I am studying the effects of customer interaction on the probability that the customer will adopt a recommendation we make to them. For example, we might send out a first email, then a follow-up email one week later, then a final follow-up phone call. I've identified the Cox Proportional Hazards model (with time-varying covariates) as a strong candidate for doing exactly this.

I've prepared my data in a form expected by the coxph function in the R survival package. I form a dataframe uptake with the appropriate start, stop, n_touchpoint, and success columns. I fit the model like this:

conv_model <- 
  coxph(Surv(start, stop, success) ~ n_touchpoint,
        data = uptake)

Here is the output from calling summary on the model:

> summary(conv_model)
coxph(formula = Surv(start, stop, success) ~ n_touchpoint, data = uptake)

  n= 289256, number of events= 8806 

                coef exp(coef) se(coef)     z Pr(>|z|)    
n_touchpoint 1.09517   2.98968  0.01818 60.23   <2e-16 ***
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

             exp(coef) exp(-coef) lower .95 upper .95
n_touchpoint      2.99     0.3345     2.885     3.098

Concordance= 0.575  (se = 0.002 )
Rsquare= 0.009   (max possible= 0.5 )
Likelihood ratio test= 2690  on 1 df,   p=<2e-16
Wald test            = 3628  on 1 df,   p=<2e-16
Score (logrank) test = 3348  on 1 df,   p=<2e-16

So the model seems to say that the number of touchpoints is highly significant, and that each additional touchpoint roughly triples the hazard.

But how do I know that my model can be used for predicting future conversion attempts? In normal regression I would know how to use cross-validation, i.e. splitting my data set in a training set and a test set, but how do I validate the conv_model object on my test set?

I've found similar questions below, but I did not find the answers very helpful:

Meaning of R's coxph output

How to do ROC-analysis in R with a Cox model

Cox model vs logistic regression

Interpretation and validation of a Cox proportional hazards regression model using R in plain English

How to do ROC-analysis in R with a Cox model

How to validate Cox Proportional Hazards model?

Model testing - Cox proportional hazards model


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