Calculating AUC for Generalized Linear Models Fitted Using Imputed Data with the MICE Package in R.

Introduction to Calculating AUC for a glm Model on Imputed Data Using MICE Package

In this article, we will explore the concept of Area Under the Curve (AUC) and its application in evaluating the performance of logistic regression models. Specifically, we will delve into calculating AUC for a generalized linear model (glm) fitted using data imputed by the Multiple Imputation with Chained Equations (MICE) package.

The MICE package is a powerful tool for handling missing data in R. It provides an efficient method for creating multiple imputations of the dataset, which can be used to train separate models for each imputation. This approach enables us to account for the uncertainty associated with the imputed data and provide more accurate estimates of model performance.

Understanding AUC

AUC (Area Under the Curve) is a widely used metric for evaluating the performance of binary classification models, such as logistic regression. It represents the proportion of true positives that are correctly classified above the threshold. In other words, it measures how well the model can distinguish between positive and negative classes.

The AUC value ranges from 0 (worst possible performance) to 1 (best possible performance). An AUC value close to 1 indicates a good model, while an AUC value near 0 suggests poor model performance.

Overview of MICE Package

The MICE package provides an efficient method for multiple imputation using the Chained Equations approach. This method involves iteratively imputing missing values based on previous imputed values until convergence is reached.

Here’s a high-level overview of how the MICE package works:

Initialize the dataset and identify the variables with missing values.
Create an imputation model using a specified imputation method (e.g., pmm, reg, or norm).
Impute missing values in one variable based on the imputed values of other variables.
Repeat step 3 until convergence is reached or a maximum number of iterations is specified.

Calculating AUC for Separate Models

To calculate AUC for each separate model fitted using the MICE package, we can use the perperformance function from the ROC (Receiver Operating Characteristic) package in R.

Here’s an example code snippet:

library(ROCR)
library(mice)

# Create a synthetic dataset with missing values
set.seed(500)
n <- 100
x1 <- rnorm(n)
x2 <- rnorm(n)
y <- ifelse(x1 + x2 > 5, 1, 0)
data <- data.frame(y, x1, x2)
_missing_data <- data.frame(y = NA, x1 = NA, x2 = NA)

# Impute missing values using MICE package
impData <- mice(_missing_data, m=5, maxit=50, meth='pmm', seed=500, printFlag = FALSE)

# Fit logistic models using imputed datasets
mymodelFit1 <- with(data = impData$analysis_set[1], exp = glm(y ~ x1 + x2, family = binomial(link = "logit")))
mymodelFit2 <- with(data = impData$analysis_set[2], exp = glm(y ~ x1 + x2, family = binomial(link = "logit")))

# Calculate AUC for separate models
prob1 <- predict(mymodelFit1, newdata=data, type="response")
pred1 <- prediction(prob1, data$y)
perf1 <- performance(pred1, measure = "tpr", x.measure = "fpr")
auc1 <- performance(pred1, measure = "auc")

prob2 <- predict(mymodelFit2, newdata=data, type="response")
pred2 <- prediction(prob2, data$y)
perf2 <- performance(pred2, measure = "tpr", x.measure = "fpr")
auc2 <- performance(pred2, measure = "auc")

# Extract AUC values
auc1_val <- auc1@performance[[1]]@x.values
auc2_val <- auc2@performance[[1]]@x.values

# Print AUC values
print(paste("AUC for model 1:", auc1_val))
print(paste("AUC for model 2:", auc2_val))

Calculating AUC for the Pooled Model

To calculate AUC for the pooled model, we can use a similar approach as before but with some modifications. The idea is to create separate models using each imputed dataset and then pool the results by taking the average or weighted average of the model performances.

Here’s an example code snippet:

# Create a pooled model performance object
pool_pred <- prediction(prob, data$y)

# Calculate AUC for the pooled model
perf_pool <- performance(pool_pred, measure = "tpr", x.measure = "fpr")
auc_pool <- performance(perf_pool, measure = "auc")

# Extract AUC value
auc_pool_val <- auc_pool@performance[[1]]@x.values

# Print AUC value
print(paste("AUC for pooled model:", auc_pool_val))

Discussion and Conclusion

In this article, we explored the concept of calculating AUC for a generalized linear model fitted using data imputed by the MICE package. We discussed how to calculate AUC for separate models using the ROC package in R and also showed how to create a pooled model performance object and extract its AUC value.

The main takeaway from this article is that you can use the MICE package to handle missing data in logistic regression models and evaluate their performance using AUC. By understanding how to calculate AUC for separate models, you can assess the individual contributions of each imputed dataset, while pooling model performances provides a more comprehensive evaluation of the overall model performance.

Common Misconceptions

AUC is always a good metric: While AUC is a widely used and effective metric for evaluating binary classification models, it’s not perfect. For example, AUC values can be sensitive to class imbalance issues or outliers in the data.
MICE package handles missing data perfectly: The MICE package provides an efficient method for handling missing data, but there may be situations where more advanced imputation methods are required.

Future Work

Using other imputation methods: In addition to the pmm and reg imputation methods used in this article, you can explore other methods such as norm, mean, or even machine learning-based approaches.
Handling complex datasets: As data complexity increases, you may need to consider more advanced techniques for handling missing values and evaluating model performance.

Last modified on 2024-02-25