cutp: *cut p*oint for a continuous variable in a model fit with...
In survMisc: Miscellaneous Functions for Survival Data
Description
Usage
Arguments
Details
Value
References
Examples
Description
Determine the optimal cut point for a continuous variable
in a coxph or survfit model.
Usage
1
2
3
4
5
6
7
Arguments
x
A survfit or coxph object
defCont
definition of a continuous variable.
If the variable has > defCont unique values, it
is treated as continuous and a cut point is determined.
...
Additional arguments (not implemented).
Details
For a cut point mu, of a predictor K,
the variable is split
into two groups, those >= mu and
those < mu.
The score (or log-rank) statistic, sc,
is calculated for each unique element
k in K and uses
-
e1[i] the number of events
-
n1[i] the number at risk
in those above the cut point, respectively.
The basic statistic is
sc[k] = sum (e1[i] - n1[i] * e[i] / n[i])
The sum is taken across times with observed events, to D,
the largest of these.
It is normalized (standardized), in the case of censoring,
by finding s^2 which is:
s^2 = (1 / (D - 1)) *
sum[i:D](1 - sum[j:i](1 / (D - j + 1))^2 )
The test statistic is then
Q = max(abs(sc[k])) / s * sqrt((D - 1))
Under the null hypothesis that the chosen cut point
does not predict survival,
the distribution of Q has a limiting distibution which
is the supremum of the
absolute value of a Brownian bridge:
p= P(Q >= q) = 2 sum[i:Inf](-1)^(i + 1) * e^(-2 * i^2 *q^2)
Value
A list of data.tables.
There is one list element per continuous variable.
Each has a column with possible values of the cut point
(i.e. unique values of the variable), and the
additional columns:
U
The score (log-rank) test for a model with the variable 'cut'
into into those >= the cutpoint and those below.
Q
The test statistic.
p
The p-value.
The tables are ordered by p-value, lowest first.
References
Contal C, O'Quigley J, 1999.
An application of changepoint methods in studying the
effect of age on survival in breast cancer.
Computational Statistics & Data Analysis 30(3):253–70.
ScienceDirect (paywall)
Mandrekar JN, Mandrekar, SJ, Cha SS, 2003.
Cutpoint Determination Methods in Survival Analysis using SAS.
Proceedings of the 28th SAS Users Group International Conference (SUGI). Paper 261-28.
SAS (free)
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
## Mandrekar et al. above
data("bmt", package="KMsurv")
b1 <- bmt[bmt$group==1, ] # ALL patients
c1 <- coxph(Surv(t2, d3) ~ z1, data=b1) # z1=age
c1 <- cutp(c1)$z1
data.table::setorder(c1, "z1")
## [] below is used to print data.table to console
c1[]
## Not run:
## compare to output from survival::coxph
matrix(
unlist(
lapply(26:30,
function(i) c(i, summary(coxph(Surv(t2, d3) ~ z1 >= i, data=b1))$sctest))),
ncol=5,
dimnames=list(c("age", "score_test", "df", "p")))
cutp(coxph(Surv(t2, d3) ~ z1, data=bmt[bmt$group==2, ]))$z1[]
cutp(coxph(Surv(t2, d3) ~ z1, data=bmt[bmt$group==3, ]))[[1]][]
## K&M. Example 8.3, pg 273-274.
data("kidtran", package="KMsurv")
k1 <- kidtran
## patients who are male and black
k2 <- k1[k1$gender==1 & k1$race==2, ]
c2 <- coxph(Surv(time, delta) ~ age, data=k2)
print(cutp(c2))
## check significance of computed value
summary(coxph(Surv(time, delta) ~ age >= 58, data=k2))
k3 <- k1[k1$gender==2 & k1$race==2, ]
c3 <- coxph(Surv(time, delta) ~ age, data=k3)
print(cutp(c3))
## doesn't apply to binary variables e.g. gender
print(cutp(coxph(Surv(time, delta) ~ age + gender, data=k1)))
## End(Not run)
Example output
Loading required package: survival
z1 U Q p
1: 15 0.0000000 0.00000000 1.00000000
2: 17 0.7502634 0.16683217 1.00000000
3: 18 0.4232100 0.09410701 1.00000000
4: 19 0.7427106 0.16515268 1.00000000
5: 20 0.2724980 0.06059396 1.00000000
6: 21 0.2736081 0.06084081 1.00000000
7: 22 0.7416005 0.16490584 1.00000000
8: 23 2.1637208 0.48113533 0.97474717
9: 24 1.2170637 0.27063210 0.99999955
10: 26 3.2474808 0.72212539 0.67415725
11: 27 4.7286924 1.05149469 0.21883201
12: 28 5.6821864 1.26351820 0.08209497
13: 29 4.7785156 1.06257363 0.20885364
14: 30 3.4222249 0.76098233 0.60871287
15: 32 2.5916317 0.57628765 0.89403817
16: 36 3.6068403 0.80203429 0.54083616
17: 37 2.8074971 0.62428851 0.83058351
18: 39 2.1070787 0.46854011 0.98060360
19: 40 1.6013513 0.35608416 0.99958127
20: 42 0.9736842 0.21651309 1.00000000
[,1] [,2] [,3] [,4] [,5]
age 26.0000000 27.00000000 28.000000000 29.000000000 30.00000000
score_test 1.9195957 4.91019534 9.453363533 8.646732729 5.27806670
df 1.0000000 1.00000000 1.000000000 1.000000000 1.00000000
p 0.1659012 0.02669862 0.002107622 0.003276484 0.02159571
z1 U Q p
1: 28 4.5270838 0.98359005 0.2880073
2: 30 3.6540586 0.79390968 0.5540826
3: 29 3.5720297 0.77608743 0.5834910
4: 27 3.4147519 0.74191601 0.6407884
5: 26 3.3621348 0.73048399 0.6600702
6: 23 3.2577394 0.70780224 0.6982105
7: 32 2.9489805 0.64071882 0.8062345
8: 21 2.7450586 0.59641315 0.8689962
9: 22 2.6623427 0.57844164 0.8914769
10: 33 2.6009944 0.56511262 0.9068426
11: 25 2.5662010 0.55755312 0.9150305
12: 31 2.1869171 0.47514690 0.9776622
13: 34 1.5691590 0.34092790 0.9998194
14: 17 1.4697921 0.31933865 0.9999563
15: 43 1.4453431 0.31402668 0.9999706
16: 19 1.3875985 0.30148062 0.9999894
17: 35 1.1830743 0.25704408 0.9999999
18: 50 1.1477159 0.24936184 1.0000000
19: 37 1.1170831 0.24270631 1.0000000
20: 18 0.8706633 0.18916719 1.0000000
21: 16 0.7077287 0.15376673 1.0000000
22: 14 0.5953967 0.12936060 1.0000000
23: 46 0.5523192 0.12000123 1.0000000
24: 45 0.5415682 0.11766539 1.0000000
25: 15 0.1123319 0.02440612 1.0000000
26: 13 0.0000000 0.00000000 1.0000000
z1 U Q p
z1 U Q p
1: 23 3.49406081 0.639185853 0.8085528
2: 24 3.48042241 0.636690912 0.8123064
3: 22 3.14860843 0.575990538 0.8943891
4: 18 2.96035766 0.541552891 0.9310460
5: 27 2.60302171 0.476183657 0.9771747
6: 15 2.47567206 0.452886955 0.9864839
7: 25 2.10593236 0.385248638 0.9984030
8: 17 2.10118201 0.384379635 0.9984585
9: 20 1.96745839 0.359916910 0.9994909
10: 47 1.95138095 0.356975784 0.9995615
11: 14 1.87505233 0.343012611 0.9997958
12: 35 1.79422679 0.328226795 0.9999188
13: 29 1.69326776 0.309757860 0.9999789
14: 19 1.58586761 0.290110617 0.9999963
15: 11 1.57860647 0.288782302 0.9999967
16: 33 1.33417447 0.244067145 1.0000000
17: 50 1.32930492 0.243176335 1.0000000
18: 45 1.14416212 0.209307245 1.0000000
19: 8 0.88417564 0.161746631 1.0000000
20: 37 0.78709903 0.143987926 1.0000000
21: 40 0.75155349 0.137485403 1.0000000
22: 32 0.74325904 0.135968059 1.0000000
23: 41 0.62293656 0.113956871 1.0000000
24: 48 0.57689090 0.105533510 1.0000000
25: 39 0.40983241 0.074972673 1.0000000
26: 36 0.34440367 0.063003470 1.0000000
27: 31 0.31877771 0.058315586 1.0000000
28: 44 0.31062750 0.056824628 1.0000000
29: 43 0.15725524 0.028767481 1.0000000
30: 52 0.04518513 0.008265939 1.0000000
31: 7 0.00000000 0.000000000 1.0000000
z1 U Q p
$age
age U Q p
1: 58 2.6324038 0.80293399 0.5393762
2: 57 2.4538287 0.74846514 0.6297514
3: 64 2.4501868 0.74735429 0.6316225
4: 63 2.4172171 0.73729790 0.6485770
5: 39 2.4102361 0.73516853 0.6521689
6: 62 2.3171861 0.70678650 0.6999099
7: 55 2.2687723 0.69201937 0.7244766
8: 38 2.1567961 0.65786446 0.7797318
9: 60 2.1129700 0.64449664 0.8004834
10: 37 2.0567651 0.62735307 0.8261290
11: 36 1.8910105 0.57679472 0.8934379
12: 52 1.8893288 0.57628175 0.8940451
13: 59 1.8273697 0.55738302 0.9152103
14: 40 1.8219100 0.55571772 0.9169593
15: 56 1.8202578 0.55521376 0.9174847
16: 30 1.8104842 0.55223264 0.9205569
17: 54 1.7082776 0.52105764 0.9488589
18: 44 1.6557991 0.50505070 0.9606225
19: 65 1.6357561 0.49893720 0.9646209
20: 43 1.5557681 0.47453930 0.9779446
21: 53 1.3875202 0.42322046 0.9939575
22: 42 1.3826608 0.42173825 0.9942233
23: 33 1.3778787 0.42027962 0.9944762
24: 51 1.3712143 0.41824682 0.9948146
25: 47 1.1385707 0.34728603 0.9997394
26: 32 1.0843323 0.33074228 0.9999041
27: 23 1.0532184 0.32125195 0.9999498
28: 41 1.0426363 0.31802420 0.9999603
29: 50 1.0311897 0.31453277 0.9999694
30: 31 0.9638931 0.29400600 0.9999946
31: 46 0.8799251 0.26839415 0.9999997
32: 28 0.8511069 0.25960403 0.9999999
33: 66 0.8418331 0.25677534 0.9999999
34: 45 0.6666687 0.20334682 1.0000000
35: 27 0.6450299 0.19674658 1.0000000
36: 26 0.4719227 0.14394553 1.0000000
37: 22 0.4400556 0.13422545 1.0000000
38: 25 0.4266073 0.13012347 1.0000000
39: 49 0.3511406 0.10710467 1.0000000
40: 21 0.3400245 0.10371405 1.0000000
41: 24 0.1532494 0.04674404 1.0000000
42: 48 0.1510785 0.04608187 1.0000000
43: 7 0.0000000 0.00000000 1.0000000
age U Q p
Call:
coxph(formula = Surv(time, delta) ~ age >= 58, data = k2)
n= 92, number of events= 14
coef exp(coef) se(coef) z Pr(>|z|)
age >= 58TRUE 1.4279 4.1700 0.6386 2.236 0.0253 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
age >= 58TRUE 4.17 0.2398 1.193 14.58
Concordance= 0.607 (se = 0.068 )
Rsquare= 0.045 (max possible= 0.697 )
Likelihood ratio test= 4.21 on 1 df, p=0.04
Wald test = 5 on 1 df, p=0.03
Score (logrank) test = 5.87 on 1 df, p=0.02
$age
age U Q p
1: 48 3.0965494 0.94450736 0.3342762
2: 46 2.9554945 0.90148289 0.3906865
3: 44 2.9089872 0.88729727 0.4105065
4: 45 2.4986631 0.76214050 0.6067715
5: 59 2.1335713 0.65078043 0.7908033
6: 57 1.9887986 0.60662196 0.8553949
7: 54 1.9678086 0.60021962 0.8639918
8: 43 1.9062716 0.58144964 0.8878512
9: 23 1.7606838 0.53704256 0.9352296
10: 50 1.6157334 0.49282988 0.9683466
11: 40 1.5754543 0.48054397 0.9750458
12: 42 1.4885296 0.45403026 0.9861038
13: 61 1.3664319 0.41678810 0.9950475
14: 56 1.3543248 0.41309521 0.9956016
15: 21 1.3038525 0.39770017 0.9974177
16: 49 1.2498111 0.38121652 0.9986476
17: 39 1.2334880 0.37623765 0.9989071
18: 38 1.1194601 0.34145694 0.9998136
19: 25 1.0496831 0.32017360 0.9999535
20: 37 0.9784052 0.29843247 0.9999919
21: 66 0.9652148 0.29440914 0.9999944
22: 36 0.8643773 0.26365176 0.9999998
23: 52 0.7901217 0.24100236 1.0000000
24: 35 0.7503494 0.22887105 1.0000000
25: 64 0.7323542 0.22338216 1.0000000
26: 33 0.6363215 0.19409034 1.0000000
27: 41 0.6284213 0.19168064 1.0000000
28: 31 0.5222936 0.15930964 1.0000000
29: 27 0.4304879 0.13130713 1.0000000
30: 20 0.2473325 0.07544120 1.0000000
31: 55 0.2105542 0.06422311 1.0000000
32: 13 0.0000000 0.00000000 1.0000000
age U Q p
$age
age U Q p
1: 40 40.40605202 3.484347686 5.698629e-11
2: 41 39.54197790 3.409835713 1.592076e-10
3: 39 38.67195782 3.334811000 4.380090e-10
4: 42 37.87058656 3.265706101 1.090613e-09
5: 43 37.10139207 3.199375914 2.571272e-09
6: 44 36.78899819 3.172437154 3.624434e-09
7: 47 35.80605086 3.087674351 1.047454e-08
8: 37 35.49550181 3.060894678 1.455975e-08
9: 46 35.07167226 3.024346452 2.271601e-08
10: 38 34.42598779 2.968666942 4.427615e-08
11: 48 34.41154407 2.967421412 4.493573e-08
12: 45 34.32611283 2.960054393 4.903670e-08
13: 36 33.66162344 2.902753272 9.601072e-08
14: 35 31.63925009 2.728357320 6.844021e-07
15: 34 31.45310148 2.712305110 8.150219e-07
16: 49 29.73992576 2.564572293 3.875194e-06
17: 33 29.03407432 2.503704386 7.182061e-06
18: 50 27.32166442 2.356037609 3.016949e-05
19: 54 27.06228888 2.333670797 3.721154e-05
20: 52 26.40574646 2.277054970 6.272117e-05
21: 32 25.76574596 2.221865607 1.030572e-04
22: 51 25.63836525 2.210881147 1.135981e-04
23: 53 24.37173644 2.101655550 2.914142e-04
24: 55 24.10930856 2.079025524 3.521170e-04
25: 31 22.97605279 1.981301126 7.786405e-04
26: 57 21.57222515 1.860244419 1.973649e-03
27: 56 21.41141659 1.846377365 2.187335e-03
28: 30 21.16090486 1.824774908 2.563300e-03
29: 29 19.85958435 1.712557731 5.670030e-03
30: 60 17.85326132 1.539545851 1.747024e-02
31: 58 17.38936899 1.499542880 2.227897e-02
32: 59 17.33350331 1.494725397 2.293107e-02
33: 28 16.49111184 1.422083191 3.503179e-02
34: 27 16.01111106 1.380691134 4.418015e-02
35: 62 14.04795046 1.211401293 1.062470e-01
36: 26 13.99498896 1.206834248 1.086188e-01
37: 61 13.97097529 1.204763470 1.097085e-01
38: 25 13.18577001 1.137052618 1.506106e-01
39: 64 12.81369996 1.104967785 1.738749e-01
40: 24 12.61622656 1.087939000 1.873270e-01
41: 63 12.47504385 1.075764347 1.974330e-01
42: 23 10.82315045 0.933316109 3.484025e-01
43: 65 10.22397437 0.881647170 4.185632e-01
44: 22 8.46275060 0.729771012 6.612726e-01
45: 66 8.22319308 0.709113174 6.960158e-01
46: 21 6.87680316 0.593009512 8.734014e-01
47: 18 4.88309424 0.421085388 9.943376e-01
48: 20 4.64660947 0.400692524 9.971215e-01
49: 19 4.44718677 0.383495644 9.985133e-01
50: 17 4.01016523 0.345809829 9.997602e-01
51: 67 3.96429379 0.341854183 9.998092e-01
52: 16 3.68785050 0.318015562 9.999603e-01
53: 14 3.33450631 0.287545523 9.999971e-01
54: 13 2.97522755 0.256563726 9.999999e-01
55: 68 2.23387467 0.192634411 1.000000e+00
56: 12 2.15499415 0.185832283 1.000000e+00
57: 11 1.79204023 0.154533564 1.000000e+00
58: 8 1.53346552 0.132235810 1.000000e+00
59: 7 1.23679181 0.106652654 1.000000e+00
60: 6 0.91447708 0.078858387 1.000000e+00
61: 70 0.73710839 0.063563298 1.000000e+00
62: 5 0.71007700 0.061232291 1.000000e+00
63: 3 0.53351020 0.046006352 1.000000e+00
64: 2 0.24714577 0.021312199 1.000000e+00
65: 71 0.15880390 0.013694186 1.000000e+00
66: 75 0.06901279 0.005951202 1.000000e+00
67: 1 0.00000000 0.000000000 1.000000e+00
age U Q p
$gender
[1] NaN
survMisc documentation built on May 2, 2019, 5:14 p.m.
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Description Usage Arguments Details Value References Examples
Description
Determine the optimal cut point for a continuous variable
in a coxph or survfit model.
Usage
1 2 3 4 5 6 7 |
Arguments
x |
A |
defCont |
definition of a continuous variable.
|
... |
Additional arguments (not implemented). |
Details
For a cut point mu, of a predictor K,
the variable is split
into two groups, those >= mu and
those < mu.
The score (or log-rank) statistic, sc,
is calculated for each unique element
k in K and uses
-
e1[i] the number of events
-
n1[i] the number at risk
in those above the cut point, respectively.
The basic statistic is
sc[k] = sum (e1[i] - n1[i] * e[i] / n[i])
The sum is taken across times with observed events, to D,
the largest of these.
It is normalized (standardized), in the case of censoring,
by finding s^2 which is:
s^2 = (1 / (D - 1)) * sum[i:D](1 - sum[j:i](1 / (D - j + 1))^2 )
The test statistic is then
Q = max(abs(sc[k])) / s * sqrt((D - 1))
Under the null hypothesis that the chosen cut point does not predict survival, the distribution of Q has a limiting distibution which is the supremum of the absolute value of a Brownian bridge:
p= P(Q >= q) = 2 sum[i:Inf](-1)^(i + 1) * e^(-2 * i^2 *q^2)
Value
A list of data.tables.
There is one list element per continuous variable.
Each has a column with possible values of the cut point
(i.e. unique values of the variable), and the
additional columns:
U |
The score (log-rank) test for a model with the variable 'cut' into into those >= the cutpoint and those below. |
Q |
The test statistic. |
p |
The p-value. |
The tables are ordered by p-value, lowest first.
References
Contal C, O'Quigley J, 1999. An application of changepoint methods in studying the effect of age on survival in breast cancer. Computational Statistics & Data Analysis 30(3):253–70. ScienceDirect (paywall)
Mandrekar JN, Mandrekar, SJ, Cha SS, 2003. Cutpoint Determination Methods in Survival Analysis using SAS. Proceedings of the 28th SAS Users Group International Conference (SUGI). Paper 261-28. SAS (free)
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | ## Mandrekar et al. above
data("bmt", package="KMsurv")
b1 <- bmt[bmt$group==1, ] # ALL patients
c1 <- coxph(Surv(t2, d3) ~ z1, data=b1) # z1=age
c1 <- cutp(c1)$z1
data.table::setorder(c1, "z1")
## [] below is used to print data.table to console
c1[]
## Not run:
## compare to output from survival::coxph
matrix(
unlist(
lapply(26:30,
function(i) c(i, summary(coxph(Surv(t2, d3) ~ z1 >= i, data=b1))$sctest))),
ncol=5,
dimnames=list(c("age", "score_test", "df", "p")))
cutp(coxph(Surv(t2, d3) ~ z1, data=bmt[bmt$group==2, ]))$z1[]
cutp(coxph(Surv(t2, d3) ~ z1, data=bmt[bmt$group==3, ]))[[1]][]
## K&M. Example 8.3, pg 273-274.
data("kidtran", package="KMsurv")
k1 <- kidtran
## patients who are male and black
k2 <- k1[k1$gender==1 & k1$race==2, ]
c2 <- coxph(Surv(time, delta) ~ age, data=k2)
print(cutp(c2))
## check significance of computed value
summary(coxph(Surv(time, delta) ~ age >= 58, data=k2))
k3 <- k1[k1$gender==2 & k1$race==2, ]
c3 <- coxph(Surv(time, delta) ~ age, data=k3)
print(cutp(c3))
## doesn't apply to binary variables e.g. gender
print(cutp(coxph(Surv(time, delta) ~ age + gender, data=k1)))
## End(Not run)
|
Example output
Loading required package: survival
z1 U Q p
1: 15 0.0000000 0.00000000 1.00000000
2: 17 0.7502634 0.16683217 1.00000000
3: 18 0.4232100 0.09410701 1.00000000
4: 19 0.7427106 0.16515268 1.00000000
5: 20 0.2724980 0.06059396 1.00000000
6: 21 0.2736081 0.06084081 1.00000000
7: 22 0.7416005 0.16490584 1.00000000
8: 23 2.1637208 0.48113533 0.97474717
9: 24 1.2170637 0.27063210 0.99999955
10: 26 3.2474808 0.72212539 0.67415725
11: 27 4.7286924 1.05149469 0.21883201
12: 28 5.6821864 1.26351820 0.08209497
13: 29 4.7785156 1.06257363 0.20885364
14: 30 3.4222249 0.76098233 0.60871287
15: 32 2.5916317 0.57628765 0.89403817
16: 36 3.6068403 0.80203429 0.54083616
17: 37 2.8074971 0.62428851 0.83058351
18: 39 2.1070787 0.46854011 0.98060360
19: 40 1.6013513 0.35608416 0.99958127
20: 42 0.9736842 0.21651309 1.00000000
[,1] [,2] [,3] [,4] [,5]
age 26.0000000 27.00000000 28.000000000 29.000000000 30.00000000
score_test 1.9195957 4.91019534 9.453363533 8.646732729 5.27806670
df 1.0000000 1.00000000 1.000000000 1.000000000 1.00000000
p 0.1659012 0.02669862 0.002107622 0.003276484 0.02159571
z1 U Q p
1: 28 4.5270838 0.98359005 0.2880073
2: 30 3.6540586 0.79390968 0.5540826
3: 29 3.5720297 0.77608743 0.5834910
4: 27 3.4147519 0.74191601 0.6407884
5: 26 3.3621348 0.73048399 0.6600702
6: 23 3.2577394 0.70780224 0.6982105
7: 32 2.9489805 0.64071882 0.8062345
8: 21 2.7450586 0.59641315 0.8689962
9: 22 2.6623427 0.57844164 0.8914769
10: 33 2.6009944 0.56511262 0.9068426
11: 25 2.5662010 0.55755312 0.9150305
12: 31 2.1869171 0.47514690 0.9776622
13: 34 1.5691590 0.34092790 0.9998194
14: 17 1.4697921 0.31933865 0.9999563
15: 43 1.4453431 0.31402668 0.9999706
16: 19 1.3875985 0.30148062 0.9999894
17: 35 1.1830743 0.25704408 0.9999999
18: 50 1.1477159 0.24936184 1.0000000
19: 37 1.1170831 0.24270631 1.0000000
20: 18 0.8706633 0.18916719 1.0000000
21: 16 0.7077287 0.15376673 1.0000000
22: 14 0.5953967 0.12936060 1.0000000
23: 46 0.5523192 0.12000123 1.0000000
24: 45 0.5415682 0.11766539 1.0000000
25: 15 0.1123319 0.02440612 1.0000000
26: 13 0.0000000 0.00000000 1.0000000
z1 U Q p
z1 U Q p
1: 23 3.49406081 0.639185853 0.8085528
2: 24 3.48042241 0.636690912 0.8123064
3: 22 3.14860843 0.575990538 0.8943891
4: 18 2.96035766 0.541552891 0.9310460
5: 27 2.60302171 0.476183657 0.9771747
6: 15 2.47567206 0.452886955 0.9864839
7: 25 2.10593236 0.385248638 0.9984030
8: 17 2.10118201 0.384379635 0.9984585
9: 20 1.96745839 0.359916910 0.9994909
10: 47 1.95138095 0.356975784 0.9995615
11: 14 1.87505233 0.343012611 0.9997958
12: 35 1.79422679 0.328226795 0.9999188
13: 29 1.69326776 0.309757860 0.9999789
14: 19 1.58586761 0.290110617 0.9999963
15: 11 1.57860647 0.288782302 0.9999967
16: 33 1.33417447 0.244067145 1.0000000
17: 50 1.32930492 0.243176335 1.0000000
18: 45 1.14416212 0.209307245 1.0000000
19: 8 0.88417564 0.161746631 1.0000000
20: 37 0.78709903 0.143987926 1.0000000
21: 40 0.75155349 0.137485403 1.0000000
22: 32 0.74325904 0.135968059 1.0000000
23: 41 0.62293656 0.113956871 1.0000000
24: 48 0.57689090 0.105533510 1.0000000
25: 39 0.40983241 0.074972673 1.0000000
26: 36 0.34440367 0.063003470 1.0000000
27: 31 0.31877771 0.058315586 1.0000000
28: 44 0.31062750 0.056824628 1.0000000
29: 43 0.15725524 0.028767481 1.0000000
30: 52 0.04518513 0.008265939 1.0000000
31: 7 0.00000000 0.000000000 1.0000000
z1 U Q p
$age
age U Q p
1: 58 2.6324038 0.80293399 0.5393762
2: 57 2.4538287 0.74846514 0.6297514
3: 64 2.4501868 0.74735429 0.6316225
4: 63 2.4172171 0.73729790 0.6485770
5: 39 2.4102361 0.73516853 0.6521689
6: 62 2.3171861 0.70678650 0.6999099
7: 55 2.2687723 0.69201937 0.7244766
8: 38 2.1567961 0.65786446 0.7797318
9: 60 2.1129700 0.64449664 0.8004834
10: 37 2.0567651 0.62735307 0.8261290
11: 36 1.8910105 0.57679472 0.8934379
12: 52 1.8893288 0.57628175 0.8940451
13: 59 1.8273697 0.55738302 0.9152103
14: 40 1.8219100 0.55571772 0.9169593
15: 56 1.8202578 0.55521376 0.9174847
16: 30 1.8104842 0.55223264 0.9205569
17: 54 1.7082776 0.52105764 0.9488589
18: 44 1.6557991 0.50505070 0.9606225
19: 65 1.6357561 0.49893720 0.9646209
20: 43 1.5557681 0.47453930 0.9779446
21: 53 1.3875202 0.42322046 0.9939575
22: 42 1.3826608 0.42173825 0.9942233
23: 33 1.3778787 0.42027962 0.9944762
24: 51 1.3712143 0.41824682 0.9948146
25: 47 1.1385707 0.34728603 0.9997394
26: 32 1.0843323 0.33074228 0.9999041
27: 23 1.0532184 0.32125195 0.9999498
28: 41 1.0426363 0.31802420 0.9999603
29: 50 1.0311897 0.31453277 0.9999694
30: 31 0.9638931 0.29400600 0.9999946
31: 46 0.8799251 0.26839415 0.9999997
32: 28 0.8511069 0.25960403 0.9999999
33: 66 0.8418331 0.25677534 0.9999999
34: 45 0.6666687 0.20334682 1.0000000
35: 27 0.6450299 0.19674658 1.0000000
36: 26 0.4719227 0.14394553 1.0000000
37: 22 0.4400556 0.13422545 1.0000000
38: 25 0.4266073 0.13012347 1.0000000
39: 49 0.3511406 0.10710467 1.0000000
40: 21 0.3400245 0.10371405 1.0000000
41: 24 0.1532494 0.04674404 1.0000000
42: 48 0.1510785 0.04608187 1.0000000
43: 7 0.0000000 0.00000000 1.0000000
age U Q p
Call:
coxph(formula = Surv(time, delta) ~ age >= 58, data = k2)
n= 92, number of events= 14
coef exp(coef) se(coef) z Pr(>|z|)
age >= 58TRUE 1.4279 4.1700 0.6386 2.236 0.0253 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
age >= 58TRUE 4.17 0.2398 1.193 14.58
Concordance= 0.607 (se = 0.068 )
Rsquare= 0.045 (max possible= 0.697 )
Likelihood ratio test= 4.21 on 1 df, p=0.04
Wald test = 5 on 1 df, p=0.03
Score (logrank) test = 5.87 on 1 df, p=0.02
$age
age U Q p
1: 48 3.0965494 0.94450736 0.3342762
2: 46 2.9554945 0.90148289 0.3906865
3: 44 2.9089872 0.88729727 0.4105065
4: 45 2.4986631 0.76214050 0.6067715
5: 59 2.1335713 0.65078043 0.7908033
6: 57 1.9887986 0.60662196 0.8553949
7: 54 1.9678086 0.60021962 0.8639918
8: 43 1.9062716 0.58144964 0.8878512
9: 23 1.7606838 0.53704256 0.9352296
10: 50 1.6157334 0.49282988 0.9683466
11: 40 1.5754543 0.48054397 0.9750458
12: 42 1.4885296 0.45403026 0.9861038
13: 61 1.3664319 0.41678810 0.9950475
14: 56 1.3543248 0.41309521 0.9956016
15: 21 1.3038525 0.39770017 0.9974177
16: 49 1.2498111 0.38121652 0.9986476
17: 39 1.2334880 0.37623765 0.9989071
18: 38 1.1194601 0.34145694 0.9998136
19: 25 1.0496831 0.32017360 0.9999535
20: 37 0.9784052 0.29843247 0.9999919
21: 66 0.9652148 0.29440914 0.9999944
22: 36 0.8643773 0.26365176 0.9999998
23: 52 0.7901217 0.24100236 1.0000000
24: 35 0.7503494 0.22887105 1.0000000
25: 64 0.7323542 0.22338216 1.0000000
26: 33 0.6363215 0.19409034 1.0000000
27: 41 0.6284213 0.19168064 1.0000000
28: 31 0.5222936 0.15930964 1.0000000
29: 27 0.4304879 0.13130713 1.0000000
30: 20 0.2473325 0.07544120 1.0000000
31: 55 0.2105542 0.06422311 1.0000000
32: 13 0.0000000 0.00000000 1.0000000
age U Q p
$age
age U Q p
1: 40 40.40605202 3.484347686 5.698629e-11
2: 41 39.54197790 3.409835713 1.592076e-10
3: 39 38.67195782 3.334811000 4.380090e-10
4: 42 37.87058656 3.265706101 1.090613e-09
5: 43 37.10139207 3.199375914 2.571272e-09
6: 44 36.78899819 3.172437154 3.624434e-09
7: 47 35.80605086 3.087674351 1.047454e-08
8: 37 35.49550181 3.060894678 1.455975e-08
9: 46 35.07167226 3.024346452 2.271601e-08
10: 38 34.42598779 2.968666942 4.427615e-08
11: 48 34.41154407 2.967421412 4.493573e-08
12: 45 34.32611283 2.960054393 4.903670e-08
13: 36 33.66162344 2.902753272 9.601072e-08
14: 35 31.63925009 2.728357320 6.844021e-07
15: 34 31.45310148 2.712305110 8.150219e-07
16: 49 29.73992576 2.564572293 3.875194e-06
17: 33 29.03407432 2.503704386 7.182061e-06
18: 50 27.32166442 2.356037609 3.016949e-05
19: 54 27.06228888 2.333670797 3.721154e-05
20: 52 26.40574646 2.277054970 6.272117e-05
21: 32 25.76574596 2.221865607 1.030572e-04
22: 51 25.63836525 2.210881147 1.135981e-04
23: 53 24.37173644 2.101655550 2.914142e-04
24: 55 24.10930856 2.079025524 3.521170e-04
25: 31 22.97605279 1.981301126 7.786405e-04
26: 57 21.57222515 1.860244419 1.973649e-03
27: 56 21.41141659 1.846377365 2.187335e-03
28: 30 21.16090486 1.824774908 2.563300e-03
29: 29 19.85958435 1.712557731 5.670030e-03
30: 60 17.85326132 1.539545851 1.747024e-02
31: 58 17.38936899 1.499542880 2.227897e-02
32: 59 17.33350331 1.494725397 2.293107e-02
33: 28 16.49111184 1.422083191 3.503179e-02
34: 27 16.01111106 1.380691134 4.418015e-02
35: 62 14.04795046 1.211401293 1.062470e-01
36: 26 13.99498896 1.206834248 1.086188e-01
37: 61 13.97097529 1.204763470 1.097085e-01
38: 25 13.18577001 1.137052618 1.506106e-01
39: 64 12.81369996 1.104967785 1.738749e-01
40: 24 12.61622656 1.087939000 1.873270e-01
41: 63 12.47504385 1.075764347 1.974330e-01
42: 23 10.82315045 0.933316109 3.484025e-01
43: 65 10.22397437 0.881647170 4.185632e-01
44: 22 8.46275060 0.729771012 6.612726e-01
45: 66 8.22319308 0.709113174 6.960158e-01
46: 21 6.87680316 0.593009512 8.734014e-01
47: 18 4.88309424 0.421085388 9.943376e-01
48: 20 4.64660947 0.400692524 9.971215e-01
49: 19 4.44718677 0.383495644 9.985133e-01
50: 17 4.01016523 0.345809829 9.997602e-01
51: 67 3.96429379 0.341854183 9.998092e-01
52: 16 3.68785050 0.318015562 9.999603e-01
53: 14 3.33450631 0.287545523 9.999971e-01
54: 13 2.97522755 0.256563726 9.999999e-01
55: 68 2.23387467 0.192634411 1.000000e+00
56: 12 2.15499415 0.185832283 1.000000e+00
57: 11 1.79204023 0.154533564 1.000000e+00
58: 8 1.53346552 0.132235810 1.000000e+00
59: 7 1.23679181 0.106652654 1.000000e+00
60: 6 0.91447708 0.078858387 1.000000e+00
61: 70 0.73710839 0.063563298 1.000000e+00
62: 5 0.71007700 0.061232291 1.000000e+00
63: 3 0.53351020 0.046006352 1.000000e+00
64: 2 0.24714577 0.021312199 1.000000e+00
65: 71 0.15880390 0.013694186 1.000000e+00
66: 75 0.06901279 0.005951202 1.000000e+00
67: 1 0.00000000 0.000000000 1.000000e+00
age U Q p
$gender
[1] NaN
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