Qualitative Predictors

# Exploring Qualitative Predictors in Medical Data Regression Models
# In my journey of analyzing medical data, I find it intriguing to observe how regression models can seamlessly integrate both quantitative and qualitative predictors. Real-world datasets, especially those in the medical field, often present a mix of variable types, which opens up avenues for nuanced analysis. My recent project delves into these complexities, exploring how qualitative predictors such as treatment type and patient region can provide meaningful insights when modeled alongside quantitative variables like age and BMI.
# 
# Understanding the Dataset and Predictors
# I began my analysis by exploring a dataset centered around patient outcomes following specific medical treatments. The dataset contains a variety of predictors: some quantitative, such as age and BMI, and others qualitative, including treatment type and region. Recognizing the significance of these qualitative predictors, I took steps to incorporate them into my regression models. For instance, the Treatment_Type variable captures whether a patient received Drug A, Drug B, or no treatment at all. Similarly, the Region variable identifies whether a patient resides in an urban, rural, or suburban area.
# 
# Incorporating Dummy Variables
# To integrate these qualitative predictors into my regression models, I created dummy variables. For the Treatment_Type predictor, I defined two new variables: Treatment_A and Treatment_B. Patients who received Drug A were coded as 1 in the Treatment_A variable, while those who received Drug B were assigned a value of 1 in the Treatment_B variable. Patients who did not receive any treatment served as the baseline group.
# 
# I fitted a regression model that combined these dummy variables with quantitative predictors such as age and BMI. This approach allowed me to examine how outcomes differed between the treatment groups. I found that the coefficients for Treatment_A and Treatment_B represented the differences in outcomes for patients receiving these treatments compared to those in the baseline group.
# 
# Analyzing Predictors with Multiple Levels
# The Region variable presented another interesting challenge. With three levels—Urban, Rural, and Suburban—a single dummy variable was insufficient. I addressed this by creating two dummy variables: Region_Urban and Region_Rural. The Suburban category served as the baseline. By including these variables in my regression model, I could explore how outcomes varied across regions.
# 
# Interpreting the coefficients for Region_Urban and Region_Rural, I observed differences in outcomes for patients in urban and rural areas compared to those in suburban areas. The intercept in this model represented the average outcome for suburban patients, while the coefficients for the dummy variables highlighted the deviations for urban and rural patients.
# 
# Insights and Reflections
# Through this project, I realized the power of coding qualitative variables in uncovering hidden patterns in medical data. For instance, I could determine whether treatment outcomes varied significantly based on the type of treatment or the patient’s region. While the dummy variable approach is straightforward, it offers a robust framework for including qualitative predictors in regression models.
# 
# I also reflected on the importance of interpretation. The choice of baseline group, while arbitrary, affects how coefficients are understood. For example, the intercept represents the average outcome for the baseline group, and the dummy variable coefficients denote deviations from this baseline. These interpretations are critical for drawing meaningful conclusions from the data.
# 
# Conclusion
# Analyzing medical data requires a thoughtful approach to handling both quantitative and qualitative predictors. By incorporating dummy variables, I was able to model complex relationships and uncover insights that might otherwise go unnoticed. This project not only deepened my understanding of regression modeling but also highlighted the importance of flexibility and creativity in data analysis. The ability to adapt regression models for qualitative predictors is a skill I continue to refine, and I am excited to apply these techniques to future projects. Through this work, I have come to appreciate the rich storytelling potential of data and the valuable insights it can yield when analyzed with care and precision.

# I load the necessary libraries for my analysis
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(GGally)

## Warning: package 'GGally' was built under R version 4.4.2

## Loading required package: ggplot2

## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2

library(ggplot2)
library(readxl)

## Warning: package 'readxl' was built under R version 4.4.2

# I start by reading in my medical dataset and inspecting its structure
my_medical_data <- read_excel("C:/Users/jacob/Downloads/my_medical_data.xlsx")

# I explore the dataset to identify qualitative predictors
# In my case, 'Treatment_Type' and 'Region' are qualitative variables
# Let's create dummy variables for 'Treatment_Type'

# I find it fascinating that regression models can incorporate qualitative predictors, 
# which often appear in real-world datasets. For instance, in a medical dataset, 
# qualitative variables like smoking status (smoker or non-smoker) or patient region (urban, rural, suburban) can offer meaningful insights.

# I aim to analyze a dataset involving patient outcomes after specific treatments. 
# My dataset includes patient characteristics such as age, BMI, and treatment type. 
# Some predictors are quantitative, like age and BMI, while others are qualitative, like treatment type (e.g., drug A, drug B, or no treatment).

my_medical_data <- my_medical_data %>%
  mutate(Treatment_A = ifelse(Treatment_Type == "Drug_A", 1, 0),
         Treatment_B = ifelse(Treatment_Type == "Drug_B", 1, 0))

# I create a regression model using both quantitative and dummy variables

# I love analyzing how dummy variables impact my regression results. 
# For example, I created two dummy variables: `Treatment_A` and `Treatment_B`. 
# These represent whether a patient received Drug A or Drug B, respectively. 
# The baseline group consists of patients who did not receive any treatment.

# Inspect the Outcome variable to check its levels
table(my_medical_data$Outcome)

## 
##  Improved No_Change  Worsened 
##      1753      1659      1686

# Convert Outcome to a numeric variable
my_medical_data$Outcome <- ifelse(my_medical_data$Outcome == "Improved", 1,
                          ifelse(my_medical_data$Outcome == "No_Change", 0,
                          ifelse(my_medical_data$Outcome == "Worsened", -1, NA)))

# Check for NA values and remove rows with NA in the Outcome variable
my_medical_data <- na.omit(my_medical_data)

# Re-fit the linear model after cleaning the data
model <- lm(Outcome ~ Age + BMI + Treatment_A + Treatment_B, data = my_medical_data)

# Summarize the model
summary(model)

## 
## Call:
## lm(formula = Outcome ~ Age + BMI + Treatment_A + Treatment_B, 
##     data = my_medical_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.04711 -1.00033 -0.01405  0.97462  1.02286 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept)  0.0467392  0.0643534   0.726    0.468
## Age         -0.0003957  0.0005482  -0.722    0.470
## BMI         -0.0003492  0.0018463  -0.189    0.850
## Treatment_A  0.0144111  0.0281475   0.512    0.609
## Treatment_B -0.0204752  0.0281682  -0.727    0.467
## 
## Residual standard error: 0.8215 on 5093 degrees of freedom
## Multiple R-squared:  0.0004112,  Adjusted R-squared:  -0.0003738 
## F-statistic: 0.5238 on 4 and 5093 DF,  p-value: 0.7183

# Next, I address the 'Region' variable, which has three levels: Urban, Rural, Suburban

# I find that coding qualitative variables is a powerful technique. 
# For example, the `Region` variable has three levels: Urban, Rural, and Suburban. 
# I use dummy variables `Region_Urban` and `Region_Rural` to represent Urban and Rural regions, with Suburban as the baseline. 
# This approach helps me understand regional differences in patient outcomes.

# To handle this, I create dummy variables for 'Urban' and 'Rural' (Suburban is the baseline)
my_medical_data <- my_medical_data %>%
  mutate(Region_Urban = ifelse(Region == "Urban", 1, 0),
         Region_Rural = ifelse(Region == "Rural", 1, 0))

# I create another regression model, now including the region dummy variables

# By interpreting the results, I notice the intercept now represents the average outcome for patients in suburban areas. 
# The coefficients for `Region_Urban` and `Region_Rural` reflect the differences in outcomes for urban and rural patients compared to suburban ones.

model_region <- lm(Outcome ~ Age + BMI + Region_Urban + Region_Rural, data = my_medical_data)

# I summarize this model to understand how regional differences impact outcomes
summary(model_region)

## 
## Call:
## lm(formula = Outcome ~ Age + BMI + Region_Urban + Region_Rural, 
##     data = my_medical_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.04441 -1.00121 -0.01341  0.97520  1.01964 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)
## (Intercept)   0.0461219  0.0642818   0.717    0.473
## Age          -0.0004005  0.0005486  -0.730    0.465
## BMI          -0.0002912  0.0018472  -0.158    0.875
## Region_Urban  0.0112606  0.0283744   0.397    0.691
## Region_Rural -0.0193267  0.0282420  -0.684    0.494
## 
## Residual standard error: 0.8215 on 5093 degrees of freedom
## Multiple R-squared:  0.0003484,  Adjusted R-squared:  -0.0004367 
## F-statistic: 0.4438 on 4 and 5093 DF,  p-value: 0.777

# First I loaded additional libraries for summarizing model results
library(broom)

## Warning: package 'broom' was built under R version 4.4.2

library(kableExtra)

## 
## Attaching package: 'kableExtra'

## The following object is masked from 'package:dplyr':
## 
##     group_rows

# I Tidy the model results using the broom package
model_summary <- tidy(model)

# I generated a colorful table using kableExtra
model_summary %>%
  mutate(
    p.value = ifelse(p.value < 0.001, "<0.001", round(p.value, 3)), # Format p-values
    term = gsub("\\(Intercept\\)", "Intercept", term) # Rename intercept for clarity
  ) %>%
  kable("html", caption = "Regression Model Summary (Treatment Effect)") %>%
  kable_styling(full_width = FALSE, bootstrap_options = c("striped", "hover", "condensed")) %>%
  row_spec(0, background = "#4CAF50", color = "white", bold = TRUE) %>% # Style header row
  column_spec(1, bold = TRUE, width = "2in") %>% # Style term column
  column_spec(2:5, width = "1.5in") # Style numerical columns

Regression Model Summary (Treatment Effect)

term	estimate	std.error	statistic	p.value
Intercept	0.0467392	0.0643534	0.7262902	0.468
Age	-0.0003957	0.0005482	-0.7218473	0.470
BMI	-0.0003492	0.0018463	-0.1891622	0.850
Treatment_A	0.0144111	0.0281475	0.5119859	0.609
Treatment_B	-0.0204752	0.0281682	-0.7268893	0.467

# Interpreting Regression Results
# In my exploration of how various factors influence medical outcomes, I developed a regression model incorporating predictors such as Age, BMI, and treatment types (Treatment_A and Treatment_B). The results of this analysis provided valuable insights, although none of the predictors demonstrated statistical significance. Here is my interpretation of the findings.
# 
# The intercept of the model, with an estimate of 0.0467, represents the predicted outcome when all predictors are set to zero. While this value serves as a baseline reference, it is not statistically significant, with a p-value of 0.468, suggesting limited interpretive value.
# 
# When examining the effect of age, I observed a small negative relationship with the outcome. The coefficient for Age is -0.0003957, indicating that for every additional year of age, the outcome decreases by a marginal amount, holding all other variables constant. However, the p-value of 0.470 indicates that this effect is not statistically significant. This suggests that age may not play a meaningful role in predicting the outcome within this dataset.
# 
# Similarly, BMI also showed a negligible negative relationship with the outcome, with a coefficient of -0.0003492. This means that for every one-unit increase in BMI, the outcome decreases slightly, holding other variables constant. However, like age, BMI has a high p-value of 0.850, indicating no statistically significant association with the outcome.
# 
# The effects of treatment types were also analyzed. Patients who received Treatment_A had an estimated outcome that was 0.0144 higher compared to those who did not receive treatment. Meanwhile, those who received Treatment_B had an estimated outcome that was 0.0205 lower than the baseline group. Despite these observed differences, the p-values for Treatment_A (0.609) and Treatment_B (0.467) suggest that neither treatment had a statistically significant impact on the outcome.
# 
# These results imply that none of the predictors—Age, BMI, Treatment_A, or Treatment_B—are significant contributors to the variability in the outcome. This lack of significance might be due to several factors. It is possible that the dataset lacks sufficient power to detect meaningful effects, or that critical predictors were omitted from the model. Another consideration is potential multicollinearity or other modeling issues that could obscure the relationships between the predictors and the outcome.
# 
# While these findings did not reveal statistically significant relationships, they provided an opportunity to reflect on the modeling process and consider ways to refine future analyses. For instance, incorporating interaction terms or additional predictors might improve the model's explanatory power. Additionally, exploring a larger or more diverse dataset could help detect subtle effects that were not evident in this analysis.
# 
# # In conclusion, although the results did not identify significant predictors, this analysis highlights the importance of iterative refinement in statistical modeling. Each step in the process contributes to a deeper understanding of the data and offers insights into potential improvements for future work. This project has reinforced the value of rigor and adaptability in data analysis, qualities I will continue to apply in future endeavors.