Cancer Prediction Appendix

load libraries/packages that are needed:

library(caret)
library("ggplot2")
library("caTools")
library("corrplot")
library(dplyr)
library(partykit)
library("e1071")
library(reshape2)
library(pROC)
library(gridExtra)
library(grid)
library(ggfortify)
library(purrr)
library(nnet)

load in data:

cancer <- read.csv(file = "~/Downloads/CancerData.csv", header = T, stringsAsFactors = T)
str(cancer)

'data.frame':   569 obs. of  32 variables:
 $ id                     : int  842302 842517 84300903 84348301 84358402 843786 844359 84458202 844981 84501001 ...
 $ diagnosis              : Factor w/ 2 levels "B","M": 2 2 2 2 2 2 2 2 2 2 ...
 $ radius_mean            : num  18 20.6 19.7 11.4 20.3 ...
 $ texture_mean           : num  10.4 17.8 21.2 20.4 14.3 ...
 $ perimeter_mean         : num  122.8 132.9 130 77.6 135.1 ...
 $ area_mean              : num  1001 1326 1203 386 1297 ...
 $ smoothness_mean        : num  0.1184 0.0847 0.1096 0.1425 0.1003 ...
 $ compactness_mean       : num  0.2776 0.0786 0.1599 0.2839 0.1328 ...
 $ concavity_mean         : num  0.3001 0.0869 0.1974 0.2414 0.198 ...
 $ concave.points_mean    : num  0.1471 0.0702 0.1279 0.1052 0.1043 ...
 $ symmetry_mean          : num  0.242 0.181 0.207 0.26 0.181 ...
 $ fractal_dimension_mean : num  0.0787 0.0567 0.06 0.0974 0.0588 ...
 $ radius_se              : num  1.095 0.543 0.746 0.496 0.757 ...
 $ texture_se             : num  0.905 0.734 0.787 1.156 0.781 ...
 $ perimeter_se           : num  8.59 3.4 4.58 3.44 5.44 ...
 $ area_se                : num  153.4 74.1 94 27.2 94.4 ...
 $ smoothness_se          : num  0.0064 0.00522 0.00615 0.00911 0.01149 ...
 $ compactness_se         : num  0.049 0.0131 0.0401 0.0746 0.0246 ...
 $ concavity_se           : num  0.0537 0.0186 0.0383 0.0566 0.0569 ...
 $ concave.points_se      : num  0.0159 0.0134 0.0206 0.0187 0.0188 ...
 $ symmetry_se            : num  0.03 0.0139 0.0225 0.0596 0.0176 ...
 $ fractal_dimension_se   : num  0.00619 0.00353 0.00457 0.00921 0.00511 ...
 $ radius_worst           : num  25.4 25 23.6 14.9 22.5 ...
 $ texture_worst          : num  17.3 23.4 25.5 26.5 16.7 ...
 $ perimeter_worst        : num  184.6 158.8 152.5 98.9 152.2 ...
 $ area_worst             : num  2019 1956 1709 568 1575 ...
 $ smoothness_worst       : num  0.162 0.124 0.144 0.21 0.137 ...
 $ compactness_worst      : num  0.666 0.187 0.424 0.866 0.205 ...
 $ concavity_worst        : num  0.712 0.242 0.45 0.687 0.4 ...
 $ concave.points_worst   : num  0.265 0.186 0.243 0.258 0.163 ...
 $ symmetry_worst         : num  0.46 0.275 0.361 0.664 0.236 ...
 $ fractal_dimension_worst: num  0.1189 0.089 0.0876 0.173 0.0768 ...

percentage of women affected in benign and malignant stage

cancer %>% count(diagnosis)%>%group_by(diagnosis) %>%
  summarize(perc_dx = round((n / 569)* 100, 2))

split the data into traning and testing sets

set.seed(123)
m = nrow(cancer)
index <- sample(m, 0.7 * m)
train <- cancer[index, ]
test <- cancer[-index, ]

fitControl <- trainControl(method="cv",number = 5, preProcOptions = list(thresh = 0.99), 
classProbs = TRUE, summaryFunction = twoClassSummary)

MODELS:

• LOGISTIC REGRESSION

fit.glm <- glm(diagnosis~. ,data = train, family = binomial)

Warning: glm.fit: algorithm did not convergeWarning: glm.fit: fitted probabilities numerically 0 or 1 occurred

summary(fit.glm)

Call:
glm(formula = diagnosis ~ ., family = binomial, data = train)

Deviance Residuals: 
       Min          1Q      Median          3Q         Max  
-3.591e-04  -2.000e-08  -2.000e-08   2.000e-08   3.472e-04  

Coefficients:
                          Estimate Std. Error z value Pr(>|z|)
(Intercept)             -5.832e+03  5.180e+05  -0.011    0.991
id                      -2.095e-08  1.228e-04   0.000    1.000
radius_mean             -2.236e+03  1.273e+05  -0.018    0.986
texture_mean             2.641e+01  2.997e+03   0.009    0.993
perimeter_mean           3.004e+02  1.821e+04   0.016    0.987
area_mean                2.074e+00  4.989e+02   0.004    0.997
smoothness_mean          1.398e+04  1.232e+06   0.011    0.991
compactness_mean        -1.668e+04  8.069e+05  -0.021    0.984
concavity_mean           3.519e+03  1.120e+06   0.003    0.997
concave.points_mean     -3.693e+03  9.503e+05  -0.004    0.997
symmetry_mean           -3.767e+03  6.776e+05  -0.006    0.996
fractal_dimension_mean   3.097e+04  3.739e+06   0.008    0.993
radius_se                1.845e+03  8.399e+05   0.002    0.998
texture_se               2.050e+02  3.057e+04   0.007    0.995
perimeter_se            -1.177e+02  7.423e+04  -0.002    0.999
area_se                 -3.242e+00  3.928e+03  -0.001    0.999
smoothness_se            1.304e+04  3.644e+06   0.004    0.997
compactness_se           2.530e+04  1.874e+06   0.014    0.989
concavity_se            -9.865e+03  7.101e+05  -0.014    0.989
concave.points_se        3.037e+04  3.865e+06   0.008    0.994
symmetry_se             -1.051e+04  2.320e+06  -0.005    0.996
fractal_dimension_se    -2.169e+05  1.734e+07  -0.013    0.990
radius_worst             6.174e+02  7.152e+04   0.009    0.993
texture_worst           -4.770e+00  4.297e+03  -0.001    0.999
perimeter_worst         -2.910e+01  1.216e+04  -0.002    0.998
area_worst              -2.417e+00  3.463e+02  -0.007    0.994
smoothness_worst        -2.426e+03  9.558e+05  -0.003    0.998
compactness_worst       -1.587e+03  2.274e+05  -0.007    0.994
concavity_worst          9.678e+02  3.196e+05   0.003    0.998
concave.points_worst     5.978e+03  5.235e+05   0.011    0.991
symmetry_worst           3.358e+03  4.933e+05   0.007    0.995
fractal_dimension_worst  8.747e+03  1.827e+06   0.005    0.996

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 5.1500e+02  on 397  degrees of freedom
Residual deviance: 1.4747e-06  on 366  degrees of freedom
AIC: 64

Number of Fisher Scoring iterations: 25

prob.glm <- predict(fit.glm,test, type="response")
pred.glm <- factor(prob.glm > .5, levels=c(FALSE, TRUE),
                     labels=c("benign", "malignant"))
perf.logit <- table(test$diagnosis, pred.glm,
                    dnn=c("Actual","Predicted"))
perf.logit

      Predicted
Actual benign malignant
     B     94         4
     M      2        71

performance(perf.logit)

Sensitivity = 0.97
Specificity = 0.96
Positive Predictive Value = 0.95
Negative Predictive Value = 0.98
Accuracy = 0.96

• DECISION TREE

fit.tree <- ctree(diagnosis~., data=train)
plot(fit.tree, main="Conditional Inference Tree")

pred.tree <- predict(fit.tree, test)
confusionMatrix(pred.tree, test$diagnosis, positive="M")

Confusion Matrix and Statistics

          Reference
Prediction  B  M
         B 93 14
         M  5 59
                                          
               Accuracy : 0.8889          
                 95% CI : (0.8319, 0.9318)
    No Information Rate : 0.5731          
    P-Value [Acc > NIR] : < 2e-16         
                                          
                  Kappa : 0.7693          
                                          
 Mcnemar's Test P-Value : 0.06646         
                                          
            Sensitivity : 0.8082          
            Specificity : 0.9490          
         Pos Pred Value : 0.9219          
         Neg Pred Value : 0.8692          
             Prevalence : 0.4269          
         Detection Rate : 0.3450          
   Detection Prevalence : 0.3743          
      Balanced Accuracy : 0.8786          
                                          
       'Positive' Class : M               
                                          

• KNN MODEL

fit.knn <- train(diagnosis~.,data = train, method="knn", metric="ROC", preProcess = c('center', 'scale'),
tuneLength=10,trControl=fitControl)

pred.knn <- predict(fit.knn,test)

cm_knn <- confusionMatrix(pred.knn, test$diagnosis, positive = "M")
cm_knn

Confusion Matrix and Statistics

          Reference
Prediction  B  M
         B 97  8
         M  1 65
                                          
               Accuracy : 0.9474          
                 95% CI : (0.9024, 0.9757)
    No Information Rate : 0.5731          
    P-Value [Acc > NIR] : <2e-16          
                                          
                  Kappa : 0.8911          
                                          
 Mcnemar's Test P-Value : 0.0455          
                                          
            Sensitivity : 0.8904          
            Specificity : 0.9898          
         Pos Pred Value : 0.9848          
         Neg Pred Value : 0.9238          
             Prevalence : 0.4269          
         Detection Rate : 0.3801          
   Detection Prevalence : 0.3860          
      Balanced Accuracy : 0.9401          
                                          
       'Positive' Class : M               
                                          

Evaluate Models

performance <- function(table, n=2){
  tn = table[1,1]
  fp = table[1,2] 
  fn = table[2,1]
  tp = table[2,2]
  
  sensitivity = tp/(tp+fn) # recall
  specificity = tn/(tn+fp) 
  ppp = tp/(tp+fp) # precision
  npp = tn/(tn+fn)
  hitrate = (tp+tn)/(tp+tn+fp+fn) # accuracy
  
  result <- paste("Sensitivity = ", round(sensitivity, n) ,
                  "\nSpecificity = ", round(specificity, n),
                  "\nPositive Predictive Value = ", round(ppp, n),
                  "\nNegative Predictive Value = ", round(npp, n),
                  "\nAccuracy = ", round(hitrate, n), "\n", sep="")
  
  cat(result)
}