battenr

# Title: Calculating Probability of Censoring

# Description: Inverse probability of censoring weighting (IPCW) can be used to remove the potential selection bias 
# caused by censoring. There are different ways to calculate the probability of censoring. The goal of this code was 
# to examine whether the two methods produced the same result. 

# Setup ----

#... Libraries 

battenr

# Title: Demonstration of the Central Limit Theorem

# Description: The purpose of this script is to simulate data for three different 
# distributions (normal, logistic and poisson) for four different sample sizes. 
# Each of these is then plotted to demonstrate how the sampling distribution 
# changes with increasing sizes of the sample. 


# Setup ----

battenr

# Title: Conditioning on a Collider

# Description: Directed acyclic graphs (DAGs) are a great tool that can be 
# used to guide variable selection. Colliders, a variable where two arrowheads meet, 
# should not be adjusted for since they can induce bias. This code aims to prove
# and quantify the bias using a simple example. 

# Setup ----

#... Libraries ----

battenr

# Title: Plotting Distributions for PS Methods

# Description: An example of plotting the distributions before and after
# IPTW of two confounders. 

# Setup ----

#... Libraries ----

library(tidyverse) # ol faithful

battenr

# Title: Demonstration of How Power Can Vary

# Description: The purpose of this script is to show how power can vary
# based on effect size and sample size. Power is calculated for several scenarios
# then plotted to demonstrate the importance of power/sample size. 

# Setup ----

library(tidyverse) # ol faithful

battenr

# Title: Demonstration of Standard Error

# Description: The purpose of this script is to demonstrate standard error. 
# A sample is repeatedly drawn then the mean is calculated. The result, each 
# sample mean is then plotted 

# Setup ----

library(tidyverse) # ol faithful

battenr

# Title: Demonstration of P-Value

# Description: The purpose of this script is to demonstrate what a 
# p-value is. A logistic regression was used and the difference in deviances for 
# including the main effect in the model vs not (aka Likelihood Ratio Test).

# Setup ----

library(tidyverse) # ol faithful

battenr

# Title: Demonstration of Confidence Intervals

# Description: The purpose of this script is to simulate data to show what a 
# confidence interval is. The goal is to highlight that the 95% has to do 
# with us repeatedly sampling the value. 

# Setup ----

library(tidyverse) # ol faithful
library(ggridges) # used for ridge plot

battenr

# Title: Dichotomization Can Reduce Precision (SE)

# Description: Demonstrating how dichotomization of a continuous covariate
# can reduce precision (showing this based on the standard error)

# Setup ----

library(tidyverse) # ol' faithful

# Parameters for the Simulation ----

battenr

# Title: Demonstration of Power Loss 

# Description: Demonstrating the reduction in power by dichotomizing a covariate. 

# Setup ----

library(tidyverse) # ol faithful 
library(broom) # for tidying the model results

# Function for Estimating Treatment Effect ----