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")
breastcancer = breastcancer|>
janitor::clean_names()# 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)
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)
##
## 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) 58.98164 4.18486 14.094 < 2e-16 ***
## age -0.04220 0.04138 -1.020 0.30787
## raceOther 5.58194 1.84998 3.017 0.00257 **
## raceWhite 3.67154 1.40193 2.619 0.00885 **
## marital_statusMarried 0.71309 1.11566 0.639 0.52276
## marital_statusSeparated -6.24605 3.52093 -1.774 0.07614 .
## marital_statusSingle -0.03560 1.37859 -0.026 0.97940
## marital_statusWidowed -0.78933 1.80857 -0.436 0.66254
## 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_statusPositive 8.61299 1.68605 5.108 3.4e-07 ***
## progesterone_statusPositive 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]