**March 3, 2020**

In this worksheet, we will use the libraries tidyverse, plotROC, and ggthemes:

```
library(tidyverse)
theme_set(theme_bw(base_size=12)) # set default ggplot2 theme
library(plotROC)
library(ggthemes)
```

We continue working with the biopsy data set:

`biopsy <- read_csv("http://wilkelab.org/classes/SDS348/data_sets/biopsy.csv")`

```
## Parsed with column specification:
## cols(
## clump_thickness = col_double(),
## uniform_cell_size = col_double(),
## uniform_cell_shape = col_double(),
## marg_adhesion = col_double(),
## epithelial_cell_size = col_double(),
## bare_nuclei = col_double(),
## bland_chromatin = col_double(),
## normal_nucleoli = col_double(),
## mitoses = col_double(),
## outcome = col_character()
## )
```

`biopsy$outcome <- factor(biopsy$outcome) # make outcome a factor`

The following code splits the biopsy data set into a random training and test set:

```
train_fraction <- 0.4 # fraction of data for training purposes
set.seed(126) # set the seed to make the partition reproductible
train_size <- floor(train_fraction * nrow(biopsy)) # number of observations in training set
train_indices <- sample(1:nrow(biopsy), size = train_size)
train_data <- biopsy[train_indices, ] # get training data
test_data <- biopsy[-train_indices, ] # get test data
```

Fit a logistic regression model on the training data set, then predict the outcome on the test data set, and plot the resulting ROC curves. Limit the x-axis range from 0 to 0.15 to zoom into the ROC curve. (Hint: Do **not** use `coord_fixed()`

.)

```
# model to use:
# outcome ~ clump_thickness + uniform_cell_size + uniform_cell_shape
glm_out <- glm(
outcome ~ clump_thickness + uniform_cell_size + uniform_cell_shape,
data = train_data,
family = binomial
)
# results data frame for training data
df_train <- data.frame(
predictor = predict(glm_out, train_data),
known_truth = train_data$outcome,
data_name = "training"
)
# results data frame for test data
df_test <- data.frame(
predictor = predict(glm_out, test_data),
known_truth = test_data$outcome,
data_name = "test"
)
df_combined <- rbind(df_train, df_test)
ggplot(df_combined, aes(d = known_truth, m = predictor, color = data_name)) +
geom_roc(n.cuts = 0) +
xlim(0, 0.15) +
scale_color_colorblind()
```

```
## Warning in verify_d(data$d): D not labeled 0/1, assuming benign = 0 and
## malignant = 1!
```

You can calculate the areas under the ROC curves by running `calc_auc()`

on a plot generated with `geom_roc()`

(see previous worksheet). Use this function to calculate the area under the training and test curve for the model `outcome ~ clump_thickness`

. For this exercise, generate a new set of training and test datasets with a different fraction of training data from before.

```
train_fraction <- 0.2 # fraction of data for training purposes
set.seed(123) # set the seed to make the partition reproductible
train_size <- floor(train_fraction * nrow(biopsy)) # number of observations in training set
train_indices <- sample(1:nrow(biopsy), size = train_size)
train_data <- biopsy[train_indices, ] # get training data
test_data <- biopsy[-train_indices, ] # get test data
# fit the model on the training data
glm_out <- glm(
outcome ~ clump_thickness,
data = train_data,
family = binomial
)
# predict outcomes for the training data
df_train <- data.frame(
predictor = predict(glm_out, train_data),
known_truth = train_data$outcome,
data_name = "training"
)
# predict outcomes for the test data
df_test <- data.frame(
predictor = predict(glm_out, test_data),
known_truth = test_data$outcome,
data_name = "test"
)
df_combined <- rbind(df_train, df_test)
p <- ggplot(df_combined, aes(d = known_truth, m = predictor, color = data_name)) +
geom_roc(n.cuts = 0)
calc_auc(p)
```

```
## Warning in verify_d(data$d): D not labeled 0/1, assuming benign = 0 and
## malignant = 1!
```

```
## PANEL group AUC
## 1 1 1 0.9214427
## 2 1 2 0.9050554
```

Write code that combines the AUC values calculated by `calc_auc()`

with the correct group names and orders the output in descending order of AUC. (Hint: We have seen similar code in the previous worksheet.)

```
data_name <- unique(df_combined$data_name)
data_info <- data.frame(
data_name,
group = order(data_name)
)
left_join(data_info, calc_auc(p)) %>%
select(-group, -PANEL) %>%
arrange(desc(AUC))
```

```
## Warning in verify_d(data$d): D not labeled 0/1, assuming benign = 0 and
## malignant = 1!
```

`## Joining, by = "group"`

```
## data_name AUC
## 1 training 0.9214427
## 2 test 0.9050554
```