Data Science Asked by Ajay H on January 28, 2021
I’ve been looking into the Cox Regression method for Survival Analysis in Churn Prediction. Cox regression will allow us to determine the probability that a subscriber will unsubscribe after a time $t$, defined by the hazard rate:
$$
h(t lvert X_i ) = h_0(t)expbig( boldsymbol{beta} ^Tboldsymbol{X}_{i} big)
$$
Where
$h_0(t)$: Baseline Hazard is a prior Probability that any customer churns at time t when all influencing factors are 0.
$boldsymbol{beta} in mathbb{R}^D$: Exponent of each Coefficient gives us a Hazard ratio. These should be constant w.r.t time (proportionality assumption).
$boldsymbol{X}in mathbb{R}^{Ntimes D}$: Set of $N$ sample customers
Problem: Proportionality Hazard Assumption: Cox regression makes an assumption that the Hazard Ratios should remain constant through time $t$. For example, for a covariate $X_1$ = “gender”, say $beta_1=1.8$. In english, it means male subscribers tend to leave the service $80%$ more than females after a time $t$. However, this $80%$ should hold for any time $t$.
This is usually an unreasonable constrain for many variables. But there are other methods that can incorporate variables that don’t follow the proportional hazards assumption.
I was just reading up on stratified cox regression. The only apparent downside here is:
Question: Is pseudo-observations similar? Does it have less/more rigid constraints? Even so, how is it’s performance considering I have copious amounts of data?
I suggest using a model with more relaxed assumptions on proportionality of hazards. In my work I use piecewise constant hazard model, which works wonderfully. Its assumption is that the hazards are proportional in a time interval. It allows using numerical covariates with splines, and time-dependent covariates. Moreover in my experience the model is usually very well calibrated and does not overfit much.
Answered by Gino_JrDataScientist on January 28, 2021
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