14.4 Proportional Hazards Model
The examples in these notes use the following data sets.
14.4.1 Xelox
Data from a Phase II clinical trial of Xeloda and exaliplatin given before surgery to advanced gastric cancer patients with para-aortic lymph node metastasis. timeWeeks is survival time; delta is the censoring indicator (1 = death, 0 = censored).
## timeWeeks delta
## 1 4 1
## 2 8 1
## 3 8 1
## 4 8 1
## 5 9 1
## 6 11 114.4.2 pancreatic
Data from a Phase II clinical trial of patients with locally advanced or metastatic pancreatic cancer. Column stage is a covariate indicating the diagnosis (LA = locally advance, M = metastatic); the event of interest is either progression or death. There was no censoring in this data because none of the subjects lived very long.
## stage onstudy progression death
## 1 M 12/16/2005 2/2/2006 10/19/2006
## 2 M 1/6/2006 2/26/2006 4/19/2006
## 3 LA 2/3/2006 8/2/2006 1/19/2007
## 4 M 3/30/2006 . 5/11/2006
## 5 LA 4/27/2006 3/11/2007 5/29/2007
## 6 M 5/7/2006 6/25/2006 10/11/200614.4.3 prostateSurvival
There are two outcomes of interest indicated by status, death from prostate cancer, and death from other causes, a competing risks survival analysis problem.
## grade stage ageGroup survTime status
## 1 mode T1c 80+ 18 0
## 2 mode T1ab 75-79 23 0
## 3 poor T1c 75-79 37 0
## 4 mode T2 70-74 27 0
## 5 mode T1c 70-74 42 0
## 6 poor T2 75-79 38 214.4.4 pharmacoSmoking
The primary outcome variable ttr is the time from randomization until relapse (return to smoking). Individuals who remained non-smokers for six months were censored.
## id ttr relapse grp age gender race employment yearsSmoking
## 1 21 182 0 patchOnly 36 Male white ft 26
## 2 113 14 1 patchOnly 41 Male white other 27
## 3 39 5 1 combination 25 Female white other 12
## 4 80 16 1 combination 54 Male white ft 39
## 5 87 0 1 combination 45 Male white other 30
## 6 29 182 0 combination 43 Male hispanic ft 30
## levelSmoking ageGroup2 ageGroup4 priorAttempts longestNoSmoke
## 1 heavy 21-49 35-49 0 0
## 2 heavy 21-49 35-49 3 90
## 3 heavy 21-49 21-34 3 21
## 4 heavy 50+ 50-64 0 0
## 5 heavy 21-49 35-49 0 0
## 6 heavy 21-49 35-49 2 182514.4.5 hepatoCellular
Overall and recurrence-free survival of patients with hepatocellular carcinoma. The survival outcomes are OS (overall survival) and RFS (recurrence-free survival), and the corresponding censoring indicators are Death and Recurrance.
## Number Age Gender HBsAg Cirrhosis ALT AST AFP Tumorsize Tumordifferentiation
## 1 1 57 0 1 1 1 2 2 2 1
## 2 2 58 1 0 0 1 1 2 1 1
## 3 3 65 1 0 0 1 1 2 2 2
## 4 4 54 1 1 0 2 1 2 2 2
## 5 5 71 1 1 0 2 2 2 2 2
## 6 6 32 1 0 0 2 2 2 2 2
## Vascularinvasion Tumormultiplicity Capsulation TNM BCLC OS Death RFS
## 1 0 1 0 2 1 83 0 13
## 2 0 1 1 1 1 81 0 81
## 3 1 1 1 2 2 79 0 79
## 4 0 1 1 1 1 76 0 76
## 5 1 2 0 2 2 7 1 3
## 6 0 1 0 1 1 13 1 3
## Recurrence CXCL17T CXCL17P CXCL17N CD4T CD4N CD8T CD8N CD20T CD20N
## 1 1 113.947238 299.325404 138.247177 2.6 0 190.6 126.8 20.95 13.05
## 2 0 54.071542 63.468462 6.214912 NA NA NA NA NA NA
## 3 0 22.188831 34.470336 22.131934 NA NA NA NA NA NA
## 4 0 8.442809 16.002843 11.146906 NA NA NA NA NA NA
## 5 1 8.271131 22.034540 32.271196 NA NA NA NA NA NA
## 6 1 13.708073 6.423604 0.000000 NA NA NA NA NA NA
## CD57T CD57N CD15T CD15N CD68T CD68N CD4NR CD8NR CD20NR CD57NR
## 1 15.86 0 72.8 23.85 47.48125 50.29444 0 0.5925387 0.06098289 0
## 2 NA NA NA NA NA NA NA NA NA NA
## 3 NA NA NA NA NA NA NA NA NA NA
## 4 NA NA NA NA NA NA NA NA NA NA
## 5 NA NA NA NA NA NA NA NA NA NA
## 6 NA NA NA NA NA NA NA NA NA NA
## CD15NR CD68NR CD4TR CD8TR CD20TR CD57TR CD15TR
## 1 0.1114515 0.2350269 0.007422395 0.5441186 0.05980738 0.04527661 0.2078271
## 2 NA NA NA NA NA NA NA
## 3 NA NA NA NA NA NA NA
## 4 NA NA NA NA NA NA NA
## 5 NA NA NA NA NA NA NA
## 6 NA NA NA NA NA NA NA
## CD68TR Ki67 CD34
## 1 0.1355479 6.0435 57079.5
## 2 NA NA NA
## 3 NA NA NA
## 4 NA NA NA
## 5 NA NA NA
## 6 NA NA NA14.4.6 GBSG2
14.4.7 Unemp
UnempDur contains time to re-employment of 3,343 unemployed persons.
Column censor1 indicates the re-employment event in a full-time job. Column spell indicates the length of time unemployed in number of two-week intervals.
## # A tibble: 2 x 2
## censor1 n
## <dbl> <int>
## 1 0 2270
## 2 1 1073## [1] 5 13 21 3 9+ 11+## time status
## Min. : 1.000 Min. :0.000
## 1st Qu.: 2.000 1st Qu.:0.000
## Median : 5.000 Median :0.000
## Mean : 6.248 Mean :0.321
## 3rd Qu.: 9.000 3rd Qu.:1.000
## Max. :28.000 Max. :1.000