#CHAPTER FOUR ##PRESENTATION OF RESULTS Descriptive Statistics
load(file="heartdata.rda")
library(survival)
summary(heartdata)## id age anaemia creatinine.phosphokinase
## Min. : 1.0 Min. :40.00 negative:170 Min. : 23.0
## 1st Qu.: 75.5 1st Qu.:51.00 positive:129 1st Qu.: 116.5
## Median :150.0 Median :60.00 Median : 250.0
## Mean :150.0 Mean :60.83 Mean : 581.8
## 3rd Qu.:224.5 3rd Qu.:70.00 3rd Qu.: 582.0
## Max. :299.0 Max. :95.00 Max. :7861.0
## diabetes ejection.fraction High.blood.pressure platelets
## negative:174 Min. :14.00 negative:194 Min. : 25100
## positive:125 1st Qu.:30.00 positive:105 1st Qu.:212500
## Median :38.00 Median :262000
## Mean :38.08 Mean :263358
## 3rd Qu.:45.00 3rd Qu.:303500
## Max. :80.00 Max. :850000
## serum.creatinine serum.sodium sex smoking time
## Min. :0.500 Min. :113.0 female:105 non smoker:203 Min. : 4.0
## 1st Qu.:0.900 1st Qu.:134.0 male :194 smoker : 96 1st Qu.: 73.0
## Median :1.100 Median :137.0 Median :115.0
## Mean :1.394 Mean :136.6 Mean :130.3
## 3rd Qu.:1.400 3rd Qu.:140.0 3rd Qu.:203.0
## Max. :9.400 Max. :148.0 Max. :285.0
## death.event age.range
## survive:203 adults:155
## died : 96 aging : 85
## aged : 52
## NA's : 7
##
## Inferential Statistics
res.aov <- aov(time ~ smoking, data = heartdata)
summary(res.aov)## Df Sum Sq Mean Sq F value Pr(>F)
## smoking 1 936 936 0.155 0.694
## Residuals 297 1794205 6041res.aov1 <- aov(time ~ sex, data = heartdata)
summary(res.aov1)## Df Sum Sq Mean Sq F value Pr(>F)
## sex 1 437 437 0.072 0.788
## Residuals 297 1794704 6043res.aov2 <- aov(time ~ anaemia, data = heartdata)
summary(res.aov2)## Df Sum Sq Mean Sq F value Pr(>F)
## anaemia 1 35899 35899 6.061 0.0144 *
## Residuals 297 1759243 5923
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1res.aov3 <- aov(time ~ diabetes, data = heartdata)
summary(res.aov3)## Df Sum Sq Mean Sq F value Pr(>F)
## diabetes 1 2042 2042 0.338 0.561
## Residuals 297 1793100 6037res.aov4 <- aov(time ~ death.event, data = heartdata)
summary(res.aov4)## Df Sum Sq Mean Sq F value Pr(>F)
## death.event 1 498494 498494 114.2 <2e-16 ***
## Residuals 297 1296647 4366
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1res.aov5 <- aov(time ~ age.range, data = heartdata)
res.aov5## Call:
## aov(formula = time ~ age.range, data = heartdata)
##
## Terms:
## age.range Residuals
## Sum of Squares 54735.9 1701352.1
## Deg. of Freedom 2 289
##
## Residual standard error: 76.72699
## Estimated effects may be unbalanced
## 7 observations deleted due to missingnessCox Proportional Hazards Model Estimation
model.heart<-coxph(Surv(time,death.event)~age+anaemia+diabetes+High.blood.pressure+smoking+platelets+ejection.fraction+serum.creatinine+creatinine.phosphokinase+serum.sodium, data=heartdata, id=id)
summary(model.heart)## Call:
## coxph(formula = Surv(time, death.event) ~ age + anaemia + diabetes +
## High.blood.pressure + smoking + platelets + ejection.fraction +
## serum.creatinine + creatinine.phosphokinase + serum.sodium,
## data = heartdata, id = id)
##
## n= 299, number of events= 96
##
## coef exp(coef) se(coef) robust se z
## age 4.526e-02 1.046e+00 9.216e-03 9.461e-03 4.784
## anaemiapositive 4.415e-01 1.555e+00 2.155e-01 2.137e-01 2.066
## diabetespositive 1.491e-01 1.161e+00 2.221e-01 2.307e-01 0.646
## High.blood.pressurepositive 4.977e-01 1.645e+00 2.144e-01 2.120e-01 2.348
## smokingsmoker 3.013e-02 1.031e+00 2.256e-01 2.262e-01 0.133
## platelets -2.702e-07 1.000e+00 1.107e-06 1.024e-06 -0.264
## ejection.fraction -4.749e-02 9.536e-01 1.035e-02 1.189e-02 -3.992
## serum.creatinine 3.220e-01 1.380e+00 7.045e-02 6.616e-02 4.866
## creatinine.phosphokinase 2.113e-04 1.000e+00 9.842e-05 1.002e-04 2.109
## serum.sodium -4.308e-02 9.578e-01 2.338e-02 2.646e-02 -1.628
## Pr(>|z|)
## age 1.72e-06 ***
## anaemiapositive 0.0388 *
## diabetespositive 0.5180
## High.blood.pressurepositive 0.0189 *
## smokingsmoker 0.8940
## platelets 0.7919
## ejection.fraction 6.55e-05 ***
## serum.creatinine 1.14e-06 ***
## creatinine.phosphokinase 0.0349 *
## serum.sodium 0.1035
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## age 1.0463 0.9557 1.0271 1.0659
## anaemiapositive 1.5550 0.6431 1.0229 2.3640
## diabetespositive 1.1608 0.8614 0.7386 1.8245
## High.blood.pressurepositive 1.6450 0.6079 1.0857 2.4925
## smokingsmoker 1.0306 0.9703 0.6615 1.6057
## platelets 1.0000 1.0000 1.0000 1.0000
## ejection.fraction 0.9536 1.0486 0.9316 0.9761
## serum.creatinine 1.3798 0.7247 1.2120 1.5709
## creatinine.phosphokinase 1.0002 0.9998 1.0000 1.0004
## serum.sodium 0.9578 1.0440 0.9094 1.0088
##
## Concordance= 0.741 (se = 0.027 )
## Likelihood ratio test= 81.07 on 10 df, p=3e-13
## Wald test = 97.31 on 10 df, p=<2e-16
## Score (logrank) test = 88.06 on 10 df, p=1e-14, Robust = 49.3 p=4e-07
##
## (Note: the likelihood ratio and score tests assume independence of
## observations within a cluster, the Wald and robust score tests do not).Diagnostic Checking Checking Proportional Hazards
model.heart1 <- coxph(Surv(time, death.event) ~ age + anaemia + High.blood.pressure + ejection.fraction + serum.creatinine + creatinine.phosphokinase, data=heartdata, id=id)
model.heart1## Call:
## coxph(formula = Surv(time, death.event) ~ age + anaemia + High.blood.pressure +
## ejection.fraction + serum.creatinine + creatinine.phosphokinase,
## data = heartdata, id = id)
##
##
## 1:2 coef exp(coef) se(coef) robust se
## age 4.361e-02 1.045e+00 8.853e-03 8.955e-03
## anaemiapositive 3.933e-01 1.482e+00 2.129e-01 2.116e-01
## High.blood.pressurepositive 4.668e-01 1.595e+00 2.129e-01 2.110e-01
## ejection.fraction -5.179e-02 9.495e-01 1.005e-02 1.136e-02
## serum.creatinine 3.483e-01 1.417e+00 6.550e-02 5.801e-02
## creatinine.phosphokinase 1.965e-04 1.000e+00 9.856e-05 9.807e-05
##
## 1:2 z p
## age 4.869 1.12e-06
## anaemiapositive 1.858 0.0631
## High.blood.pressurepositive 2.212 0.0270
## ejection.fraction -4.558 5.17e-06
## serum.creatinine 6.005 1.92e-09
## creatinine.phosphokinase 2.003 0.0452
##
## States: 1= (s0), 2= died
##
## Likelihood ratio test=77.02 on 6 df, p=1.474e-14
## n= 299, number of events= 96cox.zph(model.heart1)## chisq df p
## age 0.1774 1 0.674
## anaemia 0.0062 1 0.937
## High.blood.pressure 0.0105 1 0.918
## ejection.fraction 5.0657 1 0.024
## serum.creatinine 1.8459 1 0.174
## creatinine.phosphokinase 0.8805 1 0.348
## GLOBAL 9.8324 6 0.132par(mfrow=c(2, 2))
plot(cox.zph(model.heart1))
#END