04_logistic-regressions_2024.Rmd

---
title: "04_logistic-regressions"
author: "Caroline & Patrycja"
date: '2023-07-13'
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

```{r}
rm(list=ls())
```


# Initial operations on the dataset

## call libraries

```{r}
library(tidyverse)
library(dplyr)
library (broom)
```

## load the preprocessed data into R environement

```{r}
port_preprocessed_data <- readRDS("02_preprocessed_port_data.rds")
head(port_preprocessed_data)
```

## inspect variables/ column names

```{r}
colnames(port_preprocessed_data)
```



# Logistic Regressions 


Predictor 1: did you find your sessions with ieso helpful (yes; no) 

Predictor 2: how much have your symptoms and day-to-day functioning improved after the sessions with ieso (much better; little better; no change; little worse; much worse) 


**PV1**: retrospectively_reported_improvement (much better(4); little better(3); no change(2); little worse(1); much worse(0))
**PV2**: retrospectively_treatment_helpful (yes(1); no(0))
**PV1&PV2**: retrospectively_reported_improvement & retrospectively_treatment_helpful
**Covariates**: No of sessions, gender, age 

**OV1**: recovered (yes; no)
**OV2**: reliable improvement (yes; no)
**OV3**: reliable recovery (yes; no)

Guidance websites: (1) \<<https://rcompanion.org/rcompanion/e_07.html>\>
(2) \<<https://rcompanion.org/rcompanion/e_07.html>\> (3)
\<<https://www.statology.org/assumptions-of-logistic-regression/>\>


## change yes/no in OVs into 1 and 0



```{r}
# Modify "yes" and "no" values to numeric values (1 and 0) while keeping NA values as NA
port_preprocessed_data <- port_preprocessed_data %>%
  dplyr::mutate(recovered = ifelse(is.na(recovered), NA, ifelse(recovered == "yes", 1, 0)),
                reliable_improvement = ifelse(is.na(reliable_improvement), NA, ifelse(reliable_improvement == "yes", 1, 0)),
                reliable_recovery = ifelse(is.na(reliable_recovery), NA, ifelse(reliable_recovery == "yes", 1, 0)))

```

```{r}
#change demographics_gender into a numeric variable 
#(non_binary -> 0, male -> 1, female -> 2)
port_preprocessed_data <- port_preprocessed_data %>%
  mutate(demographics_gender = ifelse(demographics_gender == "female", 2,
                                      ifelse(demographics_gender == "male", 1, 0)))


```

```{r}
#Renaming the age variable as a different name was used for it in the preprocessing script 

port_preprocessed_data <- port_preprocessed_data %>%
  rename(demographics_age_at_screening = demographics_age_at_screening_years)
```

# **Logistic regressions for OV1: RECOVERED**

## PV1: retrospectively_reported_improvement


## Assumptions-checking of Logistic Regression ov1_pv1

(1) Outcome variable is binary - **checked**
(2) The observations are independent - **checked** (they come from separate individuals)
(3) No severe multicolinearity among the exploratory variables
(4) No extreme outliers
(5) Linear relationship between predictor variables and the logit of
    outcome variable

##load packages

```{r}
library(tidyverse)
library(broom)
theme_set(theme_classic())

```

```{r}
unique(port_preprocessed_data$recovered)

```


```{r}
# Fit the logistic regression model ov1_pv1
log_reg_ov1_pv1 <- glm(recovered ~ retrospectively_reported_improvement + ieso_treatment_completed_total  + demographics_gender + demographics_age_at_screening, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov1_pv1)

```
```{r}
# Predict the probability (p) of symptom improvement
probabilities_ov1_pv1 <- predict(log_reg_ov1_pv1, type = "response")
predicted.classes <- ifelse(probabilities_ov1_pv1 > 0.5, "pos", "neg")
print(predicted.classes)

```
## ASSUMPTION 3: (3) No severe multicolinearity among the exploratory variables
 Investigating multicolinearity by looking at the variance inflation factor

The Variance Inflation Factor (VIF) measures the severity of multicollinearity in regression analysis. It is a statistical concept that indicates the increase in the variance of a regression coefficient as a result of collinearity.

The value for VIF starts at 1 and has no upper limit. A general rule of thumb for interpreting VIFs is as follows:

A value of 1 indicates there is no correlation between a given predictor variable and any other predictor variables in the model.
A value between 1 and 5 indicates moderate correlation between a given predictor variable and other predictor variables in the model, but this is often not severe enough to require attention.
A value greater than 5 indicates potentially severe correlation between a given predictor variable and other predictor variables in the model. In this case, the coefficient estimates and p-values in the regression output are likely unreliable.

```{r}
library(car)
vif(log_reg_ov1_pv1)
```

**as all values well below 5 -> no excessive colinearity between predictor variables**

## Calculating correlation matrix for log_reg_ov1_pv1

```{r}
#create a dataset with variables solely used in log_reg_ov1_pv1
#data_log_reg_ov1_pv1 = port_preprocessed_data %>%
#  select(recovered, retrospectively_reported_improvement, ieso_treatment_completed_total, demographics_gender, #demographics_age_at_screening)
```


```{r} 
#library("psych")
#corr.test(data_log_reg_ov1_pv1, adjust = "none")
```
**correlations between the predictor variable and covariates are weak**

## ASSUMPTION 4:(4) No extreme outliers


```{r}
#visualizing the Cook's distance values
plot(log_reg_ov1_pv1, which = 4, id.n = 3)
```
Cook's distance is considered high if it's above 0.5
Cook's Distance is a measure of how influential an instance is to the computation of a regression, e.g. if the instance is removed would the estimated coeficients of the underlying model be substantially changed? Because of this, Cook's Distance is generally used to detect outliers in standard, OLS regression. 

In fact, a general rule of thumb is that D(i) > 4/n is a good threshold for determining highly influential points as outliers -> 4/137 =~ 0.03

So we have 3ish outliers - should we ignore them?? 


```{r}
# Extract model results
model.data <- augment(log_reg_ov1_pv1) %>% 
  mutate(index = 1:n()) 
#The data for the top 3 largest values, according to the Cook's distance, can be displayed as follow:
model.data %>% top_n(3, .cooksd)
#Plot the standardized residuals:
ggplot(model.data, aes(index, .std.resid)) + 
  geom_point(aes(color = retrospectively_reported_improvement), alpha = .5) +
  theme_bw()
#Filter potential influential data points:
model.data %>% 
  filter(abs(.std.resid) > 3)

```

**all datapoints are well within 2SD of the mean**


## ASSUMPTION 5: (5) Linear relationship between predictor variables and the logit of outcome variable

## Remove qualitative variables from the original data frame and bind the logit values to the data:

```{r}

# Select only numeric predictors
log_reg_predictors_ov1_pv1 <- port_preprocessed_data %>%
  select(ieso_treatment_completed_total, demographics_age_at_screening, demographics_gender, retrospectively_reported_improvement)
# Bind the logit and tidying the data for plot
log_reg_predictors_ov1_pv1 <- log_reg_predictors_ov1_pv1 %>%
  mutate(logit = log(probabilities_ov1_pv1/(1-probabilities_ov1_pv1))) %>%
  gather(key = "predictors", value = "predictor.value", -logit)

```

## Create scatterplots

```{r}
ggplot(log_reg_predictors_ov1_pv1, aes(logit, predictor.value))+
  geom_point(size = 0.5, alpha = 0.5) +
  geom_smooth(method = "loess") + 
  theme_bw() + 
  facet_wrap(~predictors, scales = "free_y")
```

**there is a linear relationship bewteen the retrospectively_reported_improvement and iapt:recovered**

# PV2: retrospectively_treatment_helpful

## Assumptions-checking of Logistic Regression ov1_pv2

(1) Outcome variable is binary - **checked**
(2) The observations are independent - **checked** (they come from separate individuals)
(3) No severe multicolinearity among the exploratory variables
(4) No extreme outliers
(5) Linear relationship between predictor variables and the logit of
    outcome variable


```{r}
# Fit the logistic regression model ov1_pv2
log_reg_ov1_pv2 <- glm(recovered ~ retrospectively_treatment_helpful + ieso_treatment_completed_total  + demographics_gender + demographics_age_at_screening, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov1_pv2)

```
```{r}
# Predict the probability (p) of symptom improvement
probabilities_ov1_pv2 <- predict(log_reg_ov1_pv2, type = "response")
predicted.classes <- ifelse(probabilities_ov1_pv2 > 0.5, "pos", "neg")
print(predicted.classes)

```
## ASSUMPTION 3: (3) No severe multicolinearity among the exploratory variables
 

```{r}
library(car)
vif(log_reg_ov1_pv2)
```

**as all values well below 5 -> no excessive colinearity between predictor variables**

## Calculating correlation matrix for log_reg_ov1_pv2

```{r}
#create a dataset with variables solely used in log_reg_ov1_pv2
data_log_reg_ov1_pv2 = port_preprocessed_data %>%
  select(recovered, retrospectively_treatment_helpful, ieso_treatment_completed_total, demographics_gender, demographics_age_at_screening)
```


```{r} 
#corr.test(data_log_reg_ov1_pv2, adjust = "none")
```
**correlations between the predictor variable and covariates are weak**

## ASSUMPTION 4:(4) No extreme outliers


```{r}
#visualizing the Cook's distance values
plot(log_reg_ov1_pv2, which = 4, id.n = 3)
```

So we have 3 or 4ish outliers - should we ignore them?? 


```{r} 
# Are these outliers within 2 standard deviations of the mean?

# Extract model results
model.data <- augment(log_reg_ov1_pv2) %>% 
  mutate(index = 1:n()) 
#The data for the top 3 largest values, according to the Cook's distance, can be displayed as follow:
model.data %>% top_n(3, .cooksd)
#Plot the standardized residuals:
ggplot(model.data, aes(index, .std.resid)) + 
  geom_point(aes(color = retrospectively_treatment_helpful), alpha = .5) +
  theme_bw()
#Filter potential influential data points:
model.data %>% 
  filter(abs(.std.resid) > 3)

```

**one datapoint is slightly above 2SD from the mean**


## ASSUMPTION 5: (5) Linear relationship between predictor variables and the logit of outcome variable

## Remove qualitative variables from the original data frame and bind the logit values to the data:

```{r}

# Select only numeric predictors
log_reg_predictors_ov1_pv2 <- port_preprocessed_data %>%
  select(ieso_treatment_completed_total, demographics_age_at_screening, demographics_gender, retrospectively_treatment_helpful)
# Bind the logit and tidying the data for plot
log_reg_predictors_ov1_pv2 <- log_reg_predictors_ov1_pv2 %>%
  mutate(logit = log(probabilities_ov1_pv2/(1-probabilities_ov1_pv2))) %>%
  gather(key = "predictors", value = "predictor.value", -logit)

```

## Create scatterplots

```{r}
ggplot(log_reg_predictors_ov1_pv2, aes(logit, predictor.value))+
  geom_point(size = 0.5, alpha = 0.5) +
  geom_smooth(method = "loess") + 
  theme_bw() + 
  facet_wrap(~predictors, scales = "free_y")
```

**linear relationships between pvs and ov**

# PV1 & PV2: retrospectively_reported_improvement and retrospectively_treatment_helpful

## Assumptions-checking of Logistic Regression ov1_pv1_pv2

(1) Outcome variable is binary - **checked**
(2) The observations are independent - **checked** (they come from separate individuals)
(3) No severe multicolinearity among the exploratory variables
(4) No extreme outliers
(5) Linear relationship between predictor variables and the logit of
    outcome variable


```{r}
# Fit the logistic regression model ov1_pv1_pv2
log_reg_ov1_pv1_pv2 <- glm(recovered ~ retrospectively_reported_improvement  + retrospectively_treatment_helpful +  ieso_treatment_completed_total  + demographics_gender + demographics_age_at_screening, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov1_pv1_pv2)

```

```{r}
# Predict the probability (p) of symptom improvement
probabilities_ov1_pv1_pv2 <- predict(log_reg_ov1_pv1_pv2, type = "response")
predicted.classes <- ifelse(probabilities_ov1_pv1_pv2 > 0.5, "pos", "neg")
print(predicted.classes)

```
## ASSUMPTION 3: (3) No severe multicolinearity among the exploratory variables
 Investigating multicolinearity by looking at the variance inflation factor


```{r}
library(car)
vif(log_reg_ov1_pv1_pv2)
```

**as all values well below 5 -> no excessive colinearity between predictor variables**

## Calculating correlation matrix for log_reg_ov1_pv1_pv2

```{r}
#create a dataset with variables solely used in log_reg_ov1_pv1_pv2
data_log_reg_ov1_pv1_pv2 = port_preprocessed_data %>%
  select(recovered,retrospectively_reported_improvement, retrospectively_treatment_helpful, ieso_treatment_completed_total, demographics_gender, demographics_age_at_screening)
```


```{r} 
#corr.test(data_log_reg_ov1_pv1_pv2, adjust = "none")
```
**correlations between 2 PVs of interest (retrospectively_reported_improvement and retrospectively_treatment_helpful) is .63**

## ASSUMPTION 4:(4) No extreme outliers


```{r}
#visualizing the Cook's distance values
plot(log_reg_ov1_pv1_pv2, which = 4, id.n = 3)
```
So we have some outliers - should we ignore them?? 


```{r} 
# Are these outliers within 2 standard deviations of the mean?

# Extract model results
model.data <- augment(log_reg_ov1_pv1_pv2) %>% 
  mutate(index = 1:n()) 
#The data for the top 3 largest values, according to the Cook's distance, can be displayed as follow:
model.data %>% top_n(3, .cooksd)
#Plot the standardized residuals:
ggplot(model.data, aes(index, .std.resid)) + 
  geom_point(aes(color = retrospectively_reported_improvement), alpha = .5) +
  theme_bw()
#Filter potential influential data points:
model.data %>% 
  filter(abs(.std.resid) > 3)

```

**one datapoint is slightly above 2SD from the mean**


## ASSUMPTION 5: (5) Linear relationship between predictor variables and the logit of outcome variable

## Remove qualitative variables from the original data frame and bind the logit values to the data:

```{r}
# Select only numeric predictors
log_reg_predictors_ov1_pv1_pv2 <- port_preprocessed_data %>%
  select(ieso_treatment_completed_total, demographics_age_at_screening, demographics_gender, retrospectively_treatment_helpful, retrospectively_reported_improvement)
# Bind the logit and tidying the data for plot
log_reg_predictors_ov1_pv1_pv2 <- log_reg_predictors_ov1_pv1_pv2 %>%
  mutate(logit = log(probabilities_ov1_pv1_pv2/(1-probabilities_ov1_pv1_pv2))) %>%
  gather(key = "predictors", value = "predictor.value", -logit)

```

## Create scatterplots

```{r}
ggplot(log_reg_predictors_ov1_pv1_pv2, aes(logit, predictor.value))+
  geom_point(size = 0.5, alpha = 0.5) +
  geom_smooth(method = "loess") + 
  theme_bw() + 
  facet_wrap(~predictors, scales = "free_y")
```

**linear relationships between pvs and ov**

# **Logistic regressions for OV2: RELIABLE_IMPROVEMENT**

## PV1: retrospectively_reported_improvement

## Assumptions-checking of Logistic Regression ov2_pv1

(1) Outcome variable is binary - checked
(2) The observations are independent - checked (they come from separate individuals)
(3) No severe multicolinearity among the exploratory variables
(4) No extreme outliers
(5) Linear relationship between predictor variables and the logit of
    outcome variable

##load packages

```{r}
library(tidyverse)
library(broom)
theme_set(theme_classic())

```


```{r}
# Fit the logistic regression model ov2_pv1
log_reg_ov2_pv1 <- glm(reliable_improvement ~ retrospectively_reported_improvement + ieso_treatment_completed_total  + demographics_gender + demographics_age_at_screening, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov2_pv1)

```


```{r}
# Predict the probability (p) of symptom improvement
probabilities_ov2_pv1 <- predict(log_reg_ov2_pv1, type = "response")
predicted.classes <- ifelse(probabilities_ov2_pv1 > 0.5, "pos", "neg")
print(predicted.classes)

```

## ASSUMPTION 3: (3) No severe multicolinearity among the exploratory variables
 

```{r}
library(car)
vif(log_reg_ov2_pv1)
```

**as all values well below 5 -> no excessive colinearity between predictor variables**

## Calculating correlation matrix for log_reg_ov2_pv1

```{r}
#create a dataset with variables solely used in log_reg_ov1_pv1
data_log_reg_ov2_pv1 = port_preprocessed_data %>%
  select(reliable_improvement, retrospectively_reported_improvement, ieso_treatment_completed_total, demographics_gender, demographics_age_at_screening)
```


```{r} 
library("psych")
corr.test(data_log_reg_ov2_pv1, adjust = "none")
```
**ieso_treatment_completed_total and age - 0.39, gender and retrospectively reported improvement - 0.37**

## ASSUMPTION 4:(4) No extreme outliers


```{r}
#visualizing the Cook's distance values
plot(log_reg_ov2_pv1, which = 4, id.n = 3)
```
**some outliers**


```{r}
# Extract model results
model.data <- augment(log_reg_ov2_pv1) %>% 
  mutate(index = 1:n()) 
#The data for the top 3 largest values, according to the Cook's distance, can be displayed as follow:
model.data %>% top_n(3, .cooksd)
#Plot the standardized residuals:
ggplot(model.data, aes(index, .std.resid)) + 
  geom_point(aes(color = retrospectively_reported_improvement), alpha = .5) +
  theme_bw()
#Filter potential influential data points:
model.data %>% 
  filter(abs(.std.resid) > 3)

```

**2 datapoints are marginally beyond 2SD of the mean**


## ASSUMPTION 5: (5) Linear relationship between predictor variables and the logit of outcome variable

## Remove qualitative variables from the original data frame and bind the logit values to the data:

```{r}

# Select only numeric predictors
log_reg_predictors_ov2_pv1 <- port_preprocessed_data %>%
  select(ieso_treatment_completed_total, demographics_age_at_screening, demographics_gender, retrospectively_reported_improvement)
# Bind the logit and tidying the data for plot
log_reg_predictors_ov2_pv1 <- log_reg_predictors_ov2_pv1 %>%
  mutate(logit = log(probabilities_ov2_pv1/(1-probabilities_ov2_pv1))) %>%
  gather(key = "predictors", value = "predictor.value", -logit)

```

## Create scatterplots

```{r}
ggplot(log_reg_predictors_ov2_pv1, aes(logit, predictor.value))+
  geom_point(size = 0.5, alpha = 0.5) +
  geom_smooth(method = "loess") + 
  theme_bw() + 
  facet_wrap(~predictors, scales = "free_y")
```

**there is a linear relationship bewteen the retrospectively_reported_improvement and iapt:reliable improvement**

# PV2: retrospectively_treatment_helpful

## Assumptions-checking of Logistic Regression ov2_pv2

(1) Outcome variable is binary - **checked**
(2) The observations are independent - **checked** (they come from separate individuals)
(3) No severe multicolinearity among the exploratory variables
(4) No extreme outliers
(5) Linear relationship between predictor variables and the logit of
    outcome variable


```{r}
# Fit the logistic regression model ov2_pv2
log_reg_ov2_pv2 <- glm(reliable_improvement ~ retrospectively_treatment_helpful + ieso_treatment_completed_total  + demographics_gender + demographics_age_at_screening, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov2_pv2)

```
```{r}
# Predict the probability (p) of symptom improvement
probabilities_ov2_pv2 <- predict(log_reg_ov2_pv2, type = "response")
predicted.classes <- ifelse(probabilities_ov2_pv2 > 0.5, "pos", "neg")
print(predicted.classes)

```
## ASSUMPTION 3: (3) No severe multicolinearity among the exploratory variables


```{r}
library(car)
vif(log_reg_ov2_pv2)
```

**as all values well below 5 -> no excessive colinearity between predictor variables**

## Calculating correlation matrix for log_reg_ov2_pv2

```{r}
#create a dataset with variables solely used in log_reg_ov1_pv2
data_log_reg_ov2_pv2 = port_preprocessed_data %>%
  select(reliable_improvement, retrospectively_treatment_helpful, ieso_treatment_completed_total, demographics_gender, demographics_age_at_screening)
```


```{r} 
#corr.test(data_log_reg_ov2_pv2, adjust = "none")
```
**no of treatments and restrospecovely treatment helpful = .36**

## ASSUMPTION 4:(4) No extreme outliers

```{r}
#visualizing the Cook's distance values
plot(log_reg_ov2_pv2, which = 4, id.n = 3)
```
So we have some outliers - should we ignore them?? 

```{r} 
# Are these outliers within 2 standard deviations of the mean?

# Extract model results
model.data <- augment(log_reg_ov2_pv2) %>% 
  mutate(index = 1:n()) 
#The data for the top 3 largest values, according to the Cook's distance, can be displayed as follow:
model.data %>% top_n(3, .cooksd)
#Plot the standardized residuals:
ggplot(model.data, aes(index, .std.resid)) + 
  geom_point(aes(color = retrospectively_treatment_helpful), alpha = .5) +
  theme_bw()
#Filter potential influential data points:
model.data %>% 
  filter(abs(.std.resid) > 3)

```

**all datapoints are roughly within 1.5SD from the mean**


## ASSUMPTION 5: (5) Linear relationship between predictor variables and the logit of outcome variable

## Remove qualitative variables from the original data frame and bind the logit values to the data:

```{r}

# Select only numeric predictors
log_reg_predictors_ov2_pv2 <- port_preprocessed_data %>%
  select(ieso_treatment_completed_total, demographics_age_at_screening, demographics_gender, retrospectively_treatment_helpful)
# Bind the logit and tidying the data for plot
log_reg_predictors_ov2_pv2 <- log_reg_predictors_ov2_pv2 %>%
  mutate(logit = log(probabilities_ov2_pv2/(1-probabilities_ov2_pv2))) %>%
  gather(key = "predictors", value = "predictor.value", -logit)

```

## Create scatterplots

```{r}
ggplot(log_reg_predictors_ov2_pv2, aes(logit, predictor.value))+
  geom_point(size = 0.5, alpha = 0.5) +
  geom_smooth(method = "loess") + 
  theme_bw() + 
  facet_wrap(~predictors, scales = "free_y")
```

**linear relationships between pvs and ov**

# PV1 & PV2: retrospectively_reported_improvement and retrospectively_treatment_helpful

## Assumptions-checking of Logistic Regression ov2_pv1_pv2

(1) Outcome variable is binary - **checked**
(2) The observations are independent - **checked** (they come from separate individuals)
(3) No severe multicolinearity among the exploratory variables
(4) No extreme outliers
(5) Linear relationship between predictor variables and the logit of
    outcome variable


```{r}
# Fit the logistic regression model ov1_pv1_pv2
log_reg_ov2_pv1_pv2 <- glm(reliable_improvement ~ retrospectively_reported_improvement  + retrospectively_treatment_helpful +  ieso_treatment_completed_total  + demographics_gender + demographics_age_at_screening, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov2_pv1_pv2)

```

```{r}
# Predict the probability (p) of symptom improvement
probabilities_ov2_pv1_pv2 <- predict(log_reg_ov2_pv1_pv2, type = "response")
predicted.classes <- ifelse(probabilities_ov1_pv1_pv2 > 0.5, "pos", "neg")
print(predicted.classes)

```
## ASSUMPTION 3: (3) No severe multicolinearity among the exploratory variables
 Investigating multicolinearity by looking at the variance inflation factor


```{r}
library(car)
vif(log_reg_ov2_pv1_pv2)
```

**as all values well below 5 -> no excessive colinearity between predictor variables**

## Calculating correlation matrix for log_reg_ov2_pv1_pv2

```{r}
#create a dataset with variables solely used in log_reg_ov1_pv2
data_log_reg_ov2_pv1_pv2 = port_preprocessed_data %>%
  select(reliable_improvement,retrospectively_reported_improvement, retrospectively_treatment_helpful, ieso_treatment_completed_total, demographics_gender, demographics_age_at_screening)
```


```{r} 
#corr.test(data_log_reg_ov2_pv1_pv2, adjust = "none")
```
**correlations between 2 PVs of interest (retrospectively_reported_improvement and retrospectively_treatment_helpful) is .63**

## ASSUMPTION 4:(4) No extreme outliers


```{r}
#visualizing the Cook's distance values
plot(log_reg_ov2_pv1_pv2, which = 4, id.n = 3)
```

So we have some outliers - should we ignore them?? 


```{r} 
# Are these outliers within 2 standard deviations of the mean?

# Extract model results
model.data <- augment(log_reg_ov2_pv1_pv2) %>% 
  mutate(index = 1:n()) 
#The data for the top 3 largest values, according to the Cook's distance, can be displayed as follow:
model.data %>% top_n(3, .cooksd)
#Plot the standardized residuals:
ggplot(model.data, aes(index, .std.resid)) + 
  geom_point(aes(color = retrospectively_reported_improvement), alpha = .5) +
  theme_bw()
#Filter potential influential data points:
model.data %>% 
  filter(abs(.std.resid) > 3)

```

**3 data points are marginally beyond 2SD from the mean**


## ASSUMPTION 5: (5) Linear relationship between predictor variables and the logit of outcome variable

## Remove qualitative variables from the original data frame and bind the logit values to the data:

```{r}

# Select only numeric predictors
log_reg_predictors_ov2_pv1_pv2 <- port_preprocessed_data %>%
  select(ieso_treatment_completed_total, demographics_age_at_screening, demographics_gender, retrospectively_treatment_helpful, retrospectively_reported_improvement)
# Bind the logit and tidying the data for plot
log_reg_predictors_ov2_pv1_pv2 <- log_reg_predictors_ov2_pv1_pv2 %>%
  mutate(logit = log(probabilities_ov2_pv1_pv2/(1-probabilities_ov2_pv1_pv2))) %>%
  gather(key = "predictors", value = "predictor.value", -logit)

```

## Create scatterplots

```{r}
ggplot(log_reg_predictors_ov2_pv1_pv2, aes(logit, predictor.value))+
  geom_point(size = 0.5, alpha = 0.5) +
  geom_smooth(method = "loess") + 
  theme_bw() + 
  facet_wrap(~predictors, scales = "free_y")
```

**linear relationships between pvs and ov**

# **Logistic regressions for OV3: RELIABLE_RECOVERY**

## PV1: retrospectively_reported_improvement

## Assumptions-checking of Logistic Regression ov3_pv1

(1) Outcome variable is binary - **checked**
(2) The observations are independent - **checked** (they come from separate individuals)
(3) No severe multicolinearity among the exploratory variables
(4) No extreme outliers
(5) Linear relationship between predictor variables and the logit of
    outcome variable

```{r}
# Fit the logistic regression model ov3_pv1
log_reg_ov3_pv1 <- glm(reliable_recovery ~ retrospectively_reported_improvement + ieso_treatment_completed_total  + demographics_gender + demographics_age_at_screening, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov3_pv1)

```


```{r}
# Predict the probability (p) of symptom improvement
probabilities_ov3_pv1 <- predict(log_reg_ov3_pv1, type = "response")
predicted.classes <- ifelse(probabilities_ov3_pv1 > 0.5, "pos", "neg")
print(predicted.classes)

```

## ASSUMPTION 3: (3) No severe multicolinearity among the exploratory variables
 

```{r}
library(car)
vif(log_reg_ov3_pv1)
```

**as all values well below 5 -> no excessive colinearity between predictor variables**

## Calculating correlation matrix for log_reg_ov3_pv1

```{r}
#create a dataset with variables solely used in log_reg_ov1_pv1
data_log_reg_ov3_pv1 = port_preprocessed_data %>%
  select(reliable_recovery, retrospectively_reported_improvement, ieso_treatment_completed_total, demographics_gender, demographics_age_at_screening)
```


```{r} 
library("psych")
corr.test(data_log_reg_ov3_pv1, adjust = "none")
```
**ieso_treatment_completed_total and retrospectively reported improvement - 0.39**

## ASSUMPTION 4:(4) No extreme outliers


```{r}
#visualizing the Cook's distance values
plot(log_reg_ov3_pv1, which = 4, id.n = 3)
```
**some outliers - mostly datapoint 77**


```{r}
# Extract model results
model.data <- augment(log_reg_ov3_pv1) %>% 
  mutate(index = 1:n()) 
#The data for the top 3 largest values, according to the Cook's distance, can be displayed as follow:
model.data %>% top_n(3, .cooksd)
#Plot the standardized residuals:
ggplot(model.data, aes(index, .std.resid)) + 
  geom_point(aes(color = retrospectively_reported_improvement), alpha = .5) +
  theme_bw()
#Filter potential influential data points:
model.data %>% 
  filter(abs(.std.resid) > 3)

```

**all datapoints within 2SD of the mean**


## ASSUMPTION 5: (5) Linear relationship between predictor variables and the logit of outcome variable

## Remove qualitative variables from the original data frame and bind the logit values to the data:

```{r}

# Select only numeric predictors
log_reg_predictors_ov3_pv1 <- port_preprocessed_data %>%
  select(ieso_treatment_completed_total, demographics_age_at_screening, demographics_gender, retrospectively_reported_improvement)
# Bind the logit and tidying the data for plot
log_reg_predictors_ov3_pv1 <- log_reg_predictors_ov3_pv1 %>%
  mutate(logit = log(probabilities_ov3_pv1/(1-probabilities_ov3_pv1))) %>%
  gather(key = "predictors", value = "predictor.value", -logit)

```

## Create scatterplots

```{r}
ggplot(log_reg_predictors_ov3_pv1, aes(logit, predictor.value))+
  geom_point(size = 0.5, alpha = 0.5) +
  geom_smooth(method = "loess") + 
  theme_bw() + 
  facet_wrap(~predictors, scales = "free_y")
```


**there is a linear relationship between the retrospectively_reported_improvement and iapt:reliable recovery**

# PV2: retrospectively_treatment_helpful

## Assumptions-checking of Logistic Regression ov3_pv2

(1) Outcome variable is binary - **checked**
(2) The observations are independent - **checked** (they come from separate individuals)
(3) No severe multicolinearity among the exploratory variables
(4) No extreme outliers
(5) Linear relationship between predictor variables and the logit of
    outcome variable


```{r}
# Fit the logistic regression model ov3_pv2
log_reg_ov3_pv2 <- glm(reliable_recovery ~ retrospectively_treatment_helpful + ieso_treatment_completed_total  + demographics_gender + demographics_age_at_screening, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov3_pv2)

```
```{r}
# Predict the probability (p) of symptom improvement
probabilities_ov3_pv2 <- predict(log_reg_ov3_pv2, type = "response")
predicted.classes <- ifelse(probabilities_ov3_pv2 > 0.5, "pos", "neg")
print(predicted.classes)

```
## ASSUMPTION 3: (3) No severe multicolinearity among the exploratory variables


```{r}
library(car)
vif(log_reg_ov3_pv2)
```

**as all values well below 5 -> no excessive colinearity between predictor variables**

## Calculating correlation matrix for log_reg_ov2_pv2

```{r}
#create a dataset with variables solely used in log_reg_ov3_pv2
data_log_reg_ov3_pv2 = port_preprocessed_data %>%
  select(reliable_recovery, retrospectively_treatment_helpful, ieso_treatment_completed_total, demographics_gender, demographics_age_at_screening)
```


```{r} 
#corr.test(data_log_reg_ov3_pv2, adjust = "none")
```
**no of treatments and restrospecovely treatment helpful = .36**

## ASSUMPTION 4:(4) No extreme outliers


```{r}
#visualizing the Cook's distance values
plot(log_reg_ov3_pv2, which = 4, id.n = 3)
```
So we have some outliers - should we ignore them?? 


```{r} 
# Are these outliers within 2 standard deviations of the mean?

# Extract model results
model.data <- augment(log_reg_ov3_pv2) %>% 
  mutate(index = 1:n()) 
#The data for the top 3 largest values, according to the Cook's distance, can be displayed as follow:
model.data %>% top_n(3, .cooksd)
#Plot the standardized residuals:
ggplot(model.data, aes(index, .std.resid)) + 
  geom_point(aes(color = retrospectively_treatment_helpful), alpha = .5) +
  theme_bw()
#Filter potential influential data points:
model.data %>% 
  filter(abs(.std.resid) > 3)

```

**all datapoints are within 2SD from the mean**


## ASSUMPTION 5: (5) Linear relationship between predictor variables and the logit of outcome variable

## Remove qualitative variables from the original data frame and bind the logit values to the data:

```{r}

# Select only numeric predictors
log_reg_predictors_ov3_pv2 <- port_preprocessed_data %>%
  select(ieso_treatment_completed_total, demographics_age_at_screening, demographics_gender, retrospectively_treatment_helpful)
# Bind the logit and tidying the data for plot
log_reg_predictors_ov3_pv2 <- log_reg_predictors_ov3_pv2 %>%
  mutate(logit = log(probabilities_ov3_pv2/(1-probabilities_ov3_pv2))) %>%
  gather(key = "predictors", value = "predictor.value", -logit)

```

## Create scatterplots

```{r}
ggplot(log_reg_predictors_ov3_pv2, aes(logit, predictor.value))+
  geom_point(size = 0.5, alpha = 0.5) +
  geom_smooth(method = "loess") + 
  theme_bw() + 
  facet_wrap(~predictors, scales = "free_y")
```

**linear relationships between pvs and ov**

# PV1 & PV2: retrospectively_reported_improvement and retrospectively_treatment_helpful

## Assumptions-checking of Logistic Regression ov3_pv1_pv2

(1) Outcome variable is binary - **checked**
(2) The observations are independent - **checked** (they come from separate individuals)
(3) No severe multicolinearity among the exploratory variables
(4) No extreme outliers
(5) Linear relationship between predictor variables and the logit of
    outcome variable


```{r}
# Fit the logistic regression model ov3_pv1_pv2
log_reg_ov3_pv1_pv2 <- glm(reliable_recovery ~ retrospectively_reported_improvement  + retrospectively_treatment_helpful +  ieso_treatment_completed_total  + demographics_gender + demographics_age_at_screening, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov3_pv1_pv2)

```

```{r}
# Predict the probability (p) of symptom improvement
probabilities_ov3_pv1_pv2 <- predict(log_reg_ov3_pv1_pv2, type = "response")
predicted.classes <- ifelse(probabilities_ov3_pv1_pv2 > 0.5, "pos", "neg")
print(predicted.classes)

```
## ASSUMPTION 3: (3) No severe multicolinearity among the exploratory variables
 Investigating multicolinearity by looking at the variance inflation factor


```{r}
library(car)
vif(log_reg_ov3_pv1_pv2)
```

**as all values well below 5 -> no excessive colinearity between predictor variables**

## Calculating correlation matrix for log_reg_ov3_pv1_pv2

```{r}
#create a dataset with variables solely used in log_reg_ov1_pv2
data_log_reg_ov3_pv1_pv2 = port_preprocessed_data %>%
  select(reliable_recovery,retrospectively_reported_improvement, retrospectively_treatment_helpful, ieso_treatment_completed_total, demographics_gender, demographics_age_at_screening)
```


```{r} 
#corr.test(data_log_reg_ov3_pv1_pv2, adjust = "none")
```
**correlations between 2 PVs of interest (retrospectively_reported_improvement and retrospectively_treatment_helpful) is .63; additionaly between no of sessions attended and retrospectively related improvement and retrospectively treatment helpful - 0.37 and 0.36, retrospectively**

## ASSUMPTION 4:(4) No extreme outliers


```{r}
#visualizing the Cook's distance values
plot(log_reg_ov3_pv1_pv2, which = 4, id.n = 3)
```

So we have some outliers (especially datapont 77) - should we ignore them?? 


```{r} 
# Are these outliers within 2 standard deviations of the mean?

# Extract model results
model.data <- augment(log_reg_ov3_pv1_pv2) %>% 
  mutate(index = 1:n()) 
#The data for the top 3 largest values, according to the Cook's distance, can be displayed as follow:
model.data %>% top_n(3, .cooksd)
#Plot the standardized residuals:
ggplot(model.data, aes(index, .std.resid)) + 
  geom_point(aes(color = retrospectively_reported_improvement), alpha = .5) +
  theme_bw()
#Filter potential influential data points:
model.data %>% 
  filter(abs(.std.resid) > 3)

```

**all datapoints are within 2SD from the mean**


## ASSUMPTION 5: (5) Linear relationship between predictor variables and the logit of outcome variable

## Remove qualitative variables from the original data frame and bind the logit values to the data:

```{r}

# Select only numeric predictors
log_reg_predictors_ov3_pv1_pv2 <- port_preprocessed_data %>%
  select(ieso_treatment_completed_total, demographics_age_at_screening, demographics_gender, retrospectively_treatment_helpful, retrospectively_reported_improvement)
# Bind the logit and tidying the data for plot
log_reg_predictors_ov3_pv1_pv2 <- log_reg_predictors_ov3_pv1_pv2 %>%
  mutate(logit = log(probabilities_ov3_pv1_pv2/(1-probabilities_ov3_pv1_pv2))) %>%
  gather(key = "predictors", value = "predictor.value", -logit)

```

## Create scatterplots

```{r}
ggplot(log_reg_predictors_ov3_pv1_pv2, aes(logit, predictor.value))+
  geom_point(size = 0.5, alpha = 0.5) +
  geom_smooth(method = "loess") + 
  theme_bw() + 
  facet_wrap(~predictors, scales = "free_y")
```

**linear relationships between pvs and ov**


## PREDICTING THE PROBABILITIES


# Visualise log_reg_ov1_pv1
```{r}
library(ggplot2)
library(visreg)
library(extrafont)

# Import system fonts - only supports TrueType fonts
# font_import() # This can take a while

# Set the font to Calibri
theme_set(theme_bw(base_family = "Calibri"))

# Modify font size
theme_update(plot.title = element_text(size = 12, face = "bold"),
             axis.title.x = element_text(size = 12),
             axis.title.y = element_text(size = 12),
             axis.text.x = element_text(size = 12),
             axis.text.y = element_text(size = 12),
             legend.text = element_text(size = 12),
             legend.title = element_text(size = 12))

# Define plot
visreg(log_reg_ov1_pv1, "retrospectively_reported_improvement", 
       gg = TRUE, 
       scale = "response",
       jitter = TRUE) +
  
  # Modify y-axis label to present in two lines
  labs(y = "Probability of Recovery(Yes)", 
       x = "Improvement",
       title = "Relationship Between Improvement Categories\nand NHSTT Treatment Outcome - Recovery",
       subtitle = "Controlling For: Number of Treatment Sessions, Gender, and Age") +
  
  # Replace numeric values on the x-axis with corresponding labels
  scale_x_continuous(labels = c("Much Worse", "Little Worse", "No Change", "Little Better", "Much Better")) +
  
  # Modify theme to APA7 style
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank(),
        axis.line = element_line(linewidth = 1),
        axis.ticks = element_line(linewidth = 0.5),
        legend.position = "bottom",
        legend.justification = "center",
        legend.box = "horizontal")


```




# Visualise log_reg_ov1_pv2

```{r}

library(ggplot2)
library(visreg)
library(extrafont)

# Import system fonts - only supports TrueType fonts
# font_import() # This can take a while

# Set the font to Calibri
theme_set(theme_bw(base_family = "Calibri"))

# Modify font size
theme_update(plot.title = element_text(size = 12, face = "bold"),
             axis.title.x = element_text(size = 12),
             axis.title.y = element_text(size = 12),
             axis.text.x = element_text(size = 12),
             axis.text.y = element_text(size = 12),
             legend.text = element_text(size = 12),
             legend.title = element_text(size = 12))
# Convert 'retrospectively_treatment_helpful' column to a factor with labels "No" and "Yes"
#log_reg_ov1_pv2$retrospectively_treatment_helpful <- #factor(log_reg_ov1_pv2$retrospectively_treatment_helpful, levels = c(0, 1), labels = c("No", "Yes"))

# Define plot
visreg(log_reg_ov1_pv2, "retrospectively_treatment_helpful", 
       gg = TRUE, 
       scale = "response",
       jitter = TRUE) +
  
  # Modify y-axis label to present in two lines
  labs(y = "Probability of Recovery(Yes)", 
       x = "Helpfulness",
       title = "Relationship Between Helpfulness Categories\nand NHSTT Treatment Outcome - Recovery",
       subtitle = "Controlling For: Number of Treatment Sessions, Gender, and Age") +
     
  # Replace 0 and 1 on the x-axis with "No" and "Yes"
 #scale_x_continuous(labels = c("No", "Yes")) +
  # Modify theme to APA7 style
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank(),
        axis.line = element_line(linewidth = 1),
        axis.ticks = element_line(linewidth = 0.5),
        legend.position = "bottom",
        legend.justification = "center",
        legend.box = "horizontal")

```
# Visualise log_reg_ov1_pv1_pv2

```{r}

library(ggplot2)
library(visreg)
library(extrafont)

# Import system fonts - only supports TrueType fonts
# font_import() # This can take a while

# Set the font to Calibri
theme_set(theme_bw(base_family = "Calibri"))

# Modify font size
theme_update(plot.title = element_text(size = 12, face = "bold"),
             axis.title.x = element_text(size = 12),
             axis.title.y = element_text(size = 12),
             axis.text.x = element_text(size = 12),
             axis.text.y = element_text(size = 12),
             legend.text = element_text(size = 12),
             legend.title = element_text(size = 12))

# Define plot
visreg(log_reg_ov1_pv1_pv2, "retrospectively_reported_improvement", 
       gg = TRUE, 
       scale = "response",
       jitter = TRUE) +
  
  # Modify y-axis label to present in two lines
  labs(y = "Probability of Recovery(Yes)", 
       x = "Improvement",
       title = "Relationship Between Improvement Categories\nand NHSTT Treatment Outcome - Recovery,\nAccounting for Helpfulness",
       subtitle = "Controlling For: Number of Treatment Sessions, Gender, and Age") +
  
    # Replace numeric values on the x-axis with corresponding labels
  scale_x_continuous(labels = c("Much Worse", "Little Worse", "No Change", "Little Better", "Much Better")) +
  
  # Modify theme to APA7 style
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank(),
        axis.line = element_line(linewidth = 1),
        axis.ticks = element_line(linewidth = 0.5),
        legend.position = "bottom",
        legend.justification = "center",
        legend.box = "horizontal")

```
# Visualise log_reg_ov2_pv1

```{r}

library(ggplot2)
library(visreg)
library(extrafont)

# Import system fonts - only supports TrueType fonts
# font_import() # This can take a while

# Set the font to Calibri
theme_set(theme_bw(base_family = "Calibri"))

# Modify font size
theme_update(plot.title = element_text(size = 12, face = "bold"),
             axis.title.x = element_text(size = 12),
             axis.title.y = element_text(size = 12),
             axis.text.x = element_text(size = 12),
             axis.text.y = element_text(size = 12),
             legend.text = element_text(size = 12),
             legend.title = element_text(size = 12))

# Define plot
visreg(log_reg_ov2_pv1, "retrospectively_reported_improvement", 
       gg = TRUE, 
       scale = "response",
       jitter = TRUE) +
  
  # Modify y-axis label to present in two lines
  labs(y = "Probability of Reliable Improvement(Yes)", 
       x = "Improvement",
       title = "Relationship Between Improvement Categories\nand NHSTT Treatment Outcome - Reliable Improvement",
       subtitle = "Controlling For: Number of Treatment Sessions, Gender, and Age") +
  
  # Replace numeric values on the x-axis with corresponding labels
  scale_x_continuous(labels = c("Much Worse", "Little Worse", "No Change", "Little Better", "Much Better")) +
  
  # Modify theme to APA7 style
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank(),
        axis.line = element_line(linewidth = 1),
        axis.ticks = element_line(linewidth = 0.5),
        legend.position = "bottom",
        legend.justification = "center",
        legend.box = "horizontal")

```

# Visualise log_reg_ov2_pv2

```{r}

library(ggplot2)
library(visreg)
library(extrafont)

# Import system fonts - only supports TrueType fonts
# font_import() # This can take a while

# Set the font to Calibri
theme_set(theme_bw(base_family = "Calibri"))

# Modify font size
theme_update(plot.title = element_text(size = 12, face = "bold"),
             axis.title.x = element_text(size = 12),
             axis.title.y = element_text(size = 12),
             axis.text.x = element_text(size = 12),
             axis.text.y = element_text(size = 12),
             legend.text = element_text(size = 12),
             legend.title = element_text(size = 12))

# Define plot
visreg(log_reg_ov2_pv2, "retrospectively_treatment_helpful", 
       gg = TRUE, 
       scale = "response") +
  
  # Modify y-axis label to present in two lines
  labs(y = "Probability of Reliable Improvement(Yes)", 
       x = "Helpfulness",
       title = "Relationship Between Helpfulness Categories\nand NHSTT Treatment Outcome - Reliable Improvement",
       subtitle = "Controlling For: Number of Treatment Sessions, Gender, and Age") +
  
  # Modify theme to APA7 style
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank(),
        axis.line = element_line(linewidth = 1),
        axis.ticks = element_line(linewidth = 0.5),
        legend.position = "bottom",
        legend.justification = "center",
        legend.box = "horizontal")

```
# Visualise log_reg_ov2_pv1_pv2

```{r}

library(ggplot2)
library(visreg)
library(extrafont)

# Import system fonts - only supports TrueType fonts
# font_import() # This can take a while

# Set the font to Calibri
theme_set(theme_bw(base_family = "Calibri"))

# Modify font size
theme_update(plot.title = element_text(size = 12, face = "bold"),
             axis.title.x = element_text(size = 12),
             axis.title.y = element_text(size = 12),
             axis.text.x = element_text(size = 12),
             axis.text.y = element_text(size = 12),
             legend.text = element_text(size = 12),
             legend.title = element_text(size = 12))

# Define plot
visreg(log_reg_ov2_pv1_pv2, "retrospectively_reported_improvement", 
       gg = TRUE, 
       scale = "response",
       jitter = TRUE) +
  
  # Modify y-axis label to present in two lines
  labs(y = "Probability of Reliable Improvement(Yes)", 
       x = "Improvement",
       title = "Relationship Between Improvement Categories\nand NHSTT Treatment Outcome - Reliable Improvement,\nAccounting for Helpfulness",
       subtitle = "Controlling For: Number of Treatment Sessions, Gender, and Age") +
  
  # Replace numeric values on the x-axis with corresponding labels
  scale_x_continuous(labels = c("Much Worse", "Little Worse", "No Change", "Little Better", "Much Better")) +
  
  # Modify theme to APA7 style
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank(),
        axis.line = element_line(linewidth = 1),
        axis.ticks = element_line(linewidth = 0.5),
        legend.position = "bottom",
        legend.justification = "center",
        legend.box = "horizontal")

```

# Visualise log_reg_ov3_pv1

```{r}

library(ggplot2)
library(visreg)
library(extrafont)

# Import system fonts - only supports TrueType fonts
# font_import() # This can take a while

# Set the font to Calibri
theme_set(theme_bw(base_family = "Calibri"))

# Modify font size
theme_update(plot.title = element_text(size = 12, face = "bold"),
             axis.title.x = element_text(size = 12),
             axis.title.y = element_text(size = 12),
             axis.text.x = element_text(size = 12),
             axis.text.y = element_text(size = 12),
             legend.text = element_text(size = 12),
             legend.title = element_text(size = 12))

# Define plot
visreg(log_reg_ov3_pv1, "retrospectively_reported_improvement", 
       gg = TRUE, 
       scale = "response",
       jitter = TRUE) +
  
  # Modify y-axis label to present in two lines
  labs(y = "Probability of Reliable Recovery(Yes)", 
       x = "Improvement",
       title = "Relationship Between Improvement Categories\nand NHSTT Treatment Outcome - Reliable Recovery",
       subtitle = "Controlling For: Number of Treatment Sessions, Gender, and Age") +
  
# Replace numeric values on the x-axis with corresponding labels
  scale_x_continuous(labels = c("Much Worse", "Little Worse", "No Change", "Little Better", "Much Better")) +
  
  # Modify theme to APA7 style
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank(),
        axis.line = element_line(linewidth = 1),
        axis.ticks = element_line(linewidth = 0.5),
        legend.position = "bottom",
        legend.justification = "center",
        legend.box = "horizontal")

```

# Visualise log_reg_ov3_pv2

```{r}

library(ggplot2)
library(visreg)
library(extrafont)

# Import system fonts - only supports TrueType fonts
# font_import() # This can take a while

# Set the font to Calibri
theme_set(theme_bw(base_family = "Calibri"))

# Modify font size
theme_update(plot.title = element_text(size = 12, face = "bold"),
             axis.title.x = element_text(size = 12),
             axis.title.y = element_text(size = 12),
             axis.text.x = element_text(size = 12),
             axis.text.y = element_text(size = 12),
             legend.text = element_text(size = 12),
             legend.title = element_text(size = 12))

# Define plot
visreg(log_reg_ov3_pv2, "retrospectively_treatment_helpful", 
       gg = TRUE, 
       scale = "response",
       jitter = TRUE) +
  
  # Modify y-axis label to present in two lines
  labs(y = "Probability of Reliable Recovery(Yes)", 
       x = "Helpfulness",
       title = "Relationship Between Helpfulness Categories\nand NHSTT Treatment Outcome - Reliable Recovery",
       subtitle = "Controlling For: Number of Treatment Sessions, Gender, and Age") +
  
  # Modify theme to APA7 style
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank(),
        axis.line = element_line(linewidth = 1),
        axis.ticks = element_line(linewidth = 0.5),
        legend.position = "bottom",
        legend.justification = "center",
        legend.box = "horizontal")

```
# Visualise log_reg_ov3_pv1_pv2

```{r}

library(ggplot2)
library(visreg)
library(extrafont)

# Import system fonts - only supports TrueType fonts
# font_import() # This can take a while

# Set the font to Calibri
theme_set(theme_bw(base_family = "Calibri"))

# Modify font size
theme_update(plot.title = element_text(size = 12, face = "bold"),
             axis.title.x = element_text(size = 12),
             axis.title.y = element_text(size = 12),
             axis.text.x = element_text(size = 12),
             axis.text.y = element_text(size = 12),
             legend.text = element_text(size = 12),
             legend.title = element_text(size = 12))

# Define plot
visreg(log_reg_ov3_pv1_pv2, "retrospectively_reported_improvement", 
       gg = TRUE, 
       scale = "response",
       jitter = TRUE) +
  
  # Modify y-axis label to present in two lines
  labs(y = "Probability of Reliable Recovery(Yes)", 
       x = "Improvement",
       title = "Relationship Between Improvement Categories\nand NHSTT Treatment Outcome - Reliable Recovery,\nAccounting for Helpfulness",
       subtitle = "Controlling For: Number of Treatment Sessions, Gender, and Age") +
  # Replace numeric values on the x-axis with corresponding labels
  scale_x_continuous(labels = c("Much Worse", "Little Worse", "No Change", "Little Better", "Much Better")) +
  
  # Modify theme to APA7 style
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank(),
        axis.line = element_line(linewidth = 1),
        axis.ticks = element_line(linewidth = 0.5),
        legend.position = "bottom",
        legend.justification = "center",
        legend.box = "horizontal")

```

## COHEN'S KAPPA for iapt treatment outcomes and Retrospective Reports of Treatment Helpfulness

```{r}
#install.packages("irr")  # Install the irr package if you haven't already
library(irr)             # Load the irr package
#CONTINGENCY TABLE for recovered 
contingency_table = table(port_preprocessed_data$recovered, port_preprocessed_data$retrospectively_treatment_helpful)



print(contingency_table)

# Calculate the proportion of participants in each category
proportion_table_a <- prop.table(contingency_table, margin = 1)

print(proportion_table_a)

```
```{r}
# reference: https://www.statology.org/cohens-kappa-in-r/
library(psych)
cohen.kappa(x=cbind(port_preprocessed_data$retrospectively_treatment_helpful, port_preprocessed_data$recovered))

##NO AGREEMENT (.064) BETWEEN RECOVERED AND RETROSPECTIVELY TREATMENT HELPFUL
```
```{r}
contingency_table2 = table(port_preprocessed_data$reliable_improvement, port_preprocessed_data$retrospectively_treatment_helpful)
print(contingency_table2)
cohen.kappa(x=cbind(port_preprocessed_data$retrospectively_treatment_helpful, port_preprocessed_data$reliable_improvement))
##NO AGREEMENT (.058) BETWEEN RELIABLE IMPROVEMENT AND RETROSPECTIVELY TREATMENT HELPFUL

# Calculate the proportion of participants in each category
proportion_table_b <- prop.table(contingency_table2, margin = 1)

print(proportion_table_b)
```

```{r}
contingency_table3 = table(port_preprocessed_data$reliable_recovery, port_preprocessed_data$retrospectively_treatment_helpful)
print(contingency_table3)
cohen.kappa(x=cbind(port_preprocessed_data$retrospectively_treatment_helpful, port_preprocessed_data$reliable_recovery))
##NO AGREEMENT (.056) BETWEEN RELIABLE RECOVERY AND RETROSPECTIVELY TREATMENT HELPFUL

# Calculate the proportion of participants in each category
proportion_table_c <- prop.table(contingency_table3, margin = 1)

print(proportion_table_c)
table(port_preprocessed_data$reliable_recovery)
```


```{r}

# Create a contingency table using the table() function
cross_tab <- table(port_preprocessed_data$recovered,port_preprocessed_data$retrospectively_reported_improvement)

# Calculate the proportion of participants in each category
proportion_table <- prop.table(cross_tab, margin = 1)

# Display the proportion table
print(proportion_table)

```

```{r}
# Create a contingency table using the table() function
cross_tab2 <- table(port_preprocessed_data$reliable_improvement, port_preprocessed_data$retrospectively_reported_improvement)

# Calculate the proportion of participants in each category
proportion_table2 <- prop.table(cross_tab2, margin = 1)

# Display the proportion table
print(proportion_table2)
```
```{r}
# Create a contingency table using the table() function
cross_tab3 <- table(port_preprocessed_data$reliable_recovery, port_preprocessed_data$retrospectively_reported_improvement)

# Calculate the proportion of participants in each category
proportion_table3 <- prop.table(cross_tab3, margin = 1)

# Display the proportion table
print(proportion_table3)
```
```{r}
table(port_preprocessed_data$reliable_recovery)
table(port_preprocessed_data$recovered)
```

## AGREEMENT PLOTS



```{r}
#Calculating the proportions for the IMPROVEMENT plot 
#Reminder about the encoding of the columns:
#   NHS Talking Therapies categories : 1 = Yes, 2 = No 
#   Improvement variable : 
      # 4 = Much better
      # 3 = Little better
      # 2 = No change
      # 1 = Little worse
      # 0 = Much worse

#RECOVERY YES 
#N participants in each Yes or No
recovered_distribution <- table(port_preprocessed_data$recovered)
print(recovered_distribution)

# Filter data for prcpts with a value of 1 in 'recovered'
recovered_yes_participants <- port_preprocessed_data[port_preprocessed_data$recovered == 1, ]

# Calculating the frequency of values for participants with recovered = 1
frequency_recovered_yes <- table(recovered_yes_participants$retrospectively_reported_improvement)

# Print the frequency table
print(frequency_recovered_yes)

#RECOVERY NO

# Filter data for prcpts with a value of 0 in 'recovered'
recovered_no_participants <- port_preprocessed_data[port_preprocessed_data$recovered == 0, ]

# Calculating the frequency of values for participants with recovered = 0
frequency_recovered_no <- table(recovered_no_participants$retrospectively_reported_improvement)

# Print the frequency table
print(frequency_recovered_no)

```

```{r}
#RELIABLE IMPROVEMENT YES 
#N participants in each Yes or No
RI_distribution <- table(port_preprocessed_data$reliable_improvement)
print(RI_distribution)

# Filter data for prcpts with a value of 1 in 'recovered'
RI_yes_participants <- port_preprocessed_data[port_preprocessed_data$reliable_improvement == 1, ]

# Calculating the frequency of values for participants with recovered = 1
frequency_RI_yes <- table(RI_yes_participants$retrospectively_reported_improvement)

# Print the frequency table
print(frequency_RI_yes)

#RELIABLE IMPROVEMENT NO
# Filter data for prcpts with a value of 0 in 'recovered'
RI_no_participants <- port_preprocessed_data[port_preprocessed_data$reliable_improvement == 0, ]

# Calculating the frequency of values for participants with recovered = 0
frequency_RI_no <- table(RI_no_participants$retrospectively_reported_improvement)

# Print the frequency table
print(frequency_RI_no)
```


```{r}
#RELIABLE RECOVERY YES 
#N participants in each Yes or No
RR_distribution <- table(port_preprocessed_data$reliable_recovery)
print(RR_distribution)

# Filter data for prcpts with a value of 1 in 'recovered'
RR_yes_participants <- port_preprocessed_data[port_preprocessed_data$reliable_recovery == 1, ]

# Calculating the frequency of values for participants with recovered = 1
frequency_RR_yes <- table(RR_yes_participants$retrospectively_reported_improvement)

# Print the frequency table
print(frequency_RR_yes)

#RELIABLE RCOVERY NO
# Filter data for prcpts with a value of 0 in 'recovered'
RR_no_participants <- port_preprocessed_data[port_preprocessed_data$reliable_recovery == 0, ]

# Calculating the frequency of values for participants with recovered = 0
frequency_RR_no <- table(RR_no_participants$retrospectively_reported_improvement)

# Print the frequency table
print(frequency_RR_no)
```



```{r}
# Load the required library
library(ggplot2)

# Create a data frame 
data_helpfulness <- data.frame(
  Variable = rep(c("Recovery", "Reliable Improvement", "Reliable Recovery"), each = 4),
  Agreement = rep(c("Yes Yes", "No No", "Yes No", "No Yes"), times = 3),
  Proportion = c(0.46, 0.21, 0.06, 0.27, 0.48, 0.16, 0.09, 0.27, 0.36, 0.23, 0.05, 0.36)
)

# Specify desired order of levels for the Agreement factor
agreement_order <- c("No No", "Yes No", "No Yes", "Yes Yes")


# Create the agreement figure using ggplot2
agreement_plot_helpfulness <- ggplot(data_helpfulness, aes(x = Proportion, y = Variable, fill = factor(Agreement, levels = agreement_order))) +
  geom_bar(stat = "identity", position = "stack", width = 0.3) +
  scale_fill_manual(values = c("Yes Yes" = "#117733", "No No" = "#882255", "Yes No" = "#88CCEE", "No Yes" = "#332288")) +
  labs(title = expression("Agreement Between " * italic("Helpfulness") * " \n and NHS Talking Therapies Treatment Outcomes")) +
  theme_minimal() +
  theme(
    axis.title = element_blank(),  # Remove axis titles
    legend.title = element_blank(),
    text = element_text(size = 12),
    legend.text = element_text(size = 12),  # Adjust legend label font size
    axis.text.y = element_text(size = 12),  # Adjust y-axis text (variable names) font size# Remove legend title
    )

# Print the plot
print(agreement_plot_helpfulness)



```


```{r}
# Load the required library

library(ggplot2)

# Create a data frame with your data
data_improvement <- data.frame(
  Variable = rep(c("Recovery: Yes","Recovery: No", "Reliable Improvement: Yes", "Reliable Improvement: No", "Reliable Recovery: Yes", "Reliable Recovery: No"), each = 5),
  Improvement = rep(c("Much Better", "Little Better", "No Change","Little Worse", "Much Worse"), times = 6),
  Proportion = c(0.390625,
                0.468750,
                0.140625,
                0.000000,
                0.000000,
                0.083333,
                0.433333,
                0.400000,
                0.050000,
                0.033333,
                0.376623,
                0.493506,
                0.129870,
                0.000000,
                0.000000,
                0.086207,
                0.413793,
                0.413793,
                0.051724,
                0.034483,
                0.444444,
                0.444444,
                0.111111,
                0.000000,
                0.000000,
                0.085714,
                0.457143,
                0.385714,
                0.042857,
                0.028571)
                )

#The values above were not entered manually but pasted from an excel sheet where the proportions were calculated 
# Specify the desired order of levels for the Improvement factor
improvement_order <- c("Much Worse", "Little Worse", "No Change", "Little Better", "Much Better")

# Create the agreement figure using ggplot2
agreement_plot_improvement <- ggplot(data_improvement, aes(x = Proportion, y = Variable, fill = factor(Improvement, levels = improvement_order))) +
  geom_bar(stat = "identity", position = "stack", width = 0.5) +
  scale_fill_manual(values = c("Much Better" = "#117733", "Little Better" = "#332288", "No Change" = "#88CCEE", "Little Worse" = "#DDCC77", "Much Worse" = "#882255")) +
  labs(title = expression("Agreement Between " * italic("Helpfulness") * " \n and NHS Talking Therapies Treatment Outcomes")) +
  theme_minimal() +
  theme(
    axis.title = element_blank(),  # Remove axis titles
    legend.title = element_blank(),
    text = element_text(size = 12),
    legend.text = element_text(size = 12),  # Adjust legend label font size
    axis.text.y = element_text(size = 12)  # Adjust y-axis text (variable names) font size
  )

# Print the plot
print(agreement_plot_improvement)

```
```{r}
library(patchwork) 
agreement_plot_combined = agreement_plot_helpfulness + agreement_plot_improvement + plot_layout(nrow=2)
print(agreement_plot_combined)
```
## REVISED FOREST PLOT

```{r}
library(sjPlot)
log_reg_forest_plot <- plot_models(log_reg_ov1_pv2, log_reg_ov1_pv1, log_reg_ov1_pv1_pv2, log_reg_ov2_pv2, log_reg_ov2_pv1, log_reg_ov2_pv1_pv2, log_reg_ov3_pv2, log_reg_ov3_pv1, log_reg_ov3_pv1_pv2,
  transform = "exp",
  std.est = NULL,
  std.response = TRUE,
  rm.terms = c("ieso_treatment_completed_total", "demographics_gender", "demographics_age_at_screening"),
  title = NULL,
  m.labels = NULL,
  legend.title = "Models",
  legend.pval.title = "p",
  axis.labels = c("Improvement", "Helpfulness"),
  axis.title = "Odds Ratios (95% CI)",
  axis.lim = NULL,
  wrap.title = 50,
  wrap.labels = 25,
  wrap.legend.title = 20,
  grid.breaks = NULL,
  dot.size = 3,
  line.size = NULL,
  value.size = NULL,
  spacing = 0.5,
  colors =  c("#332288", "#88CCEE", "#88CCEE", "#117733", "#999933", "#999933", "#DDCC77", "#882255","#882255"),
  show.values = FALSE,
  show.legend = TRUE,
  show.intercept = FALSE,
  show.p = TRUE,
  p.shape = TRUE,
  p.threshold = c(0.05),
  p.adjust = NULL,
  ci.lvl = 0.95,
  robust = FALSE,
  vcov.fun = NULL,
  vcov.type = NULL,
  vcov.args = NULL,
  vline.color = "black",
  digits = 2,
  grid = FALSE,
  auto.label = TRUE,
  prefix.labels = c("none", "varname", "label")
)+
theme(axis.text.x = element_text(size=12),axis.text.y = element_text(size = 12)) +
  theme_minimal()

print(log_reg_forest_plot)
```

```{r}

##Computing the logistic regressions again without the covariates of number of treatment sessions, gender, and age following a reviewer comment
#The B at the and of the labels is used to signify that they are aprt of a second set of analyses, where the regressions were conducted without the covariates. 

# Fit the logistic regression model ov1_pv1
log_reg_ov1_pv1_B <- glm(recovered ~ retrospectively_reported_improvement, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov1_pv1_B)

odds_ratios_log_reg_ov1_pv1_B <- exp(coef(log_reg_ov1_pv1_B))

odds_ratios_log_reg_ov1_pv1_B


# Fit the logistic regression model ov1_pv2
log_reg_ov1_pv2_B <- glm(recovered ~ retrospectively_treatment_helpful, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov1_pv2_B)

odds_ratios_log_reg_ov1_pv2_B <- exp(coef(log_reg_ov1_pv2_B))

odds_ratios_log_reg_ov1_pv2_B


# Fit the logistic regression model ov1_pv1_pv2
log_reg_ov1_pv1_pv2_B <- glm(recovered ~ retrospectively_reported_improvement  + retrospectively_treatment_helpful,
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov1_pv1_pv2_B)

odds_ratios_log_reg_ov1_pv1_pv2_B <- exp(coef(log_reg_ov1_pv1_pv2_B))

odds_ratios_log_reg_ov1_pv1_pv2_B

# Fit the logistic regression model ov2_pv1
log_reg_ov2_pv1_B <- glm(reliable_improvement ~ retrospectively_reported_improvement, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov2_pv1_B)

odds_ratios_log_reg_ov2_pv1_B <- exp(coef(log_reg_ov2_pv1_B))

odds_ratios_log_reg_ov2_pv1_B

# Fit the logistic regression model ov2_pv2
log_reg_ov2_pv2_B <- glm(reliable_improvement ~ retrospectively_treatment_helpful, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov2_pv2_B)

odds_ratios_log_reg_ov2_pv2_B <- exp(coef(log_reg_ov2_pv2_B))

odds_ratios_log_reg_ov2_pv2_B

# Fit the logistic regression model ov1_pv1_pv2
log_reg_ov2_pv1_pv2_B <- glm(reliable_improvement ~ retrospectively_reported_improvement  + retrospectively_treatment_helpful, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov2_pv1_pv2_B)

odds_ratios_log_reg_ov2_pv1_pv2_B <- exp(coef(log_reg_ov2_pv1_pv2_B))

odds_ratios_log_reg_ov2_pv1_pv2_B

# Fit the logistic regression model ov3_pv1
log_reg_ov3_pv1_B <- glm(reliable_recovery ~ retrospectively_reported_improvement, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov3_pv1_B)

odds_ratios_log_reg_ov3_pv1_B<- exp(coef(log_reg_ov3_pv1_B))

odds_ratios_log_reg_ov3_pv1_B

# Fit the logistic regression model ov3_pv2
log_reg_ov3_pv2_B <- glm(reliable_recovery ~ retrospectively_treatment_helpful, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov3_pv2_B)

odds_ratios_log_reg_ov3_pv2_B <- exp(coef(log_reg_ov3_pv2_B))

odds_ratios_log_reg_ov3_pv2_B

# Fit the logistic regression model ov3_pv1_pv2
log_reg_ov3_pv1_pv2_B <- glm(reliable_recovery ~ retrospectively_reported_improvement  + retrospectively_treatment_helpful, 
                       data = port_preprocessed_data, 
                       family = binomial)

summary(log_reg_ov3_pv1_pv2_B)

odds_ratios_log_reg_ov3_pv1_pv2_B <- exp(coef(log_reg_ov3_pv1_pv2_B))

odds_ratios_log_reg_ov3_pv1_pv2_B



```