2023-11-29
knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE)
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.3 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ ggplot2 3.4.3 ✔ tibble 3.2.1
## ✔ lubridate 1.9.2 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(MASS) # boxcox##
## Attaching package: 'MASS'
##
## The following object is masked from 'package:dplyr':
##
## select
library(performance) # vif
library(ggpubr)# import data
breastcancer = read_csv("./data/Project_2_data.csv")
#Data Cleaning
breastcancer_1 = breastcancer|>
janitor::clean_names()|>
mutate(
race = as_factor(race),
marital_status = factor(marital_status, levels = c("Single", "Married", "Divorced", "Separated", "Widowed")),
t_stage = factor(t_stage, levels = c("T1", "T2", "T3", "T4")),
n_stage = factor(n_stage, levels = c("N1", "N2", "N3")),
x6th_stage = factor(x6th_stage, levels = c("IIA", "IIB", "IIIA", "IIIB", "IIIC")),
differentiate = factor(differentiate, levels = c("Moderately differentiated", "Poorly differentiated", "Undifferentiated", "Well differentiated")),
grade = factor(grade, levels = c("1", "2", "3", "anaplastic; Grade IV")),
a_stage = factor(a_stage, levels = c("Distant", "Regional")),
estrogen_status = as_factor(estrogen_status),
progesterone_status = as_factor(progesterone_status),
status = ifelse(status == "Dead", 1, 0),
status = as_factor(status))
breastcancer_clean = breastcancer_1|>
mutate(node_positive_prop = reginol_node_positive/regional_node_examined,
node_positive_prop = round(node_positive_prop, 4))
breastcancer_clean## # A tibble: 4,024 × 17
## age race marital_status t_stage n_stage x6th_stage differentiate grade
## <dbl> <fct> <fct> <fct> <fct> <fct> <fct> <fct>
## 1 68 White Married T1 N1 IIA Poorly different… 3
## 2 50 White Married T2 N2 IIIA Moderately diffe… 2
## 3 58 White Divorced T3 N3 IIIC Moderately diffe… 2
## 4 58 White Married T1 N1 IIA Poorly different… 3
## 5 47 White Married T2 N1 IIB Poorly different… 3
## 6 51 White Single T1 N1 IIA Moderately diffe… 2
## 7 51 White Married T1 N1 IIA Well differentia… 1
## 8 40 White Married T2 N1 IIB Moderately diffe… 2
## 9 40 White Divorced T4 N3 IIIC Poorly different… 3
## 10 69 White Married T4 N3 IIIC Well differentia… 1
## # ℹ 4,014 more rows
## # ℹ 9 more variables: a_stage <fct>, tumor_size <dbl>, estrogen_status <fct>,
## # progesterone_status <fct>, regional_node_examined <dbl>,
## # reginol_node_positive <dbl>, survival_months <dbl>, status <fct>,
## # node_positive_prop <dbl>
# fit a model with all the predictors
fit1 = lm(survival_months ~ age + race + marital_status + t_stage + n_stage + x6th_stage + differentiate + grade + a_stage + tumor_size + estrogen_status + progesterone_status + regional_node_examined + reginol_node_positive, data = breastcancer_clean)
summary(fit1)##
## Call:
## lm(formula = survival_months ~ age + race + marital_status +
## t_stage + n_stage + x6th_stage + differentiate + grade +
## a_stage + tumor_size + estrogen_status + progesterone_status +
## regional_node_examined + reginol_node_positive, data = breastcancer_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -74.685 -15.591 1.087 18.126 56.245
##
## Coefficients: (4 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 72.83328 3.67741 19.806 < 2e-16 ***
## age -0.04220 0.04138 -1.020 0.30787
## raceBlack -3.67154 1.40193 -2.619 0.00885 **
## raceOther 1.91040 1.32287 1.444 0.14878
## marital_statusMarried 0.74868 1.02626 0.730 0.46572
## marital_statusDivorced 0.03560 1.37859 0.026 0.97940
## marital_statusSeparated -6.21046 3.48494 -1.782 0.07481 .
## marital_statusWidowed -0.75373 1.77315 -0.425 0.67080
## t_stageT2 -1.61447 1.69125 -0.955 0.33984
## t_stageT3 0.73762 2.76338 0.267 0.78954
## t_stageT4 -2.25092 4.48353 -0.502 0.61567
## n_stageN2 -0.58607 1.98650 -0.295 0.76799
## n_stageN3 -3.37649 2.67197 -1.264 0.20642
## x6th_stageIIB 0.53765 1.82506 0.295 0.76832
## x6th_stageIIIA -0.65701 2.36107 -0.278 0.78082
## x6th_stageIIIB 3.32794 5.15941 0.645 0.51895
## x6th_stageIIIC NA NA NA NA
## differentiatePoorly differentiated -0.98945 0.85155 -1.162 0.24533
## differentiateUndifferentiated -2.95238 5.21782 -0.566 0.57154
## differentiateWell differentiated -0.02110 1.07890 -0.020 0.98440
## grade2 NA NA NA NA
## grade3 NA NA NA NA
## gradeanaplastic; Grade IV NA NA NA NA
## a_stageRegional 4.36505 2.67211 1.634 0.10243
## tumor_size -0.05649 0.03434 -1.645 0.10002
## estrogen_statusNegative -8.61299 1.68605 -5.108 3.4e-07 ***
## progesterone_statusNegative -1.60271 1.10116 -1.455 0.14562
## regional_node_examined 0.10692 0.04828 2.214 0.02686 *
## reginol_node_positive -0.31396 0.14259 -2.202 0.02774 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.47 on 3999 degrees of freedom
## Multiple R-squared: 0.04476, Adjusted R-squared: 0.03903
## F-statistic: 7.808 on 24 and 3999 DF, p-value: < 2.2e-16
# residual vs fitted plot:
plot(fit1, which = 1) #funning of the data points
# QQ plot: detect normality of residuals and outliers
plot(fit1, which = 2) #deviations at the tails 
# Scale-Location: check the assumption of equal variance
plot(fit1, which = 3)
# Residual v.s. Leverage: identify influential cases
plot(fit1, which = 4)
#Box-Cox result indicates that we might not need transformation on y
plot(fit1)
boxcox(fit1)
# Check for Multicollinearity
# Calculate the variance inflation factor (VIF)
check_collinearity(fit1) # based on the results, we have to stratify for different stage levels if we include them in our model## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance
## age 1.10 [ 1.07, 1.14] 1.05 0.91
## race 1.06 [ 1.03, 1.11] 1.03 0.94
## marital_status 1.12 [ 1.09, 1.17] 1.06 0.89
## differentiate 1.14 [ 1.10, 1.18] 1.07 0.88
## a_stage 1.27 [ 1.23, 1.32] 1.13 0.79
## tumor_size 4.19 [ 3.97, 4.43] 2.05 0.24
## estrogen_status 1.41 [ 1.36, 1.47] 1.19 0.71
## progesterone_status 1.39 [ 1.33, 1.44] 1.18 0.72
## regional_node_examined 1.22 [ 1.18, 1.27] 1.10 0.82
## reginol_node_positive 4.23 [ 4.01, 4.47] 2.06 0.24
## Tolerance 95% CI
## [0.88, 0.94]
## [0.90, 0.97]
## [0.86, 0.92]
## [0.85, 0.91]
## [0.76, 0.81]
## [0.23, 0.25]
## [0.68, 0.73]
## [0.69, 0.75]
## [0.79, 0.85]
## [0.22, 0.25]
##
## High Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance Tolerance 95% CI
## t_stage 64.44 [60.64, 68.49] 8.03 0.02 [0.01, 0.02]
## n_stage 28.84 [27.15, 30.63] 5.37 0.03 [0.03, 0.04]
## x6th_stage 90.22 [84.88, 95.89] 9.50 0.01 [0.01, 0.01]