The non-zero mean SIMEX: Improving estimation in the face of measurement error

The simulation extrapolation method developed by Cook and Stefanski (1995) is a simulation based technique for estimating and reducing bias due to additive measurement error armed only with knowledge of the variance of the measurement error distribution. However there are many instances in which validation data are not available, and measurement error is known not to have mean zero. For example, in assessing phylogenetic cluster size of HIV viruses, cluster size is systematically underestimated since clustering can only be performed on the viruses of those individuals who have presented for testing. In this setting, it is not possible to obtain validation data; however, using knowledge gleaned from the literature, the distribution of the errors may be estimated. In this work, we extend the simulation extrapolation procedure to accommodate errors with non-zero means, motivated by an interest in determining behavioural correlates of HIV phylogenetic cluster size. We provide theoretical justication for the generalization to the non-zero mean measurement error case, proving its consistency and demonstrating its performance via simulation. We then apply the result to data from a the province of Quebec in Canada to show that ndings from a

[1]  Xihong Lin,et al.  Functional Inference in Frailty Measurement Error Models for Clustered Survival Data Using the SIMEX Approach , 2003 .

[2]  S. Sanjosé,et al.  Occupational exposure to endocrine disruptors and lymphoma risk in a multi-centric European study , 2015, British Journal of Cancer.

[3]  Raymond J. Carroll,et al.  Asymptotics For The Simex Estimator In Structural Measurement Error Models , 1994 .

[4]  F. Kronenberg,et al.  American Journal of Epidemiology Practice of Epidemiology Estimating the Single Nucleotide Polymorphism Genotype Misclassification from Routine Double Measurements in a Large Epidemiologic Sample , 2022 .

[5]  Sander Greenland,et al.  Multiple-imputation for measurement-error correction. , 2006, International journal of epidemiology.

[6]  Michel Roger,et al.  Phylogenetic inferences on HIV-1 transmission: implications for the design of prevention and treatment interventions. , 2013, AIDS.

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

[8]  J. R. Cook,et al.  Simulation-Extrapolation: The Measurement Error Jackknife , 1995 .

[9]  Raymond J. Carroll,et al.  Bias Analysis and SIMEX Approach in Generalized Linear Mixed Measurement Error Models , 1998 .

[10]  Yi Shang.  Measurement Error Adjustment Using the SIMEX Method: An Application to Student Growth Percentiles , 2012 .

[11]  J. R. Cook,et al.  Simulation-Extrapolation Estimation in Parametric Measurement Error Models , 1994 .

[12]  Dipankar Bandyopadhyay,et al.  An investigation of the MC‐SIMEX method with application to measurement error in periodontal outcomes , 2009, Statistics in medicine.

[13]  Raymond J. Carroll,et al.  Asymptotics for the SIMEX Estimator in Nonlinear Measurement Error Models , 1996 .

[14]  A. Rambaut,et al.  Episodic Sexual Transmission of HIV Revealed by Molecular Phylodynamics , 2008, PLoS medicine.

[15]  Leon Jay Gleser,et al.  Simex approaches to measurement error in roc studies , 2000 .

[16]  Stéphane Hué,et al.  HIV-1 pol gene variation is sufficient for reconstruction of transmissions in the era of antiretroviral therapy , 2004, AIDS.

[17]  Wenqing He,et al.  SIMEX R Package for Accelerated Failure Time Models with Covariate Measurement Error , 2012 .

[18]  E. Moodie,et al.  HIV Sexual Networks: The Montreal Experience , 2012 .

[19]  J. Benichou,et al.  The performance of functional methods for correcting non‐Gaussian measurement error within Poisson regression: corrected excess risk of lung cancer mortality in relation to radon exposure among French uranium miners , 2012, Statistics in medicine.

[20]  Erik M. Volz,et al.  Inferring the Source of Transmission with Phylogenetic Data , 2013, PLoS Comput. Biol..

[21]  Roger A. Sugden,et al.  Multiple Imputation for Nonresponse in Surveys , 1988 .

[22]  D. Ruppert,et al.  Measurement Error in Nonlinear Models , 1995 .

[23]  M. Wainberg,et al.  Future of Phylogeny in HIV Prevention , 2013, Journal of acquired immune deficiency syndromes.

[24]  Esther Fearnhill,et al.  Transmission Network Parameters Estimated From HIV Sequences for a Nationwide Epidemic , 2011, The Journal of infectious diseases.