Over the course of our work, we encounter countless numbers in hours upon hours of meetings. We are both expected and hoping to infer information about risks and opportunities. Often, we see surface level numbers and are missing key information. Fortunately, from my experience, the decision-makers behind the scenes almost always seem to be aware of the numbers we are missing. Here’s an example where people often hear a number that needs more context—it is totally imagined for this article and not based on any real events I have experienced:
For paid dates in October, our average receipt to paid date decreased by 0.25 days from September’s figure. This has been brought to you by Yesbot, the new AI decisioning tool.
To which I say, “Yes, but . . .” Nobody discussed remains unpaid. A company could be delinquent on aged claims, and that will cause the average observed payment lag to “improve” by decreasing. In the spirit of an annual meeting Professionalism skit, here’s an outlandish phone call:
Pat: Rusty, your contract says that you earn a million-dollar bonus if the 2025 average received to paid date is under eight days. Are you aware?
Rusty: Sure, Pat. And I met the target. Pardon me, I can’t hear you.
Rusty [muted]: Ed, can you shut the enclosure please?
Pat: Andy received an email from you telling everyone to avoid working any claim over seven days old. It even advised sending people home early for the holidays. You announced it at Thanksgiving as part of your gratitude mailing. Do you remember?
Rusty: Yes. What a beautiful send-off! We then dropped our average payment lag below the bonus target. I moved overseas after that last hurrah at New Year’s. My retirement has been wonderful here.
Pat: But . . .
Rusty: Consider the prior end of year, when we ended the year with no inventory over 30 days old. That meant starting the new year off 100% in compliance with prompt pay law. Then our December closeout of the year was the best on record. We didn’t pay one cent of interest in December. That’s an improvement over our best year yet!
Pat: About that. Because you didn’t pay anything, we owe a lot of . . .
Rusty: Hold on.
Rusty [muted]: Yes, right here. I ordered both the pillow and banana smoothie. Oh! A little umbrella. Thank you. That’s for you. Yes, I’m serious. You earned it.
[Click]
What did Rusty do? Rusty took advantage of the fact that the chosen risk metric could not detect a problem. By not paying any claims over seven days old, Rusty forced the average under seven for the month. By all appearances, things are wonderful. But in February, the new administrator has found the problem.
Claim administrators are smarter than this. They understand that the pending inventory must be monitored, and it keeps everyone honest. But what is the real way to measure payment speed? Before we begin, let’s not forget that many in the health industry, including the author, were reluctant to learn actuarial models related to life insurance. Applying the mortality model to claims illustrates the importance of a well-rounded actuarial model education. On with the illustration.
A Point in Time Mortality Refresher
The following example was selected for several reasons:
- It is a mortality problem with short lifespans.
- It is a stepping-stone to the less traditional application of claims.
- The mathematical ingredients are delivered via a story without ambiguity.
- The author has a lifelong affinity for peppers.
Rex farms pepper plants. He brings them indoors and winterizes them in an old bomb shelter before reviving them in the spring sunlight. Only a portion of the plants come back to life, but he always has enough backup starters to end the season with a thousand. Oddly, in 20 years of doing this, he has never had one wake up a fourth time. Every plant that has ever woken up produced that season and was put to sleep in the winter. He has been making what he thinks are improvements, and since he started recording data, he has noticed he’s had to start fewer plants over time. He wants to know whether his plants are living longer. As expected in the Actuarial Fantasy World, he asked an actuary for help.
Table 1 shows the “what was planted and what woke up” numbers, with the remaining unmonitored population making a thousand total.
Table 1
Collected Pepper Plant Data
Assume that for any collection of plants, the estimate of their survival rate is the number of survivors divided by the number that had the opportunity to survive. This is a Bernoulli model.
Looking at the 2018 to 2019 winter transition, the mortality model emerges from the Bernoulli trial observations, as shown in Table 2.
Table 2
Organized Data and Calculations
This makes the average lifetime of each plant 2.452 seasons.
We can do this for each year, as demonstrated in Table 3.
Table 3
Annual Observed Average Lifetime in Seasons
Indeed, as time passed, the pepper farmer received more harvests from each plant.
The Mortality of Claims
Let’s return to a scenario more like the one with Pat and Rusty. For a claim received on November 1 and paid on November 5, the “average observed payment lag” method counts this claim as a four and earned Rusty a nice cabana.
And in the “mortality” model, we count the claim as an observation to five experiments. Did a zero-day-old claim get paid? Did a one-day-old claim get paid? You get the idea. Here’s a trick that may help it make sense: If a claim has the same likelihood of payment every day, then its lifetime to payment in days is a geometric random variable with support at zero.
Consider a business scenario. We want to analyze November activity. Let’s examine some claims and see how they would fall into the “claim mortality” model. If we know how old a claim was “when we started trying to pay it and when we stopped trying to pay it,” we know the collection of November Bernoulli experiments to which it belongs.
Four questions, to be answered in data collection before grouping, populate Table 4:
- Was it open in November?
- How old was the claim, at its earliest, in November?
- How old was the claim, at its oldest, in November?
- Did we pay it?
Table 4
Claim Census Sample
These would count in the model as shown in Table 5.
Table 5
Modeling Data Transformation
What’s in It for Actuaries?
More work, of course. A claim data set was constructed by simulation, with the intent to make a nice distribution shape and lack resemblance to any line of business. These claim patterns are simulated and should not be used to extrapolate anything about an actual claims population.
We account for the observations as follows:
- Claims enter observation by being received during the period or by being open at the beginning of the period.
- Claims exit by being paid or by remaining open at period end.
- We can compute the age of any claim at these moments in time.
- Claims do not close and reopen; they are observed for any day between entry and exit.
- Therefore, the observations are calculated recursively as follows:
- For N = 0, Observations 0 = Entries 0.
- Observations N + 1 = Observations N – Exits N + Entries N + 1.
Table 6 and Figure 1 show “claim mortality” calculation through 31 days.
Table 6
Claim Mortality Calculation for One Month
Figure 1
Claim Survival Distribution
- We have the full historical probability distribution over the observed range (aside from any tail assumption) to help make probability inferences about the anticipated future timing of claim payments.
- In this example, the lifetime to payment (Expected Value) computation is available immediately.
- Lifetime to payment is a statistically unbiased metric for a claim team’s operational productivity in a month.
- Under the illustrated setup, simply avoiding older claims would not improve the measure in the same way it improves the paid-claims-only average.
- If a claim team focuses on aged claims and pays them, the metric improves.
- This technique is easily adapted to business days only.
- The number of business days elapsed between two dates is also an integer over identical support.
- There are some direct applications to insurance work.
- If a claim is held today completing Day 22, how likely is it to exceed Day 30?
- P (Claim Paid 31 or After | Claim Paid 23 or After) = 0.0162 / 0.0385 = 0.42
- How often in general does the team comply with a 30-day prompt pay goal?
- According to the preceding model, the company fails to comply 1.62% of the time. Note that the actual compliance rate for November is not available here since some observations are paid in October but “30 day due” in November.
- In predictive modeling, can we fit a target variable for whether a claim is likely to be paid with interest?
- Claims aged zero could potentially be identified to get a head start.
- Since we know the probability timing stream of information, can we easily compute an interest reserve?
- We have a discount assumption, a claim interest assumption, a future payment timing probability distribution and the expected paid amount; an interest reserve calculation awaits.
- How much time and money do claim payment initiatives and improvements really save?
- This model inherits the well-established and robust mathematical framework from the mortality distribution. All of the ordinary probability distribution assumption constraints are satisfied.
- The probability and timing of payments provides important information that an actuary may use to estimate how much expected interest will be paid on claims held. Using this, it can provide a financial insight into the value of claim processing initiatives.
- If a claim is held today completing Day 22, how likely is it to exceed Day 30?
- Were any real claims used in this article?
- I work for a sophisticated company that works very hard to avoid that. So, of course not!
- Were any pepper plants harmed in the creation of this article?
- No, and sadly, no peppers were eaten.
This article is provided for informational and educational purposes only. Neither the Society of Actuaries nor the respective authors’ employers make any endorsement, representation or guarantee with regard to any content, and disclaim any liability in connection with the use or misuse of any information provided herein. This article should not be construed as professional or financial advice. Statements of fact and opinions expressed herein are those of the individual authors and are not necessarily those of the Society of Actuaries or the respective authors’ employers.
Russ Greenlee, FSA, is director of actuarial services at USHEALTH Group. Russ can be reached at GreenleeR@ushealthgroup.com.