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Among the many R packages, there is the outbreaks package. It contains datasets on epidemics, on of which is from the 2013 outbreak of influenza A H7N9 in China, as analysed by Kucharski et al (2014). I will be using their data as an example to test whether we can use Machine Learning algorithms for predicting disease outcome.

To do so, I selected and extracted features from the raw data, including age, days between onset and outcome, gender, whether the patients were hospitalised, etc. Missing values were imputed and different model algorithms were used to predict outcome (death or recovery). The prediction accuracy, sensitivity and specificity. The thus prepared dataset was devided into training and testing subsets. The test subset contained all cases with an unknown outcome. Before I applied the models to the test data, I further split the training data into validation subsets.

The tested modeling algorithms were similarly successful at predicting the outcomes of the validation data. To decide on final classifications, I compared predictions from all models and defined the outcome “Death” or “Recovery” as a function of all models, whereas classifications with a low prediction probability were flagged as “uncertain”. Accounting for this uncertainty led to a 100% correct classification of the validation test set.

The training cases with unknown outcome were then classified based on the same algorithms. From 57 unknown cases, 14 were classified as “Recovery”, 10 as “Death” and 33 as uncertain.

## The data

The dataset contains case ID, date of onset, date of hospitalisation, date of outcome, gender, age, province and of course the outcome: Death or Recovery. I can already see that there are a couple of missing values in the data, which I will deal with later.

# install and load package
if (!require("outbreaks")) install.packages("outbreaks")
library(outbreaks)
fluH7N9.china.2013_backup <- fluH7N9.china.2013 # back up original dataset in case something goes awry along the way

# convert ? to NAs
fluH7N9.china.2013$age[which(fluH7N9.china.2013$age == "?")] <- NA

# create a new column with case ID
fluH7N9.china.2013$case.ID <- paste("case", fluH7N9.china.2013$case.ID, sep = "_")
##   case.ID date.of.onset date.of.hospitalisation date.of.outcome outcome gender age province
## 1  case_1    2013-02-19                          2013-03-04   Death      m  87 Shanghai
## 2  case_2    2013-02-27              2013-03-03      2013-03-10   Death      m  27 Shanghai
## 3  case_3    2013-03-09              2013-03-19      2013-04-09   Death      f  35    Anhui
## 4  case_4    2013-03-19              2013-03-27                      f  45  Jiangsu
## 5  case_5    2013-03-19              2013-03-30      2013-05-15 Recover      f  48  Jiangsu
## 6  case_6    2013-03-21              2013-03-28      2013-04-26   Death      f  32  Jiangsu

Before I start preparing the data for Machine Learning, I want to get an idea of the distribution of the data points and their different variables by plotting. Most provinces have only a handful of cases, so I am combining them into the category “other” and keep only Jiangsu, Shanghai and Zhejian and separate provinces.

# gather for plotting with ggplot2
library(tidyr)
fluH7N9.china.2013_gather <- fluH7N9.china.2013 %>%
gather(Group, Date, date.of.onset:date.of.outcome)

# rearrange group order
fluH7N9.china.2013_gather$Group <- factor(fluH7N9.china.2013_gather$Group, levels = c("date.of.onset", "date.of.hospitalisation", "date.of.outcome"))

# rename groups
library(plyr)
fluH7N9.china.2013_gather$Group <- mapvalues(fluH7N9.china.2013_gather$Group, from = c("date.of.onset", "date.of.hospitalisation", "date.of.outcome"),
to = c("Date of onset", "Date of hospitalisation", "Date of outcome"))

# renaming provinces
fluH7N9.china.2013_gather$province <- mapvalues(fluH7N9.china.2013_gather$province,
from = c("Anhui", "Beijing", "Fujian", "Guangdong", "Hebei", "Henan", "Hunan", "Jiangxi", "Shandong", "Taiwan"),
to = rep("Other", 10))

# add a level for unknown gender
levels(fluH7N9.china.2013_gather$gender) <- c(levels(fluH7N9.china.2013_gather$gender), "unknown")
fluH7N9.china.2013_gather$gender[is.na(fluH7N9.china.2013_gather$gender)] <- "unknown"

# rearrange province order so that Other is the last
fluH7N9.china.2013_gather$province <- factor(fluH7N9.china.2013_gather$province, levels = c("Jiangsu",  "Shanghai", "Zhejiang", "Other"))

# convert age to numeric
fluH7N9.china.2013_gather$age <- as.numeric(as.character(fluH7N9.china.2013_gather$age))

library(ggplot2)
my_theme <- function(base_size = 12, base_family = "sans"){
theme_minimal(base_size = base_size, base_family = base_family) +
theme(
axis.text = element_text(size = 12),
axis.text.x = element_text(angle = 45, vjust = 0.5, hjust = 0.5),
axis.title = element_text(size = 14),
panel.grid.major = element_line(color = "grey"),
panel.grid.minor = element_blank(),
panel.background = element_rect(fill = "aliceblue"),
strip.background = element_rect(fill = "lightgrey", color = "grey", size = 1),
strip.text = element_text(face = "bold", size = 12, color = "black"),
legend.position = "bottom",
legend.justification = "top",
legend.box = "horizontal",
legend.box.background = element_rect(colour = "grey50"),
legend.background = element_blank(),
panel.border = element_rect(color = "grey", fill = NA, size = 0.5)
)
}

# plotting raw data
ggplot(data = fluH7N9.china.2013_gather, aes(x = Date, y = age, fill = outcome)) +
stat_density2d(aes(alpha = ..level..), geom = "polygon") +
geom_jitter(aes(color = outcome, shape = gender), size = 1.5) +
geom_rug(aes(color = outcome)) +
labs(
fill = "Outcome",
color = "Outcome",
alpha = "Level",
shape = "Gender",
x = "Date in 2013",
y = "Age",
title = "2013 Influenza A H7N9 cases in China",
subtitle = "Dataset from 'outbreaks' package (Kucharski et al. 2014)",
caption = ""
) +
facet_grid(Group ~ province) +
my_theme() +
scale_shape_manual(values = c(15, 16, 17)) +
scale_color_brewer(palette="Set1", na.value = "grey50") +
scale_fill_brewer(palette="Set1")


Gives this plot:

This plot shows the dates of onset, hospitalisation and outcome (if known) of each data point. Outcome is marked by color and age shown on the y-axis. Gender is marked by point shape. The density distribution of date by age for the cases seems to indicate that older people died more frequently in the Jiangsu and Zhejiang province than in Shanghai and in other provinces. When we look at the distribution of points along the time axis, it suggests that their might be a positive correlation between the likelihood of death and an early onset or early outcome.

I also want to know how many cases there are for each gender and province and compare the genders’ age distribution.

fluH7N9.china.2013_gather_2 <- fluH7N9.china.2013_gather[, -4] %>%
gather(group_2, value, gender:province)

fluH7N9.china.2013_gather_2$value <- mapvalues(fluH7N9.china.2013_gather_2$value, from = c("m", "f", "unknown", "Other"),
to = c("Male", "Female", "Unknown gender", "Other province"))

fluH7N9.china.2013_gather_2$value <- factor(fluH7N9.china.2013_gather_2$value,
levels = c("Female", "Male", "Unknown gender", "Jiangsu", "Shanghai", "Zhejiang", "Other province"))

p1 <- ggplot(data = fluH7N9.china.2013_gather_2, aes(x = value, fill = outcome, color = outcome)) +
geom_bar(position = "dodge", alpha = 0.7, size = 1) +
my_theme() +
scale_fill_brewer(palette="Set1", na.value = "grey50") +
scale_color_brewer(palette="Set1", na.value = "grey50") +
labs(
color = "",
fill = "",
x = "",
y = "Count",
title = "2013 Influenza A H7N9 cases in China",
subtitle = "Gender and Province numbers of flu cases",
caption = ""
)

p2 <- ggplot(data = fluH7N9.china.2013_gather, aes(x = age, fill = outcome, color = outcome)) +
geom_density(alpha = 0.3, size = 1) +
geom_rug() +
scale_color_brewer(palette="Set1", na.value = "grey50") +
scale_fill_brewer(palette="Set1", na.value = "grey50") +
my_theme() +
labs(
color = "",
fill = "",
x = "Age",
y = "Density",
title = "",
subtitle = "Age distribution of flu cases",
caption = ""
)

library(gridExtra)
library(grid)
grid.arrange(p1, p2, ncol = 2)

Gives this plot:

In the dataset, there are more male than female cases and correspondingly, we see more deaths, recoveries and unknown outcomes in men than in women. This is potentially a problem later on for modeling because the inherent likelihoods for outcome are not directly comparable between the sexes. Most unknown outcomes were recorded in Zhejiang. Similarly to gender, we don’t have an equal distribution of data points across provinces either. When we look at the age distribution it is obvious that people who died tended to be slightly older than those who recovered. The density curve of unknown outcomes is more similar to that of death than of recovery, suggesting that among these people there might have been more deaths than recoveries. And lastly, I want to plot how many days passed between onset, hospitalisation and outcome for each case.

ggplot(data = fluH7N9.china.2013_gather, aes(x = Date, y = age, color = outcome)) +
geom_point(aes(shape = gender), size = 1.5, alpha = 0.6) +
geom_path(aes(group = case.ID)) +
facet_wrap( ~ province, ncol = 2) +
my_theme() +
scale_shape_manual(values = c(15, 16, 17)) +
scale_color_brewer(palette="Set1", na.value = "grey50") +
scale_fill_brewer(palette="Set1") +
labs(
color = "Outcome",
shape = "Gender",
x = "Date in 2013",
y = "Age",
title = "2013 Influenza A H7N9 cases in China",
subtitle = "Dataset from 'outbreaks' package (Kucharski et al. 2014)",
caption = "\nTime from onset of flu to outcome."
)


Gives this plot which shows that there are many missing values in the dates, so it is hard to draw a general conclusion.

### Features

In Machine Learning-speak features are the variables used for model training. Using the right features dramatically influences the accuracy of the model.

Because we don’t have many features, I am keeping age as it is, but I am also generating new features:

• from the date information I am calculating the days between onset and outcome and between onset and hospitalisation
• I am converting gender into numeric values with 1 for female and 0 for male
• similarly, I am converting provinces to binary classifiers (yes == 1, no == 0) for Shanghai, Zhejiang, Jiangsu and other provinces
• the same binary classification is given for whether a case was hospitalised, and whether they had an early onset or early outcome (earlier than the median date)
# preparing the data frame for modeling
#
library(dplyr)

dataset <- fluH7N9.china.2013 %>%
mutate(hospital = as.factor(ifelse(is.na(date.of.hospitalisation), 0, 1)),
gender_f = as.factor(ifelse(gender == "f", 1, 0)),
province_Jiangsu = as.factor(ifelse(province == "Jiangsu", 1, 0)),
province_Shanghai = as.factor(ifelse(province == "Shanghai", 1, 0)),
province_Zhejiang = as.factor(ifelse(province == "Zhejiang", 1, 0)),
province_other = as.factor(ifelse(province == "Zhejiang" | province == "Jiangsu" | province == "Shanghai", 0, 1)),
days_onset_to_outcome = as.numeric(as.character(gsub(" days", "",
as.Date(as.character(date.of.outcome), format = "%Y-%m-%d") -
as.Date(as.character(date.of.onset), format = "%Y-%m-%d")))),
days_onset_to_hospital = as.numeric(as.character(gsub(" days", "",
as.Date(as.character(date.of.hospitalisation), format = "%Y-%m-%d") -
as.Date(as.character(date.of.onset), format = "%Y-%m-%d")))),
age = as.numeric(as.character(age)),
early_onset = as.factor(ifelse(date.of.onset < summary(fluH7N9.china.2013$date.of.onset)[[3]], 1, 0)), early_outcome = as.factor(ifelse(date.of.outcome < summary(fluH7N9.china.2013$date.of.outcome)[[3]], 1, 0))) %>%
subset(select = -c(2:4, 6, 8))
rownames(dataset) <- dataset$case.ID dataset <- dataset[, -1] ## Imputing missing values When looking at the dataset I created for modeling, it is obvious that we have quite a few missing values. The missing values from the outcome column are what I want to predict but for the rest I would either have to remove the entire row from the data or impute the missing information. I decided to try the latter with the mice package. # impute missing data library(mice) dataset_impute <- mice(dataset[, -1], print = FALSE) # recombine imputed data frame with the outcome column dataset_complete <- merge(dataset[, 1, drop = FALSE], mice::complete(dataset_impute, 1), by = "row.names", all = TRUE) rownames(dataset_complete) <- dataset_complete$Row.names
dataset_complete <- dataset_complete[, -1]


## Test, train and validation datasets

For building the model, I am separating the imputed data frame into training and test data. Test data are the 57 cases with unknown outcome.

summary(dataset$outcome) ## Death Recover NA's ## 32 47 57 The training data will be further devided for validation of the models: 70% of the training data will be kept for model building and the remaining 30% will be used for model testing. I am using the caret package for modeling. train_index <- which(is.na(dataset_complete$outcome))
train_data <- dataset_complete[-train_index, ]
test_data  <- dataset_complete[train_index, -1]

library(caret)
set.seed(27)
val_index <- createDataPartition(train_data$outcome, p = 0.7, list=FALSE) val_train_data <- train_data[val_index, ] val_test_data <- train_data[-val_index, ] val_train_X <- val_train_data[,-1] val_test_X <- val_test_data[,-1] ## Decision trees To get an idea about how each feature contributes to the prediction of the outcome, I first built a decision tree based on the training data using rpart and rattle. library(rpart) library(rattle) library(rpart.plot) library(RColorBrewer) set.seed(27) fit <- rpart(outcome ~ ., data = train_data, method = "class", control = rpart.control(xval = 10, minbucket = 2, cp = 0), parms = list(split = "information")) fancyRpartPlot(fit) Gives this plot: This randomly generated decision tree shows that cases with an early outcome were most likely to die when they were 68 or older, when they also had an early onset and when they were sick for fewer than 13 days. If a person was not among the first cases and was younger than 52, they had a good chance of recovering, but if they were 82 or older, they were more likely to die from the flu. ## Feature Importance Not all of the features I created will be equally important to the model. The decision tree already gave me an idea of which features might be most important but I also want to estimate feature importance using a Random Forest approach with repeated cross validation. # prepare training scheme control <- trainControl(method = "repeatedcv", number = 10, repeats = 10) # train the model set.seed(27) model <- train(outcome ~ ., data = train_data, method = "rf", preProcess = NULL, trControl = control) # estimate variable importance importance <- varImp(model, scale=TRUE) # prepare for plotting importance_df_1 <- importance$importance
importance_df_1$group <- rownames(importance_df_1) importance_df_1$group <- mapvalues(importance_df_1$group, from = c("age", "hospital2", "gender_f2", "province_Jiangsu2", "province_Shanghai2", "province_Zhejiang2", "province_other2", "days_onset_to_outcome", "days_onset_to_hospital", "early_onset2", "early_outcome2" ), to = c("Age", "Hospital", "Female", "Jiangsu", "Shanghai", "Zhejiang", "Other province", "Days onset to outcome", "Days onset to hospital", "Early onset", "Early outcome" )) f = importance_df_1[order(importance_df_1$Overall, decreasing = FALSE), "group"]

importance_df_2 <- importance_df_1


### Elastic-Net Regularized Generalized Linear Models

Lasso or elastic net regularization for generalized linear model regression are based on linear regression models and is useful when we have feature correlation in our model. This model classified 13 out of 23 cases correctly.

set.seed(27)
model_glmnet <- caret::train(outcome ~ .,
data = val_train_data,
method = "glmnet",
preProcess = NULL,
trControl = trainControl(method = "repeatedcv", number = 10, repeats = 10, verboseIter = FALSE))

### Penalized Discriminant Analysis

set.seed(27)
model_pda <- caret::train(outcome ~ .,
data = val_train_data,
method = "pda",
preProcess = NULL,
trControl = trainControl(method = "repeatedcv", number = 10, repeats = 10, verboseIter = FALSE))

### Nearest Shrunken Centroids

Nearest Shrunken Centroids computes a standardized centroid for each class and shrinks each centroid toward the overall centroid for all classes. This model classified 15 out of 23 cases correctly.

set.seed(27)
model_pam <- caret::train(outcome ~ .,
data = val_train_data,
method = "pam",
preProcess = NULL,
trControl = trainControl(method = "repeatedcv", number = 10, repeats = 10, verboseIter = FALSE))

### Partial Least Squares

Partial least squares regression combined principal component analysis and multiple regression and is useful for modeling with correlated features. This model classified 15 out of 23 cases correctly.

set.seed(27)
model_pls <- caret::train(outcome ~ .,
data = val_train_data,
method = "pls",
preProcess = NULL,
trControl = trainControl(method = "repeatedcv", number = 10, repeats = 10, verboseIter = FALSE))
confusionMatrix(predict(model_pls, val_test_data[, -1]), val_test_data$outcome) ### Comparing accuracy of models All models were similarly accurate. # Create a list of models models <- list(rf = model_rf, glmnet = model_glmnet, kknn = model_kknn, pda = model_pda, slda = model_slda, pam = model_pam, C5.0Tree = model_C5.0Tree, pls = model_pls) # Resample the models resample_results <- resamples(models) # Generate a summary summary(resample_results, metric = c("Kappa", "Accuracy")) bwplot(resample_results , metric = c("Kappa","Accuracy")) Gives this plot: ### Combined results of predicting validation test samples To compare the predictions from all models, I summed up the prediction probabilities for Death and Recovery from all models and calculated the log2 of the ratio between the summed probabilities for Recovery by the summed probabilities for Death. All cases with a log2 ratio bigger than 1.5 were defined as Recover, cases with a log2 ratio below -1.5 were defined as Death, and the remaining cases were defined as uncertain. results <- data.frame(randomForest = predict(model_rf, newdata = val_test_data[, -1], type="prob"), glmnet = predict(model_glmnet, newdata = val_test_data[, -1], type="prob"), kknn = predict(model_kknn, newdata = val_test_data[, -1], type="prob"), pda = predict(model_pda, newdata = val_test_data[, -1], type="prob"), slda = predict(model_slda, newdata = val_test_data[, -1], type="prob"), pam = predict(model_pam, newdata = val_test_data[, -1], type="prob"), C5.0Tree = predict(model_C5.0Tree, newdata = val_test_data[, -1], type="prob"), pls = predict(model_pls, newdata = val_test_data[, -1], type="prob")) results$sum_Death <- rowSums(results[, grep("Death", colnames(results))])
results$sum_Recover <- rowSums(results[, grep("Recover", colnames(results))]) results$log2_ratio <- log2(results$sum_Recover/results$sum_Death)
results$true_outcome <- val_test_data$outcome
results$pred_outcome <- ifelse(results$log2_ratio > 1.5, "Recover", ifelse(results$log2_ratio < -1.5, "Death", "uncertain")) results$prediction <- ifelse(results$pred_outcome == results$true_outcome, "CORRECT",
ifelse(results$pred_outcome == "uncertain", "uncertain", "wrong")) All predictions based on all models were either correct or uncertain. ### Predicting unknown outcomes The above models will now be used to predict the outcome of cases with unknown fate. set.seed(27) model_rf <- caret::train(outcome ~ ., data = train_data, method = "rf", preProcess = NULL, trControl = trainControl(method = "repeatedcv", number = 10, repeats = 10, verboseIter = FALSE)) model_glmnet <- caret::train(outcome ~ ., data = train_data, method = "glmnet", preProcess = NULL, trControl = trainControl(method = "repeatedcv", number = 10, repeats = 10, verboseIter = FALSE)) model_kknn <- caret::train(outcome ~ ., data = train_data, method = "kknn", preProcess = NULL, trControl = trainControl(method = "repeatedcv", number = 10, repeats = 10, verboseIter = FALSE)) model_pda <- caret::train(outcome ~ ., data = train_data, method = "pda", preProcess = NULL, trControl = trainControl(method = "repeatedcv", number = 10, repeats = 10, verboseIter = FALSE)) model_slda <- caret::train(outcome ~ ., data = train_data, method = "slda", preProcess = NULL, trControl = trainControl(method = "repeatedcv", number = 10, repeats = 10, verboseIter = FALSE)) model_pam <- caret::train(outcome ~ ., data = train_data, method = "pam", preProcess = NULL, trControl = trainControl(method = "repeatedcv", number = 10, repeats = 10, verboseIter = FALSE)) model_C5.0Tree <- caret::train(outcome ~ ., data = train_data, method = "C5.0Tree", preProcess = NULL, trControl = trainControl(method = "repeatedcv", number = 10, repeats = 10, verboseIter = FALSE)) model_pls <- caret::train(outcome ~ ., data = train_data, method = "pls", preProcess = NULL, trControl = trainControl(method = "repeatedcv", number = 10, repeats = 10, verboseIter = FALSE)) models <- list(rf = model_rf, glmnet = model_glmnet, kknn = model_kknn, pda = model_pda, slda = model_slda, pam = model_pam, C5.0Tree = model_C5.0Tree, pls = model_pls) # Resample the models resample_results <- resamples(models) bwplot(resample_results , metric = c("Kappa","Accuracy")) Gives this plot: Here again, the accuracy is similar in all models. The final results are calculate as described above. results <- data.frame(randomForest = predict(model_rf, newdata = test_data, type="prob"), glmnet = predict(model_glmnet, newdata = test_data, type="prob"), kknn = predict(model_kknn, newdata = test_data, type="prob"), pda = predict(model_pda, newdata = test_data, type="prob"), slda = predict(model_slda, newdata = test_data, type="prob"), pam = predict(model_pam, newdata = test_data, type="prob"), C5.0Tree = predict(model_C5.0Tree, newdata = test_data, type="prob"), pls = predict(model_pls, newdata = test_data, type="prob")) results$sum_Death <- rowSums(results[, grep("Death", colnames(results))])
results$sum_Recover <- rowSums(results[, grep("Recover", colnames(results))]) results$log2_ratio <- log2(results$sum_Recover/results$sum_Death)
results$predicted_outcome <- ifelse(results$log2_ratio > 1.5, "Recover", ifelse(results$log2_ratio < -1.5, "Death", "uncertain")) From 57 cases, 14 were defined as Recover, 10 as Death and 33 as uncertain. results_combined <- merge(results[, -c(1:16)], fluH7N9.china.2013[which(fluH7N9.china.2013$case.ID %in% rownames(results)), ],
by.x = "row.names", by.y = "case.ID")
results_combined <- results_combined[, -c(2, 3, 8, 9)]
results_combined_gather <- results_combined %>%
gather(group_dates, date, date.of.onset:date.of.hospitalisation)

results_combined_gather$group_dates <- factor(results_combined_gather$group_dates, levels = c("date.of.onset", "date.of.hospitalisation"))

results_combined_gather$group_dates <- mapvalues(results_combined_gather$group_dates, from = c("date.of.onset", "date.of.hospitalisation"),
to = c("Date of onset", "Date of hospitalisation"))

results_combined_gather$gender <- mapvalues(results_combined_gather$gender, from = c("f", "m"),
to = c("Female", "Male"))
levels(results_combined_gather$gender) <- c(levels(results_combined_gather$gender), "unknown")
results_combined_gather$gender[is.na(results_combined_gather$gender)] <- "unknown"
results_combined_gather$age <- as.numeric(as.character(results_combined_gather$age))

ggplot(data = results_combined_gather, aes(x = date, y = log2_ratio, color = predicted_outcome)) +
geom_jitter(aes(size = age), alpha = 0.3) +
geom_rug() +
facet_grid(gender ~ group_dates) +
labs(
color = "Predicted outcome",
size = "Age",
x = "Date in 2013",
y = "log2 ratio of prediction Recover vs Death",
title = "2013 Influenza A H7N9 cases in China",
subtitle = "Predicted outcome",
caption = ""
) +
my_theme() +
scale_color_brewer(palette="Set1") +
scale_fill_brewer(palette="Set1")

Gives this plot:

The comparison of date of onset, data of hospitalisation, gender and age with predicted outcome shows that predicted deaths were associated with older age than predicted Recoveries. Date of onset does not show an obvious bias in either direction.

## Conclusions

This dataset posed a couple of difficulties to begin with, like unequal distribution of data points across variables and missing data. This makes the modeling inherently prone to flaws. However, real life data isn’t perfect either, so I went ahead and tested the modeling success anyway. By accounting for uncertain classification with low predictions probability, the validation data could be classified accurately. However, for a more accurate model, these few cases don’t give enough information to reliably predict the outcome. More cases, more information (i.e. more features) and fewer missing data would improve the modeling outcome. Also, this example is only applicable for this specific case of flu. In order to be able to draw more general conclusions about flu outcome, other cases and additional information, for example on medical parameters like preexisting medical conditions, disase parameters, demographic information, etc. would be necessary. All in all, this dataset served as a nice example of the possibilities (and pitfalls) of machine learning applications and showcases a basic workflow for building prediction models with R.