287 lines
13 KiB
Plaintext
287 lines
13 KiB
Plaintext
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R Under development (unstable) (2023-05-10 r84417) -- "Unsuffered Consequences"
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Copyright (C) 2023 The R Foundation for Statistical Computing
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Platform: x86_64-pc-linux-gnu (64-bit)
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R is free software and comes with ABSOLUTELY NO WARRANTY.
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You are welcome to redistribute it under certain conditions.
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Type 'license()' or 'licence()' for distribution details.
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R is a collaborative project with many contributors.
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Type 'contributors()' for more information and
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'citation()' on how to cite R or R packages in publications.
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Type 'demo()' for some demos, 'help()' for on-line help, or
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'help.start()' for an HTML browser interface to help.
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Type 'q()' to quit R.
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> options(na.action=na.exclude) # preserve missings
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> options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type
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> library(survival)
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>
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> expect <- survexp(futime ~ 1,
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+ rmap = list(age=(accept.dt - birth.dt), sex=1,
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+ year=accept.dt, race='white'), jasa, cohort=F,
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+ ratetable=survexp.usr)
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>
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> survdiff(Surv(jasa$futime, jasa$fustat) ~ offset(expect))
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Call:
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survdiff(formula = Surv(jasa$futime, jasa$fustat) ~ offset(expect))
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Observed Expected Z p
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75.000 0.587 -97.119 0.000
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> # Now fit the 6 models found in Kalbfleisch and Prentice, p139
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> sfit.1 <- coxph(Surv(start, stop, event)~ (age + surgery)*transplant,
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+ jasa1, method='breslow')
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> sfit.2 <- coxph(Surv(start, stop, event)~ year*transplant,
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+ jasa1, method='breslow')
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> sfit.3 <- coxph(Surv(start, stop, event)~ (age + year)*transplant,
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+ jasa1, method='breslow')
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> sfit.4 <- coxph(Surv(start, stop, event)~ (year +surgery) *transplant,
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+ jasa1, method='breslow')
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> sfit.5 <- coxph(Surv(start, stop, event)~ (age + surgery)*transplant + year ,
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+ jasa1, method='breslow')
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> sfit.6 <- coxph(Surv(start, stop, event)~ age*transplant + surgery + year,
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+ jasa1, method='breslow')
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>
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> summary(sfit.1)
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Call:
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coxph(formula = Surv(start, stop, event) ~ (age + surgery) *
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transplant, data = jasa1, method = "breslow")
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n= 170, number of events= 75
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coef exp(coef) se(coef) z Pr(>|z|)
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age 0.01386 1.01395 0.01813 0.765 0.445
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surgery -0.54652 0.57896 0.61091 -0.895 0.371
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transplant 0.11572 1.12268 0.32729 0.354 0.724
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age:transplant 0.03473 1.03534 0.02725 1.274 0.202
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surgery:transplant -0.29037 0.74799 0.75819 -0.383 0.702
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exp(coef) exp(-coef) lower .95 upper .95
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age 1.014 0.9862 0.9786 1.051
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surgery 0.579 1.7272 0.1748 1.917
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transplant 1.123 0.8907 0.5911 2.132
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age:transplant 1.035 0.9659 0.9815 1.092
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surgery:transplant 0.748 1.3369 0.1692 3.306
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Concordance= 0.595 (se = 0.037 )
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Likelihood ratio test= 12.45 on 5 df, p=0.03
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Wald test = 11.62 on 5 df, p=0.04
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Score (logrank) test = 12.02 on 5 df, p=0.03
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> sfit.2
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Call:
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coxph(formula = Surv(start, stop, event) ~ year * transplant,
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data = jasa1, method = "breslow")
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coef exp(coef) se(coef) z p
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year -0.2652 0.7671 0.1051 -2.522 0.0117
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transplant -0.2871 0.7504 0.5137 -0.559 0.5762
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year:transplant 0.1371 1.1469 0.1409 0.973 0.3306
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Likelihood ratio test=8.61 on 3 df, p=0.03488
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n= 170, number of events= 75
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> summary(sfit.3)
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Call:
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coxph(formula = Surv(start, stop, event) ~ (age + year) * transplant,
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data = jasa1, method = "breslow")
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n= 170, number of events= 75
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coef exp(coef) se(coef) z Pr(>|z|)
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age 0.01558 1.01571 0.01734 0.899 0.36887
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year -0.27413 0.76023 0.10588 -2.589 0.00962 **
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transplant -0.59388 0.55218 0.54222 -1.095 0.27339
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age:transplant 0.03380 1.03438 0.02795 1.209 0.22653
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year:transplant 0.20228 1.22419 0.14247 1.420 0.15566
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---
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Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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exp(coef) exp(-coef) lower .95 upper .95
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age 1.0157 0.9845 0.9818 1.0508
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year 0.7602 1.3154 0.6178 0.9356
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transplant 0.5522 1.8110 0.1908 1.5981
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age:transplant 1.0344 0.9668 0.9792 1.0926
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year:transplant 1.2242 0.8169 0.9259 1.6185
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Concordance= 0.63 (se = 0.036 )
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Likelihood ratio test= 14.85 on 5 df, p=0.01
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Wald test = 13.77 on 5 df, p=0.02
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Score (logrank) test = 14.06 on 5 df, p=0.02
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> sfit.4
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Call:
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coxph(formula = Surv(start, stop, event) ~ (year + surgery) *
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transplant, data = jasa1, method = "breslow")
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coef exp(coef) se(coef) z p
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year -0.2541 0.7756 0.1077 -2.360 0.0183
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surgery -0.2365 0.7894 0.6282 -0.377 0.7065
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transplant -0.2969 0.7431 0.5054 -0.588 0.5568
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year:transplant 0.1653 1.1797 0.1416 1.167 0.2431
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surgery:transplant -0.5499 0.5770 0.7759 -0.709 0.4785
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Likelihood ratio test=12.36 on 5 df, p=0.03021
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n= 170, number of events= 75
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> sfit.5
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Call:
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coxph(formula = Surv(start, stop, event) ~ (age + surgery) *
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transplant + year, data = jasa1, method = "breslow")
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coef exp(coef) se(coef) z p
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age 0.01504 1.01516 0.01760 0.855 0.3928
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surgery -0.42025 0.65689 0.61564 -0.683 0.4948
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transplant 0.07412 1.07694 0.33113 0.224 0.8229
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year -0.13631 0.87258 0.07097 -1.921 0.0548
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age:transplant 0.02691 1.02728 0.02712 0.992 0.3210
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surgery:transplant -0.29656 0.74337 0.75800 -0.391 0.6956
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Likelihood ratio test=16.2 on 6 df, p=0.0127
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n= 170, number of events= 75
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> sfit.6
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Call:
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coxph(formula = Surv(start, stop, event) ~ age * transplant +
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surgery + year, data = jasa1, method = "breslow")
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coef exp(coef) se(coef) z p
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age 0.01527 1.01539 0.01750 0.873 0.3828
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transplant 0.04457 1.04558 0.32171 0.139 0.8898
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surgery -0.62113 0.53734 0.36786 -1.688 0.0913
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year -0.13608 0.87278 0.07090 -1.919 0.0550
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age:transplant 0.02703 1.02740 0.02714 0.996 0.3193
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Likelihood ratio test=16.06 on 5 df, p=0.006687
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n= 170, number of events= 75
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>
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> # Survival curve for an "average" subject,
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> # done once as overall, once via individual method
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> surv1 <- survfit(sfit.1, newdata=list(age=-2, surgery=0, transplant=0))
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> newdata <- data.frame(start=c(0,50,100), stop=c(50,100, max(jasa1$stop)),
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+ event=c(1,1,1), age=rep(-2,3), surgery=rep(0,3),
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+ transplant=rep(0,3), name=c("Smith", "Smith", "Smith"))
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> surv2 <- survfit(sfit.1, newdata, id=name)
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> # Have to use unclass to avoid [.survfit trying to pick curves,
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> # remove the final element "call" because it won't match, nor will newdata
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> ii <- match(c("newdata", "call"), names(surv1))
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> all.equal(unclass(surv1)[-ii],
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+ unclass(surv2)[-ii])
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[1] TRUE
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>
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>
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> # Survival curve for a subject of age 50, with prior surgery, tx at 6 months
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> # Remember that 'age' in jasa 1 was centered at 48
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> data <- data.frame(start=c(0,183), stop=c(183,3*365), event=c(1,1),
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+ age=c(2,2), surgery=c(1,1), transplant=c(0,1), id=c(1,1))
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> summary(survfit(sfit.1, data, id=id))
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Call: survfit(formula = sfit.1, newdata = data, id = id)
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time n.risk n.event survival std.err lower 95% CI upper 95% CI
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0.5 103 1 0.994 0.00722 0.980 1.000
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1.0 102 3 0.975 0.01860 0.939 1.000
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2.0 99 3 0.956 0.02914 0.900 1.000
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4.0 96 2 0.943 0.03605 0.875 1.000
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5.0 94 2 0.930 0.04286 0.849 1.000
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7.0 92 1 0.923 0.04623 0.837 1.000
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8.0 91 1 0.917 0.04959 0.824 1.000
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11.0 89 1 0.910 0.05294 0.812 1.000
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15.0 88 3 0.890 0.06278 0.775 1.000
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16.0 85 1 0.883 0.06608 0.763 1.000
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17.0 84 1 0.877 0.06928 0.751 1.000
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20.0 83 2 0.864 0.07538 0.728 1.000
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27.0 81 1 0.857 0.07849 0.716 1.000
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29.0 80 1 0.850 0.08160 0.705 1.000
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31.0 78 1 0.844 0.08473 0.693 1.000
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34.0 77 1 0.837 0.08786 0.681 1.000
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35.0 76 1 0.830 0.09098 0.669 1.000
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36.0 75 1 0.823 0.09412 0.658 1.000
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38.0 74 1 0.816 0.09727 0.646 1.000
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39.0 72 2 0.802 0.10349 0.623 1.000
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42.0 70 1 0.795 0.10664 0.611 1.000
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44.0 69 1 0.788 0.10982 0.600 1.000
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49.0 68 1 0.781 0.11300 0.588 1.000
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50.0 67 1 0.774 0.11614 0.577 1.000
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52.0 66 1 0.767 0.11925 0.565 1.000
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57.0 65 1 0.760 0.12238 0.554 1.000
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60.0 64 1 0.752 0.12552 0.542 1.000
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65.0 63 1 0.745 0.12866 0.531 1.000
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67.0 62 2 0.730 0.13494 0.508 1.000
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68.0 60 1 0.722 0.13809 0.497 1.000
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71.0 59 2 0.707 0.14420 0.474 1.000
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76.0 57 1 0.699 0.14729 0.463 1.000
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77.0 56 1 0.691 0.15043 0.451 1.000
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79.0 55 1 0.683 0.15362 0.439 1.000
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80.0 54 1 0.674 0.15680 0.428 1.000
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84.0 53 1 0.666 0.16005 0.416 1.000
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89.0 52 1 0.657 0.16326 0.404 1.000
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95.0 51 1 0.648 0.16648 0.392 1.000
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99.0 50 1 0.639 0.16972 0.380 1.000
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101.0 49 1 0.630 0.17293 0.368 1.000
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109.0 47 1 0.621 0.17611 0.356 1.000
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148.0 45 1 0.611 0.17927 0.344 1.000
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152.0 44 1 0.601 0.18236 0.332 1.000
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164.0 43 1 0.592 0.18551 0.320 1.000
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185.0 41 1 0.583 0.12737 0.380 0.894
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187.0 40 1 0.574 0.12889 0.370 0.891
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206.0 39 1 0.565 0.13036 0.359 0.888
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218.0 38 1 0.556 0.13180 0.349 0.885
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262.0 37 1 0.546 0.13320 0.339 0.881
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284.0 35 2 0.527 0.13585 0.318 0.874
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307.0 33 1 0.517 0.13707 0.308 0.869
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333.0 32 1 0.507 0.13823 0.297 0.865
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339.0 31 1 0.497 0.13930 0.287 0.861
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342.0 29 1 0.486 0.14029 0.276 0.856
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583.0 21 1 0.471 0.14187 0.261 0.850
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674.0 17 1 0.452 0.14361 0.243 0.843
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732.0 16 1 0.433 0.14506 0.225 0.835
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851.0 14 1 0.410 0.14622 0.204 0.825
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979.0 11 1 0.383 0.14698 0.180 0.813
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995.0 10 1 0.356 0.14735 0.158 0.801
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1031.0 9 1 0.330 0.14743 0.137 0.792
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>
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> # These should all give the same answer
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> # When there are offsets, the default curve is always for someone with
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> # the mean offset.
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> j.age <- jasa$age -48
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> fit1 <- coxph(Surv(futime, fustat) ~ j.age, data=jasa)
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> fit2 <- coxph(Surv(futime, fustat) ~ j.age, jasa, init=fit1$coef, iter=0)
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> fit3 <- coxph(Surv(start, stop, event) ~ age, jasa1)
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> fit4 <- coxph(Surv(start, stop, event) ~ offset(age*fit1$coef), jasa1)
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>
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> s1 <- survfit(fit1, list(j.age=fit3$means), censor=FALSE)
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> s2 <- survfit(fit2, list(j.age=fit3$means), censor=FALSE)
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> s3 <- survfit(fit3, censor=FALSE)
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> s4 <- survfit(fit4, censor=FALSE)
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>
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> all.equal(s1$surv, s2$surv)
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[1] TRUE
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> all.equal(s1$surv, s3$surv)
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[1] TRUE
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> all.equal(s1$surv, s4$surv)
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[1] TRUE
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>
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> # Still the same answer, fit multiple strata at once
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> # Strata 1 has independent coefs of strata 2, so putting in
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> # the other data should not affect it
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> ll <- nrow(jasa1)
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> ss <- rep(0:1, c(ll,ll))
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> tdata <- with(jasa1, data.frame(start=rep(start,2), stop=rep(stop,2),
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+ event=rep(event,2), ss=ss, age=rep(age,2),
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+ age2 = (rep(age,2))^2 * ss))
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> fit <- coxph(Surv(start, stop, event) ~ age*strata(ss) + age2, tdata)
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> # Above replaced these 2 lines, which kill Splus5 as of 8/98
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> # Something with data frames, I expect.
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> #fit <- coxph(Surv(rep(start,2), rep(stop,2), rep(event,2)) ~
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> # rep(age,2)*strata(ss) + I(rep(age,2)^2*ss) )
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> all.equal(fit$coef[1], fit3$coef)
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[1] TRUE
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> s5 <- survfit(fit, data.frame(age=fit3$means, age2=0, ss=0), censor=FALSE)
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> all.equal(s5$surv[1:(s5$strata[1])], s3$surv)
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[1] TRUE
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>
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>
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>
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> proc.time()
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user system elapsed
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1.011 0.101 1.104
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