# How to estimate Breslow type Baseline Hazard for mixture cure model?

I have done the following bit myself:

#Prediction using Mixture Cure Modelling
pd<-smcure(Surv(Line_Tenure_In_Days,Churn_Flag) ~ Months_On_Device,cureform = ~ Months_On_Device,data=df_acn4,model = "ph",nboot=100,Var=TRUE)
printsmcure(pd)

predm <- predictsmcure(pd,newX=c(0,1),newZ=c(0,1),model = "ph")
predm_predict<-predm$$prediction as.data.frame(predm_predict) uncure_prob<-predm$$newuncureprob
as.data.frame(uncure_prob)
plotpredictsmcure(predm,model="ph")


Now my aim is to obtain the individual survival probabilities at a fixed time instance using Mixture Cure model for which I am using this smcure() in R.

Questions: I am well aware of the mixture cure model see(https://deepblue.lib.umich.edu/bitstream/handle/2027.42/65901/j.0006-341X.2000.00227.x.pdf?sequence=1&isAllowed=y)

titled Estimation in a Cox Proportional Hazards Cure Model

I am well aware of the smcure() in R.

I also know the Breslow type estimator to calculate $$\Lambda_0(t|Y=1)=\Sigma_{i:t_i\le t}{\dfrac{d_i}{\Sigma_{l \in R_i}w_l^{m}e^{z_l^T.\beta}}}$$

And finally $$S_{pop}(t∣X, Z) = π(z)S(t∣X) + 1 - π(z)$$

Now how do I obtain $$\Lambda_0(t|Y=1)$$ in R for the mixture cure model?

How do I obtain $$S_{pop}(t∣X, Z) = π(z)S(t∣X) + 1 - π(z)$$ for individual observations using the smcure() in R?(By this I mean the following: Is there an equivalent of predict(smcureobject,type="lp") that which we used to do find out the linear predictors in Cox PH model for individual observations?)

I give you how I obtained the individual survival probabilities using CoxPh in R

cox_Jan_Aug <-coxph(Surv(Line_Tenure_In_Days,Churn_Flag)~Months_On_Device+Subscriber_Activity_Price_Plan_Code+Months_On_Price_Plan+Price_Plan_Change_Flag+Total_MOU+Total_Calls+Market_Name+BYOD_Indicator1,method = "breslow")
summary(cox_Jan_Aug)
pred_Jan_Aug <- survfit(cox_Jan_Aug)
plot(pred_Jan_Aug,fun=function(y)log(y/(1-y)), ylab="Logit S(t)",col="Red")

plot(pred_Jan_Aug,
main = 'Cox Regression Plot',col="Blue",width=1,height=1)
abline(h = 0.5,col="Red")
summary(pred_Jan_Aug)
pred_coef_times_vars4<- predict(cox_Jan_Aug,type = "lp")
basehaz_Jan_Aug <- basehaz(cox_Jan_Aug)

predicted_on_15thday4 <- as.data.frame((exp(-basehaz_Jan_Aug[16,1]))^(exp(pred_coef_times_vars4)))
colnames(predicted_on_15thday4)<- 'predicted survival probability on 15th day'

predicted_on_20thday4 <- as.data.frame((exp(-basehaz_Jan_Aug[21,1]))^(exp(pred_coef_times_vars4)))
colnames(predicted_on_20thday4)<- 'predicted survival probability on 20th day'

predicted_on_30thday4 <- as.data.frame((exp(-basehaz_Jan_Aug[31,1]))^(exp(pred_coef_times_vars4)))
colnames(predicted_on_30thday4)<- 'predicted survival probability on 30th day'

Indiv_Prob_Jan_Aug <- cbind(predicted_on_15thday4,predicted_on_20thday4$$predicted survival probability on 20th day,predicted_on_30thday4$$predicted survival probability on 30th day,Line_Tenure_In_Days,Total_MOU,Churn_Flag,Months_On_Device,Months_On_Price_Plan,Price_Plan_Change_Flag,Total_Calls,BYOD_Indicator1,Subscriber_Activity_Price_Plan_Code)
write.csv(Indiv_Prob_Jan_Aug,file = "Individual Probabilities on Jan through August.csv")


A few words:

• Please try not to downvote this post for not posting the original data here
• Please try to use any standard data like e1684 dataset.
• smsurv looks like what you're after. NB: the "mixture cure model" is an abuse of terminology. Farwell and Sy appropriately referred to such models as mixture or cure models: Cox models where an unobserved proportion of individuals are not at risk for the event. NB also: "mixture models" have come to take a different meaning over time. If the smcure function gives you some posterior probability of being not-at-risk, you can classify based on thresholds, fit the normal Cox model only among those at risk, and use the basehaz function. Oct 18, 2018 at 14:00
• instructing people to not downvote you seems like shady site etiquette. Are you not able to makea reproducible example yourself with "standard data like the e1684 dataset"? Oct 18, 2018 at 14:04