battenr

# Title: Increasing Sample Size Doesn't Fix Bias

# Description: Demonstrating that increasing sample size doesn't fix bias. 
# Note: this code was written with the help of Gemini

# Setup ----

#.. Libraries ----

library(tidyverse) # ol faithful

battenr

# Title: Bayesian Joint Modelling Approach

# Description: Demonstrating how a Bayesian approach can be useful. For this example, we are going to model 
# the outcome and the treatment at the same time. 

# Setup ----

#... Libraries ----

library(tidyverse) # ol faithful 

battenr

# Title: How Complete Case Analysis Impacts Results

# Description: This code demonstrates how complete case analysis can impact your results
# differently for different missing data mechanisms. 

# Setup ----

#... Libraries ----

library(tidyverse) # ol faithful

battenr

# Title: Why Adjusting for All Variables is Problematic

# Description: It's easy to think that adjusting for all variables is helpful. 
# For causal inference, it's very problematic. This code simulates data, then fits a 
# generalized linear model. Bias and the Monte Carlo Standard Error of bias are calculated
# to compare results from two scenarios: 

# 1. Adjusting for all variables
# 2. Adjusting for correct variables (only confounder, not mediator, not collider)

battenr

# Title: Modelling Confounding

# Description: Demonstrating how it's important to consider the relationship between
# variables. Directed acyclic graphs (DAGs) are helpful to identify what to 
# adjust for, and what not to. However, we need to also consider the relationship
# that we are trying to model. 

# This code simulates data, where there is a nonlinear relationship between 
# sleep (z1) and happiness (y). The relationship is plotted, and two models fit. 
# One model assuming a linear relationship (incorrectly), one model assuming 

battenr

# Title: Table 2 Fallacy - Example ----

# Description: When interpreting results, if the goal is causal inference, 
# it's important to consider pathways between the exposure and outcome. 
# If the exposure of interest changes, so do the pathways. This is known as 
# the Table 2 Fallacy. 

# This code demonstrates the Table 2 Fallacy. Highly recommend the paper 
# The table 2 fallacy: presenting and interpreting confounder and modifier coefficients
# by Westreich & Greenland 

battenr

# Title: Restricted Mean Survival Time 

# Description: When using time-to-event outcomes, a common effect measure is 
# the hazard ratio. For causal inference, there are several problems with this measure
# including selection bias, and a strange interpretability. 

# Luckily there are alternatives! 

# One such alternative is the restricted mean survival time. This code demonstrates 
# the RMST. 

battenr

# Title: Truncating Weights for Inverse Probability Weighting 

# Description: When using inverse probability weights, it is recommended to stabilize weights. 
# If there are extreme weights, truncating them can help reduce variance. 

# This code demonstrates the benefit of truncating the weights 
# (that is setting the values > some threshold, to that threshold). 
# For example, setting weights > 95th percentile to the 95th percentile

# Setup ----

battenr

# Title: Adjusting for Variable for Precision ----

# Description: In causal inference, we know to adjust for confounding and avoid 
# adjusting for colliders. However, what if a variable is not a confounder, collider 
# or a mediator. Should we adjust? 

# Note: The variable must be included in a directed acyclic graph (DAG)
# because it's a common cause of a pair of variables. 

# For this example we are going to look at: 

battenr

# Title: Outliers in Causal Inference

# Description: Outliers can cause problems. This code shows how 
# we can add some data that we know are outliers (since we added them). 

# Setup ----

#... Libraries ----

library(tidyverse) # ol' faithful