Packages
library(readxl)
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(neuralnet)
##
## Attaching package: 'neuralnet'
## The following object is masked from 'package:dplyr':
##
## compute
library(ggplot2)
Import Data
data_cancer <- read_excel("Cancer vs AP_Xray_Stage_Grade_Age.xlsx", sheet = "Sheet1")
glimpse(data_cancer)
## Rows: 300
## Columns: 6
## $ AP <dbl> 128, 46, 165, 102, 42, 52, 112, 146, 157, 174, 135, 144, 136, 63…
## $ XRay <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0…
## $ Stage <dbl> 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1…
## $ Grade <dbl> 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0…
## $ Age <dbl> 54, 55, 53, 50, 61, 55, 52, 55, 59, 60, 66, 60, 53, 61, 66, 63, …
## $ Y <dbl> 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0…
head(data_cancer)
## # A tibble: 6 × 6
## AP XRay Stage Grade Age Y
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 128 0 1 1 54 1
## 2 46 0 1 1 55 0
## 3 165 0 0 1 53 1
## 4 102 0 1 1 50 1
## 5 42 0 1 0 61 0
## 6 52 0 1 0 55 0
Dibuat Faktor
data_cancer1 <- data_cancer
data_cancer1$XRay <- as.factor(data_cancer1$XRay)
data_cancer1$Stage <- as.factor(data_cancer1$Stage)
data_cancer1$Grade <- as.factor(data_cancer1$Grade)
Subset Data
set.seed(122)
r <- runif(nrow(data_cancer1))
data_cancer2 <- cbind(data_cancer1, r)
data_cancer2 <- data_cancer2[order(data_cancer2$r),]
data_cancer2 <- data_cancer2[1:200, c('AP', 'XRay', 'Stage', 'Grade', 'Age', 'Y')]
head(data_cancer2)
## AP XRay Stage Grade Age Y
## 8 146 0 1 0 55 1
## 24 83 0 0 0 56 0
## 187 80 0 1 1 50 0
## 27 119 0 1 1 69 1
## 281 84 0 1 0 55 0
## 214 44 1 1 1 66 1
nrow(data_cancer2)
## [1] 200
Eksplorasi Data
summary(data_cancer2)
## AP XRay Stage Grade Age Y
## Min. : 41.00 0:100 0: 92 0: 97 Min. :49.00 Min. :0.000
## 1st Qu.: 73.75 1:100 1:108 1:103 1st Qu.:54.00 1st Qu.:0.000
## Median :109.50 Median :59.00 Median :1.000
## Mean :110.20 Mean :59.06 Mean :0.685
## 3rd Qu.:146.00 3rd Qu.:64.00 3rd Qu.:1.000
## Max. :190.00 Max. :70.00 Max. :1.000
library(ggplot2)
ggplot(data_cancer2, aes(x = factor(1), fill = XRay)) + geom_bar(width = 1) + scale_fill_brewer(palette="Set2") + coord_polar("y") + stat_count(geom = "text", aes(label = stat(count)), position=position_stack(vjust=0.5), colour="white")
## Warning: `stat(count)` was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(count)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
ggplot(data_cancer2, aes(x = factor(1), fill = Stage)) + geom_bar(width = 1) + scale_fill_brewer(palette="Accent") + coord_polar("y") + stat_count(geom = "text", aes(label = stat(count)), position=position_stack(vjust=0.5), colour="white")
ggplot(data_cancer2, aes(x = factor(1), fill = Grade)) + geom_bar(width = 1) + coord_polar("y") + stat_count(geom = "text", aes(label = stat(count)), position=position_stack(vjust=0.5), colour="white")
ggplot(data_cancer2, aes(x=XRay, fill=as.factor(Y)))+geom_bar(position = "stack") + ylab("count") + geom_text(stat = 'count', aes(label = stat(count)), position = position_stack(vjust = 0.5), size = 3, color = "white") + labs(fill = 'Y') + scale_fill_brewer(palette="Set2")
ggplot(data_cancer2, aes(x=Stage, fill=as.factor(Y)))+geom_bar(position = "stack") + ylab("count") + geom_text(stat = 'count', aes(label = stat(count)), position = position_stack(vjust = 0.5), size = 3, color = "white") + labs(fill = 'Y') + scale_fill_brewer(palette="Accent")
ggplot(data_cancer2, aes(x=Grade, fill=as.factor(Y)))+geom_bar(position = "stack") + ylab("count")+ geom_text(stat = 'count', aes(label = stat(count)), position = position_stack(vjust = 0.5), size = 3, color = "white") + labs(fill = 'Y')
get_box_stats <- function(y, upper_limit = max(y) * 1.15) {
return(data.frame(
y = 0.95 * upper_limit,
label = paste(
"Count =", length(y), "\n",
"Mean =", round(mean(y), 2), "\n",
"Median =", round(median(y), 2), "\n"
)
))
}
ggplot(data_cancer2, aes(x = Y, y = AP, group = Y)) + geom_boxplot(fill = c("#999162", "#668291")) + stat_summary(fun.data = get_box_stats, geom = "text", hjust = 0.5, vjust = 0.8)
ggplot(data_cancer2, aes(x = Y, y = Age, group = Y)) + geom_boxplot(fill = c("#E6A700", "#76B4E9")) + stat_summary(fun.data = get_box_stats, geom = "text", hjust = 0.5, vjust = 0.9)
ggplot(data_cancer2, aes(x = AP, y = Y)) +
geom_point(aes(color = 'coral'))
ggplot(data_cancer2, aes(x = Age, y = Y)) +
geom_point(aes(color='coral'))
ggplot(data_cancer2, aes(x = factor(1), fill = as.factor(Y))) + geom_bar(width = 1) + scale_fill_brewer(palette="Dark2") + coord_polar("y") + labs(fill = 'Y') + stat_count(geom = "text", aes(label = stat(count)), position=position_stack(vjust=0.5), colour="white")
Split Data
set.seed(122)
log_sample <- sample(c(TRUE, FALSE), nrow(data_cancer2),
replace=TRUE, prob=c(0.8,0.2))
log_train_data <- data_cancer2[log_sample, ]
log_test_data <- data_cancer2[!log_sample, ]
glimpse(log_train_data); glimpse(log_test_data)
## Rows: 158
## Columns: 6
## $ AP <dbl> 80, 119, 84, 44, 184, 51, 178, 132, 177, 125, 68, 89, 157, 119, …
## $ XRay <fct> 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1…
## $ Stage <fct> 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1…
## $ Grade <fct> 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1…
## $ Age <dbl> 50, 69, 55, 66, 51, 61, 62, 53, 50, 63, 65, 58, 59, 56, 50, 68, …
## $ Y <dbl> 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1…
## Rows: 42
## Columns: 6
## $ AP <dbl> 146, 83, 83, 122, 136, 151, 79, 59, 58, 135, 45, 62, 102, 58, 12…
## $ XRay <fct> 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0…
## $ Stage <fct> 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1…
## $ Grade <fct> 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0…
## $ Age <dbl> 55, 56, 56, 61, 54, 65, 52, 62, 50, 64, 63, 63, 66, 56, 68, 55, …
## $ Y <dbl> 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0…
Eksplorasi
library(DataExplorer)
plot_histogram(data_cancer2)
plot_bar(data_cancer2)
plot_boxplot(data_cancer2, by='Y')
Regresi Logistik
model1_log <- glm(Y~., data = log_train_data, family = 'binomial')
summary(model1_log)
##
## Call:
## glm(formula = Y ~ ., family = "binomial", data = log_train_data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.307981 2.351900 -0.556 0.578117
## AP 0.044874 0.008511 5.272 1.35e-07 ***
## XRay1 2.755007 0.668962 4.118 3.82e-05 ***
## Stage1 2.389997 0.620304 3.853 0.000117 ***
## Grade1 1.429076 0.500288 2.857 0.004283 **
## Age -0.091964 0.040389 -2.277 0.022790 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 192.35 on 157 degrees of freedom
## Residual deviance: 119.19 on 152 degrees of freedom
## AIC: 131.19
##
## Number of Fisher Scoring iterations: 6
Odds Ratio
exp(model1_log$coefficients)
## (Intercept) AP XRay1 Stage1 Grade1 Age
## 0.2703654 1.0458961 15.7211456 10.9134577 4.1748408 0.9121383
library(ggplot2)
log_train_data %>%
mutate(prob = ifelse(Y == "1", 1, 0)) %>%
ggplot(aes(model1_log$fitted.values, prob)) +
geom_point(alpha = .05) +
geom_smooth(formula=y~x, method = "glm", method.args = list(family = "binomial")) +
ggtitle("Logistic regression model fit") +
xlab("Fit") +
ylab("Probability of Y")+
theme_minimal()
model1_log$coefficients
## (Intercept) AP XRay1 Stage1 Grade1 Age
## -1.30798105 0.04487401 2.75500666 2.38999668 1.42907622 -0.09196366
exp(model1_log$coefficients)
## (Intercept) AP XRay1 Stage1 Grade1 Age
## 0.2703654 1.0458961 15.7211456 10.9134577 4.1748408 0.9121383
Matriks Konfusi Data Latih
pred_train1 <- round(predict(model1_log, newdata = log_train_data, type = 'response'))
result_Y1 <- data_frame(log_train_data$Y, pred_train1)
## Warning: `data_frame()` was deprecated in tibble 1.1.0.
## ℹ Please use `tibble()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
length(pred_train1)
## [1] 158
head(result_Y1, 10)
## # A tibble: 10 × 2
## `log_train_data$Y` pred_train1
## <dbl> <dbl>
## 1 0 1
## 2 1 1
## 3 0 0
## 4 1 1
## 5 1 1
## 6 0 0
## 7 1 1
## 8 1 1
## 9 1 1
## 10 0 1
library(caret)
## Loading required package: lattice
confusionMatrix(as.factor(log_train_data$Y), as.factor(pred_train1))
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 30 17
## 1 14 97
##
## Accuracy : 0.8038
## 95% CI : (0.7332, 0.8626)
## No Information Rate : 0.7215
## P-Value [Acc > NIR] : 0.01129
##
## Kappa : 0.5218
##
## Mcnemar's Test P-Value : 0.71944
##
## Sensitivity : 0.6818
## Specificity : 0.8509
## Pos Pred Value : 0.6383
## Neg Pred Value : 0.8739
## Prevalence : 0.2785
## Detection Rate : 0.1899
## Detection Prevalence : 0.2975
## Balanced Accuracy : 0.7663
##
## 'Positive' Class : 0
##
Matriks Konfusi Data Uji
pred_test1 <- round(predict(model1_log, newdata = log_test_data, type = 'response'))
pred_test2 <- predict(model1_log, newdata = log_test_data, type = 'response')
result_Y2 <- data.frame(log_test_data$Y, pred_test1)
head(result_Y2, 10)
## log_test_data.Y pred_test1
## 8 1 1
## 24 0 0
## 233 0 1
## 239 1 1
## 104 0 0
## 154 1 1
## 53 1 1
## 107 0 0
## 58 0 0
## 65 1 1
Confusion Matrix
confusionMatrix(as.factor(log_test_data$Y), as.factor(pred_test1))
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 12 4
## 1 1 25
##
## Accuracy : 0.881
## 95% CI : (0.7437, 0.9602)
## No Information Rate : 0.6905
## P-Value [Acc > NIR] : 0.003711
##
## Kappa : 0.7382
##
## Mcnemar's Test P-Value : 0.371093
##
## Sensitivity : 0.9231
## Specificity : 0.8621
## Pos Pred Value : 0.7500
## Neg Pred Value : 0.9615
## Prevalence : 0.3095
## Detection Rate : 0.2857
## Detection Prevalence : 0.3810
## Balanced Accuracy : 0.8926
##
## 'Positive' Class : 0
##
ROC
library(pROC)
## Type 'citation("pROC")' for a citation.
##
## Attaching package: 'pROC'
## The following objects are masked from 'package:stats':
##
## cov, smooth, var
roc1 <- roc(log_train_data$Y, model1_log$fitted.values, plot = T)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
roc2 <- roc(log_test_data$Y, pred_test2, plot = T)
## Setting levels: control = 0, case = 1
## Setting direction: controls < cases
plot(roc1, col = 'green', main = 'Plot ROC Regresi Logistik', lty=1); plot(roc2, add = TRUE, lty=2, col = 'red'); legend("right", c("Train", "Test"), lty=1:2, col = c("green", "red"), bty="n", inset=c(0,-0.15))
ggroc(list(Train = roc1, Test = roc2), aes = c('linetype')) + labs(linetype = 'Data')
roc1$auc; roc2$auc
## Area under the curve: 0.8823
## Area under the curve: 0.8942
Artificial Neural Network - 1
Split Data
set.seed(122)
r <- runif(nrow(data_cancer))
data_cancer3 <- cbind(data_cancer, r)
data_cancer3 <- data_cancer3[order(data_cancer3$r),]
data_cancer3 <- data_cancer3[1:200, c('AP', 'XRay', 'Stage', 'Grade', 'Age', 'Y')]
head(data_cancer3)
## AP XRay Stage Grade Age Y
## 8 146 0 1 0 55 1
## 24 83 0 0 0 56 0
## 187 80 0 1 1 50 0
## 27 119 0 1 1 69 1
## 281 84 0 1 0 55 0
## 214 44 1 1 1 66 1
nrow(data_cancer3)
## [1] 200
nn_sample <- sample(c(TRUE, FALSE), nrow(data_cancer3),
replace=TRUE, prob=c(0.8,0.2))
nn_train_data <- data_cancer3[nn_sample, ]
nn_test_data <- data_cancer3[!nn_sample, ]
glimpse(nn_train_data); glimpse(nn_test_data)
## Rows: 157
## Columns: 6
## $ AP <dbl> 146, 83, 80, 119, 44, 184, 51, 132, 83, 177, 125, 68, 89, 119, 1…
## $ XRay <dbl> 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0…
## $ Stage <dbl> 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0…
## $ Grade <dbl> 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0…
## $ Age <dbl> 55, 56, 50, 69, 66, 51, 61, 53, 56, 50, 63, 65, 58, 56, 50, 64, …
## $ Y <dbl> 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0…
## Rows: 43
## Columns: 6
## $ AP <dbl> 84, 178, 157, 170, 89, 114, 99, 151, 179, 105, 135, 45, 62, 43, …
## $ XRay <dbl> 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1…
## $ Stage <dbl> 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1…
## $ Grade <dbl> 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1…
## $ Age <dbl> 55, 62, 59, 68, 64, 63, 50, 65, 69, 61, 64, 63, 63, 55, 57, 68, …
## $ Y <dbl> 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1…
Model
library(neuralnet)
set.seed(122)
h <- c(3, 2)
nn_log_lin <- neuralnet(Y~., data = nn_train_data, act.fct = 'logistic',
linear.output = T, hidden = h)
nn_tanh_lin <- neuralnet(Y~., data = nn_train_data, act.fct = 'tanh',
linear.output = T, hidden = h)
nn_log_nonlin <- neuralnet(Y~., data = nn_train_data, act.fct = 'logistic',
linear.output = F, hidden = h)
nn_tanh_nonlin <- neuralnet(Y~., data = nn_train_data, act.fct = 'tanh',
linear.output = F, hidden = h)
# error
nn_error <- data.frame('NN Logistic Linear' = nn_log_lin$result.matrix[1],
'NN Logistic Nonlinear' = nn_log_nonlin$result.matrix[1],
'NN Tan-H Linear' = nn_tanh_lin$result.matrix[1],
'NN Tan-H Nonlinear' = nn_tanh_nonlin$result.matrix[1])
nn_error
## NN.Logistic.Linear NN.Logistic.Nonlinear NN.Tan.H.Linear NN.Tan.H.Nonlinear
## 1 9.287747 9.009976 13.81471 17.71338
model1_nn <- nn_log_nonlin
plot(model1_nn)
library(nnet)
library(devtools)
## Loading required package: usethis
source_url('https://gist.githubusercontent.com/fawda123/7471137/raw/466c1474d0a505ff044412703516c34f1a4684a5/nnet_plot_update.r')
## ℹ SHA-1 hash of file is "74c80bd5ddbc17ab3ae5ece9c0ed9beb612e87ef"
plot.nnet(model1_nn)
## Loading required package: scales
## Loading required package: reshape
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pred_train2 <- neuralnet::compute(model1_nn, nn_train_data)
pred_test2 <- neuralnet::compute(model1_nn, nn_test_data)
predtrain_nn <- ifelse(pred_train2$net.result > 0.5, 1, 0)
predtest_nn <- ifelse(pred_test2$net.result > 0.5, 1, 0)
Confusion Matrix
confusionMatrix(as.factor(nn_train_data$Y), as.factor(predtrain_nn))
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 39 15
## 1 6 97
##
## Accuracy : 0.8662
## 95% CI : (0.8028, 0.9153)
## No Information Rate : 0.7134
## P-Value [Acc > NIR] : 4.498e-06
##
## Kappa : 0.6914
##
## Mcnemar's Test P-Value : 0.08086
##
## Sensitivity : 0.8667
## Specificity : 0.8661
## Pos Pred Value : 0.7222
## Neg Pred Value : 0.9417
## Prevalence : 0.2866
## Detection Rate : 0.2484
## Detection Prevalence : 0.3439
## Balanced Accuracy : 0.8664
##
## 'Positive' Class : 0
##
confusionMatrix(as.factor(nn_test_data$Y), as.factor(predtest_nn))
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 6 3
## 1 5 29
##
## Accuracy : 0.814
## 95% CI : (0.666, 0.9161)
## No Information Rate : 0.7442
## P-Value [Acc > NIR] : 0.1930
##
## Kappa : 0.4804
##
## Mcnemar's Test P-Value : 0.7237
##
## Sensitivity : 0.5455
## Specificity : 0.9062
## Pos Pred Value : 0.6667
## Neg Pred Value : 0.8529
## Prevalence : 0.2558
## Detection Rate : 0.1395
## Detection Prevalence : 0.2093
## Balanced Accuracy : 0.7259
##
## 'Positive' Class : 0
##
Kurva ROC
roc3 <- roc(nn_train_data$Y, pred_train2$net.result, plot = T)
## Setting levels: control = 0, case = 1
## Warning in roc.default(nn_train_data$Y, pred_train2$net.result, plot = T):
## Deprecated use a matrix as predictor. Unexpected results may be produced,
## please pass a numeric vector.
## Setting direction: controls < cases
roc4 <- roc(nn_test_data$Y, pred_test2$net.result, plot = T)
## Setting levels: control = 0, case = 1
## Warning in roc.default(nn_test_data$Y, pred_test2$net.result, plot = T):
## Deprecated use a matrix as predictor. Unexpected results may be produced,
## please pass a numeric vector.
## Setting direction: controls < cases
ggroc(list(Train = roc3, Test = roc4), aes = c('linetype')) + labs(linetype = 'Data')
roc3$auc; roc4$auc
## Area under the curve: 0.831
## Area under the curve: 0.7418
ggroc(list(Logistic = roc1, ANN = roc3), aes = c('linetype')) + labs(linetype = 'Data Latih')
ggroc(list(Logistic = roc2, ANN = roc4), aes = c('linetype')) + labs(linetype = 'Data Uji')
