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In epidemiological studies, misclassification error, especially differential misclassification, has serious implications. Different sensitivity levels, specificity levels, prevalence rates and odds ratios were simulated. Interaction graphics were constructed to study bias in the different settings, and the effect of the different factors on bias was described using linear models. One hundred per cent of the biases caused by NDME were negative.
The effect of the sensitivity and specificity in classifying exposure, the prevalence of exposure in controls and true OR differed between positive and negative biases.
The use of valid exposure classification instruments with high sensitivity and high specificity is recommended to mitigate this type of bias. Case-control studies are commonly utilized, especially for studying rare diseases 1 1.
Rothman K, Greenland S. Modern Epidemiology. Philadelphia: Lippincott Raven Publishers, Cancer Epidemiology: Principles and Methods. Both case identification and control selection should be carried out with the greatest possible rigor. Lack of rigor could lead to systematic errors and consequently to invalid results 3 3.
Similarly, if the exposure, the disease or both are misclassified, the association measures, the odds ratio OR and the conclusions will be biased 1 1. In any epidemiological study, the inappropriate classification of the exposure or of the disease is known as misclassification error, which can be divided into two types: non-differential misclassification error NDME or differential misclassification error DME. This type of error is usually found in studies that investigate socially unacceptable behaviour or behaviours considered private that can generate shame or stigma 4 4.
Misclassification bias: diversity in conceptualisations about having 'had sex'. Sex Health ; 7: Measuring psychotropic drug exposures in register-based studies - validity of a dosage assumption of one unit per day in older Finns. Int J Methods Psychiatr Res ; 22 2 : It is known that NDME biases the risk estimate typically represented by an odds ratio in case-control studies towards the null hypothesis 2 2.
Bross I. Misclassification in 2x2 tables. Newell D. Errors in the interpretation of errors in epidemiology. Keys A, Kihlberg J. Effect of misclassification on estimated relative prevalence of a characteristic: Part I. Two populations infallibly distinguished: Part II.
Errors in two variables. Effects of misclassification in epidemiologic studies. Public Health Rep ; Goldberg J. Effects of misclassification on bias in difference between 2 proportions and relative odds in fourfold table. J Am Stat Assoc ; 7. When will nondifferential misclassification of an exposure preserve the direction of a trend.
Am J Epidemiol ; 6 : Szklo M, Nieto F. Conceptos y aplicaciones. Consider a 2 x 2 contingency table in any type of epidemiological study that represents the results observed among non-diseased and diseased individuals as a function of the exposure variable, where a and b represent, respectively, the number of diseased and non-diseased exposed individuals and c and d represent the number of diseased and non-diseased unexposed individuals, respectively.
Exposure misclassification error occurs when the diseased group and the non-diseased group are considered to be exposed although they were not and unexposed although they were 6 6. A similar situation would occur if error arose in the classification of the disease. Equations 1 to 4 show how misclassification error affects the frequencies in the 2 x 2 table.
These equations have been derived by us using equation 9 from the Vogel and Geffeller paper 13 1. In these equations, a and a' indicate, respectively, the true and observed numbers of diseased persons exposed, b and b' the true and observed numbers of non-diseased exposed, c and c' the true and observed numbers of diseased unexposed, and d and d' the true and observed numbers of non-diseased unexposed.
The reasoning behind these equations is that the group of diseased individuals will include a percentage of truly exposed subjects a who will be classified as such by a certain instrument laboratory test, survey, etc. This percentage corresponds to the sensitivity of the instrument for classifying subjects as exposed Se D. In addition, some of the individuals who were truly not exposed c will be classified by the instrument as exposed.
This percentage represents the instrument's false positive rate 1 - Sp D. Therefore, among diseased individuals, the number of subjects classified by the instrument as exposed 1- Sp D will be equal to the fraction of individuals correctly classified, aSe D , in addition to the fraction of individuals incorrectly classified, c 1 - Sp D.
Similarly, the number of diseased subjects classified by the instrument as unexposed c ' is equal to the fraction of individuals correctly classified as such, cSp D , plus the fraction of individuals incorrectly classified, a 1 - Se D. Likewise, the number of subjects classified as exposed and unexposed by an instrument in a non-diseased population b' and d' is determined by the sensitivity and specificity of the instrument in that population Se N and Sp D.
The subjects classified as exposed b' will correspond to the fraction of individuals correctly classified, bSe N , plus the fraction of individuals incorrectly classified d 1 - Sp N. Similarly, the subjects classified as unexposed d' will equal the fraction of individuals correctly classified, dSp N , added to the fraction of individuals incorrectly classified, b 1 - Se N.
A similar situation would occur with other risk measures employed in different epidemiological designs. Using equations 5 to 8, it is possible to use the true table frequencies to replace the corresponding sensitivities and specificities for the following formulas derived also by the authors from the equations described above:.
However, this is not always possible. Therefore, in this article, the effect of misclassification error differential and non-differential on odds ratio estimates is simulated using a case-control design.
This effect is simulated as a function of the sensitivity and specificity of the exposure classification given different prevalence rates of the exposure among the controls and different true ORs to describe how misclassification error occurs and to identify possible trends. These trends may guide the discussion of results in this type of studies when there are deficiencies in the classification instruments.
To study the effect of misclassification error on the estimation of the OR, we used different scenarios with variations in the sensitivity and specificity of the exposure classification for cases and controls, the prevalence of the exposure among the controls and the OR. The effect was measured according to the bias produced by varying these parameters. By definition, bias is the difference between the estimated OR and the true OR 14 Daniel W, Cross C.
USA: Wiley, Relative bias expressed as a percentage is the quotient between this difference and the true OR expressed in hundreds.
Negative bias values indicate underestimates of the OR, and positive bias values indicate overestimates. Likewise, bias values close to zero indicate the absence of bias. Simulation studies employed in various areas of research are very useful to understand the behaviour of certain phenomena under different virtual scenarios prompted by researchers through some specialized software.
In statistical robustness studies these are very common to observe the behaviour of an estimator under different scenarios that could occur in reality. Given the similarity between the simulation studies and experimental studies, this last approach is used to quantify the effect of misclassification in case-control studies 15 Salazar JC, Baena A.
Dyna revfacnacminas. For this, we have considered six factors:. A total of 2, scenarios were generated 4 5 x 2 2. One hundred of these scenarios comprised the NDME analysis because the factors 1 and 3 levels as well as the factors 2 and 4 levels were the same.
Therefore, the number of factors considered in this analysis was reduced to four. Interaction graphics were used to study relative bias as a function of the factors that varied, estimating the median bias for each group of combinations. Using linear models, the effect of the varying factors i. Because positive relative bias occurred only with DME, which presented a high level of variability, the DME analyses were stratified according to the sign of the bias.
Because of the high variability, a natural logarithmic transformation was used for the DME outcome in the linear models.
For this analysis, we created a categorical variable with three levels:. Spearman's correlation coefficient was used to assess the relationships between the different levels of the DME analysis factors and positive, absent or negative bias. P-values less than or equal to 0. The R statistical package R CoreTeam R: A language and environment for statistical computing. R scripts are available on request from the corresponding author.
Thumbnail Figure 1. Relative bias of the risk estimation Odds Ratio in a case-control study under the effect of non-differential misclassification error according to different levels of sensitivity and specificity of exposure classification, exposure prevalence in controls and true odds ratio. Finally, we observed less bias in the estimates of moderate odds ratios.
As opposed to the NDME analysis, the results of the DME are complex, not only because of the number of factors involved in the simulations but also because they do not produce a trend that clearly describes the effect of DME in relation to the combinations of factors.
Therefore, the DME analysis is presented in a discriminatory manner according to the type of bias: negative or positive. Figures 2 to 4 correspond to the medians of the relative biases for different combinations of the six factors included in this analysis.
High levels of sensitivity and specificity of the exposure classification among the cases Se Ca and Sp Ca , respectively reduce the bias, but they reduce positive bias more than negative bias Figures 2A and 2B. A similar effect is observed for the sensitivity and specificity of the exposure classification among the controls Se Co and Sp Co , respectively , although the effect is less clear for Se Co Figures 3A and 3B. With regard to the prevalence of the exposure among the controls, the bias is lower when the exposure prevalence is high, independent of the sensitivity or specificity of the exposure classification, both for the cases and for the controls Figures 2C to 2F and 3C to 3F.
Regarding the specificity, the effect was the opposite of that observed for NDME. When the levels of sensitivity and specificity were combined with the levels of the true ORs for the cases and the controls, no clear pattern of bias was observed Figures 2G , 2H , 3G and 3H.
After combining Se Ca , Sp Ca , Se Co and Sp Co , we observed that the bias decreased with high levels of specificity more than with sensitivity in both the cases and the controls. However, these trends were not very clear Figures 4A to 4H.
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Rothman K. Differential misclassification arising from nondifferential errors in exposure measurement. Am J Epidemiol ; Sven HI. En: Introduction to occupational epi-demiology.