American Journal of Epidemiology Advance Access originally published online on January 17, 2008
American Journal of Epidemiology 2008 167(4):502-503; doi:10.1093/aje/kwm387
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LETTERS TO THE EDITOR |
RE: "EFFECTS OF PAST AND RECENT BLOOD PRESSURE AND CHOLESTEROL LEVEL ON CORONARY HEART DISEASE AND STROKE MORTALITY, ACCOUNTING FOR MEASUREMENT ERROR"
1 Medical Statistics Unit, London School of Hygiene and Tropical Medicine, London WC1E 7HT, United Kingdom
2 MRC Biostatistics Unit, Institute of Public Health, University of Cambridge, Cambridge CB2 0SR, United Kingdom
(e-mail: jonathan.bartlett{at}lshtm.ac.uk)
We read with interest the recent paper by Boshuizen et al. (1) exploring the associations between mortality risk and current versus past values of systolic blood pressure (SBP) and serum cholesterol. We applaud their recognition that risk in a particular period may depend on both current and past exposure levels, and that these exposures may contribute differentially to current risk. However, we would like to highlight an assumption made under the two-step approach used by Boshuizen et al. to adjust for measurement error, which appears to have been violated in at least one of the analyses reported.
In their paper, Boshuizen et al. use the two-step approach of Tsiatis et al. (2), which is essentially a form of regression calibration and as such makes the usual assumption that measurement error is nondifferential. The approach involves fitting a linear mixed model to longitudinal error-prone measurements of the exposures of interest—SBP and cholesterol. The mixed model is used to obtain empirical Bayes estimates of the true exposure levels 25 years previously and at the current age. In the second stage, the authors use these empirical Bayes values to fit a number of different Cox regression models, either using exposure at a single time point (hence not adjusted for levels at other time points) (table 4) or entering exposure at both time points simultaneously (tables 5 and 6).
When fitting a model containing the true exposure level at a single point in time, Boshuizen et al. aim to estimate the unadjusted association between that true exposure level and disease. It is clear that because of confounding, these unadjusted associations may not represent causal associations. Our point, however, is that the methods used may yield biased estimates of these unadjusted associations. This is because they assume that measurement error is nondifferential, and this assumption is false if the true exposure level at the other time point is independently associated with risk.
For example, Boshuizen et al.'s results (table 5) suggest that after adjustment for SBP at the current age, SBP 25 years previously is independently associated with risk of coronary heart disease mortality. If this is the case and a Cox model is fitted with only SBP at the current age (table 4) but measurements from 25 years previously are used at the linear mixed model stage, the estimates of the unadjusted association of current SBP will be biased (3). This is because measurements of SBP 25 years previously are related to the outcome, after conditioning on the true exposure of interest (in this case, current SBP), thus violating the nondifferential error assumption.
It is important to realize that whether measurement error can be considered nondifferential depends on the final model being fitted. If we use error-prone measurements of a variable at the regression calibration stage but omit the variable from the analysis model, the resulting estimates for other variables will be unbiased only if the omitted variable has no independent association with the outcome.
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ACKNOWLEDGMENTS |
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Conflict of interest: none declared.
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References |
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 TOP References |
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- Boshuizen HC, Lanti M, Menotti A, et al. Effects of past and recent blood pressure and cholesterol level on coronary heart disease and stroke mortality, accounting for measurement error. Am J Epidemiol (2007) 165:398–409.
[Abstract/Free Full Text] - Tsiatis AA, DeGruttola V, Wulfsohn MS. Modeling the relationship of survival to longitudinal data measured with error: applications to survival and CD4 counts in patients with AIDS. J Am Stat Assoc (1995) 90:27–37.[CrossRef][Web of Science]
- Frost C, White IR. The effect of measurement error in risk factors that change over time in cohort studies: do simple methods overcorrect for ‘regression dilution’? Int J Epidemiol (2005) 34:1359–68.
[Abstract/Free Full Text]
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  H. C. Boshuizen, M. Lanti, A. Menotti, J. Moschandreas, H. Tolonen, A. Nissinen, S. Nedeljkovic, A. Kafatos, and D. Kromhout THE AUTHORS REPLY Am. J. Epidemiol., February 15, 2008; 167(4): 503 - 504. [Full Text] [PDF]
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