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Suppose you have a set of insurance claims and you want to predict the probability that a claim will give rise to a complaint from some features of the claim at a certain point in time such as time from the first notification of loss to claim closure, time to first payment, etc.

The starting point is a data set of claims with some measures at time t and a flag for claims that currently have a complaint open on them. The dataset is quite unbalanced as the complaint rate is <3%.

I was thinking to model the response variable Y ('the claim has triggered a complaint') as a Bernoulli random variable and then to use logistic regression to model the probability of a claim triggering a complaint.

Do you think that this is an appropriate starting point? If so, what would you suggest to be careful with? If not, what other models would you use instead to model this probability?

Ideally, I want to update these probabilities as the claim progresses through its lifecycle, but I want to avoid Bayesian methods at this stage.

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  • $\begingroup$ Yup. That’s what I would do as a first cut at this type of data. I wouldn’t worry too much about the complaint rate unless you have a very small number of complaints (like that 3% represents 10 total complaints). Working with probabilities alleviates the much discussed issues with unbalanced classes. $\endgroup$ May 25, 2019 at 18:53
  • $\begingroup$ @Matthew thanks for your reply, I'm glad to see that I'm going in the right direction. Could you just expand a bit on why the fact that the dataset is unbalanced is not a concern in this context? $\endgroup$ May 25, 2019 at 20:59
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    $\begingroup$ Class imbalance doesn't really affect the ability of logistic regression to estimate probabilities. If you think about it, there's really no reason it should, by virtue of estimating probabilities it can just adjust the results to take into account the prior probability of ending up in either class. You can confirm this with simulation experiments. It does affect the way you would create a classification rule given a logistic regression, naively thresholding at 0.5 is problematic in this situation, for example. There's a few detailed threads about this on CV if you search. $\endgroup$ May 25, 2019 at 23:12
  • $\begingroup$ Right, I see. Actually, I'm also interested in building a classification rule based on logistic regression to categorise claims as either ' will develop into a complaint' or not. Could you send the links to the threads on CV that you were mentioning in your latest comment, please? c $\endgroup$ May 26, 2019 at 5:51

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