Misclassification Bias
Misclassification bias can be assessed with the function misclassification. Confidence intervals for corrected association due to exposure misclassification are also directly available, or the estimates can also be bootstrapped (see below). The confidence intervals from the variance of the corrected odds ratio estimator in the misclassification function are computed as in Greenland et al. and Chu et al., when adjusting for exposure misclassification using sensitivity and specificity. Using the example in Chu et al. of a case-control study of cigarette smoking and invasive pneumococcal disease, the unadjusted odds ratio is 4.32, with a 95% confidence interval of 2.96 to 6.31. Let’s say the sensitivity of self-reported smoking is 94% and specificity is 97%, for both the case and control groups:
misclassification(matrix(c(126, 92, 71, 224),
dimnames = list(c("Case", "Control"),
c("Smoking +", "Smoking - ")),
nrow = 2, byrow = TRUE),
type = "exposure",
bias_parms = c(0.94, 0.94, 0.97, 0.97))## --Observed data--
## Outcome: Case
## Comparing: Smoking + vs. Smoking -
##
## Smoking + Smoking -
## Case 126 92
## Control 71 224
##
## 2.5% 97.5%
## Observed Relative Risk: 2.196866 1.796016 2.687181
## Observed Odds Ratio: 4.320882 2.958402 6.310846
## ---
## 2.5% 97.5%
## Misclassification Bias Corrected Relative Risk: 2.377254
## Misclassification Bias Corrected Odds Ratio: 5.024508 3.282534 7.690912The corrected odds ratio is now 5.02, with a widened 95% confidence interval (3.28 to 7.69). Note the bias despite the large sensitivity and specificity.
You can even reproduce the contour plots in Chu et al. paper!
dat <- expand.grid(Se = seq(0.582, 1, 0.02),
Sp = seq(0.762, 1, 0.02))
dat$OR_c <- apply(dat, 1,
function(x) misclassification(matrix(c(126, 92, 71, 224),
nrow = 2, byrow = TRUE),
type = "exposure",
bias_parms = c(x[1], x[1], x[2], x[2]))$adj.measures[2, 1])
dat$OR_c <- round(dat$OR_c, 2)
library(ggplot2)
library(directlabels)
p1 <- ggplot(dat, aes(x = Se, y = Sp, z = OR_c)) +
geom_contour(aes(colour = ..level..), breaks = c(4.32, 6.96, 8.56, 12.79, 23.41, 432.1)) +
annotate("text", x = 1, y = 1, label = "4.32", size = 3) +
scale_fill_gradient(limits = range(dat$OR_c), high = 'red', low = 'green') +
scale_x_continuous(breaks = seq(0.5, 1, .1), expand = c(0,0)) +
scale_y_continuous(breaks = seq(0.5, 1, .1), expand = c(0,0)) +
coord_fixed(ylim = c(0.5, 1.025), xlim = c(0.5, 1.025)) +
scale_colour_gradient(guide = 'none') +
xlab("Sensitivity") +
ylab("Specificity") +
ggtitle("Estimates of Corrected OR")
direct.label(p1, list("far.from.others.borders", "calc.boxes", "enlarge.box",
hjust = 1, vjust = -.5, box.color = NA, cex = .6,
fill = "transparent", "draw.rects"))
Contour plot of point estimates of corrected odds ratio (OR)
dat$ORc_lci <- apply(dat, 1,
function(x) misclassification(matrix(c(126, 92, 71, 224),
nrow = 2, byrow = TRUE),
type = "exposure",
bias_parms = c(x[1], x[1], x[2], x[2]))$adj.measures[2, 2])
dat$ORc_lci <- round(dat$ORc_lci, 2)
p3 <- ggplot(dat, aes(x = Se, y = Sp, z = ORc_lci)) +
geom_contour(aes(colour = ..level..),
breaks = c(4.05, 4.64, 5.68, 7.00, 9.60)) +
annotate("text", x = 1, y = 1, label = "2.96", size = 3) +
scale_fill_gradient(limits = range(dat$ORc_lci), high = 'red', low = 'green') +
scale_x_continuous(breaks = seq(0.5, 1, .1), expand = c(0,0)) +
scale_y_continuous(breaks = seq(0.5, 1, .1), expand = c(0,0)) +
coord_fixed(ylim = c(0.5, 1.025), xlim = c(0.5, 1.025)) +
scale_colour_gradient(guide = 'none') +
xlab("Sensitivity") +
ylab("Specificity") +
ggtitle("95% LCI of Corrected OR")
direct.label(p3, list("far.from.others.borders", "calc.boxes", "enlarge.box",
hjust = 1, vjust = -.5, box.color = NA, cex = .6,
fill = "transparent", "draw.rects"))
Contour plot of 95% lower confidence limit of corrected OR
The bias analysis for exposure misclassification can also use positive and negative predictive values. Bodnar et al. evaluated the accuracy of maternal prepregnancy BMI and gestational weight gain (GWG) data derived from the Pennsylvania state birth certificates against information collected from the medical record. To estimate positive and negative predictive values, a validation study was conducted by randomly sampling women conditional on their reported BMI category and term/preterm status. BMI was obtained from medical records for these sampled women and used as a gold standard for BMI category, allowing to determine positive and negative predictive values: PPVD1 = 65%, PPVD0 = 74%, NPVD1 = 100%, NPVD0 = 98%. The analysis is the following.
misclassification(matrix(c(599, 4978, 31175, 391851),
dimnames = list(c("Preterm", "Term"), c("Underweight", "Normal weight")),
nrow = 2, byrow = TRUE),
type = "exposure_pv",
bias_parms = c(0.65, 0.74, 1, 0.98))## --Observed data--
## Outcome: Preterm
## Comparing: Underweight vs. Normal weight
##
## Underweight Normal weight
## Preterm 599 4978
## Term 31175 391851
##
## 2.5% 97.5%
## Observed Relative Risk: 1.502808 1.381743 1.634480
## Observed Odds Ratio: 1.512469 1.388465 1.647547
## ---
## 2.5% 97.5%
## Misclassification Bias Corrected Relative Risk: 0.9528156
## Misclassification Bias Corrected Odds Ratio: 0.9522211Note that using predictive values relates to the prevalence of the true exposure status, which might not be the same in every populations.
Covariate misclassification is available via the function misclassification.cov. For example, the paper by Berry et al. looked if misclassification of the confounding variable in vitro fertilization (IVF), a confounder, resulted wrongly on an association between increase folic acid and having twins. IVF increases the risk of twins, and women undergoing IVF might be more likely to take folic acid supplements, i.e. IVF would be a confounder between vitamins and twins. Data on IVF were not available and a proxy for it was used, period of involuntary childlessness. However, it was a poor proxy for IVF, with a sensitivity of 60% and a specificity of 95%. These bias parameters were assumed to be nondifferential. Here’s the code with episensr:
misclassification.cov(array(c(1319, 38054, 5641, 405546, 565, 3583,
781, 21958, 754, 34471, 4860, 383588),
dimnames = list(c("Twins+", "Twins-"),
c("Folic acid+", "Folic acid-"),
c("Total", "IVF+", "IVF-")),
dim = c(2, 2, 3)),
bias_parms = c(.6, .6, .95, .95))## --Observed data--
## Outcome: Twins+
## Comparing: Folic acid+ vs. Folic acid-
##
## , , Total
##
## Folic acid+ Folic acid-
## Twins+ 1319 5641
## Twins- 38054 405546
##
## , , IVF+
##
## Folic acid+ Folic acid-
## Twins+ 565 781
## Twins- 3583 21958
##
## , , IVF-
##
## Folic acid+ Folic acid-
## Twins+ 754 4860
## Twins- 34471 383588
##
##
## 2.5% 97.5%
## Observed Relative Risk: 2.441910 2.301898 2.590437
## Observed Odds Ratio: 2.491888 2.344757 2.648251
## ---
## Observed Corrected
## SMR RR adjusted for confounder: 2.261738 1.000235
## RR due to confounding by misclassified confounder: 1.079661 2.441337
## Mantel-Haenszel RR adjusted for confounder: 2.228816 1.000187
## MH RR due to confounding by misclassified confounder: 1.095608 2.441452
## SMR OR adjusted for confounder: 2.337898 1.000304
## OR due to confounding by misclassified confounder: 1.065867 2.491131
## Mantel-Haenszel OR adjusted for confounder: 2.290469 1.000215
## MH OR due to confounding by misclassified confounder: 1.087938 2.491351While the non-adjusted analysis showed that women taking folic acid were 2.44 times more likely to have twins, after correcting for the misclassification of IVF, risk ratio is now null (= 1.0).
