Cáncer de Mama - Árbol de Decisión
Librerías
# install.packages("rpart")
# install.packages("rpart.plot")
library(rpart)
library(rpart.plot)Importar la base de datos
cancer <- read.csv("cancer_de_mama.csv")
colnames(cancer)[colnames(cancer) == "X...diagnosis"] <- "diagnosis"
cancer$diagnosis <- as.factor(cancer$diagnosis)Entender la base de datos
El dataset contiene mediciones de núcleos celulares obtenidas mediante imágenes digitalizadas de biopsias de mama. Cada fila es un paciente y la variable objetivo indica si el tumor es Maligno (M) o Benigno (B).
str(cancer)## 'data.frame': 569 obs. of 31 variables:
## $ 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 ...summary(cancer)## diagnosis radius_mean texture_mean perimeter_mean area_mean
## B:357 Min. : 6.981 Min. : 9.71 Min. : 43.79 Min. : 143.5
## M:212 1st Qu.:11.700 1st Qu.:16.17 1st Qu.: 75.17 1st Qu.: 420.3
## Median :13.370 Median :18.84 Median : 86.24 Median : 551.1
## Mean :14.127 Mean :19.29 Mean : 91.97 Mean : 654.9
## 3rd Qu.:15.780 3rd Qu.:21.80 3rd Qu.:104.10 3rd Qu.: 782.7
## Max. :28.110 Max. :39.28 Max. :188.50 Max. :2501.0
## smoothness_mean compactness_mean concavity_mean concave.points_mean
## Min. :0.05263 Min. :0.01938 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.08637 1st Qu.:0.06492 1st Qu.:0.02956 1st Qu.:0.02031
## Median :0.09587 Median :0.09263 Median :0.06154 Median :0.03350
## Mean :0.09636 Mean :0.10434 Mean :0.08880 Mean :0.04892
## 3rd Qu.:0.10530 3rd Qu.:0.13040 3rd Qu.:0.13070 3rd Qu.:0.07400
## Max. :0.16340 Max. :0.34540 Max. :0.42680 Max. :0.20120
## symmetry_mean fractal_dimension_mean radius_se texture_se
## Min. :0.1060 Min. :0.04996 Min. :0.1115 Min. :0.3602
## 1st Qu.:0.1619 1st Qu.:0.05770 1st Qu.:0.2324 1st Qu.:0.8339
## Median :0.1792 Median :0.06154 Median :0.3242 Median :1.1080
## Mean :0.1812 Mean :0.06280 Mean :0.4052 Mean :1.2169
## 3rd Qu.:0.1957 3rd Qu.:0.06612 3rd Qu.:0.4789 3rd Qu.:1.4740
## Max. :0.3040 Max. :0.09744 Max. :2.8730 Max. :4.8850
## perimeter_se area_se smoothness_se compactness_se
## Min. : 0.757 Min. : 6.802 Min. :0.001713 Min. :0.002252
## 1st Qu.: 1.606 1st Qu.: 17.850 1st Qu.:0.005169 1st Qu.:0.013080
## Median : 2.287 Median : 24.530 Median :0.006380 Median :0.020450
## Mean : 2.866 Mean : 40.337 Mean :0.007041 Mean :0.025478
## 3rd Qu.: 3.357 3rd Qu.: 45.190 3rd Qu.:0.008146 3rd Qu.:0.032450
## Max. :21.980 Max. :542.200 Max. :0.031130 Max. :0.135400
## concavity_se concave.points_se symmetry_se fractal_dimension_se
## Min. :0.00000 Min. :0.000000 Min. :0.007882 Min. :0.0008948
## 1st Qu.:0.01509 1st Qu.:0.007638 1st Qu.:0.015160 1st Qu.:0.0022480
## Median :0.02589 Median :0.010930 Median :0.018730 Median :0.0031870
## Mean :0.03189 Mean :0.011796 Mean :0.020542 Mean :0.0037949
## 3rd Qu.:0.04205 3rd Qu.:0.014710 3rd Qu.:0.023480 3rd Qu.:0.0045580
## Max. :0.39600 Max. :0.052790 Max. :0.078950 Max. :0.0298400
## radius_worst texture_worst perimeter_worst area_worst
## Min. : 7.93 Min. :12.02 Min. : 50.41 Min. : 185.2
## 1st Qu.:13.01 1st Qu.:21.08 1st Qu.: 84.11 1st Qu.: 515.3
## Median :14.97 Median :25.41 Median : 97.66 Median : 686.5
## Mean :16.27 Mean :25.68 Mean :107.26 Mean : 880.6
## 3rd Qu.:18.79 3rd Qu.:29.72 3rd Qu.:125.40 3rd Qu.:1084.0
## Max. :36.04 Max. :49.54 Max. :251.20 Max. :4254.0
## smoothness_worst compactness_worst concavity_worst concave.points_worst
## Min. :0.07117 Min. :0.02729 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.11660 1st Qu.:0.14720 1st Qu.:0.1145 1st Qu.:0.06493
## Median :0.13130 Median :0.21190 Median :0.2267 Median :0.09993
## Mean :0.13237 Mean :0.25427 Mean :0.2722 Mean :0.11461
## 3rd Qu.:0.14600 3rd Qu.:0.33910 3rd Qu.:0.3829 3rd Qu.:0.16140
## Max. :0.22260 Max. :1.05800 Max. :1.2520 Max. :0.29100
## symmetry_worst fractal_dimension_worst
## Min. :0.1565 Min. :0.05504
## 1st Qu.:0.2504 1st Qu.:0.07146
## Median :0.2822 Median :0.08004
## Mean :0.2901 Mean :0.08395
## 3rd Qu.:0.3179 3rd Qu.:0.09208
## Max. :0.6638 Max. :0.20750head(cancer)## diagnosis radius_mean texture_mean perimeter_mean area_mean smoothness_mean
## 1 M 17.99 10.38 122.80 1001.0 0.11840
## 2 M 20.57 17.77 132.90 1326.0 0.08474
## 3 M 19.69 21.25 130.00 1203.0 0.10960
## 4 M 11.42 20.38 77.58 386.1 0.14250
## 5 M 20.29 14.34 135.10 1297.0 0.10030
## 6 M 12.45 15.70 82.57 477.1 0.12780
## compactness_mean concavity_mean concave.points_mean symmetry_mean
## 1 0.27760 0.3001 0.14710 0.2419
## 2 0.07864 0.0869 0.07017 0.1812
## 3 0.15990 0.1974 0.12790 0.2069
## 4 0.28390 0.2414 0.10520 0.2597
## 5 0.13280 0.1980 0.10430 0.1809
## 6 0.17000 0.1578 0.08089 0.2087
## fractal_dimension_mean radius_se texture_se perimeter_se area_se
## 1 0.07871 1.0950 0.9053 8.589 153.40
## 2 0.05667 0.5435 0.7339 3.398 74.08
## 3 0.05999 0.7456 0.7869 4.585 94.03
## 4 0.09744 0.4956 1.1560 3.445 27.23
## 5 0.05883 0.7572 0.7813 5.438 94.44
## 6 0.07613 0.3345 0.8902 2.217 27.19
## smoothness_se compactness_se concavity_se concave.points_se symmetry_se
## 1 0.006399 0.04904 0.05373 0.01587 0.03003
## 2 0.005225 0.01308 0.01860 0.01340 0.01389
## 3 0.006150 0.04006 0.03832 0.02058 0.02250
## 4 0.009110 0.07458 0.05661 0.01867 0.05963
## 5 0.011490 0.02461 0.05688 0.01885 0.01756
## 6 0.007510 0.03345 0.03672 0.01137 0.02165
## fractal_dimension_se radius_worst texture_worst perimeter_worst area_worst
## 1 0.006193 25.38 17.33 184.60 2019.0
## 2 0.003532 24.99 23.41 158.80 1956.0
## 3 0.004571 23.57 25.53 152.50 1709.0
## 4 0.009208 14.91 26.50 98.87 567.7
## 5 0.005115 22.54 16.67 152.20 1575.0
## 6 0.005082 15.47 23.75 103.40 741.6
## smoothness_worst compactness_worst concavity_worst concave.points_worst
## 1 0.1622 0.6656 0.7119 0.2654
## 2 0.1238 0.1866 0.2416 0.1860
## 3 0.1444 0.4245 0.4504 0.2430
## 4 0.2098 0.8663 0.6869 0.2575
## 5 0.1374 0.2050 0.4000 0.1625
## 6 0.1791 0.5249 0.5355 0.1741
## symmetry_worst fractal_dimension_worst
## 1 0.4601 0.11890
## 2 0.2750 0.08902
## 3 0.3613 0.08758
## 4 0.6638 0.17300
## 5 0.2364 0.07678
## 6 0.3985 0.12440Distribución del diagnóstico
tabla <- table(cancer$diagnosis)
porcentaje <- round(prop.table(tabla) * 100, 2)
barplot(tabla,
col = c("steelblue", "tomato"),
main = "Distribución del Diagnóstico",
xlab = "Diagnóstico (B = Benigno, M = Maligno)",
ylab = "Número de pacientes")
cat("Benigno: ", tabla["B"], "(", porcentaje["B"], "%)\n")## Benigno: 357 ( 62.74 %)cat("Maligno: ", tabla["M"], "(", porcentaje["M"], "%)\n")## Maligno: 212 ( 37.26 %)Preparación de datos
Variables
El dataset tiene 30 variables numéricas agrupadas en 3 grupos por cada una de las 10 características celulares:
| Grupo | Descripción |
|---|---|
_mean |
Valor promedio de la característica |
_se |
Error estándar (variabilidad) |
_worst |
Peor valor (más extremo) observado |
Las 10 características medidas son: radio, textura, perímetro, área, suavidad, compacidad, concavidad, puntos cóncavos, simetría y dimensión fractal.
# Verificar — sin valores NA
cat("Total de NAs en el dataset:", sum(is.na(cancer)), "\n")## Total de NAs en el dataset: 0str(cancer$diagnosis)## Factor w/ 2 levels "B","M": 2 2 2 2 2 2 2 2 2 2 ...Crear árbol de decisión
arbol <- rpart(diagnosis ~ ., data = cancer, method = "class")
rpart.plot(arbol,
extra = 104,
fallen.leaves = TRUE,
main = "Árbol de Decisión - Cáncer de Mama",
cex = 0.75)
Importancia de variables
importancia <- sort(arbol$variable.importance, decreasing = TRUE)
top10 <- head(importancia, 10)
par(mar = c(10, 4, 4, 2)) # margen inferior ampliado para etiquetas verticales
barplot(top10,
main = "Top 10 Variables más Importantes",
col = "steelblue",
las = 2,
ylab = "Importancia",
cex.names = 0.8)
par(mar = c(5, 4, 4, 2)) # restaurar márgenes por defectoConclusiones
- El árbol clasifica tumores como Malignos (M) o Benignos (B) usando mediciones celulares del núcleo.
- Las variables del grupo
_worst(peores valores observados) tienden a ser las más importantes, especialmenteperimeter_worstyconcave.points_mean— indicando que la forma más extrema del núcleo es el mejor predictor. - Tumores malignos tienden a tener núcleos más grandes e irregulares que los benignos.
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