Chapter 5 Competing Risks
The below code illustrates how to perform a Cox regression using a cause-specific hazard for competing risks models.
leaders$lost = factor(leaders$lost, 0:3, labels = c("In-Office", "Constitutional", "Natural", "Non-Constitutional"))
cox_nat <- coxph(Surv(years, lost == "Natural") ~ manner + start+military + age + conflict + loginc + growth + pop + land + literacy + factor(region), data = leaders)
summary(cox_nat)## Call:
## coxph(formula = Surv(years, lost == "Natural") ~ manner + start +
## military + age + conflict + loginc + growth + pop + land +
## literacy + factor(region), data = leaders)
##
## n= 438, number of events= 27
## (34 observations deleted due to missingness)
##
## coef exp(coef) se(coef) z Pr(>|z|)
## manner 3.747e-01 1.455e+00 6.633e-01 0.565 0.572
## start -5.403e-02 9.474e-01 3.386e-02 -1.596 0.111
## military -3.646e-01 6.945e-01 7.409e-01 -0.492 0.623
## age 7.386e-02 1.077e+00 1.840e-02 4.015 5.95e-05 ***
## conflict -2.609e-01 7.704e-01 4.720e-01 -0.553 0.580
## loginc 3.285e-01 1.389e+00 2.673e-01 1.229 0.219
## growth 8.817e-02 1.092e+00 8.518e-02 1.035 0.301
## pop 1.991e-03 1.002e+00 2.138e-03 0.931 0.352
## land -3.969e-05 1.000e+00 1.781e-04 -0.223 0.824
## literacy -8.796e-03 9.912e-01 1.260e-02 -0.698 0.485
## factor(region)1 -6.427e-01 5.259e-01 8.360e-01 -0.769 0.442
## factor(region)2 -7.776e-01 4.595e-01 9.031e-01 -0.861 0.389
## factor(region)3 6.591e-01 1.933e+00 7.852e-01 0.839 0.401
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## manner 1.4546 0.6875 0.39644 5.337
## start 0.9474 1.0555 0.88657 1.012
## military 0.6945 1.4400 0.16255 2.967
## age 1.0767 0.9288 1.03853 1.116
## conflict 0.7704 1.2980 0.30548 1.943
## loginc 1.3889 0.7200 0.82251 2.345
## growth 1.0922 0.9156 0.92423 1.291
## pop 1.0020 0.9980 0.99780 1.006
## land 1.0000 1.0000 0.99961 1.000
## literacy 0.9912 1.0088 0.96707 1.016
## factor(region)1 0.5259 1.9015 0.10217 2.707
## factor(region)2 0.4595 2.1763 0.07827 2.698
## factor(region)3 1.9330 0.5173 0.41484 9.007
##
## Concordance= 0.819 (se = 0.046 )
## Likelihood ratio test= 32.42 on 13 df, p=0.002
## Wald test = 29.47 on 13 df, p=0.006
## Score (logrank) test = 33.21 on 13 df, p=0.002The following code illustrates how to do a competing risk model with Fine-Gray model.
# Cumulative Incidence Functions #
cif.dat=leaders[leaders$lost!="In-Office",]
cif.tenure=cif.dat$years
cif.status=cif.dat$lost
cif.leaders=cuminc(cif.tenure,cif.status,rho=0)
ggcompetingrisks(cif.leaders)
# Cox Regression Competing Risks #
tenure=leaders$years
View(leaders)
status.leaders=leaders$lost
x=leaders[,3:12]
x$africa=ifelse(leaders$region==1,1,0)
x$asia=ifelse(leaders$region==2,1,0)
x$latin=ifelse(leaders$region==3,1,0)
gray.natural=crr(tenure,status.leaders,x,failcode="Natural")## 34 cases omitted due to missing values## Competing Risks Regression
##
## Call:
## crr(ftime = tenure, fstatus = status.leaders, cov1 = x, failcode = "Natural")
##
## coef exp(coef) se(coef) z p-value
## manner -7.32e-02 0.929 0.562617 -0.13007 0.9000
## start -8.33e-02 0.920 0.026453 -3.14757 0.0016
## military -2.51e-01 0.778 0.549101 -0.45674 0.6500
## age 4.75e-02 1.049 0.018127 2.62190 0.0087
## conflict -2.13e-03 0.998 0.440003 -0.00484 1.0000
## loginc 5.55e-01 1.741 0.261591 2.11995 0.0340
## growth 9.80e-02 1.103 0.128218 0.76408 0.4400
## pop 2.41e-03 1.002 0.002784 0.86500 0.3900
## land -8.76e-05 1.000 0.000189 -0.46445 0.6400
## literacy -6.71e-03 0.993 0.011000 -0.60956 0.5400
## africa 4.44e-01 1.559 0.710063 0.62578 0.5300
## asia -6.97e-01 0.498 0.821035 -0.84936 0.4000
## latin 1.22e-01 1.129 0.625890 0.19434 0.8500
##
## exp(coef) exp(-coef) 2.5% 97.5%
## manner 0.929 1.076 0.3085 2.800
## start 0.920 1.087 0.8736 0.969
## military 0.778 1.285 0.2653 2.283
## age 1.049 0.954 1.0121 1.087
## conflict 0.998 1.002 0.4213 2.364
## loginc 1.741 0.574 1.0427 2.907
## growth 1.103 0.907 0.8578 1.418
## pop 1.002 0.998 0.9970 1.008
## land 1.000 1.000 0.9995 1.000
## literacy 0.993 1.007 0.9721 1.015
## africa 1.559 0.641 0.3878 6.272
## asia 0.498 2.008 0.0996 2.489
## latin 1.129 0.885 0.3312 3.851
##
## Num. cases = 438 (34 cases omitted due to missing values)
## Pseudo Log-likelihood = -149
## Pseudo likelihood ratio test = 29.4 on 13 df,## 34 cases omitted due to missing values## Competing Risks Regression
##
## Call:
## crr(ftime = tenure, fstatus = status.leaders, cov1 = x, failcode = "Constitutional")
##
## coef exp(coef) se(coef) z p-value
## manner -6.20e-01 0.538 2.64e-01 -2.34926 0.0190
## start -1.79e-02 0.982 9.79e-03 -1.83105 0.0670
## military 1.22e-01 1.130 2.49e-01 0.48991 0.6200
## age 1.37e-02 1.014 8.45e-03 1.61657 0.1100
## conflict -1.67e-01 0.846 2.16e-01 -0.77554 0.4400
## loginc -1.35e-01 0.874 1.15e-01 -1.17732 0.2400
## growth 4.18e-02 1.043 3.02e-02 1.38457 0.1700
## pop 6.68e-04 1.001 8.78e-04 0.76086 0.4500
## land -2.74e-05 1.000 6.89e-05 -0.39672 0.6900
## literacy 1.88e-02 1.019 5.77e-03 3.25010 0.0012
## africa -9.43e-01 0.389 3.94e-01 -2.39044 0.0170
## asia -3.18e-03 0.997 3.69e-01 -0.00862 0.9900
## latin 8.25e-02 1.086 3.54e-01 0.23284 0.8200
##
## exp(coef) exp(-coef) 2.5% 97.5%
## manner 0.538 1.859 0.321 0.902
## start 0.982 1.018 0.964 1.001
## military 1.130 0.885 0.693 1.841
## age 1.014 0.986 0.997 1.031
## conflict 0.846 1.182 0.554 1.291
## loginc 0.874 1.145 0.697 1.094
## growth 1.043 0.959 0.983 1.106
## pop 1.001 0.999 0.999 1.002
## land 1.000 1.000 1.000 1.000
## literacy 1.019 0.981 1.007 1.031
## africa 0.389 2.568 0.180 0.844
## asia 0.997 1.003 0.484 2.053
## latin 1.086 0.921 0.542 2.174
##
## Num. cases = 438 (34 cases omitted due to missing values)
## Pseudo Log-likelihood = -814
## Pseudo likelihood ratio test = 101 on 13 df,## 34 cases omitted due to missing values## Competing Risks Regression
##
## Call:
## crr(ftime = tenure, fstatus = status.leaders, cov1 = x, failcode = "Non-Constitutional")
##
## coef exp(coef) se(coef) z p-value
## manner 7.87e-01 2.196 0.196832 3.996 6.4e-05
## start -5.61e-02 0.945 0.010553 -5.315 1.1e-07
## military -2.40e-01 0.787 0.200255 -1.199 2.3e-01
## age -1.34e-03 0.999 0.008335 -0.161 8.7e-01
## conflict 5.35e-01 1.708 0.183801 2.912 3.6e-03
## loginc -3.05e-01 0.737 0.128953 -2.363 1.8e-02
## growth -5.26e-02 0.949 0.029720 -1.769 7.7e-02
## pop -1.13e-03 0.999 0.000879 -1.284 2.0e-01
## land -2.69e-05 1.000 0.000079 -0.341 7.3e-01
## literacy -9.43e-03 0.991 0.004066 -2.320 2.0e-02
## africa -2.15e-01 0.807 0.284876 -0.753 4.5e-01
## asia -4.99e-01 0.607 0.364670 -1.369 1.7e-01
## latin 3.67e-01 1.443 0.290395 1.263 2.1e-01
##
## exp(coef) exp(-coef) 2.5% 97.5%
## manner 2.196 0.455 1.493 3.230
## start 0.945 1.058 0.926 0.965
## military 0.787 1.271 0.531 1.165
## age 0.999 1.001 0.982 1.015
## conflict 1.708 0.586 1.191 2.448
## loginc 0.737 1.356 0.573 0.949
## growth 0.949 1.054 0.895 1.006
## pop 0.999 1.001 0.997 1.001
## land 1.000 1.000 1.000 1.000
## literacy 0.991 1.009 0.983 0.999
## africa 0.807 1.239 0.462 1.410
## asia 0.607 1.648 0.297 1.240
## latin 1.443 0.693 0.817 2.550
##
## Num. cases = 438 (34 cases omitted due to missing values)
## Pseudo Log-likelihood = -855
## Pseudo likelihood ratio test = 110 on 13 df,5.1 Python code for competing risks models
In Python, you can easily use the cause-specific model (in either AFT or Cox PH models) by creating a new column with the event of interest being a “1” and censoring all other events (similar to what you did in Homework 2). However, Python is NOT able run a Fine-Gray model.