American Journal of Epidemiology Advance Access originally published online on July 5, 2007
American Journal of Epidemiology 2007 166(6):659-661; doi:10.1093/aje/kwm174
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Fewell et al. Respond to "Fuel for Debate"
From the Department of Social Medicine, University of Bristol, Bristol, United Kingdom
Correspondence to Prof. Jonathan A. C. Sterne, Department of Social Medicine, University of Bristol, Canynge Hall, Whiteladies Road, Bristol BS8 2PR, United Kingdom (e-mail: Jonathan.Sterne{at}bristol.ac.uk).
Received for publication December 13, 2006. Accepted for publication May 3, 2007.
In our paper (1), we considered the extent and patterns of bias in estimates of exposure-outcome associations that can result from residual or unmeasured confounding, when there is no true association between the exposure and the outcome. We conducted simulations with two or four confounders. When the confounders are uncorrelated, bias in the exposure effect estimate increases as the amount of residual and unmeasured confounding increases. However, patterns are more complex for correlated confounders: It is possible for the bias to increase when confounder measurement error decreases or when additional confounders are controlled for.
In his commentary, Dr. James Marshall (2) correctly identifies some limitations of our study: For example, he points out that the effects on the outcome of all confounders pointed in the same direction and that measurement errors were independent of risk and of each other. Further work examining the extent to which our findings are generalizable when such assumptions are relaxed would be of interest. We agree with Dr. Marshall that "measurement error is more than a benign influence that leads us to occasionally overlook risk factors" (2, p. 657). Marshall correctly identifies the need to build routine assessment of the extent of measurement error into epidemiologic studies and, having done so, to use methods that correct for measurement error in analyses.
Marshall states that the most significant limitation of our study was that we did not examine the effects of measurement error in the exposure of interest. We conducted additional simulation studies in which the exposure, as well as the confounders, may be measured with error. The simulation methods used were similar to those described in our paper (1) but with measurement error in the exposure as well as the confounders. The exposure intraclass correlation coefficient (ICC) was set to either 0.5 or 0.75, corresponding to a measurement error variance of 1 or 1/3. Following the addition of measurement error to the exposure variable, we divided the mismeasured variable by its standard deviation. Therefore, the estimated odds ratio for the exposure-outcome association can be interpreted as the odds ratio per standard-deviation increase in the mismeasured exposure variable. Full details of our simulation studies incorporating exposure measurement error are available in a supplement posted on the Journal's website (www.aje.oxfordjournals.org).
In general, the effect of random, nondifferential, and additive measurement error in the exposure was to attenuate estimated odds ratios towards the null. This effect of exposure measurement error has been previously described—for example, by Spearman (3), Armstrong et al. (4), and Armstrong (5). Table 1 shows the results of one of the additional simulation studies. In this simulation, there were two confounders, the correlation between the confounders was 0.5, and the ICC for exposure was 0.5. In all simulations presented in table 1, the true exposure-outcome odds ratio was 1. As expected, when there is no residual or unmeasured confounding (ICC = 1 for both Z1 and Z2 and odds ratios are adjusted for Z1 and Z2), the estimated exposure-outcome odds ratios equal the true odds ratio of 1.
|
The estimated odds ratios in table 1 are all smaller than those from corresponding simulations in which there is no exposure measurement error (1). Further, they are smaller than those estimated when there is less exposure measurement error (ICC = 0.75; data not shown). For example, in simulations in which the correlations between the confounders and exposure are 0.5 but exposure is measured without error, the maximum crude odds ratio estimated is 1.85 (1). The corresponding odds ratio in table 1 is 1.53, and when the exposure ICC is 0.75 the corresponding odds ratio is 1.69.
In general, bias in the estimated odds ratios increases with increasing measurement error in the confounders, increasing correlation between the confounders and exposure, and increasing unmeasured confounding. However, there are exceptions to these general patterns which occur when the partial correlations between exposure and confounders are negative. Consider, for example, the estimated odds ratios in the upper right portion of table 1, where the correlation between E and X1 equals 0.1 and the correlation between E and X2 equals 0.5. Bias in the estimated odds ratio may decrease as measurement error in Z1 increases. When the ICC for Z2 is 0.5, increasing measurement error in Z1 results in a slight decrease in the odds ratio adjusted for Z1 and Z2 (the adjusted odds ratio equals 1.12 when the ICC for Z1 equals 0.5, and it increases to 1.14 when Z1 is measured without error (ICC = 1)).
Reductions in bias with increasing confounder-exposure correlations can be seen in the middle portion of table 1 (correlation between E and X2 = 0.3), when the ICC for Z1 equals 1 and the ICC for Z2 equals 0.5. When the correlation between E and X1 equals 0.1, the estimated odds ratio adjusted for Z1 and Z2 in table 1 equals 1.07. As the correlation between E and X1 increases to 0.5, the estimated odds ratio decreases to 1.01. Finally, consider the estimated odds ratios in the bottom left portion of table 1 (correlation between E and X1 = 0.5 and correlation between E and X2 = 0.1). Here, a slight decrease in bias with increased unmeasured confounding is observed. When the ICCs for both confounders are 0.5, the estimated odds ratio adjusted for Z1 and Z2 is 1.12. When Z2 is omitted from the analysis, the estimated odds ratio is 1.11.
In summary, our findings on the effects of residual and unmeasured confounding appear to be generalizable to situations in which exposure, as well as confounders, is measured with error. The effect of random, nondifferential, and additive measurement error in the exposure was, as expected, to attenuate estimated exposure-outcome odds ratios towards the null. Residual and unmeasured confounding may have contributed to the incongruity that has repeatedly been observed between observational and experimental studies. This incongruity has been particularly prevalent in dietary epidemiology, although difficulties associated with noncompliance and dropout mean that clinical trials in this field are also problematic (6). We agree with Marshall (2) that triangulation of findings is key, and we consider that instrumental-variable approaches, including those utilizing functional genetic variants as instruments, have much to offer in this regard (7, 8).
 |
ACKNOWLEDGMENTS |
|---|
Conflict of interest: none declared.
|
References |
|---|
 TOP References |
|---|
- Fewell Z, Davey Smith G, Sterne JAC. The impact of residual and unmeasured confounding in epidemiologic studies: a simulation study. Am J Epidemiol (2007) 166:646–55.
[Abstract/Free Full Text] - Marshall J. Invited commentary: Fewell and colleagues—fuel for debate. Am J Epidemiol (2007) 166:656–8.
[Abstract/Free Full Text] - Spearman C. The proof and measurement of association between two things. Am J Psychol (1904) 15:72–101.[CrossRef][Web of Science]
- Armstrong BG, Whittemore AS, Howe GR. Analysis of case-control data with covariate measurement error: application to diet and colon cancer. Stat Med (1989) 8:1151–63.[Web of Science][Medline]
- Armstrong BG. The effects of measurement errors on relative risk regressions. Am J Epidemiol (1990) 132:1176–84.
[Abstract/Free Full Text] - Davey Smith G, Ebrahim S. Folate supplementation and cardiovascular disease. Lancet (2005) 366:1679–81.[CrossRef][Web of Science][Medline]
- Davey Smith G, Ebrahim S. "Mendelian randomization": can genetic epidemiology contribute to understanding environmental determinants of disease? Int J Epidemiol (2003) 32:1–22.
[Abstract/Free Full Text] - Thomas DC, Conti DV. Commentary: the concept of "Mendelian randomization." Int J Epidemiol (2004) 33:21–5.
[Free Full Text]
CiteULike 
Connotea 
Del.icio.us What's this?
Related articles in Am. J. Epidemiol.:
- The Impact of Residual and Unmeasured Confounding in Epidemiologic Studies: A Simulation Study
- Zoe Fewell, George Davey Smith, and Jonathan A. C. Sterne
Am. J. Epidemiol. 2007 166: 646-655.[Abstract] [FREE Full Text]
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||