Biostats_Lab 5

https://rpubs.com/ScottWeiner19/1063238

library(tidyverse)
library(openintro)
library(GGally)
library(broom)
library(ggplot2)
library(ggfortify)

1. Importing the Dataset

library(readr)
breast_20cancer <- read_csv("https://raw.githubusercontent.com/lwaldron/bios1/main/vignettes/breast%20cancer.csv", 
    col_types = cols(id = col_character(), 
        diagnosis = col_factor(levels = c("B", 
            "M")), ...33 = col_skip()))

bcancer <- breast_20cancer %>% mutate(diagnosis=case_match(diagnosis,
                                                           "B" ~ "Benign",
                                                           "M"~ "Malignant",
                                                        .ptype=factor(levels=c("Benign","Malignant"))))

2. Exploratory Data Analysis (EDA)

dim(bcancer)
head(bcancer)
summary(bcancer)

1. Check the dimensions of the dataset using the dim() function

Note: There are 32 variables and 568 observations

2. Preview the first few rows of the dataset using the head() function

Note: There is one character var (id), one factor (diagnosis), and the rest are all numerics

3. Use summary() to summarize the dataset.

About 2/3 of participants have benign diagnosis

distancematrix <- 1 - abs(cor(select(bcancer, -c(id,diagnosis))))
distancematrix <- data.frame(distancematrix)

plot(hclust(as.dist(distancematrix)))

ComplexHeatmap::Heatmap(distancematrix)

## Warning: The input is a data frame-like object, convert it to a matrix.

4. Identify collinear variables.

Area, radius, and perimeter are highly correlated.

bcancer2 <- bcancer %>% select(-id)

bcancer2long <- bcancer2%>% 
pivot_longer(!diagnosis,names_to = "attributes", values_to = "values") 


ggplot(bcancer2long,aes(x=diagnosis,y=values))+
  geom_boxplot()+
  facet_wrap(vars(attributes), scales="free")

5. Do any variables clearly have an association with breast cancer diagnosis?

Some of the variables that stand out, whose IQR’s do not overlap at all are “area_mean”, “area_se”, “area_worst”, “compactness_mean” “concave points mean”, and “perimeter”, as well as others.

3. Building a Logistic Regression Model

cancmod <- glm(diagnosis~area_mean,data=bcancer,family="binomial")
summary(cancmod)

## 
## Call:
## glm(formula = diagnosis ~ area_mean, family = "binomial", data = bcancer)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -2.72939  -0.46438  -0.20769   0.09969   2.73582  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -7.97313    0.68300  -11.67   <2e-16 ***
## area_mean    0.01177    0.00109   10.80   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 750.51  on 567  degrees of freedom
## Residual deviance: 325.65  on 566  degrees of freedom
## AIC: 329.65
## 
## Number of Fisher Scoring iterations: 7

Interpret the coefficients of the logistic regression model

Every unit increase of area_mean, is associated with an observed log odds increase of malignancy by 0.012.

meanplot <- ggplot(bcancer, aes(x=area_mean, y= diagnosis)) +
  geom_point()+
  geom_jitter(width=0)

meanplot

bcancer_pred <- bcancer %>% mutate(
  modpredict=fitted(cancmod))

meanplot +
  geom_line(data=bcancer_pred, aes(x=area_mean,y=1+modpredict), color="green",linewidth=1.5)

What do you notice about the data points where the predicted probabilities are 0, 0.5, and 1?

The data points at 0 predicted probability mostly have low area_mean values (<550), whereas datapoits around 0.5 probability is between 650 and 700 Probability of malignancy approaches 1 at an area_mean of 1000.

new_means <- tibble(
  area_mean = seq(300,1100,200))
mean_mean_pred <- new_means %>% 
  mutate(predProbability= predict( cancmod,new_means,type="response"))

mean_mean_pred

## # A tibble: 5 × 2
##   area_mean predProbability
##       <dbl>           <dbl>
## 1       300          0.0116
## 2       500          0.110 
## 3       700          0.565 
## 4       900          0.932 
## 5      1100          0.993