---
title: "Contextualizing Sensitivity Analysis in Observational Studies: Calculating Bias Factors for Known Covariates"
author: "
Lucy D'Agostino McGowan"
logo: img/logo.png
output: 
  flexdashboard::flex_dashboard:
    self_contained: true
    orientation: rows
    source: embed
    css: my_style.css
bibliography: ../../tutorial-manuscript.bib
---


```{r setup, include=FALSE}
library(package = flexdashboard)
library(package = tidyverse)

# Setup knitr
knitr::opts_chunk$set(
  echo = FALSE, message = FALSE, warning = FALSE,
  # Save all figures in the output dir, you have to include them explicitly
  # with an  tag
  fig.path = "../output/img/", fig.show = "hide"
)
```





## Row 1 {data-height=25}

###



  

**Contextualizing Sensitivity Analysis in Observational Studies: Calculating Bias Factors for Known Covariates**

  

  
  


  Lucy D'Agostino McGowan
   

  Robert A Greevy, Jr.
  

 
  

## Row 2 {data-height=60}

### **Background** 

_Strength of evidence provided by epidemiological and observational studies is limited by the potential of **unmeasured confounding**._

---

#### Our Recommendation 

  
  
 Include content-matter expertise


  
  
 Anchor in your data


  
  
 Calculate a hypothetical "**tipping point**" confounder

---

We recommend a [**tipping point method**](http://rpubs.com/lucymcgowan/enar2017) that builds on the Lin et al. method.

```r
## devtools::install_github("LucyMcGowan/tipr")
tip_with_binary(p1 = .5, p0 = 0, lb = 1.2, ub = 1.5)
```

* In order to choose sensible values for tipping point analyses, these methods must be anchored and contextualized in the studies at hand. For this purpose, propose calculating **“bias factors”** of known covariates.

* We extend the extensive research that has been done developing methods for assessing sensitivity to unmeasured confounding in observational studies [@Cornfield, @Bross, @Schlesselman, @Rosenbaum:1983, @Greenland, @Lin, @Schneeweiss, @Sturmer:2005bc, @VanderWeele:2011es, @Ding].

### **Plot**


  

#### Figure 1. Visual representation of bias in the Right Heart Catheterization Study.

### **Methods** 


#### Qualities of meaningful confounders


  
  
 Imbalance of **exposure**


  
  
 Predictive of **outcome** 



  
  
 Independent of **other covariates**

***

We calculate these bias factors by leaving known covariates out of the entire analysis process (both the propensity score model and the final analysis model). In the case of a binary response, such as is the case with logistic regression, a bias factor is the ratio of an observed result (OR) with and without a covariate present. 
 
$$\frac{OR_{cov^-}}{OR_{cov^+}}$$
 
Where $OR_{cov^-}$ is the odds ratio for the effect of the exposure and outcome without the covariate present in the analysis, and $OR_{cov^+}$ is the odds ratio for the effect of the exposure and outcome with the covariate present in the analysis.

We then graphically display the impact of each of the covariates along with an indication of our sensitivity analysis parameters.

In addition to the display, we will demonstrate how observed bias factors compare in three design contexts, (1) matching weights with additional direct covariate adjustment, (2) matching weights without additional direct covariate adjustment, and (3) direct covariate adjustment only. 



## Row 3 {data-height=15} 

### **Results** {data-width=50}

As an example, we use the Right Heart Catheterization [dataset](http://biostat.mc.vanderbilt.edu/wiki/Main/DataSets), originally used in Connors et al [@Connors:1996un]. We use 50 covariates to estimate the propensity of being assigned to right heart catheterization. We then fit the full analysis, leaving out one covariate at a time. Each time we estimate the effect of the exposure, right heart catheterization, on the outcome, 30 day survival, and compare it to the estimate with the fully specified analysis.

Figure 1 shows an example of the results from the weighted analysis. While many covariates do not cause much change in the result, a few, such as `pafi`, the PaO2/FIO2 ratio, `dnr1`, the DNR status on day 1, and `surv2md1`, the Support model estimate of the prob. of surviving 2 months, seem to. We believe insights such as these will help ground sensitivity to unmeasured confounding analyses for observational study research.

### **Thank you** {data-width=50}

#### Lucy D'Agostino McGowan


  
  

ld.mcgowan@vanderbilt.edu 


  
  

\@LucyMcGowan


  
  

\@LucyStats

**R Packages** 

JJ Allaire (2016). flexdashboard: R Markdown Format for Flexible
  Dashboards. R package version 0.3.  
  https://CRAN.R-project.org/package=flexdashboard

Winston Chang, Joe Cheng, JJ Allaire, Yihui Xie and Jonathan
  McPherson (2017). shiny: Web Application Framework for R. R package
  version 1.0.3. https://CRAN.R-project.org/package=shiny  

 Kazuki Yoshida and Justin Bohn. (2015). tableone: Create "Table 1"
  to Describe Baseline Characteristics. R package version 0.7.3.
  https://CRAN.R-project.org/package=tableone  

T. Lumley (2014) "survey: analysis of complex survey samples". R
  package version 3.30.  

T. Lumley (2004) Analysis of complex survey samples. Journal of
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 H. Wickham. ggplot2: Elegant Graphics for Data Analysis.
  Springer-Verlag New York, 2009.  

 R Core Team (2017). R: A language and environment for statistical
  computing. R Foundation for Statistical Computing, Vienna, Austria.
  URL https://www.R-project.org/.  

Baptiste Auguie (2016). gridExtra: Miscellaneous Functions for
  "Grid" Graphics. R package version 2.2.1.
  https://CRAN.R-project.org/package=gridExtra
  
**References**