Import data

load("./CancerSys.RData")

Kaplan Meier Analysis

Sex

cancerSys.kaplan <- cancerSys.data

cancerSys.kaplan[cancerSys.data$Sex == 0, "Sex"] <- "Female"
cancerSys.kaplan[cancerSys.data$Sex == 1, "Sex"] <- "Male"

survtest <- survdiff(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ Sex, 
                  data = cancerSys.kaplan)

round(1 - pchisq(survtest$chisq, 1), 4)

## [1] 0.014

Primary type of Cancer

cancerSys.kaplan[cancerSys.data$Primary >= 3, "Primary"] <- "Kidney and Others"
cancerSys.kaplan[cancerSys.data$Primary == 1, "Primary"] <- "Breast"
cancerSys.kaplan[cancerSys.data$Primary == 2, "Primary"] <- "Prostate"

kaplan.primary <- survfit(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ Primary, 
                  type="kaplan-meier", 
                  data = cancerSys.kaplan)

survtest <- survdiff(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ Primary, 
                  data = cancerSys.kaplan)

round(1 - pchisq(survtest$chisq, 2), 4)

## [1] 0.0872

X-Ray Pattern

cancerSys.kaplan.Xray <- cancerSys.data[!is.na(cancerSys.data$X.Ray.Pattern),]

cancerSys.kaplan.Xray[cancerSys.kaplan.Xray$X.Ray.Pattern == 1,"X.Ray.Pattern"] <- "Lystic"
cancerSys.kaplan.Xray[cancerSys.kaplan.Xray$X.Ray.Pattern == 2,"X.Ray.Pattern"] <- "Blastic"
cancerSys.kaplan.Xray[cancerSys.kaplan.Xray$X.Ray.Pattern == 3,"X.Ray.Pattern"] <- "Mixed"
cancerSys.kaplan.Xray$X.Ray.Pattern <- factor(cancerSys.kaplan.Xray$X.Ray.Pattern, c("Lystic", 
                                                                       "Blastic", "Mixed"))

survtest <- survdiff(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ X.Ray.Pattern, 
                  data = cancerSys.kaplan)

round(1 - pchisq(survtest$chisq, 2), 4)

## [1] 0.1264

NSRE

cancerSys.kaplan.NSRE <- cancerSys.data[!is.na(cancerSys.data$NSRE),]
cancerSys.kaplan.NSRE$NSRE <- as.character(lapply(cancerSys.kaplan.NSRE$NSRE, function(x){
  if(x >= 2){
    "2+"
  } else { # We want to keep the group if NSRE is lower than 3
    as.character(x)
  }
}))

survtest <- survdiff(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ NSRE, 
                  data = cancerSys.kaplan.NSRE)

round(1 - pchisq(survtest$chisq, 2), 4)

## [1] 0.8027

Extra.Mets

cancerSys.kaplan.Extra <- cancerSys.data[!is.na(cancerSys.data$Extra.Mets),]
cancerSys.kaplan.Extra[cancerSys.kaplan.Extra$Extra.Mets == 0, "Extra.Mets"] <- "No"
cancerSys.kaplan.Extra[cancerSys.kaplan.Extra$Extra.Mets == 1, "Extra.Mets"] <- "Yes"

survtest <- survdiff(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ Extra.Mets, 
                  data = cancerSys.kaplan.Extra)

round(1 - pchisq(survtest$chisq, 1), 4)

## [1] 0.0161

NTX3 > 100

cancerSys.kaplan.NTX3 <- cancerSys.long %>% filter(time == 3) %>% filter(!duplicated(Patient)) %>%
  mutate(NTX = NTX > 100)

chi.NTX3 <- survdiff(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ NTX, 
         data = cancerSys.kaplan.NTX3)

round(1-pchisq(chi.NTX3$chisq, length(chi.NTX3$n)-1),4)

## [1] 0.1497

NTX12 > 64

cancerSys.kaplan.NTX12 <- cancerSys.long %>% filter(time == 12) %>% filter(!duplicated(Patient)) %>%
  mutate(NTX = NTX > 64)

chi.NTX12 <- survdiff(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ NTX, 
         data = cancerSys.kaplan.NTX12)
round(1-pchisq(chi.NTX12$chisq, length(chi.NTX12$n)-1),4)

## [1] 0.0171

Cox Analysis

Age

cox.age <- coxph(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ Age.Diagnosis,
                 data = cancerSys.data)

summary(cox.age)

## Call:
## coxph(formula = Surv(Survival.after.begining.ZA.mo, Death.Status) ~ 
##     Age.Diagnosis, data = cancerSys.data)
## 
##   n= 147, number of events= 114 
## 
##                  coef exp(coef) se(coef)     z Pr(>|z|)   
## Age.Diagnosis 0.02155   1.02178  0.00722 2.985  0.00284 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##               exp(coef) exp(-coef) lower .95 upper .95
## Age.Diagnosis     1.022     0.9787     1.007     1.036
## 
## Concordance= 0.567  (se = 0.031 )
## Rsquare= 0.06   (max possible= 0.998 )
## Likelihood ratio test= 9.1  on 1 df,   p=0.002561
## Wald test            = 8.91  on 1 df,   p=0.002837
## Score (logrank) test = 8.96  on 1 df,   p=0.002757

Sex

cox.sex <- coxph(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ Sex,
                 data = cancerSys.data)

summary(cox.sex)

## Call:
## coxph(formula = Surv(Survival.after.begining.ZA.mo, Death.Status) ~ 
##     Sex, data = cancerSys.data)
## 
##   n= 147, number of events= 114 
## 
##      coef exp(coef) se(coef)     z Pr(>|z|)  
## Sex 0.473     1.605    0.194 2.438   0.0148 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##     exp(coef) exp(-coef) lower .95 upper .95
## Sex     1.605     0.6231     1.097     2.347
## 
## Concordance= 0.564  (se = 0.024 )
## Rsquare= 0.038   (max possible= 0.998 )
## Likelihood ratio test= 5.68  on 1 df,   p=0.01719
## Wald test            = 5.94  on 1 df,   p=0.01478
## Score (logrank) test = 6.05  on 1 df,   p=0.01389

NSRE

cox.NSRE <- coxph(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ NSRE, 
                  data = cancerSys.kaplan)

summary(cox.NSRE)

## Call:
## coxph(formula = Surv(Survival.after.begining.ZA.mo, Death.Status) ~ 
##     NSRE, data = cancerSys.kaplan)
## 
##   n= 146, number of events= 113 
##    (1 observation deleted due to missingness)
## 
##          coef exp(coef) se(coef)      z Pr(>|z|)
## NSRE -0.04838   0.95277  0.08359 -0.579    0.563
## 
##      exp(coef) exp(-coef) lower .95 upper .95
## NSRE    0.9528       1.05    0.8088     1.122
## 
## Concordance= 0.506  (se = 0.03 )
## Rsquare= 0.002   (max possible= 0.998 )
## Likelihood ratio test= 0.34  on 1 df,   p=0.5583
## Wald test            = 0.33  on 1 df,   p=0.5627
## Score (logrank) test = 0.34  on 1 df,   p=0.5627

Extra.Mets

cox.extra <- coxph(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ Extra.Mets,
                 data = cancerSys.data)

summary(cox.extra)

## Call:
## coxph(formula = Surv(Survival.after.begining.ZA.mo, Death.Status) ~ 
##     Extra.Mets, data = cancerSys.data)
## 
##   n= 146, number of events= 113 
##    (1 observation deleted due to missingness)
## 
##              coef exp(coef) se(coef)     z Pr(>|z|)  
## Extra.Mets 0.4934    1.6378   0.2069 2.384   0.0171 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##            exp(coef) exp(-coef) lower .95 upper .95
## Extra.Mets     1.638     0.6106     1.092     2.457
## 
## Concordance= 0.543  (se = 0.026 )
## Rsquare= 0.04   (max possible= 0.998 )
## Likelihood ratio test= 5.99  on 1 df,   p=0.01436
## Wald test            = 5.68  on 1 df,   p=0.01711
## Score (logrank) test = 5.79  on 1 df,   p=0.01612

NTX3

cox.NTX.3 <- coxph(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ NTX3,
                 data = cancerSys.data)

summary(cox.NTX.3)

## Call:
## coxph(formula = Surv(Survival.after.begining.ZA.mo, Death.Status) ~ 
##     NTX3, data = cancerSys.data)
## 
##   n= 107, number of events= 87 
##    (40 observations deleted due to missingness)
## 
##           coef exp(coef)  se(coef)     z Pr(>|z|)
## NTX3 0.0003295 1.0003295 0.0004303 0.766    0.444
## 
##      exp(coef) exp(-coef) lower .95 upper .95
## NTX3         1     0.9997    0.9995     1.001
## 
## Concordance= 0.572  (se = 0.035 )
## Rsquare= 0.005   (max possible= 0.998 )
## Likelihood ratio test= 0.54  on 1 df,   p=0.4611
## Wald test            = 0.59  on 1 df,   p=0.4438
## Score (logrank) test = 0.59  on 1 df,   p=0.4425

log(NTX3)

cox.NTX.3.log <- coxph(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ log(NTX3),
                 data = cancerSys.data)

summary(cox.NTX.3.log)

## Call:
## coxph(formula = Surv(Survival.after.begining.ZA.mo, Death.Status) ~ 
##     log(NTX3), data = cancerSys.data)
## 
##   n= 107, number of events= 87 
##    (40 observations deleted due to missingness)
## 
##              coef exp(coef) se(coef)     z Pr(>|z|)  
## log(NTX3) 0.20209   1.22395  0.08822 2.291    0.022 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##           exp(coef) exp(-coef) lower .95 upper .95
## log(NTX3)     1.224      0.817      1.03     1.455
## 
## Concordance= 0.572  (se = 0.035 )
## Rsquare= 0.046   (max possible= 0.998 )
## Likelihood ratio test= 5.06  on 1 df,   p=0.0245
## Wald test            = 5.25  on 1 df,   p=0.02197
## Score (logrank) test = 5.27  on 1 df,   p=0.02173

NTX3 threshold

cox.NTX.3.threshold <- coxph(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ NTX3 > 100,
                 data = cancerSys.data)

summary(cox.NTX.3.threshold)

## Call:
## coxph(formula = Surv(Survival.after.begining.ZA.mo, Death.Status) ~ 
##     NTX3 > 100, data = cancerSys.data)
## 
##   n= 107, number of events= 87 
##    (40 observations deleted due to missingness)
## 
##                  coef exp(coef) se(coef)     z Pr(>|z|)
## NTX3 > 100TRUE 0.3562    1.4279   0.2483 1.434    0.151
## 
##                exp(coef) exp(-coef) lower .95 upper .95
## NTX3 > 100TRUE     1.428     0.7004    0.8777     2.323
## 
## Concordance= 0.54  (se = 0.026 )
## Rsquare= 0.018   (max possible= 0.998 )
## Likelihood ratio test= 1.95  on 1 df,   p=0.1626
## Wald test            = 2.06  on 1 df,   p=0.1515
## Score (logrank) test = 2.08  on 1 df,   p=0.1494

NTX12

cox.NTX.12 <- coxph(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ NTX12,
                 data = cancerSys.data)

summary(cox.NTX.12)

## Call:
## coxph(formula = Surv(Survival.after.begining.ZA.mo, Death.Status) ~ 
##     NTX12, data = cancerSys.data)
## 
##   n= 51, number of events= 41 
##    (96 observations deleted due to missingness)
## 
##            coef exp(coef)  se(coef)     z Pr(>|z|)  
## NTX12 0.0013674 1.0013683 0.0007646 1.788   0.0737 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##       exp(coef) exp(-coef) lower .95 upper .95
## NTX12     1.001     0.9986    0.9999     1.003
## 
## Concordance= 0.564  (se = 0.051 )
## Rsquare= 0.05   (max possible= 0.995 )
## Likelihood ratio test= 2.64  on 1 df,   p=0.1043
## Wald test            = 3.2  on 1 df,   p=0.07371
## Score (logrank) test = 3.33  on 1 df,   p=0.06814

log(NTX12)

cox.NTX.12.log <- coxph(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ log(NTX12),
                 data = cancerSys.data)

summary(cox.NTX.12.log)

## Call:
## coxph(formula = Surv(Survival.after.begining.ZA.mo, Death.Status) ~ 
##     log(NTX12), data = cancerSys.data)
## 
##   n= 51, number of events= 41 
##    (96 observations deleted due to missingness)
## 
##              coef exp(coef) se(coef)     z Pr(>|z|)  
## log(NTX12) 0.2405    1.2719   0.1244 1.933   0.0533 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##            exp(coef) exp(-coef) lower .95 upper .95
## log(NTX12)     1.272     0.7862    0.9966     1.623
## 
## Concordance= 0.564  (se = 0.051 )
## Rsquare= 0.069   (max possible= 0.995 )
## Likelihood ratio test= 3.66  on 1 df,   p=0.05565
## Wald test            = 3.74  on 1 df,   p=0.05327
## Score (logrank) test = 3.72  on 1 df,   p=0.05368

NTX12 threshold

cox.NTX.12.threshold <- coxph(Surv(Survival.after.begining.ZA.mo, Death.Status) ~ NTX12 > 64,
                 data = cancerSys.data)

summary(cox.NTX.12.threshold)

## Call:
## coxph(formula = Surv(Survival.after.begining.ZA.mo, Death.Status) ~ 
##     NTX12 > 64, data = cancerSys.data)
## 
##   n= 51, number of events= 41 
##    (96 observations deleted due to missingness)
## 
##                  coef exp(coef) se(coef)     z Pr(>|z|)  
## NTX12 > 64TRUE 0.7882    2.1995   0.3387 2.327     0.02 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##                exp(coef) exp(-coef) lower .95 upper .95
## NTX12 > 64TRUE       2.2     0.4546     1.132     4.272
## 
## Concordance= 0.568  (se = 0.039 )
## Rsquare= 0.094   (max possible= 0.995 )
## Likelihood ratio test= 5.06  on 1 df,   p=0.02451
## Wald test            = 5.42  on 1 df,   p=0.01996
## Score (logrank) test = 5.69  on 1 df,   p=0.01711

Univariate Cox and Kaplan Meier Analysis

Loureiro et al.

February 2018

Import data

Kaplan Meier Analysis

Sex

Primary type of Cancer

X-Ray Pattern

NSRE

Extra.Mets

NTX3 > 100

NTX12 > 64

Cox Analysis

Age

Sex

NSRE

Extra.Mets

NTX3

log(NTX3)

NTX3 threshold

NTX12

log(NTX12)

NTX12 threshold