Solved – How to make prediction in survival analysis using R

predictionrsurvival

I have fitted a survival model in R which is below. However, I am not sure how to make predictions. I tried predicting the survival probability that a patient whose design matrix is X lives longer than 100 days, but no matter what design matrix I use, the probability is always 0. What do you think I am doing wrong?

library(survival)
attach
weibull <- survreg(Surv(time,status)~celltype + karno+diagtime+age+prior+trt ,dist="w")
beta[,1] <- as.matrix(c(weibull$coef))
x <- as.matrix(c(1,1,0,0,80,10,65,0,2)) #Design matrix
lambda <- beta[,1]%*%x
1 - (1 - exp(-lambda*100))

Best Answer

This is the code, copied & pasted from the help file to the function predict.survreg, which relates to predicting Weibull models:

lfit <- survreg(Surv(time, status) ~ ph.ecog, data=lung)
pct <- 1:98/100   # The 100th percentile of predicted survival is at +infinity
ptime <- predict(lfit, newdata=data.frame(ph.ecog=2), type='quantile',
                 p=pct, se=TRUE)
matplot(cbind(ptime$fit, ptime$fit + 2*ptime$se.fit,
                             ptime$fit - 2*ptime$se.fit)/30.5, 1-pct,
        xlab="Months", ylab="Survival", type='l', lty=c(1,2,2), col=1)

Hope this helps.

Related Solutions

Solved – Survival analysis for event prediction

Is the survival analysis suited for my purposes?

The only thing that makes this seem less applicable for survival analysis is:

... $TT$ might be missing if there was no event or set to time the follow-up ended.

You will need to know the last period the individual was observed to be alive at for most models. Otherwise it should be straightforward and applicable to use survival analysis. E.g. Cox proportional hazard with survival::coxph in R or a parametric models with survival::survreg.

The mean survival time, that can be computed for each record, seems a nice risk index - the lower the higher the risk is.

Yes, you can use the mean survival times or just the linear predictor for the two former mentioned (classes of) models.

How can I evaluate the performance of my model?

The $c$ index seems like a sensible choice to me as "natural" generalization of the AUC. Note that is implemented in R with e.g. Hmisc::rcorr.cens.

Solved – Conditional expected lifetime in survival analysis

One possible approach would be to predict the median survival time (i.e. the expected time at which the survival for a patient with a specific combination of characteristics would be 0.5, in other words, from that timepoint onwards it is more likely that the patient has died than that he is still alive). This can be done using functions from the rms package as follows:

library(rms)

# datadist is needed to fit the models:
dd <- datadist(colon)
options(datadist="dd")

fit <- psm(Surv(time,status)~rx+age+sex,data=colon, dist="weibull", x=TRUE, y=TRUE)

# The Quantile-function, creates a new function using your model for getting 
# quantiles of the predicted survival (by default median)
QFUN <- Quantile(fit)

# Now use QFUN to get the predicted median survival for the patients in your data
pred.med.surv <- QFUN(predict(fit,type="lp"))

# When asking for only one quantile (here 0.5), it drops dimensions of the output, so 
# you would have to use the following to bind the new variable to your data.frame 
colon$pred.med.surv <- as.numeric(dimnames(pred.med.surv)[[2]])

# For multiple quantiles of predicted survival you can use the following:
preds <- QFUN(q=c(0.25,0.5), predict(fit,type="lp"))
colon$surv0.25 <- preds[,"0.25"]
colon$surv0.5 <- preds[,"0.50"]

A few notes:

I see that you delete patients who died 'etype=2' from the dataset. This could lead to bias. In this case you want to evaluate recurrence, death is actually a competing risk for recurrence which calls for different type of survival analysis. Then it would be advisable to call in expert help.
The predicted survival time depends on the patients in the dataset you used to develop the model. If e.g. the model was build using measurements of patients at the day of their diagnosis (day 0), you should also enter the predictor values of the patients at day 0 and not those at day 2000. Since the example patient you mention has already survived up to day 2000, the model would not be valid for him, as his survival is probably longer. Or you could for example include a predictor variable indicating the time since diagnosis.
As I don't know the details of your research project, I would advise you to consult a statistician to determine a valid approach for your research project.

Hope this helps.

Best Answer

Related Solutions

Solved – Survival analysis for event prediction

Solved – Conditional expected lifetime in survival analysis

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