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I'm pondering a scenario involving some insurance data but this could be relevant in many fields. The idea is that I have a total count of some event. Let's imagine this count is the # of attorney negotiations present in a cohort of insurance claims. Lets say I have 1,000 of them in my data.

If I hypothesize that 10% of these attorney negotiations end up going to court (litigation) I want to estimate the additional amount of money spent on litigation.

What type of models or methods could I use in this scenario? I know regression is plausible but I want to be cautious of extrapolating outside of my predictor values (in this case litigation %) in the case that I want to create some extreme what-if scenarios for discussion.

It seems simple in nature but I'd like to have reasonably accurate estimates. Maybe some sort of simulation is in order? Or is an A-B Test applicable here ?

Concrete example with numbers:

Total # of Attorney Negotations: 1000
Actual data Litigation % is around 5%.
Hypothesize the additional amount spent on litigation if Litigation is 1% or 10%. 

Any suggestions would be welcome.

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  • $\begingroup$ It is very unclear what your data look like. Can you describe how they look in a spreadsheet? 1000 rows, right? What are the column variable names? What do the numbers within the columns look like? (0s and 1s? Or counts?) How many columns? Which column is the dependent variable and which are the predictors? $\endgroup$ – BigBendRegion Apr 8 at 13:44
  • $\begingroup$ @BigBendRegion 1000 rows (each row is a unique claim that had an attorney negotiation). 5% of these 1000 rows have a litigation indicator column=1. There is a payment column that says how much was spent on that claim total. The question I posed is rather hypothetical on how I would estimate the cost of litigation if instead of 50 rows I had 100 rows that had litigation, etc. Not looking for concrete number analysis, rather just ideas on how to estimate increased costs by changing the % of rows that are litigated. Generally if a claim goes to litigation it will cost more (court costs, etc.) $\endgroup$ – Coldchain9 Apr 8 at 14:13
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    $\begingroup$ Well, just run a logistic regression using how much was spent as the predictor, and the litigation indicator as the response. Draw the graph, extending outside the range of the cost variable if necessary, to see where the % gets to 10%. This is obviously very sensitive to functional specification, so try other link functions, like probit and other. Also, consider very strongly what kind of nonlinear effect cost has on litigation, because this will strongly affect the extrapolation. Of course, you are on shaky ground here, but you already know that., At least you will get some ideas. $\endgroup$ – BigBendRegion Apr 8 at 15:04
  • $\begingroup$ @BigBendRegion Thank you. My initial idea was to run a gamma GLM on the cost variable as dependent variable with the litigation indicator as a predictor (among other contributors to cost) and then using that factor I could see relatively how much litigation is contributing to the cost. By using that factor I could extrapolate it to see how much of the cost is going to litigation and then use that value to perform a what-if analysis. Its shaky ground indeed but at the end of the day I could probably create some confidence intervals about the mean litigation cost compared to non-litigation too. $\endgroup$ – Coldchain9 Apr 8 at 15:15

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