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DONNA SPIEGELMAN

“Adjusting for bias in effect estimates due to exposure measurement error in occupational and environmental epidemiology”. DONNA SPIEGELMAN. HARVARD SCHOOL OF PUBLIC HEALTH BOSTON, MA stdls@hsph.harvard.edu

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DONNA SPIEGELMAN

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  1. “Adjusting for bias in effect estimates due to exposure measurement error in occupational and environmental epidemiology” DONNA SPIEGELMAN HARVARD SCHOOL OF PUBLIC HEALTH BOSTON, MA stdls@hsph.harvard.edu And many other colleagues, including Edie Weller, Ruifeng Li, Don Milton, Ellen Eisen, Barbara Valanis, Sally Thurston, Jon Samet, Paige Williams, Russ Hauser, Roger Logan, Jon Samet, Doug Grove, Doug Dockery, Lucas Neas, Nora Horrick, Diane Gold, Mauricio Hernandez, Howard Hu, Aparna Keshaviah

  2. - NUTRITIONAL EPIDEMIOLOGY PROVIDED INITIAL IMPETUS FOR NEW STATISTICAL DEVELOPMENTS IN MEASUREMENT ERROR MODELS - METHODS DEVELOPED FOR NUTRITIONAL EPIDEMIOLOGY APPLICATIONS CANNOT OFTEN BE VALIDLY APLIED DIRECTLY TO OCCUPATIONAL AND ENVIRONMENTAL HEALTH STUDIES - IN THIS TALK, I WILL GIVE A BRIEF OVERVIEW OF SEVERAL PROBLEMS WHICH HAVE BEEN ADDRESSED BY MYSELF AND COLLEAGUES AT HSPH, MOTIVATED BY ONGOING ENVIRONMENTAL AND OCCUPATIONAL EPIDEMIOLOGIC RESEARCH AT HSPH and ELSEWHERE: • Assessment of the effect of metal working fluids on respiratory function, in machinists • Assessment of the effect of indoor NO2 exposure in on children’s respiratory function • Assessment of the effect of MTBE exposure about gasoline service station workers and commuters on general health symptoms • Assessment of the effect of in utero lead exposure on the birthweight of infants in Mexico City • Assessment of the effect of exposure to radon gas on the risk of death from lung cancer among uranium miners • Assessment of the effect of mixing anti-neoplastic drugs on the prevalence of fever among nurses

  3. Regression calibration for logistic regression with multiple surrogates for one exposure Edie A. Weller, Donna Spiegelman, Don Milton, Ellen Eisen Departments of Biostatistics, Epidemiology, and Environmental Health Harvard School of Public Health and Dana Farber Cancer Institute Journal of Statistical Planning and Inference, 2007; 137:449-461 • Occupational exposures often characterized by numerous factors of the workplace and work duration in a particular area ==> multiple surrogates describe one exposure. • Validation study: Personal exposure is commonly measured on a subset of the subjects and these values are then used to estimate average exposure by job or exposure zone. • No adjustment for bias or uncertainty in the exposure estimates. • Current methods typically assume that there is one surrogate for each exposure (for example, Rosner et al, 1989, 1990). • Propose adjustment method which allows for multiple surrogates for one exposure using a regression calibration approach.

  4. Main Study • To assess the relationship between exposure to metal working fluids (MWF) and respiratory function (United Automobile Workers Union and General Motors Corporation sponsored study, Greaves et al, 1997). • Outcome here is prevalence of wheeze • Job characteristics include metal working fluid (MWF) type, plant and machine operation (grinding or not). • Assembly workers are considered the non-exposed group. • Possible confounders include age, smoking status and race.

  5. Exposure Assessment Study (generically, the validation study) • Exposure was measured in various job zones (Woskie et al, 1994). • Intensity of exposure to MWF aerosol measured by the thoracic aerosol fraction (i.e. the sum of the two smallest size fractions measured with the personal monitors). • Full shift (8 hour) personal samples of aerosol exposure in breathing zone of automobile workers were collected in various job zones.

  6. Notation Number of workers in main study Number of workers in validation study Binary health outcome (prevalence of wheeze) Measured on all workers in main and validation study “True” exposure (thoracic aerosol fraction in mg/m3) r surrogates (plant, MWF type, machine operation) Measured on all workers in main and validation study s perfectly measured covariates (age, race, smoking status) Measured on all workers in main and validation study

  7. Assumptions • True exposure and the s-vector of covariates are related to the probability of binary outcome by the logistic function: logit where • Linear regression model is appropriate to relate the r surrogates and the s covariates to the true exposure: where • is a surrogate if , that is, knowledge of the surrogates provides no additional information if the true exposure is known. • and small, • or small

  8. Goal: To obtain point and interval estimates of and relating exposure to outcome adjusting for the covariates Problem • Quantitative measure of exposure is not measured on all subjects. • is measured on all of the subjects • and measured on subjects. • Multiple surrogates, describe exposure Solution: An extension to two closely related approaches • Rosner, Spiegelman and Willett (RSW, 1989, 1990) • Carroll, Ruppert and Stefanski (CRS, 1995)

  9. Procedure: Propose the following approach which follows RSW and assumes normality of and rare disease, or small (parameter of the small ME approximation): • Estimate from a logistic regression model of on and in subjects in main study • Estimate from a measurement error model among the validation study subjects using ordinary least squares regression. logit SAS PROC GENMOD or PROC LOGISTIC for step 1, PROC REG for step 2

  10. 3. Optimally combine the adjusted estimates for each surrogate where is the estimated variance-covariance matrix of SAS macro downloadable from my website to accomplish step 3; input to the macro is the output from PROC LOGISTIC and PROC REG http://www.hsph.harvard.edu/faculty/spiegelman/multsurr.html

  11. Association of indoor nitrogen dioxide with respiratory symptoms in children: Application of measurement error correction techniques to utilize data from multiple surrogates Li R, Weller EA, Dockery DW, Neas LM, Spiegelman D. Journal of Exposure Analysis and Environmental Epidemiology, 2006; 16:342-350.

  12. Variable Uncorrected Analysis (n1=1754) [95%CI] Measurement Error Corrected4 (n1=1754) [95%CI] Validation Study Alone (n2=1137) [95%CI] Combined Analysis (n1+n2=2891) [95%CI] NO2 (per 15 ppb increment) Surrogates2 (W) Gas stove, no pilot Gas stove, pilot Stove heater Fan Wood stove Number of rooms in the home3 Kerosene heater 0.68 [0.42, 1.10] 1.54 [0.94, 2.52] 1.61 [1.05, 2.47] 0.93 [0.81, 1.07] 0.91 [0.66, 1.25] 0.99 [0.92, 1.06] 1.41 [0.96, 2.07] 1.60 [1.10, 2.32] 0.37 [0.11, 1.29] 1.91 [0.91,3.99] 435 [0.01,>1000] 4.69 [0.21,104] 2.17 [0.17, 27.1] 1.84 [0.09, 37.0] 2.77 [0.86, 8.97] 1.41 [1.13, 1.75] 1.45 [1.20, 1.75] Table 4: NO2 and surrogates in relation to annual prevalence of respiratory symptoms1 1 Adjusted for cities, single marital status, higher education status, parental history of bronchitis or emphysema, parental history of asthma, gender, age, and the total packs of cigarette smoking inside the child’s home 2 Odds ratios & their 95% CIs are given for the effect of each surrogate, adjusted for all others and for the model covariates 3 Odds ratios & their 95% CIs are given for the effect of a one room increase, adjusted for all other surrogates and for the model covariates 4 Measurement error-corrected odds ratios are per 15 ppb NO2

  13. Table 3: Measurement error model for NO2 (ppb) (n2=1137) MEASUREMENT ERROR MODEL ( =1137) Variable name (ppb/unit increase) P-value Weights1 Intercept 18.38 1.14 <0.001 Surrogates Gas without pilot light 6.01 0.69 <0.001 .183 Gas with pilot light 10.05 0.73 <0.001 .510 Stove heater 1.17 0.95 0.218 .002 Fan -0.72 0.24 0.003 .029 Wood stove -1.94 0.53 <0.001 .044 Number of rooms in the home -0.35 0.12 0.004 .031 Kerosene heater 5.07 0.76 <0.001 .202 Confounders Watertown, Massachusetts -3.50 0.85 <0.001 Kingston and Harriman, Tennessee -8.97 0.87 <0.001 Steubenville, Ohio -4.41 0.76 <0.001 Portage and surrounding communities -9.81 0.72 <0.001 Topeka, Kansas -9.46 0.76 <0.001 Single 1.01 0.60 0.089 Parents with higher education -0.34 0.43 0.427 Parental history of bronchitis 0.72 0.46 0.116 Parental history of asthma 0.54 0.61 0.375 Girls 0.70 0.41 0.086 Age older >= 10 at first questionnaire 0.17 0.48 0.719 Parental cigarette smoking (packs/day) 1.07 0.33 0.001 1 These are the inverse of the variance of the corresponding measurement error model coefficient

  14. Environmetrics 2003; 14: 573–582 (DOI: 10.1002/env.604) Occupational exposure to methyl tertiary butyl ether in relation to key health symptom prevalence: the effect of measurement error correction Aparna P. Keshaviah, Edie Weller and Donna Spiegelman Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115, U.S.A. Department of Epidemiology, Harvard School of Public Health, Boston, MA 02115, U.S.A.

  15. Table 2. Association of prevalence of key symptoms in relation to serum MTBE levels and occupation Standard Measurement Validation study Combined analysis error corrected alone analysis ( = 328) (= 328) ( =81) ( = 409) Variable OR[95% CI] OR[95% CI] OR[95%CI] OR[95% CI] log10(MTBE) (X) 1.1[0.67, 1.77] 3.1[1.48, 6.33] 1.5[1.00, 2.25](mg/L) Surrogates (W) Commuters 1.2[0.66, 2.05] 1.56[0.29, 8.45] Car repair 1.2[0.36, 4.06] 1.16[0.44, 3.10] Other 6.3[0.71, 56.3] >100[0.00, >1000] Pump gas 1.1[0.35, 13.54] 1.05[0.61, 1.81] Reference group is Albany study participants. Adjusted for age, smoking and gender

  16. Table 3. Measurement error model for log10(blood MTBE levels) (mg/L) ( =81) Variable SE( ) p-value Intercept 0.96 0.121 <0.0001 Commuter 0.34 0.159 0.034 0.042 Car repair 1.24 0.148 <0.0001 0.21 Other 0.14 0.230 0.54 0.00 Pump gas 2.13 0.316 <0.0001 0.75 Smoke 0.062 0.130 0.64 Age# 0.070 0.057 0.23 Gender§§ 0.27 0.139 0.056 # Grouped as <35, 36–41, 42–52, 53+. §§Relative to males.

  17. Home Endotoxin Exposure and Wheeze in Infants: Correction for Bias Due to Exposure Measurement Error Nora Horick, Edie Weller, Donald K. Milton, Diane R. Gold, Ruifeng Li, and Donna Spiegelman Department of Biostatistics and Department of Environmental Health, Harvard School of Public Health, Boston, Massachusetts, USA; Channing Laboratory, Harvard Medical School, Boston, Massachusetts, USA; Department of Epidemiology, Harvard School of Public Health, Boston, Massachusetts, USA Environmental Health Perspectives Volume 114, Number 1, January 2006

  18. Regression Calibration With Heteroscedastic Variance Donna Spiegelman, Roger Logan, Douglas Grove Under review, 2010

  19. Assumptions • True exposure and the s-vector of covariates are related to the probability of binary outcome by the logistic function: logit where • Linear regression model is appropriate to relate the r surrogates (W) and the s covariates (Z) to the true exposure: • Where • ******* • is a surrogate if , that is, knowledge of the surrogates provides no additional information if the true exposure is known. • and small, • or small

  20. Derivation of estimator • Let under the rare disease assumption, and • Then,

  21. The Procedure 1. A logistic regression model of Y on X and g(X) is run in the main study to obtain and and their estimated variances 2. A weighted linear regression is run in the validation study, with weights 1/g(X), to obtain and 3. and are calculated as a function of and and efficiently combined to produce a single estimate • The asymptotically minimum variance weights and their derivation, as well as the formula for the variance of , are given in the Appendix of the manuscript.

  22. Example: ACE study prevalence of fever average weekly chemotherapeutics exposure, self-reported on questionnaire same, from on-site diary for 1-2 weeks 104 cases, 6 in validation study Valanis et al., 1993 control for =age (years), shift work (yes/no) logit

  23. Examples ACE study Corr 0.21 (0.26 outliers out) uncorrected 1.13 (1.03 - 1.23) 1.22 (1.04 - 1.43) 1.24 (1.05 - 1.48) 52 drugs mixed/day (90th-10th) controlling for age, shift, community hospital

  24. A comparison of regression calibration approaches for designs with internal validation data Sally W. Thurston, Paige L. Williams, Russ Hauser, Howard Hu, Mauricio Hernandez-Avila, and Donna SpiegelmanDepartment of Biostatistics and Computational Biology, University of Rochester Medical Center, 601 Elmwood Avenue, P.O. Box 630, Rochester, NY 14642, USA Department of Biostatistics, Harvard School of Public Health, USA Department of Environmental Health, Harvard School of Public Health, USA Centro de Investigaciones en Salud Poblacional, Instituto Nacional de Salud Publica, Cuernavaca, Morelos, Mexico Department of Epidemiology, Harvard School of Public Health, USA Channing Laboratory, Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, US JOURNAL OF STATISTICAL PLANNING AND INFERENCE 131 (1): 175-190 APR 1 2005

  25. We compare the asymptotic relative efficiency of several regression calibration methods of correcting for measurement error in studies with internal validation data, when a single covariate is measured with error. The estimators we consider are appropriate in main study/hybrid validation study designs, where the latter study includes internal validation and may include external validation data. Although all of the methods we consider produce consistent estimates, the method proposed by Spiegelman et al. (Statistics in Medicine, 20 (2001) 139) has an asymptotically smaller variance than the other methods. The methods for measurement error correction are illustrated using a study of the effect of in utero lead exposure on infant birth weight.

  26. Internal validation • Methods to compare: • “As external”: Treat internal validation (IV) data as external validation data – i.e. ignore in IV study. • “Same intercept”: Regress on for IV, for main study. • “Different intercept”: Same as (2), but allow IV study, and main study to have different intercepts. • 4. “Weighted” (Spiegelman, Carroll, Kipnis): Calculate from IV study, and from bias-corrected main study. Combine by weighting each estimate of by its inverse variance. • One can obtain closed form estimators for

  27. The different intercept method (CRS, 1st edition, p. 46) when participantis in the internal validation study, 0 otherwise when participant is in the main study, 0 otherwise Since when sampling into the internal validation study is independent of given and , estimation of this additional parameter, if correlated with could only increase the variance of the different intercept method relative to the same intercept method. This estimator is not considered any further.

  28. Asymptotic relative efficiencies • “As external” does same/worse than other 2 methods. • “Weighted” (SCK) method does much better than “same intercept” method when: • - is small. • - is large. • - is small. • Based on a grid search, “weighted” method never does • worse than “same intercept” method.

  29. Effect of bone lead on birth weight ( =577, =485) (Gonzalez-Cossio, 1997) . Corr(X,W)=0.19

  30. Summary and conclusions • In external validation (EV) situation, two regression calibration • methods give identical estimators for . • With internal validation (IV) study, 3 methods were compared: • “as external”: ignores in IV data. • “Same intercept”: uses in IV data, otherwise. • “weighted” (SCK): combines from IV, from corrected • main study, weighting each by its inverse variance. • (1) same/worse than (2), (2) same/worse than (3). • Especially important to use (3) when small, • large, and/or validation sample is small relative to • main study.

  31. Correcting for Measurement Error Bias In • Cumulative Exposure Variables: • A Cox Model For Lung Cancer Mortality • In Relation To Radon Progeny Exposure. • R. Logan • D. Spiegelman, • Departments of Epidemiology and Biostatistics • Harvard School of Public Health • Boston, MA, USA. • J. Samet • Johns Hopkins School of Public Health • Baltimore, MD, USA

  32. Original Study: Lung Cancer Mortality and Exposure to Radon Progeny In A Cohort of New Mexico Underground Uranium Miners. J. Samet, D. Pathak, M. Morgan, C. Key, A. Valdivia, J. Lubin Health Physics, vol 61, No. 6, 1991, pp 745-752

  33. Original study consisted of: • 3469 males with at least one year of underground • uranium mining experience. • Follow-up through December 31, 1985 • 70 cases of lung cancer • 408 deaths • Present study: • 3469 males with at least one year of underground • uranium mining experience. • Follow-up through December 31, 1993 • Contains 120 cases of lung cancer • 686 deaths

  34. Types of Measurements • Source of exposure data Years Spanned • 1 Individual estimates (c) 1967 – 1985 • 2 Company-section Measurements (C) 1956 – 1976 • 3 Grants clinic 1942 – 1979 • Colorado Plateau 1967 – 1985 • Overrides 1959 – 1974 • Hierarchy of data quality 1 > 2 > 3. • Assume that the individual estimates are the gold standard, • in the sense that the ‘ideal’ study would have used these • measurements for everyone. • There are 8 years of overlap between c and C, between • 1967 – 1976.

  35. Validation Study The validation study consists of 2833 pairs of individual annual measurements and annual section/company samples (c and C point exposure measurements). where and are the longest available cumulative exposure measurements for the 862 miners in the validation study.

  36. Error Model for Possible Choices: Gaussian : includes normal and other power transforms; log-normal also considered. Gamma : In the above models, is a collection of perfectly measured covariates. Model Used: A combination of gamma distribution and a point mass at 0. Where is 1 when holds and 0 otherwise.

  37. Extended Partial Likelihood function. where if if if and

  38. Results • Here is the log rate ratio corresponding to cumulative exposure. • There is about a 30% attenuation in beta due to exposure • measurement error. • Results could have policy implications since the original study played an important role in permissible exposure levels for radon

  39. Conclusions • Bias due to exposure measurement error in a major limitation to • the validity of occupational and environmental studies • Methods have been developed which accommodate the • features of study design and data distributions found in such • studies • These methods implement explicit adjust for this source of bias, • using the exposure validation study to characterize the • magnitude and other features of the measurement error • Point and interval estimates of effect are adjusted

  40. We can accommodate the following situations: • multiple surrogates for a single mis-measured exposure • heteroscedastic measurement error • internal and hybrid validation study designs • cumulative exposure variables in cohort studies • User-friendly SAS macros are available to implement many of these procedures • http://www.hsph.harvard.edu/faculty/spiegelman/blinplus.html • http://www.hsph.harvard.edu/faculty/spiegelman/multsurr.htm • http://www.mep.ki.se/%7Emarrei/software/ (for optimal main study/validation study design) • Papers have been published applying these methods to the analysis of occupational and environmental studies: you won’t be the first! • Just as we routinely adjust for confounding, we can routinely adjust for measurement error

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