AD (2011) Likelihood testing populations modeled by autoregressive process subject to the limit of detection in applications to longitudinal biomedical data. J Appl Stat 38(7):1333–1346
Gupta AK (1952) Estimation of the mean and standard deviation of a normal population from a censored sample. Biometrika 39:260–273
Pepe MS (2003) The statistical evaluation of medical tests for classification and prediction. Oxford, New York, NY
Perkins NJ, Schisterman EF, Vexler A (2009) Generalized ROC curve inference for a biomarker subject to a limit of detection and measurement error. Stat Med 28(13):1841–1860
Perkins NJ, Schisterman EF, Vexler A (2007) Receiver operating characteristic curve inference from a sample with a limit of detection. Am J Epidemiol 165:325–333
Schisterman EF, Vexler A, Whitcomb BW, Liu A (2006) The limitations due to exposure detection limits for regression models. Am J Epidemiol 163:374–383
Rubin DB, Schenker N (1986) Multiple imputation for interval estimation from simple random samples with ignorable nonresponse. J Am Stat Assoc 81(394):366–374
Vexler A, Liu A, Schisterman EF (2006) Efficient design and analysis of biospecimens with measurements subject to detection limit. Biom J 48:780–791
Schisterman EF, Vexler A, Mumford SL, Perkins NJ (2010) Hybrid pooled-unpooled design for cost-efficient measurement of biomarkers. Stat Med 29:597–613
Vexler A, Liu S, Schisterman EF (2011) Nonparametric-likelihood inference based on cost-effectively-sampled-data. J Appl Stat 38:769–783
Mumford SL, Schisterman EF, Vexler A, Liu A (2006) Pooling biospecimens and limits of detection: effects on ROC curve analysis. Biostatistics 7:585–598
Vexler A, Schisterman EF, Liu A (2008) Estimation of ROC curves based on stably distributed biomarkers subject to measurement error and pooling mixtures. Stat Med 27:280–296
Vexler A, Liu A, Schisterman EF (2010) Nonparametric deconvolution of density estimation based on observed sums. J Nonparametr Stat 22:1048–5252
R Development Core Team (2012) R: a language and environment for statistical computing. R foundation for statistical computing, Vienna, Austria. ISBN 3-900051-07-0 http://www.R-project.org
Searle SR, Casella G, McCullooch CE (1992) Variance components. Wiley, New York
DiCiccio T, Hall P, Romano J (1989) Comparison of parametric and empirical likelihood functions. Biometrika 76:465–476
Owen AB (1988) Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75:237–249
Owen AB (1991) Empirical likelihood for linear models. Ann Stat 19:1725–1747
Owen AB (2001) Empirical likelihood. Chapman & Hall/CRC, New York
Vexler A, Liu S, Kang L, Hutson AD (2009) Modifications of the empirical likelihood interval estimation with improved coverage probabilities. Commun Stat Simulation Comput 38:2171–2183
Vexler A, Yu J, Tian L, Liu S (2010) Two-sample nonparametric likelihood inference based on incomplete data with an application to a pneumonia study. Biom J 52:348–361
Vexler A, Gurevich G (2010) Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy. Comput Stat Data Anal 54:531–545
Yu J, Vexler A, Tian L (2010) Analyzing incomplete data subject to a threshold using empirical likelihood methods: an application to a pneumonia risk study in an ICU setting. Biometrics 66:123–130
Kitamura Y (1997) Empirical likelihood methods with weakly dependent processes. Ann Stat 25:2084–2102
Carlin B, Louis TA (2008) Bayes and empirical Bayes methods for data analysis. Chapman & Hall/CRC, New York
Liu A, Schisterman EF (2003) Comparison of diagnostic accuracy of biomarkers with pooled assessments. Biom J 45:631–644
Liu A, Schisterman EF, Teoh E (2004) Sample size and power calculation in comparing diagnostic accuracy of biomarkers with pooled assessments. J Appl Stat 31:49–59
Schisterman EF, Vexler A (2008) To pool or not to pool, from whether to when: applications of pooling to biospecimens subject to a limit of detection. Pediatr Perinat Epidemiol 22:486–496
Harter HL, Moore AH (1967) Asymptotic variances and covariances of maximum-likelihood estimators, from censored samples, of the parameters of Weibull and gamma populations. Ann Math Stat 38:557–570
Richardson DB, Ciampi A (2003) Effects of exposure measurement error when an exposure variable is constrained by a lower limit. Am J Epidemiol 157:355–363
Nie L, Chu H, Liu C, Cole SR, Vexler A, Schisterman EF (2010) Linear regression with an independent variable subject to a detection limit. Epidemiology 21(Suppl 4):S17–S24
Perkins NJ, Schisterman EF, Vexler A (2013) Multivariate normally distributed biomarkers subject to limits of detection and receiver operating characteristic curve inference. Acad Radiol 20:838–846
Zhang Z, Albert PS (2011) Binary regression analysis with pooled exposure measurements: a regression calibration approach. Biometrics 67:636–645
Lyles RH, Tang L, Lin J, Zhang Z, Mukherjee B (2012) Likelihood-based methods for regression analysis with binary exposure status assessed by pooling. Stat Med 31:2485–2497
Mcmahan CS, Tebbs JM, Bilder CR (2013) Regression models for group testing data with pool dilution effects. Biostatistics 14:284–298
Ma CX, Vexler A, Schisterman EF, Tian L (2011) Cost-efficient designs based on linearly associated biomarkers. J Appl Stat 38:2739–2750
Whitcomb BW, Perkins NJ, Zhang Z, Ye A, Lyles RH (2012) Assessment of skewed exposure in case-control studies with pooling. Stat Med 31:2461–2472
Vexler A, Liu A, Eliseeva E, Schisterman EF (2008) Maximum likelihood ratio tests for comparing the discriminatory ability of biomarkers subject to limit of detection. Biometrics 64:895–903
Perkins NJ, Schisterman EF (2005) The Youden index and the optimal cut-point corrected for measurement error. Biom J 47:428–441
Delaigle A, Hall P (2012) Nonparametric regression with homogeneous group testing data. Ann Stat 40:131–158
Liu A, Schisterman EF, Wu C (2006) Multistage evaluation of measurement error in a reliability study. Biometrics 62:1190–1196
Guo Y, Little RJ (2011) Regression analysis with covariates that have heteroscedastic measurement error. Stat Med 30:2278–2294
Guo Y, Little RJ, McConnell DS (2012) On using summary statistics from an external calibration sample to correct for covariate measurement error. Epidemiology 23:165–174
Albert PS, Harel O, Perkins N, Browne R (2010) Use of multiple assays subject to detection limits with regression modeling in assessing the relationship between exposure and outcome. Epidemiology 21(Suppl 4):S35–S43
Gillespie BW, Chen Q, Reichert R, Franzblau A, Hedgeman E, Lepkowski J, Adriaens P, Demond A, Luksemburg W, Garabrant DH (2010) Estimating population distributions when some data are below a limit of detection by using a reverse Kaplan-Meier estimator. Epidemiology 21:S64–S70
Herring AH (2010) Nonparametric Bayes shrinkage for assessing exposures to mixtures subject to limits of detection. Epidemiology 21(Suppl 4):S71–S76
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Vexler, A., Tao, G., Chen, X. (2015). A Toolkit for Clinical Statisticians to Fix Problems Based on Biomarker Measurements Subject to Instrumental Limitations: From Repeated Measurement Techniques to a Hybrid Pooled–Unpooled Design. In: Armstrong, D. (eds) Advanced Protocols in Oxidative Stress III. Methods in Molecular Biology, vol 1208. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-1441-8_31
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DOI: https://doi.org/10.1007/978-1-4939-1441-8_31
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