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prediction at 10 years without ICICLE and ParkWest.Rmd
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prediction at 10 years without ICICLE and ParkWest.Rmd
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---
title: "10 YEARS?"
author: "Yan Li"
date: '2022-11-02'
output: html_document
---
```{r censor for 10 years}
imp3.new12<-imp3.new%>%
filter(clus=="CamPalGN" |clus=="NYPUM"|clus=="PICNICS"|clus=="PINE" )
imp3.temp12<-survSplit(Surv(year, cens) ~ ., data = imp3.new12, cut = 10,
episode="timegroup")
imp3.12y<-subset(imp3.temp12, timegroup == 1) #only the first 10 year
```
```{r exclude ICICLE ParkWest}
imp3.12y%>%
filter(cens==1)%>% #cens==1 event
summarise(max(year),min(year),median(year))
PO0.12<-flexsurvspline(Surv(year,cens)~age10+sex+mdsupdrs3.10+hybl+mmsebltotal+clus,data=imp3.new12,k=0,scale = "odds") #log-logistic model
PO1.12<-flexsurvspline(Surv(year,cens)~age10+sex+mdsupdrs3.10+hybl+mmsebltotal+clus,data=imp3.new12,k=1,bknots = c(log(0.1067762),log(9.943874)),scale = "odds")
PO2.12<-flexsurvspline(Surv(year,cens)~age10+sex+mdsupdrs3.10+hybl+mmsebltotal+clus,data=imp3.new12,k=2,bknots = c(log(0.1067762),log(9.943874)),scale = "odds")
PH0.12<-flexsurvspline(Surv(year,cens)~age10+sex+mdsupdrs3.10+hybl+mmsebltotal+clus,data=imp3.new12,k=0,scale = "hazard")
PH1.12<-flexsurvspline(Surv(year,cens)~age10+sex+mdsupdrs3.10+hybl+mmsebltotal+clus,data=imp3.new12,k=1,bknots = c(log(0.1067762),log(9.943874)),scale = "hazard")
PH2.12<-flexsurvspline(Surv(year,cens)~age10+sex+mdsupdrs3.10+hybl+mmsebltotal+clus,data=imp3.new12,k=2,bknots = c(log(0.1067762),log(9.943874)),scale = "hazard")
```
```{r POPH compare 10 years}
AIC(PO0.12)
AIC(PO1.12) #1 knots in median
AIC(PO2.12) #2 knots one in 33% one in 67%
BIC(PO0.12)
BIC(PO1.12) #1 knots in median
BIC(PO2.12) #2 knots one in 33% one in 67%
AIC(PH0.12)
AIC(PH1.12) #1 knots in median
AIC(PH2.12) #2 knots one in 33% one in 67%
BIC(PH0.12)
BIC(PH1.12) #1 knots in median
BIC(PH2.12) #2 knots one in 33% one in 67%
#same the final is PO1
PO1.12
```
```{r Harrell Uno 7 years}
#---leave CamPalGN out----
data12y.1<-imp3.12y%>%
filter(clus!="CamPalGN")
data12y.1v<-imp3.12y%>%
filter(clus=="CamPalGN")
#Boundary knots location
data12y.1%>%
filter(cens==1)%>% #cens==1 event
summarise(max(year),min(year))
#refit model
model1.12<-flexsurvspline(Surv(year,cens)~age10+sex+mdsupdrs3.10+hybl+mmsebltotal,data=data12y.1,k=1,bknots = c(log(0.1067762),log(9.943874)),scale = "odds")
#linear predictor method 1
# Design matrix of predictors
des_matr1.12<-as.data.frame(model.matrix(~ age10+sex+mdsupdrs3.10+hybl+mmsebltotal,data=data12y.1v))
des_matr1.12$`(Intercept)` <- NULL
coef1.12<-c(model1.12$coefficients[4],model1.12$coefficients[5],model1.12$coefficients[6],model1.12$coefficients[7],model1.12$coefficients[8])
data12y.1v$lp.1.12 <- as.vector(as.matrix(des_matr1.12) %*% cbind(coef1.12))
# Harrell's C
harrell_C_1v.12 <- concordance(Surv(year,cens) ~ lp.1.12,
data12y.1v,
reverse = TRUE)
# Uno's C
Uno_C_1v.12<- concordance(Surv(year,cens) ~ lp.1.12,
data12y.1v,
reverse = TRUE,
timewt = "n/G2")
#---leave NYPUM out----
data12y.3<-imp3.12y%>%
filter(clus!="NYPUM")
data12y.3v<-imp3.12y%>%
filter(clus=="NYPUM")
#Boundary knots location
data12y.3%>%
filter(cens==1)%>% #cens==1 event
summarise(max(year),min(year))
#refit model
model3.12<-flexsurvspline(Surv(year,cens)~age10+sex+mdsupdrs3.10+hybl+mmsebltotal,data=data12y.3,k=1,bknots = c(log(0.1067762),log(9.943874)),scale = "odds")
#linear predictor
# Design matrix of predictors
des_matr3.12<-as.data.frame(model.matrix(~ age10+sex+mdsupdrs3.10+hybl+mmsebltotal,data=data12y.3v))
des_matr3.12$`(Intercept)` <- NULL
coef3.12<-c(model3.12$coefficients[4],model3.12$coefficients[5],model3.12$coefficients[6],model3.12$coefficients[7],model3.12$coefficients[8])
data12y.3v$lp.3.12 <- as.vector(as.matrix(des_matr3.12) %*% cbind(coef3.12))
# Harrell's C
harrell_C_3v.12 <- concordance(Surv(year,cens) ~ lp.3.12,
data12y.3v,
reverse = TRUE)
# Uno's C
Uno_C_3v.12<- concordance(Surv(year,cens) ~ lp.3.12,
data12y.3v,
reverse = TRUE,
timewt = "n/G2")
#---leave PICNICS out----
data12y.5<-imp3.12y%>%
filter(clus!="PICNICS")
data12y.5v<-imp3.12y%>%
filter(clus=="PICNICS")
#Boundary knots location
data12y.5%>%
filter(cens==1)%>% #cens==1 event
summarise(max(year),min(year))
#refit model
model5.12<-flexsurvspline(Surv(year,cens)~age10+sex+mdsupdrs3.10+hybl+mmsebltotal,data=data12y.5,k=1,bknots = c(log(0.5557837),log(9.596167)),scale = "odds")
#linear predictor
# Design matrix of predictors
des_matr5.12<-as.data.frame(model.matrix(~ age10+sex+mdsupdrs3.10+hybl+mmsebltotal,data=data12y.5v))
des_matr5.12$`(Intercept)` <- NULL
coef5.12<-c(model5.12$coefficients[4],model5.12$coefficients[5],model5.12$coefficients[6],model5.12$coefficients[7],model5.12$coefficients[8])
data12y.5v$lp.5.12 <- as.vector(as.matrix(des_matr5.12) %*% cbind(coef5.12))
# Harrell's C
harrell_C_5v.12 <- concordance(Surv(year,cens) ~ lp.5.12,
data12y.5v,
reverse = TRUE)
# Uno's C
Uno_C_5v.12<- concordance(Surv(year,cens) ~ lp.5.12,
data12y.5v,
reverse = TRUE,
timewt = "n/G2")
#---leave PINE out----
data12y.6<-imp3.12y%>%
filter(clus!="PINE")
data12y.6v<-imp3.12y%>%
filter(clus=="PINE")
#Boundary knots location
data12y.6%>%
filter(cens==1)%>% #cens==1 event
summarise(max(year),min(year))
#refit model
model6.12<-flexsurvspline(Surv(year,cens)~age10+sex+mdsupdrs3.10+hybl+mmsebltotal,data=data12y.6,k=1,bknots = c(log(0.1067762),log(9.943874)),scale = "odds")
#linear predictor
# Design matrix of predictors
des_matr6.12<-as.data.frame(model.matrix(~ age10+sex+mdsupdrs3.10+hybl+mmsebltotal,data=data12y.6v))
des_matr6.12$`(Intercept)` <- NULL
coef6.12<-c(model6.12$coefficients[4],model6.12$coefficients[5],model6.12$coefficients[6],model6.12$coefficients[7],model6.12$coefficients[8])
data12y.6v$lp.6.12 <- as.vector(as.matrix(des_matr6.12) %*% cbind(coef6.12))
# Harrell's C
harrell_C_6v.12 <- concordance(Surv(year,cens) ~ lp.6.12,
data12y.6v,
reverse = TRUE)
# Uno's C
Uno_C_6v.12<- concordance(Surv(year,cens) ~ lp.6.12,
data12y.6v,
reverse = TRUE,
timewt = "n/G2")
```
```{r Time-dependent AUC 10 years}
#---leave CamPalGN out----
Uno_1v.12 <-
timeROC::timeROC(
T = data12y.1v$year,
delta = data12y.1v$cens,
marker = data12y.1v$lp.1.12,
cause = 1,
weighting = "marginal",
times = 9.99,
iid = TRUE
)
#---leave NYPUM out----
Uno_3v.12 <-
timeROC::timeROC(
T = data12y.3v$year,
delta = data12y.3v$cens,
marker = data12y.3v$lp.3.12,
cause = 1,
weighting = "marginal",
times = 9.99,
iid = TRUE
)
#---leave PICNICS out----
Uno_5v.12 <-
timeROC::timeROC(
T = data12y.5v$year,
delta = data12y.5v$cens,
marker = data12y.5v$lp.5.12,
cause = 1,
weighting = "marginal",
times = 9.99,
iid = TRUE
)
#---leave PINE out----
Uno_6v.12 <-
timeROC::timeROC(
T = data12y.6v$year,
delta = data12y.6v$cens,
marker = data12y.6v$lp.6.12,
cause = 1,
weighting = "marginal",
times = 9.99,
iid = TRUE
)
Uno_1v.12
Uno_3v.12
Uno_5v.12
Uno_6v.12
```
```{r Mean calibration 10 years}
# Observed / Expected ratio
alpha <- .05
#---leave CamPalGN out----
# Observed
obj.1.12 <- summary(survfit(
Surv(year, cens) ~ 1,
data = data12y.1v),
times = 10)
obs_t.1.12 <- 1 - obj.1.12$surv
data12y.1v$pred<-predict(model1.12,newdata = data12y.1v,type = "survival",times = 10)[[2]] #survival probabilities
# Expected
exp_t.1.12 <-mean(1-data12y.1v$pred) #predicts risk, as 1 - S(t|X)
# Observed / Expected ratio
OE_t.1.12 <- obs_t.1.12 / exp_t.1.12
OE_summary.1.12 <- c(
"OE" = OE_t.1.12,
"2.5 %" = OE_t.1.12 * exp(-qnorm(1 - alpha / 2) * sqrt(1 / obj.1.12$n.event)),
"97.5 %" = OE_t.1.12 * exp(+qnorm(1 - alpha / 2) * sqrt(1 / obj.1.12$n.event))
)
OE_summary.1.12
#---leave NYPUM out----
obj.3.12 <- summary(survfit(
Surv(year, cens) ~ 1,
data = data12y.3v),
times = 10)
obs_t.3.12 <- 1 - obj.3.12$surv
data12y.3v$pred<-predict(model3.12,newdata = data12y.3v,type = "survival",times = 10)[[2]] #survival probabilities
# Expected
exp_t.3.12 <-mean(1-data12y.3v$pred) #predicts risk, as 1 - S(t|X)
# Observed / Expected ratio
OE_t.3.12 <- obs_t.3.12 / exp_t.3.12
OE_summary.3.12 <- c(
"OE" = OE_t.3.12,
"2.5 %" = OE_t.3.12 * exp(-qnorm(1 - alpha / 2) * sqrt(1 / obj.3.12$n.event)),
"97.5 %" = OE_t.3.12 * exp(+qnorm(1 - alpha / 2) * sqrt(1 / obj.3.12$n.event))
)
OE_summary.3.12
#---leave PICNICS out----
obj.5.12 <- summary(survfit(
Surv(year, cens) ~ 1,
data = data12y.5v),
times = 10)
obs_t.5.12 <- 1 - obj.5.12$surv
data12y.5v$pred<-predict(model5.12,newdata = data12y.5v,type = "survival",times = 10)[[2]] #survival probabilities
# Expected
exp_t.5.12 <-mean(1-data12y.5v$pred) #predicts risk, as 1 - S(t|X)
# Observed / Expected ratio
OE_t.5.12 <- obs_t.5.12 / exp_t.5.12
OE_summary.5.12 <- c(
"OE" = OE_t.5.12,
"2.5 %" = OE_t.5.12 * exp(-qnorm(1 - alpha / 2) * sqrt(1 / obj.5.12$n.event)),
"97.5 %" = OE_t.5.12 * exp(+qnorm(1 - alpha / 2) * sqrt(1 / obj.5.12$n.event))
)
OE_summary.5.12
#---leave PINE out----
obj.6.12 <- summary(survfit(
Surv(year, cens) ~ 1,
data = data12y.6v),
times = 10)
obs_t.6.12 <- 1 - obj.6.12$surv
data12y.6v$pred<-predict(model6.12,newdata = data12y.6v,type = "survival",times = 10)[[2]] #survival probabilities
# Expected
exp_t.6.12 <-mean(1-data12y.6v$pred) #predicts risk, as 1 - S(t|X)
# Observed / Expected ratio
OE_t.6.12 <- obs_t.6.12 / exp_t.6.12
OE_summary.6.12 <- c(
"OE" = OE_t.6.12,
"2.5 %" = OE_t.6.12 * exp(-qnorm(1 - alpha / 2) * sqrt(1 / obj.6.12$n.event)),
"97.5 %" = OE_t.6.12 * exp(+qnorm(1 - alpha / 2) * sqrt(1 / obj.6.12$n.event))
)
OE_summary.6.12
```
```{r Moderate calibration 10 years}
#moderate calibration uses smooth curves of predicted risk from a more complex ‘secondary’ Cox model against the predicted risk from the development model
#---leave CamPalGN out----
#data10y.1v$pred<-predict(model1.10,newdata = data10y.1v,type = "survival",times = 7)[[2]] #survival probabilities
# predicted risk
data12y.1v$risk <-(1-data12y.1v$pred) #predicted risk, as 1 - S(t|X),the probabilities of events
data12y.1v$risk.cll <- log(-log(1-data12y.1v$risk)) #complementary log-log link
#Check location of knots again
data12y.1v%>%
filter(cens==1)%>% #cens==1 event
summarise(max(year),min(year))
# Estimate actual risk
vcal.1.12.RP <- flexsurvspline(Surv(year, cens)~rcs(risk.cll,3), data = data12y.1v, k=1,bknots = c(log(1.147159),log(9.040383)),scale = "odds")
#survest function is to estimate survival probabilities
dat_cal.1.12 <- cbind.data.frame(
"obs" = 1 - predict(vcal.1.12.RP,
type = "survival",
times = 10,
newdata = data12y.1v)[[2]], #1-s(t=4) to get the refitted model predicted risk
"lower" = 1 - predict(vcal.1.12.RP,
type = "survival",
conf.int = T,
times = 10,
newdata = data12y.1v)[[4]],
"upper" = 1 - predict(vcal.1.12.RP,
type = "survival",
conf.int = T,
times = 10,
newdata = data12y.1v)[[3]],
"pred" = data12y.1v$risk
)
dat_cal.1.12 <- dat_cal.1.12[order(dat_cal.1.12$pred), ]
png("Cam-10y.png",width = 3500,height =2000,res = 400)
par(xaxs = "i", yaxs = "i", las = 1)
plot(
x=dat_cal.1.12$pred, #x is predicted risk from the
y=dat_cal.1.12$obs,
type = "l",
lty = 1,
xlim = c(0, 1),
ylim = c(0, 1),
lwd = 2,
xlab = "Predicted risk from developed model",
ylab = "Predicted risk from refitted model",
main = "Validation dataset is CamPalGN",
bty = "n" #no box
)
lines(dat_cal.1.12$pred,
dat_cal.1.12$lower,
type = "l",
lty = 2,
lwd = 2)
lines(dat_cal.1.12$pred,
dat_cal.1.12$upper,
type = "l",
lty = 2,
lwd = 2)
abline(0, 1, lwd = 2, lty = 2, col = 2)
legend("topleft",
c("Ideal calibration",
"Calibration curve based on secondary Royston-Parmar model",
"95% confidence interval"),
col = c(2, 1, 1),
lty = c(2, 1, 2),
lwd = c(2, 2, 2),
bty = "n",
cex = 0.8)
dev.off()
# Numerical measures
absdiff_cph.1.12 <- abs(dat_cal.1.12$pred - dat_cal.1.12$obs)
numsum_cph.1.12 <- c(
"ICI" = mean(absdiff_cph.1.12),
setNames(quantile(absdiff_cph.1.12, c(0.5, 0.9)), c("E50", "E90")),
"Emax" = max(absdiff_cph.1.12)
)
numsum_cph.1.12
#---leave NYPUM out----
# predicted risk
data12y.3v$risk <-(1-data12y.3v$pred) #predicted risk, as 1 - S(t|X),the probabilities of events
data12y.3v$risk.cll <- log(-log(1-data12y.3v$risk)) #complementary log-log link
#Check location of knots again
data12y.3v%>%
filter(cens==1)%>% #cens==1 event
summarise(max(year),min(year))
# Estimate actual risk
vcal.3.12.RP <- flexsurvspline(Surv(year, cens) ~ rcs(risk.cll,3), data = data12y.3v, k=1,bknots = c(log(0.8925394),log(9.511294)),scale = "odds")
dat_cal.3.12 <- cbind.data.frame(
"obs" = 1 - predict(vcal.3.12.RP,
type = "survival",
times = 10,
newdata = data12y.3v)[[2]], #1-s(t=4) to get the refitted model predicted risk
"lower" = 1 - predict(vcal.3.12.RP,
type = "survival",
conf.int = T,
times = 10,
newdata = data12y.3v)[[4]],
"upper" = 1 - predict(vcal.3.12.RP,
type = "survival",
conf.int = T,
times = 10,
newdata = data12y.3v)[[3]],
"pred" = data12y.3v$risk
)
dat_cal.3.12 <- dat_cal.3.12[order(dat_cal.3.12$pred), ]
png("NY-10y.png",width = 3500,height =2000,res = 400)
par(xaxs = "i", yaxs = "i", las = 1)
plot(
x=dat_cal.3.12$pred, #x is predicted risk from the
y=dat_cal.3.12$obs,
type = "l",
lty = 1,
xlim = c(0, 1),
ylim = c(0, 1),
lwd = 2,
xlab = "Predicted risk from developed model",
ylab = "Predicted risk from refitted model",
main = "Validation dataset is NYPUM",
bty = "n" #no box
)
lines(dat_cal.3.12$pred,
dat_cal.3.12$lower,
type = "l",
lty = 2,
lwd = 2)
lines(dat_cal.3.12$pred,
dat_cal.3.12$upper,
type = "l",
lty = 2,
lwd = 2)
abline(0, 1, lwd = 2, lty = 2, col = 2)
legend("topleft",
c("Ideal calibration",
"Calibration curve based on secondary Royston-Parmar model",
"95% confidence interval"),
col = c(2, 1, 1),
lty = c(2, 1, 2),
lwd = c(2, 2, 2),
bty = "n",
cex = 0.75)
dev.off()
# Numerical measures
absdiff_cph.3.12 <- abs(dat_cal.3.12$pred - dat_cal.3.12$obs)
numsum_cph.3.12 <- c(
"ICI" = mean(absdiff_cph.3.12),
setNames(quantile(absdiff_cph.3.12, c(0.5, 0.9)), c("E50", "E90")),
"Emax" = max(absdiff_cph.3.12)
)
numsum_cph.3.12
#---leave PICNICS out----
data12y.5v$risk <-(1-data12y.5v$pred) #predicted risk, as 1 - S(t|X),the probabilities of events
data12y.5v$risk.cll <- log(-log(1-data12y.5v$risk)) #complementary log-log link
#Check location of knots again
data12y.5v%>%
filter(cens==1)%>% #cens==1 event
summarise(max(year),min(year))
# Estimate actual risk
vcal.5.12.RP <- flexsurvspline(Surv(year, cens) ~ rcs(risk.cll,3), data = data10y.5v, k=1,bknots = c(log(0.1067762),log(9.943874)),scale = "odds")
dat_cal.5.12 <- cbind.data.frame(
"obs" = 1 - predict(vcal.5.12.RP,
type = "survival",
times = 10,
newdata = data12y.5v)[[2]], #1-s(t=4) to get the refitted model predicted risk
"lower" = 1 - predict(vcal.5.12.RP,
type = "survival",
conf.int = T,
times = 10,
newdata = data12y.5v)[[4]],
"upper" = 1 - predict(vcal.5.12.RP,
type = "survival",
conf.int = T,
times = 10,
newdata = data12y.5v)[[3]],
"pred" = data12y.5v$risk
)
dat_cal.5.12 <- dat_cal.5.12[order(dat_cal.5.12$pred), ]
png("PIC-10y.png",width = 3500,height =2000,res = 400)
par(xaxs = "i", yaxs = "i", las = 1)
plot(
x=dat_cal.5.12$pred, #x is predicted risk from the
y=dat_cal.5.12$obs,
type = "l",
lty = 1,
xlim = c(0, 1),
ylim = c(0, 1),
lwd = 2,
xlab = "Predicted risk from developed model",
ylab = "Predicted risk from refitted model",
main = "Validation dataset is PICNICS",
bty = "n" #no box
)
lines(dat_cal.5.12$pred,
dat_cal.5.12$lower,
type = "l",
lty = 2,
lwd = 2)
lines(dat_cal.5.12$pred,
dat_cal.5.12$upper,
type = "l",
lty = 2,
lwd = 2)
abline(0, 1, lwd = 2, lty = 2, col = 2)
legend("topleft",
c("Ideal calibration",
"Calibration curve based on secondary Royston-Parmar model",
"95% confidence interval"),
col = c(2, 1, 1),
lty = c(2, 1, 2),
lwd = c(2, 2, 2),
bty = "n",
cex = 0.75)
dev.off()
# Numerical measures
absdiff_cph.5.12 <- abs(dat_cal.5.12$pred - dat_cal.5.12$obs)
numsum_cph.5.12 <- c(
"ICI" = mean(absdiff_cph.5.12),
setNames(quantile(absdiff_cph.5.12, c(0.5, 0.9)), c("E50", "E90")),
"Emax" = max(absdiff_cph.5.12)
)
numsum_cph.5.12
#---leave PINE out----
data12y.6v$risk <-(1-data12y.6v$pred) #predicted risk, as 1 - S(t|X),the probabilities of events
data12y.6v$risk.cll <- log(-log(1-data12y.6v$risk)) #complementary log-log link
#Check location of knots again
data12y.6v%>%
filter(cens==1)%>% #cens==1 event
summarise(max(year),min(year))
# Estimate actual risk
vcal.6.12.RP <- flexsurvspline(Surv(year, cens) ~ rcs(risk.cll,3), data = data12y.6v, k=1,bknots = c(log(0.5557837),log(9.596167)),scale = "odds")
dat_cal.6.12 <- cbind.data.frame(
"obs" = 1 - predict(vcal.6.12.RP,
type = "survival",
times = 10,
newdata = data12y.6v)[[2]], #1-s(t=4) to get the refitted model predicted risk
"lower" = 1 - predict(vcal.6.12.RP,
type = "survival",
conf.int = T,
times = 10,
newdata = data12y.6v)[[4]],
"upper" = 1 - predict(vcal.6.12.RP,
type = "survival",
conf.int = T,
times = 10,
newdata = data12y.6v)[[3]],
"pred" = data12y.6v$risk
)
dat_cal.6.12 <- dat_cal.6.12[order(dat_cal.6.12$pred), ]
png("PIN-10y.png",width = 3500,height =2000,res = 400)
par(xaxs = "i", yaxs = "i", las = 1)
plot(
x=dat_cal.6.12$pred, #x is predicted risk from the
y=dat_cal.6.12$obs,
type = "l",
lty = 1,
xlim = c(0, 1),
ylim = c(0, 1),
lwd = 2,
xlab = "Predicted risk from developed model",
ylab = "Predicted risk from refitted model",
main = "Validation dataset is PINE",
bty = "n" #no box
)
lines(dat_cal.6.12$pred,
dat_cal.6.12$lower,
type = "l",
lty = 2,
lwd = 2)
lines(dat_cal.6.12$pred,
dat_cal.6.12$upper,
type = "l",
lty = 2,
lwd = 2)
abline(0, 1, lwd = 2, lty = 2, col = 2)
legend("topleft",
c("Ideal calibration",
"Calibration curve based on secondary Royston-Parmar model",
"95% confidence interval"),
col = c(2, 1, 1),
lty = c(2, 1, 2),
lwd = c(2, 2, 2),
bty = "n",
cex = 0.85)
dev.off()
# Numerical measures
absdiff_cph.6.12 <- abs(dat_cal.6.12$pred - dat_cal.6.12$obs)
numsum_cph.6.12 <- c(
"ICI" = mean(absdiff_cph.6.12),
setNames(quantile(absdiff_cph.6.12, c(0.5, 0.9)), c("E50", "E90")),
"Emax" = max(absdiff_cph.6.12)
)
numsum_cph.6.12
```
```{r Weak calibration 10 years}
#Include linear predictor in validation datasets as a predictor
#---leave CamPalGN out----
vcal.1.12.weak <- flexsurvspline(Surv(year, cens) ~risk.cll, data = data12y.1v, k=1,bknots = c(log(1.147159),log(9.040383)),scale = "odds")
data12y.1v$pred.act<-predict(vcal.1.12.weak,type = "survival",times = 10,newdata = data12y.1v)[[2]] #actual survival
data12y.1v$g_st<-log((1/data12y.1v$pred.act)-1)
val.1.12<-lm(g_st~lp.1.12,data = data12y.1v)
#lm(g_st~log((1/data12y.1v$pred)-1),data = data12y.1v)
summary(val.1.12)
calslope_summary.1.12 <- c(
"calibration slope" = val.1.12$coefficients[2],
"2.5 %" = val.1.12$coefficients[2] - 1.96 * 0.01731,
"97.5 %" = val.1.12$coefficients[2] + 1.96 * 0.01731
)
calslope_summary.1.12
#---leave NYPUM out----
vcal.3.12.weak <- flexsurvspline(Surv(year, cens) ~risk.cll, data = data12y.3v, k=1,bknots = c(log(0.8925394), log(9.511294)),scale = "odds")
data12y.3v$pred.act<-predict(vcal.3.12.weak,type = "survival",times = 10,newdata = data12y.3v)[[2]] #actual survival
data12y.3v$g_st<-log((1/data12y.3v$pred.act)-1)
val.3.12<-lm(g_st~lp.3.12,data = data12y.3v)
summary(val.3.12)
calslope_summary.3.12 <- c(
"calibration slope" = val.3.12$coefficients[2],
"2.5 %" = val.3.12$coefficients[2] - 1.96 * 0.01887,
"97.5 %" = val.3.12$coefficients[2] + 1.96 * 0.01887
)
calslope_summary.3.12
#---leave PICNICS out----
vcal.5.12.weak <- flexsurvspline(Surv(year, cens) ~risk.cll, data = data12y.5v, k=1,bknots = c(log(0.1067762), log(9.943874)),scale = "odds")
data12y.5v$pred.act<-predict(vcal.5.12.weak,type = "survival",times = 10,newdata = data12y.5v)[[2]] #actual survival
data12y.5v$g_st<-log((1/data12y.5v$pred.act)-1)
val.5.12<-lm(g_st~lp.5.12,data = data12y.5v)
summary(val.5.12)
calslope_summary.5.12 <- c(
"calibration slope" = val.5.12$coefficients[2],
"2.5 %" = val.5.12$coefficients[2] - 1.96 * 0.009372,
"97.5 %" = val.5.12$coefficients[2] + 1.96 * 0.009372
)
calslope_summary.5.12
#---leave PINE out----
vcal.6.12.weak <- flexsurvspline(Surv(year, cens) ~risk.cll, data = data12y.6v, k=1,bknots = c(log(0.5557837), log(9.596167)),scale = "odds")
data12y.6v$pred.act<-predict(vcal.6.12.weak,type = "survival",times = 10,newdata = data12y.6v)[[2]] #actual survival
data12y.6v$g_st<-log((1/data12y.6v$pred.act)-1)
val.6.12<-lm(g_st~lp.6.12,data = data12y.6v)
summary(val.6.12)
calslope_summary.6.12 <- c(
"calibration slope" = val.6.12$coefficients[2],
"2.5 %" = val.6.12$coefficients[2] - 1.96 * 0.01169,
"97.5 %" = val.6.12$coefficients[2] + 1.96 * 0.01169
)
calslope_summary.6.12
```
```{r recalibration 10 year}
#----CamPalGN-----
model1.12.re<-flexsurvspline(Surv(year,cens)~age10+sex+mdsupdrs3.10+hybl+mmsebltotal,data=data12y.1,k=1,bknots = c(log(1.147159),log(9.040383)),scale = "odds") #change the knots position
rcs.mod1.12<-as.data.frame(basis(model1.12.re$knots,log(10))) #basis spline
data12y.1v$rcs1<-rcs.mod1.12[,2]
data12y.1v$rcs2<-rcs.mod1.12[,3]
log((1-obj.1.12$surv)/mean(1-data12y.1v$pred)) #ln mean O/E risk ratio
model1.12.re$res[c("gamma0", "gamma1", "gamma2"), "est"]
data12y.1v$pred.re<-1/(1+exp(-10.9104500-0.5297541+1.6319907*data12y.1v$rcs1-0.9665124*data12y.1v$rcs2+data12y.1v$lp.1.12)) #change the knots position and s(lnt;r) but keep the linear predictor the same
(1-obj.1.12$surv)/mean(1-data12y.1v$pred.re) #Mean calibration improve
#Before is (1-obj.1.12$surv)/mean(1-data12y.1v$pred), 0.59, now is 0.78
data12y.1v$risk.re<-1-data12y.1v$pred.re
dat_cal.1.12.RP.re <- cbind.data.frame(
"obs" = 1 - predict(vcal.1.12.RP,
type = "survival",
times = 10,
newdata = data12y.1v)[[2]], #1-s(t=4) to get the refitted model predicted risk
"lower" = 1 - predict(vcal.1.12.RP,
type = "survival",
conf.int = T,
times = 10,
newdata = data12y.1v)[[4]],
"upper" = 1 - predict(vcal.1.12.RP,
type = "survival",
conf.int = T,
times = 10,
newdata = data12y.1v)[[3]],
"pred" = data12y.1v$risk.re
)
dat_cal.1.12.RP.re <- dat_cal.1.12.RP.re[order(dat_cal.1.12.RP.re$pred), ]
png("Cam-10y-re1.png",width = 3500,height =2000,res = 400)
par(xaxs = "i", yaxs = "i", las = 1)
plot(
x=dat_cal.1.12.RP.re$pred, #x is predicted risk from the
y=dat_cal.1.12.RP.re$obs,
type = "l",
lty = 1,
xlim = c(0, 1),
ylim = c(0, 1),
lwd = 2,
xlab = "Predicted risk from developed model with new boundary knots position and intercept",
ylab = "Predicted risk from refitted model",
main = "Validation dataset is CamPalGN",
bty = "n" #no box
)
lines(dat_cal.1.12.RP.re$pred,
dat_cal.1.12.RP.re$lower,
type = "l",
lty = 2,
lwd = 2)
lines(dat_cal.1.12.RP.re$pred,
dat_cal.1.12.RP.re$upper,
type = "l",
lty = 2,
lwd = 2)
abline(0, 1, lwd = 2, lty = 2, col = 2)
legend("topleft",
c("Ideal calibration",
"Calibration curve based on secondary Royston-Parmar model",
"95% confidence interval"),
col = c(2, 1, 1),
lty = c(2, 1, 2),
lwd = c(2, 2, 2),
bty = "n",
cex = 0.8)
dev.off()
# Numerical measures
absdiff_cph.1.12.RP.re <- abs(dat_cal.1.12.RP.re$pred - dat_cal.1.12.RP.re$obs)
numsum_cph.1.12.RP.re <- c(
"ICI" = mean(absdiff_cph.1.12.RP.re),
setNames(quantile(absdiff_cph.1.12.RP.re, c(0.5, 0.9)), c("E50", "E90")),
"Emax" = max(absdiff_cph.1.12.RP.re)
)
numsum_cph.1.12.RP.re
#----NYPUM-----
model3.12.re<-flexsurvspline(Surv(year,cens)~age10+sex+mdsupdrs3.10+hybl+mmsebltotal,data=data12y.3,k=1,bknots = c(log(0.8925394),log(9.511294)),scale = "odds") #change the knots position
rcs.mod3.12<-as.data.frame(basis(model3.12.re$knots,log(10))) #basis spline
data12y.3v$rcs1<-rcs.mod3.12[,2]
data12y.3v$rcs2<-rcs.mod3.12[,3]
log((1-obj.3.12$surv)/mean(1-data12y.3v$pred)) #ln mean O/E risk ratio
model3.12.re$res[c("gamma0", "gamma1", "gamma2"), "est"]
data12y.3v$pred.re<-1/(1+exp(-9.980246+0.2426892+1.511023*data12y.3v$rcs1-0.733772*data12y.3v$rcs2+data12y.3v$lp.3.12)) #change the knots position and s(lnt;r) but keep the linear predictor the same
(1-obj.3.12$surv)/mean(1-data12y.3v$pred.re) #Mean calibration improve
#Before is (1-obj.3.12$surv)/mean(1-data12y.3v$pred), 1.27, now is 1.21
data12y.3v$risk.re<-1-data12y.3v$pred.re
dat_cal.3.12.RP.re <- cbind.data.frame(
"obs" = 1 - predict(vcal.3.12.RP,
type = "survival",
times = 10,
newdata = data12y.3v)[[2]], #1-s(t=4) to get the refitted model predicted risk
"lower" = 1 - predict(vcal.3.12.RP,
type = "survival",
conf.int = T,
times = 10,
newdata = data12y.3v)[[4]],
"upper" = 1 - predict(vcal.3.12.RP,
type = "survival",
conf.int = T,
times = 10,
newdata = data12y.3v)[[3]],
"pred" = data12y.3v$risk.re
)
dat_cal.3.12.RP.re <- dat_cal.3.12.RP.re[order(dat_cal.3.12.RP.re$pred), ]
png("NY-10y-re1.png",width = 3500,height =2000,res = 400)
par(xaxs = "i", yaxs = "i", las = 1)
plot(
x=dat_cal.3.12.RP.re$pred, #x is predicted risk from the
y=dat_cal.3.12.RP.re$obs,
type = "l",
lty = 1,
xlim = c(0, 1),
ylim = c(0, 1),
lwd = 2,
xlab = "Predicted risk from developed model with new boundary knots position and intercept",
ylab = "Predicted risk from refitted model",
main = "Validation study is NYPUM",
bty = "n" #no box
)
lines(dat_cal.3.12.RP.re$pred,
dat_cal.3.12.RP.re$lower,
type = "l",
lty = 2,
lwd = 2)
lines(dat_cal.3.12.RP.re$pred,
dat_cal.3.12.RP.re$upper,
type = "l",
lty = 2,
lwd = 2)
abline(0, 1, lwd = 2, lty = 2, col = 2)
legend("topleft",
c("Ideal calibration",
"Calibration curve based on secondary Royston-Parmar model",
"95% confidence interval"),
col = c(2, 1, 1),