Multiple Bias Modeling
In episensr: Basic Sensitivity Analysis of Epidemiological Results

Epidemiologic studies can suffer from more than one bias. Bias functions in episensr can be applied sequentially to quantify bias resulting from multiple biases.

Following the example in Lash et al., we can use the study by Chien et al.. It is a case-control study looking at the association between antidepressant use and the occurrence of breast cancer. The observed OR was 1.2 [0.9--1.6].

chien <- matrix(c(118, 832, 103, 884),
                dimnames = list(c("BC+", "BC-"), c("AD+", "AD-")),
                nrow = 2, byrow = TRUE)

knitr::kable(chien)

Records on medication use differed between participants, from pharmacy records and self-reported use, leading to misclassification:

library(episensr)
chien %>%
    misclassification(., type = "exposure", bias_parms = c(.56, .58, .99, .97))

Controls and cases also enrolled into the study at different rates. We can combine the misclassification bias with a selection bias thanks to the function multiple.bias:

chien %>%
    misclassification(., type = "exposure", bias_parms = c(.56, .58, .99, .97)) %>%
    multiple.bias(., bias_function = "selection", bias_parms = c(.73, .61, .82, .76))

The association between antidepressant use and breast cancer was adjusted for various confounders (race/ethnicity, income, etc.). None of these confounders were found to change the association by more than 10%. However, for illustration, we can add the effect of a potential confounder (e.g. physical activity):

chien %>%
    misclassification(., type = "exposure", bias_parms = c(.56, .58, .99, .97)) %>%
    multiple.bias(., bias_function = "selection",
                  bias_parms = c(.73, .61, .82, .76)) %>%
    multiple.bias(., bias_function = "confounders",
                  type = "OR", bias_parms = c(.92, .3, .44))

We can do the same in a probabilistic framework:

Misclassification bias

set.seed(123)
mod1 <- chien %>%
    probsens(., type = "exposure", reps = 100000,
             seca.parms = list("trapezoidal", c(.45, .5, .6, .65)),
             seexp.parms = list("trapezoidal", c(.4, .48, .58, .63)),
             spca.parms = list("trapezoidal", c(.95, .97, .99, 1)),
             spexp.parms = list("trapezoidal", c(.96, .98, .99, 1)),
             corr.se = .8, corr.sp = .8)
mod1

plot(mod1, "or")

Selection bias

set.seed(123)
mod2 <- chien %>%
    probsens.sel(., reps = 100000,
                 case.exp = list("beta", c(8.08, 24.25)),
                 case.nexp = list("trapezoidal", c(.75, .85, .95, 1)),
                 ncase.exp = list("beta", c(12.6, 50.4)),
                 ncase.nexp = list("trapezoidal", c(0.7, 0.8, 0.9, 1)))
mod2

plot(mod2, "or")

Confounding

set.seed(123)
mod3 <- chien %>%
    probsens.conf(., reps = 100000,
                  prev.exp = list("beta", c(24.9, 58.1)),
                  prev.nexp = list("beta", c(42.9, 54.6)),
                  risk = list("trapezoidal", c(.2, .58, 1.01, 1.24)))
mod3

plot(mod3, "or")

Misclassification then selection

set.seed(123)
chien %>%
    probsens(., type = "exposure", reps = 100000,
             seca.parms = list("trapezoidal", c(.45, .5, .6, .65)),
             seexp.parms = list("trapezoidal", c(.4, .48, .58, .63)),
             spca.parms = list("trapezoidal", c(.95, .97, .99, 1)),
             spexp.parms = list("trapezoidal", c(.96, .98, .99, 1)),
             corr.se = .8, corr.sp = .8) %>%
    multiple.bias(., bias_function = "probsens.sel",
                  case.exp = list("beta", c(8.08, 24.25)),
                  case.nexp = list("trapezoidal", c(.75, .85, .95, 1)),
                  ncase.exp = list("beta", c(12.6, 50.4)),
                  ncase.nexp = list("trapezoidal", c(0.7, 0.8, 0.9, 1)))

Misclassification, selection, and confounding

set.seed(123)
mod6 <- chien %>%
    probsens(., type = "exposure", reps = 100000,
             seca.parms = list("trapezoidal", c(.45, .5, .6, .65)),
             seexp.parms = list("trapezoidal", c(.4, .48, .58, .63)),
             spca.parms = list("trapezoidal", c(.95, .97, .99, 1)),
             spexp.parms = list("trapezoidal", c(.96, .98, .99, 1)),
             corr.se = .8, corr.sp = .8) %>%
    multiple.bias(., bias_function = "probsens.sel",
                  case.exp = list("beta", c(8.08, 24.25)),
                  case.nexp = list("trapezoidal", c(.75, .85, .95, 1)),
                  ncase.exp = list("beta", c(12.6, 50.4)),
                  ncase.nexp = list("trapezoidal", c(0.7, 0.8, 0.9, 1))) %>%
    multiple.bias(., bias_function = "probsens.conf",
                  prev.exp = list("beta", c(24.9, 58.1)),
                  prev.nexp = list("beta", c(42.9, 54.6)),
                  risk = list("trapezoidal", c(.2, .58, 1.01, 1.24)))
mod6