---
title: "Multiple Bias Modeling"
author: "Denis Haine"
date: "`r Sys.Date()`"
output:
  rmarkdown::html_vignette:
    fig_caption: yes
vignette: >
  %\VignetteIndexEntry{Multiple Bias Modeling}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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.](https://link.springer.com/book/10.1007/978-3-030-82673-4), we can use the study by [Chien et
al.](https://link.springer.com/article/10.1007/s10549-005-9056-0).
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].

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

```{r chien-tab, echo=FALSE}
knitr::kable(chien)
```

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

```{r misclass_chien}
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`:

```{r misclass_sel}
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):

```{r misclass_sel_conf}
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

```{r multi_prob}
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
```
```{r plot2, warning=FALSE,message=FALSE,fig.width=6,fig.height=4}
plot(mod1, "or")
```

* Selection bias

```{r multi_prob2}
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
```

```{r plot3, warning=FALSE,message=FALSE,fig.width=6,fig.height=4}
plot(mod2, "or")
```

* Confounding

```{r multi_prob3}
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
```

```{r plot4, message=FALSE, warning=FALSE,fig.width=6,fig.height=4}
plot(mod3, "or")
```

* Misclassification then selection

```{r multi_ms}
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

```{r multi_msc}
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
```

```{r plot5, message=FALSE, warning=FALSE,fig.width=6,fig.height=4}
plot(mod6, "or")

plot(mod6, "or_tot")
```