The Art of DAR
Days in Accounts Receivable in the Healthcare Revenue Cycle
Andrew Bruce, RHIT, CPC, CPPM, RH-CBS
2021-12-14
Abstract
This is an outline of a book currently under early development. Days in Accounts Receivable (also known as DAR or Days in AR) is a common financial metric belonging to a group of ratios called efficiency ratios. It measures the average amount of time it takes for a business to collect money owed from the responsible party for services rendered and billed. As its name implies, the unit of measurement employed by this particular metric is days, or rather the average number of days from the moment a physician provides a service until the patient or guarantor pays for that service.
This number can tell you much about the financial health of the business. This book is designed to take you from knowing nothing about Days in AR to being able to interpret and make proper use of it and it’s underlying data at a very high level. You will gain a deep understanding of the mathematical and statistical foundations that form the DAR metric, as well as developing many useful techniques to solve common revenue cycle challenges.
Introduction to DAR
At its simplest, Days in AR is a mathematical formula that gives you an idea of how long your accounts receivable takes to clear. The easiest way to think of it is the number of days the average invoice will remain outstanding before payment is made. Completing your accounts receivable days formula gives you insight into how well your business (or your accounts receivables team) is at collecting payment on outstanding invoices.
The success of a practice’s billing operations is often measured in AR days. The AR balance can be reduced by receiving payments or by entering contractual or write off adjustments. It is important to manage the AR balance as claims become much more difficult to collect the older they become.
Good management of AR is also imperative to maintaining a good cash flow for the business. A poor AR process can result in loss of money to the business and result in financial strains to the owners. If all these tasks are being done properly, the days in AR number should be low, in contrast, high days in AR number will most likely tell you there is a problem in your revenue cycle.
What Does it Mean?
A growing number of Days in Accounts Receivable is symptomatic of a faulty billing process. For instance, let’s say a practice has a DAR of 95 days. This means that, on average, it takes the practice 95 days to collect it’s outstanding balances. But what exactly does this mean? Is a DAR of 95 good? Is it bad? How bad or good is it?
The Simple Answer
If you spend just a few minutes searching online, you’ll come across as many different answers as links and pages you can click on. Many practices look to organizations such as MGMA1 for industry-specific KPI2 standards or thresholds. Let’s look at a couple of these. The table below is representative of a common scale for Days in AR you will come across when searching for benchmarking standards:
library(gt)
dar_kpi_ex <- read.csv("data/dar_kpi_ex.csv") %>% janitor::clean_names()
dar_kpi_ex %>%
gt() %>%
cols_label("i_days_in_ar" = md("**Days in Accounts Receivable**"),
`performance` = md("**Performance**")) %>%
opt_row_striping(row_striping = TRUE)| Days in Accounts Receivable | Performance |
|---|---|
| 35 Days or Less | Great/Good |
| 35 - 50 Days | Average |
| 50 Days or More | Poor |
These “easy” answers are, in fact, excellent general answers. However, each medical practice is a unique animal, made up of a complex web of distinct attributes. Benchmarking standards, while a good place to start, apply to the average of all medical practices surveyed by the organization that publishes them.
The Complex Answer
Let’s go back to the DAR of 95 days and what it means for the practice from the example. The immediate insight is that it takes, on average, 95 days for this practice to collect it’s unpaid balances. The deeper insight is that at least three months of working capital is required to maintain the practice’s cash flow needs.
95 days is roughly equal to three months, thus, there’s three months of unpaid work sitting in Accounts Receivable. Therefore, if the practice is going to meet its financial obligations (i.e., payroll, rent, etc.), it’s going to need three months of cash reserves available, or it will have to borrow these amounts, which will in turn have additional repercussions.
The “ideal” average Days in AR depends entirely upon the medical practice, its customers (patients), and its customers’ payers, whether they be third-party payers or the patient themselves. It also depends on the services it supplies and the providers performing those services. Finally, it will depend on the financial situation of the practice and its stakeholders.
A practice’s DAR number can have different meanings across different types of practices as well. Having a very high DAR number can be indicative of a too-lenient policy with late-paying customers, or it could simply be standard for your specialty. On the other hand, having a very low DAR number could indicate a great working relationship with your patients, or that you have a hard-line approach to your payment policy that is alienating longtime patients and potentially cutting off new business.
A Starting Point for Further Analysis
Imagine this scenario: A tornado has hit your neighborhood while you are away and you are worried about your house. The only way to know the true state of your house is to go there and look around.
Judging the financial health of your medical practice by comparing it’s performance to industry-standard benchmarks is akin to trusting a stranger to tell you that your house is fine…while standing on the moon.
“See? It’s that dot right there, everything’s fine.”
The purpose of a good KPI (or group of KPIs) is to reduce the amount of time and cognitive load it requires to understand a large, complex set of data that is constantly being added to. The problem that many people run into is a lack of understanding of the basic foundations of these metrics and their fundamental inter-connectivity. End-users of the KPIs cannot then use them to properly anticipate and prevent the problems that they’re meant to highlight.
My proposal is a very simple one: familiarize yourself with the moving parts of the DAR metric and you will know how well it is running and what to do when it breaks down. You will be much better informed about not only Days in AR, but most every other significant KPI, as Days in AR connects to each of them in some way, however great or small.
Gross Charges as Opposed to Net Charges?
This is a great question and one that we’ll explore in more detail when we discuss the Revenue Cycle workflow. The short answer is that Net Charges excludes such things as contractual adjustments, and so it’s missing important information. Within the space of two numbers, AR Balance and Gross Charges, you can tell the story of an organization’s financial history. This idea of representing comes from the world of accounting and I find it brilliant in it’s simplicity.
To account is to bear witness. As the financial historian of a business entity, the accountant must be able to explain in the simplest terms possible, the financial events, past and present. As such, there is a restriction involved, called a monetary denominator.
Even if no reimbursement is involved, an event is described in terms of amounts of currency, rather than exhaustively describing the minutiae of each paper clip purchase. This number can be investigated extensively if the stakeholders see fit. And why wouldn’t they? It contains the entirety of the company’s financial history.
In much the same spirit, the Gross Charge figure contains the total account of work done while the Ending AR Balance is the exhaustive archive of compensation and recompense on behalf of that work.
Advantages & Disadvantages
A few more words on what the DAR metric is and is not. Again, it would not be appropriate to compare the DAR of medical practices with different specialties. For example, a cardiology group’s DAR would not compare to a plastic surgery practice’s DAR because the methods of reimbursement for these two entities are entirely different. Not only does the DAR metric depend on medical specialty, but also patient demographics, payer mix, and procedure sample.
Another disadvantage is that it is sensitive to the provider because it counts the lag time of unsubmitted claims for services already delivered. However, this lag time roughly averages across all payers, making DAR an effective comparison between payers for an individual provider, but invalidating it across multiple providers. One obvious advantage of the DAR metric is its independence of charges. The average feature of this metric eliminates sensitivity to a specific day or CPT, but it also hides the behavior shape of the AR curve.
To make up for these weaknesses, there are adjusted formulas as well as other metrics (such as PARBX3) that we’ll use to fill in these gaps.
The DAR Formula
The core idea of the calculation to determine DAR is to go through each individual claim, count the days from the Date of Service to the Date of (full) Payment, add all of those up, and divide by the total number of claims. This is an extremely laborious process, so other formulas have taken it’s place. The most commonly used is as follows:
Divide the total Gross Charges by the Number of Days in the period that you are measuring. This is the Average Daily Charge for that period.
Divide the Ending AR Balance for the same period by the Average Daily Charge. This is the average Days in AR for that period.
The Three Numbers
You need only three numbers to calculate the average Days in AR. They are the Number of Days in the Period, the total Gross Charges for that period, and the Ending AR Balance. Technically, you will also need the Average Daily Charge, but you can derive this number from two of the three essential numbers:
Number of Days in the Period
This is literally the number of days within the period for which you are measuring Days in AR. DAR is typically measured in monthly and quarterly increments, so this number will usually hover around 30, 60, 90, etc.
library(gt)
common_ndips <- read.csv("data/Common_NDIPS.csv") %>% janitor::clean_names()
common_ndips %>%
gt() %>%
cols_align(align = "left",columns = 1) %>%
cols_align(align = "left",columns = 2) %>%
cols_label("i_common_reporting_periods" = md("**Common Reporting Periods**"),
`number_of_days` = md("**Number of Days**")) %>%
opt_row_striping(row_striping = TRUE)| Common Reporting Periods | Number of Days |
|---|---|
| January | 31 |
| February | 28 |
| March | 31 |
| First Quarter | 90 |
| April | 30 |
| May | 31 |
| June | 30 |
| Second Quarter | 91 |
| July | 31 |
| August | 31 |
| September | 30 |
| Third Quarter | 92 |
| October | 31 |
| November | 30 |
| December | 31 |
| Fourth Quarter | 92 |
Total Gross Charges
Gross charges, which are usually the full fee schedule4 charges, are typically all charges generated by the practice, regardless of actual reimbursement. This figure is the total dollar amount charged during the Number of Days in the Period you are measuring. Whether billed to insurance on a claim or to a self-pay patient, all charges for the period are included here.
Average Daily Charge
This number is the total Gross Charges amount divided by the Number of Days in the Period.
Ending AR Balance
This is the AR balance at the close of business on the final day of the Period that you are measuring.
Step-by-Step Example
Let’s go through an example of the DAR calculation step-by-step. The following table contains the three data points you need to calculate Days in AR:
\[\\[3pt]\]
| Number of Days in Period | Gross Charges | Ending AR Balance |
|---|---|---|
| 30 | $131,440.30 | $203,460.50 |
\[\\[3pt]\]
STEP 1: Calculate the Average Daily Charge
First, we need to calculate the Average Daily Charge. The formula is as follows:
\[\\[3pt]\]
\[\\[3pt]\]
Take the Gross Charges from the table above, divide it by the Number of Days in the Period and our Average Daily Charge will be $4,381.34:
\[\\[3pt]\]
\[\\[3pt]\]
GCt divided by NDiP equals ADC.
131440.30/30## [1] 4381.343(Note: This is an R language coding chunk. I will be using these to show the outputs of calculations for the sake of accuracy.)
STEP 2: Calculate the Days in AR
Now that we have the three variables required by the DAR formula, we can calculate the Days in AR. The formula is as follows:
\[\\[3pt]\]
\[\begin{equation} \dfrac {\textrm{Ending AR Balance}}{\textrm{Average Daily Charge}}= {\textrm{Days in AR}} (\#eq:dartxt) \end{equation}\]\[\\[3pt]\]
Substitute the Ending AR Balance and Average Daily Charge into the formula and divide:
\[\\[3pt]\]
\[\\[3pt]\]
EARB divided by ADC equals DAR.
203460.50/4381.34## [1] 46.43796\[\\[3pt]\]
This gives us an average Days in AR of 46.44 days. Now our report table looks like this:
| Days in Period | Gross Charges | Ending AR | Avg Daily Charge | Days in AR |
|---|---|---|---|---|
| 30 | $131,440.30 | $203,460.50 | $4,381.34 | 46.44 |
\[\\[3pt]\]
Building on the DAR Formula
Now that we have a basic understanding of the formula for Days in AR, we can expand upon and rearrange it to do many other things. The formulas we will derive from the basic DAR calculation in this chapter will allow us to perform many, many different kinds of data analysis. To start off, we will include the calculation for the Average Daily Charge in the denominator of our basic DAR formula:
\[\\[3pt]\]
\[\begin{equation} {\textrm{Days in AR}}=\dfrac {\textrm{Ending AR Balance}}{\textrm{Gross Charges} \div \textrm{Number of Days in Period}} (\#eq:dar2txt) \end{equation}\]\[\\[3pt]\]
To simplify things, I’m going to begin using mathematical variables and acronyms for these numbers. They are as follows:
\[\\\]
| Variable | Acronym | Description |
|---|---|---|
| \(n\) | NDiP |
Number of Days in the Period |
| \(x\) | GCt |
Total Gross Charges for NDiP |
| \(y\) | EARB |
Ending AR Balance |
| \(c\) | ADC |
Average Daily Charge for NDiP |
| \(z\) | DAR |
Days in AR |
| \(t\) | DARt |
DAR Target |
\[\\[3pt]\]
The DAR formula can now be represented in several ways:
\[\\[1pt]\]
\[\\[1pt]\]
EARB for \(x\) DAR
What if we wanted to know the exact Ending AR Balance we would need to attain a certain number of Days in AR? First, we will need to find the formula for EARB. We have our DAR formula converted to variables to make it easier to visualize what is going on mathematically:
\[\\[3pt]\]
We can find the formula for EARB by taking the formula for DAR and solving for \(y\):
\[\\[3pt]\]
\[\begin{align} \dfrac {y}{x \div n}&={z}\\ \\ \\ \left(\frac {x}{n}\right) \dfrac {y}{x \div n}&={z} \left(\dfrac {x}{n}\right)\\ \\ \\ {y}&=\dfrac{zx}{n}\\ \\ \\ \\ {\textrm{EARB}}&=\dfrac{\textrm{DAR} \times \textrm{GCt}}{\textrm{NDiP}}\\ \\ \\ (\#eq:earbstep) \end{align}\]\[\\[3pt]\] Let’s use our table of results from the example in Chapter 2 and say that we would like to have achieved a DAR of 39.44. What Ending AR Balance would we have needed?
\[\\[1pt]\]
| NDiP (\(n\)) | GCt (\(x\)) | EARB (\(y\)) | ADC (\(c\)) | Desired DAR (\(z\)) |
|---|---|---|---|---|
| 30 | $131,440.30 | ? | $4,381.34 | 39.44 |
\[\\[3pt]\] Substituting the known variables from the table into our EARB formula and performing the calculation gives us a new EARB of $172,800.18:
\[\\[3pt]\]
\[\begin{align} {\textrm{EARB}}&=\dfrac{\textrm{DAR} \times \textrm{GCt}}{\textrm{NDiP}}\\ \\ \\ {172,800.18}&=\dfrac {39.44 \times 131,440.30}{30}\\ \\ \\ (\#eq:earbs) \end{align}\]\[\\[3pt]\]
DAR multiplied by GCt, then divided by NDiP, equals EARB.
(39.44 * 131440.30) / 30## [1] 172800.2
This is the Ending AR Balance we would need for 39.44 Days in AR.
GCt for \(x\) DAR
We can perform the same steps if we wanted to know the total Gross Charges we would need for a certain number of Days in AR. We can find the formula for GCt by taking the formula for DAR and solving for \(x\):
\[\\[3pt]\]
\[\begin{align} \dfrac {y}{x \div n}&={z}\\ \\ \\ \left(\frac {x}{n}\right) \dfrac {y}{x \div n}&={z} \left(\dfrac {x}{n}\right)\\ \\ \\ {x}&=\dfrac{yn}{z}\\ \\ \\ \\ {\textrm{GCt}}&=\dfrac{\textrm{EARB} \times \textrm{NDiP}}{\textrm{DAR}}\\ \\ \\ (\#eq:gctstep) \end{align}\]\[\\[3pt]\]
We would again like to have achieved a DAR of 39.44. What total Gross Charges would we have needed to achieve this result?
\[\\[3pt]\]
| NDiP (\(n\)) | GCt (\(x\)) | EARB (\(y\)) | ADC (\(c\)) | Desired DAR (\(z\)) |
|---|---|---|---|---|
| 30 | ? | $203,460.50 | $4,381.34 | 39.44 |
\[\\[3pt]\]
If we plug our known variables into our formula for total Gross Charges, we get a GCt of $154,762.04.
EARB multiplied by NDiP, then divided by DAR, equals GCt.
(203460.50 * 30) / 39.44## [1] 154762
The Average Daily Charge is determined in part by GCt, thus we will need to recalculate it since GCt has changed. Dividing the new GCt amount by the NDiP gives us a new ADC of $5,158.74.
GCt divided by NDiP equals ADC.
154762.04 / 30## [1] 5158.735\[\\[3pt]\]
\[ \begin{aligned} \dfrac {203,460.50 \times 30}{39.44}&={154,762.04}\\ \\ \\ \dfrac {154,762.04}{30}&={5,158.74} \end{aligned} \] \[\\[3pt]\]
NDiP for \(x\) DAR
We can perform the same steps if we wanted to know the Number of Days we’d need to attain a certain number of Days in AR. Let’s again take our original table of results and set up the calculation:
\[\\[3pt]\]
| NDiP (\(n\)) | GCt (\(x\)) | EARB (\(y\)) | ADC (\(c\)) | DAR (\(z\)) |
|---|---|---|---|---|
| 30 | $131,440.30 | $203,460.50 | $4,381.34 | 46.44 |
\[\\[3pt]\]
We have our DAR formula converted to variables:
\[ \begin{aligned} {\textrm{If:}} \ \ \ \frac {\textrm{EARB}}{\textrm{GCt} \div \textrm{NDiP}}&={\textrm{DAR}} \\ \\ \\ {\textrm{Where:}}\ \ \ {\textrm{EARB}}&=y\\ \ \ {\textrm{GCt}}&=x\\ \ \ {\textrm{NDiP}}&=n\\ \ \ {\textrm{DAR}}&=z\\ \ \ \\ \\ {\textrm{Then:}} \ \ \ \frac {y}{x \div n}&={z} \\ \end{aligned} \] \[\\[3pt]\]
To find the formula for NDiP, we take the formula for DAR and solve for \(n\), giving us:
\[\\[3pt]\]
\[ \frac {zx}{y}={n} \] \[\\[3pt]\]
Looking back at our table, we would again like to have achieved a DAR of 39.44. What Number of Days in the Period would we have needed to achieve this result?
\[\\[3pt]\]
| NDiP (\(n\)) | GCt (\(x\)) | EARB (\(y\)) | ADC (\(c\)) | Desired DAR (\(z\)) |
|---|---|---|---|---|
| ? | $131,440.30 | $203,460.50 | $4,381.34 | 39.44 |
\[\\[3pt]\]
If we plug our known variables into our formula for total Gross Charges, we get an NDiP of 25.48.
DAR multiplied by GCt, then divided by EARB, equals NDiP.
(39.44 * 131440.30) / 203460.50## [1] 25.47917
As the Average Daily Charge is determined in part by NDiP, this calculation will also change it, to $5,158.57.
GCt divided by NDiP equals ADC.
131440.30 / 25.48## [1] 5158.568\[ \begin{aligned} \dfrac {39.44 \times 131,440.30}{203,460.50}&={25.48}\\ \\ \\ \dfrac {131,440.30}{25.48}&={5,158.57} \end{aligned} \]
\[\\[3pt]\]
ADC for \(x\) DAR
This formula is going to be a bit different from the previous three. Remember, our formula for the Average Daily Charge is:
\[\\[3pt]\]
\[ \dfrac {\textrm{Gross Charges}}{\textrm{Number of Days in Period}} = {\textrm{Average Daily Charge}} \] \[\\[3pt]\]
Let’s take our DAR formula and make the appropriate adjustments:
\[ \begin{aligned} {\textrm{If:}} \ \ \ \dfrac {\textrm{EARB}}{\textrm{ADC}}&={\textrm{DAR}} \\ \\ \\ {\textrm{Where:}}\ \ \ {\textrm{EARB}}&=y\\ \ \ {\textrm{ADC}}&=c\\ \ \ {\textrm{DAR}}&=z\\ \ \ \\ \\ {\textrm{Then:}} \ \ \ \dfrac {y}{c}&={z} \\ \end{aligned} \] \[\\[3pt]\]
To find the formula for ADC, we take the formula for DAR and solve for \(c\), giving us: \[\\[3pt]\]
\[ \dfrac {y}{z}={c} \]
\[\\[3pt]\]
Looking back at our table, we would again like to have achieved a DAR of 39.44.
\[\\[3pt]\]
| NDiP (\(n\)) | GCt (\(x\)) | EARB (\(y\)) | ADC (\(c\)) | DAR (\(z\)) |
|---|---|---|---|---|
| 30 | $131,440.30 | $203,460.50 | $4,381.34 | 46.44 |
\[\\[3pt]\]
What Average Daily Charge would we have needed to achieve this result?
\[\\[3pt]\]
| NDiP (\(n\)) | GCt (\(x\)) | EARB (\(y\)) | ADC (\(c\)) | Desired DAR (\(z\)) |
|---|---|---|---|---|
| 30 | $131,440.30 | $203,460.50 | ? | 39.44 |
\[\\[3pt]\]
If we plug our known variables into our formula for Average Daily Charge, we get an ADC of $5,158.74.
EARB divided by DAR equals ADC.
203460.50 / 39.44## [1] 5158.735
As a change in ADC will effect GCt, we’ll use the ADC-centric formula for GCt to calculate it, giving us $154,762.05.
NDiP multiplied by ADC equals GCt.
30 * 5158.735## [1] 154762\[\\[3pt]\]
\[ \begin{aligned} \dfrac {203,460.50}{39.44}&={5,158.74}\\ \\ \\ {30 \times 5,158.74}&={154,762.05} \end{aligned} \]
\[\\[3pt]\]
Relationship Between the DAR Variables
In this section, we will discuss the empirical relationship between DAR and all of it’s related variables. In the last section, you might have noticed that we established two different formulas for the Average Daily Charge:
\[\\[3pt]\]
\[ \begin{aligned} \dfrac {\textrm{GCt}}{\textrm{NDiP}} &= {\textrm{ADC}} \\ \\ \\ \dfrac {\textrm{EARB}}{\textrm{DAR}} &= {\textrm{ADC}} \end{aligned} \]
\[\\[3pt]\]
If these are both true, then we can assume that both of the following equations are true:
\[\\[3pt]\]
\[ \begin{aligned} \dfrac {\textrm{GCt}}{\textrm{NDiP}} &= \dfrac {\textrm{EARB}}{\textrm{DAR}} \\ \\ \\ \dfrac {\textrm{DAR}}{\textrm{NDiP}} &= \dfrac {\textrm{EARB}}{\textrm{GCt}} \end{aligned} \]
\[\\[3pt]\]
Or, in mathematical terms:
\[\\[3pt]\]
\[ \begin{aligned} \dfrac {x}{n}&=\frac {y}{z} \\ \\ \\ \frac {z}{n}&=\frac {y}{x} \end{aligned} \]
\[\\[3pt]\]
Let’s test this equivalency out with our original report values:
\[\\[3pt]\]
| NDiP (\(n\)) | GCt (\(x\)) | EARB (\(y\)) | ADC (\(c\)) | DAR (\(z\)) |
|---|---|---|---|---|
| 30 | $131,440.30 | $203,460.50 | $4,381.34 | 46.44 |
\[\\[3pt]\]
NDiP multiplied by ADC equals GCt.
# 1. GCt divided by NDiP equals ADC
131440.30/30## [1] 4381.343# 2. EARB divided by DAR equals ADC
203460.50/46.43793010499292## [1] 4381.343# 3. EARB divided by GCt equals the DAR Ratio
203460.50/131440.30## [1] 1.547931# 4. DAR divided by NDiP equals the DAR Ratio
46.43793010499292/30## [1] 1.547931\[\\[3pt]\]
\[ \begin{aligned} \dfrac {131,440.30}{30}&=\dfrac {203,460.50}{46.43793} \\ \\ \\ \\ \dfrac {46.43793}{30}&=\dfrac {203,460.50}{131,440.30} \end{aligned} \]
\[\\[3pt]\]
Again, you’ll want to include all of the decimals in the calculation for absolute accuracy, but:
the total Gross Charges divided by the Number of Days in the Period is equal to the Ending AR Balance divided by the average Days in AR. Not only that,
the average Days in AR divided by the Number of Days in the Period is equal to the Ending AR Balance divided by the total Gross Charges.
This is an important relationship called the DAR Ratio that we’ll explore in depth in the next chapter.
\[\\[3pt]\]
Formula Quick Reference
The following tables contain summaries of the variables and formulas that we have discussed in this chapter.
| Variable | Acronym | Description |
|---|---|---|
| \(n\) | NDiP |
Number of Days in the Period |
| \(x\) | GCt |
Total Gross Charges for NDiP |
| \(y\) | EARB |
Ending AR Balance |
| \(c\) | ADC |
Average Daily Charge for NDiP |
| \(z\) | DAR |
Days in AR |
\[\\[3pt]\]
| Name | Formula | Variable Form |
|---|---|---|
| DAR1 | EARB / (GCt / NDiP) |
\(y \div (x \div n) = z\) |
| DAR2 | EARB / ADC |
\(y \div c = z\) |
| GCt1 | (EARB x NDiP) / DAR |
\((y \times n) \div z = x\) |
| GCt2 | NDiP x ADC |
\(n \times c = x\) |
| EARB1 | (DAR x GCt) / NDiP |
\((z \times x) \div n = y\) |
| EARB2 | DAR x ADC |
\(z \times c=y\) |
| NDiP1 | (DAR x GCt) / EARB |
\((z \times x) \div y = n\) |
| NDiP2 | GCt / ADC |
\(x \div c={n}\) |
| ADC1 | GCt / NDiP |
\(x \div n = c\) |
| ADC2 | EARB / DAR |
\(y \div z = c\) |
| DAR Ratio1 | EARB / GCt |
\(y \div x\) |
| DAR Ratio2 | DAR / NDiP |
\(z \div n\) |
The DAR Ratio
Overview of Ratio Types
| Ratio | A mathematical parameter used to express the relationship of one quantity to another, where one quantity is divided by another. |
| Proportion | A type of ratio in which the numerator (\(x\)) is a portion of the whole (\(x+y\)). In a proportion, the numerator is always included in the denominator. |
| Rate | A type of ratio in which there is a distinct relationship between the numerator and denominator and the denominator often implies a large base population. |
| Percentage | A unit of proportion expressed as a fraction of 100. A percentage is a dimensionless number that has no unit of measurement. |
Ratio
A ratio is a mathematical parameter used to express the relationship of one quantity to another. To calculate a ratio, one quantity is divided by another. The quotient can be greater than 1 or less than 1. For example, if seven men and five women were in a group, the ratio of men to women would be \(\dfrac {7}{5}\). This may also be written as 7:5 and verbalized as “7 to 5.”
The numbers 7 and 5 have no common factors, so this ratio cannot be simplified any further. However, if the group consisted of 6 men and 10 women, the ratio would be 6:10. Because the numbers in this ratio have a common factor of 2, the ratio can be simplified by dividing each number by 2, which simplifies the ratio to 3:5.
One more thing of note: since a ratio can be expressed as a fraction, the quotient of the fraction is another viable way of displaying a ratio:
Proportion
A proportion is a type of ratio in which \(x\) is a portion of the whole \((x+y)\). In a proportion, the numerator is always included in the denominator. For example, if two women out of a group of 10 over the age of 50 have had breast cancer, where \(x = 2\) (women who have had breast cancer) and \(y=8\) (women who have not had breast cancer), the calculation would be 2 divided by 10. The proportion of women who have had breast cancer is \(0.2\) or \(20\%\).
Rate
A rate5 is another type of ratio in which there is a distinct relationship between the numerator and denominator and the denominator often implies a large base population. A measure of time is often an intrinsic part of the denominator. The basic rule of thumb for calculating a rate is to indicate the number of times something actually happened in relation to the number of times it possibly could have happened (actual/potential).
For example, let’s say you have been eating out often in the past few weeks. To calculate the rate of meals you have eaten out in one week, divide the number of meals that you ate out (for example, 13) by the number of meals you could have eaten out (21). The calculation is:
A Note on Percentages
As you can see above, the solutions to the proportions and rates can be expressed as a percentage, while the ratio cannot. There is a very good reason for this, though not one that immediately presents itself.
A proportion and a rate can be represented as a percentage because their numerators are inherently part of their denominators. This is not so for a ratio as it’s only comparing one number to another, even though the two numbers might be of the same group.
Something about each quantity separates it from the other (in this case, gender) and, as such, we want to know how many with attribute A there are compared to how many with attribute B there are. With anything so simple, it can be easy to overthink and misunderstand the concept.
Look at the ratio example again. There are seven men and five women in a group. We want to know how many men there are and how many women there are. Nothing more, nothing less. Thus, the ratio of men to women in this group is 7 to 5.
To compare, if we wanted to know the proportions of men and women in this group, we would have to involve a numerical representation of the group as a whole. There are seven men and five women in the group. This group, then, contains a total of twelve people. We can now calculate these proportions, representing the results as percentages:
The particular aspect of a ratio that seems to confuse the most is that, as a fraction, you can divide one number by the other, leaving you with one number representing the relationship between those two numbers. This seems counterintuitive. How will 1.4 help me? What was wrong with 7:5?
\(\\\)
Let’s test out one of the “rules of thumb” from Chapter 1:
your monthly Ending Accounts Receivable Balance should never be more than 1.5 times your total Gross Monthly Charges.
\(\\\)
Suppose that your Ending AR Balance is $203,460.50 and your total Gross Monthly Charges are $131,440.30. We can represent this relationship as a ratio, and then divide:
\(\\\)
\[\begin{align} 203,460.50 &: 131,440.30 \\ \\ \dfrac {203,460.50}{131,440.30}&= 1.548 (\#eq:thumbex) \end{align}\]\(\\\)
Ok, great but what does that mean? Multiply the total Gross Monthly Charges by 1.5.:
\(\\\)
\[\begin{align} 131440.30 \times 1.5 &= 197,160.45 \\ \\ 203,460.50 &> 197,160.45 (\#eq:thumb2ex) \end{align}\]\(\\\)
It turns out that our Ending AR Balance is greater than 1.5 times our total Gross Monthly Charges.
In fact, it’s approximately 1.548 times greater, which we found out by calculating the ratio of Ending AR Balance to total Gross Charges, dividing the EARB by the GCt.
Calculating this ‘actual’ ratio, it’s ‘ideal’ counterpart and comparing the two can give you more precise insight about your practice’s billing and reimbursement performance than just DAR alone. It’s also the subject of the next section, a tool I’ve come to call the DAR Ratio.
Using The DAR Ratio
In Chapter 3, we established two formulas showing the empirical relationship between the DAR variables:
\[\\[3pt]\]
\[\\[3pt]\]
From these dependencies, we can explore several interesting avenues. One is the fact that with every passing day, a one is added to the denominator of the formulas for both Average Daily Charge and the Ideal DAR Ratio.
Another is that the maxim of “never letting your EARB exceed 1.5 times your GCt” seems to break down pretty quickly, as the NDiP climbs. But these are just two of a handful we’ll explore. Right now, let’s take a look at the Ideal DAR Ratio.
\[\\[3pt]\]
Table 4.1. Ideal DAR Ratio: 365-Day Key for 39.445 DAR.
library(tidyverse)
library(reactable)
DAR_Ratio_39_YR <- read.csv("data/DAR_Ratio_39_YR.csv")
DAR_Ratio_39_YR <- DAR_Ratio_39_YR %>%
janitor::clean_names()
DAR_Ratio_39_YR <- DAR_Ratio_39_YR %>%
rename(NDiP = n_di_p,
EARB = earb,
GCt = g_ct,
ADC = adc,
DAR = dar,
"Ideal Ratio" = ratio_benchmark)
reactable(DAR_Ratio_39_YR,
style = list(fontFamily = "Work Sans, sans-serif", fontSize = "14px"),
paginationType = "jump",
showPageSizeOptions = TRUE,
defaultPageSize = 10,
defaultColDef = colDef(
header = function(value) gsub(".", " ", value, fixed = TRUE),
align = "center",
minWidth = 70,
headerStyle = list(background = "#f7f7f8")
),
columns = list(
NDiP = colDef(align = "left"),
EARB = colDef(format = colFormat(currency = "USD", separators = TRUE, digits = 0), align = "left"),
GCt = colDef(format = colFormat(currency = "USD", separators = TRUE, digits = 2), align = "left"),
ADC = colDef(format = colFormat(currency = "USD", separators = TRUE, digits = 2), align = "left"),
DAR = colDef(align = "left"),
"Ideal Ratio" = colDef(align = "left")
),
bordered = TRUE,
highlight = TRUE,
striped = TRUE
)\[\\[3pt]\]
Table 4.1 is a sort of key for the “ideal” DAR ratio. To begin, I set the desired DAR at 39.445 and began my EARB at an arbitrary number and increased it daily by 1000. Using the formulas from Chapter 3, I calculated the GCt and ADC. Finally, to get the “Ideal” DAR Ratio, I divided the EARB by the GCt.
As you can see, dividing either the EARB by the GCt, or the DAR by the NDiP will both give you the “Ideal” Ratio for each day in the period.
\[\\[3pt]\]
Comparing the Ideal Ratio to the Actual Ratio
Why is this Ideal Ratio “ideal” though?
In this section, we will use the DAR Ratio on a mock data set containing a year’s worth of financial data from a physician’s office. My intention in doing so is to illustrate the relationship between the Ending AR Balance and the Gross Charges on a month-to-month basis and how once this relationship is understood, you will be able to quickly understand where your business or organization is at any time whether its the first month, third quarter, or last week of the year.
\[\\[3pt]\]
Table 4.2. Sample 12-Month Financial Report for Physician Office.
library(tidyverse)
library(reactable)
DAR_Feedback_Month <- read.csv("data/DAR_Feedback_Month.csv")
DAR_Feedback_Month <- DAR_Feedback_Month %>%
janitor::clean_names()
DAR_Feedback_Month <- DAR_Feedback_Month %>%
rename(Month = i_month,
NDiP = ndip,
GCt = g_ct,
EARB = earb,
ADC = adc,
DAR = dar,
Actual = actual_ratio,
Ideal = ideal_ratio,
Difference = difference)
reactable(DAR_Feedback_Month,
style = list(fontFamily = "Work Sans, sans-serif", fontSize = "14px"),
#paginationType = "jump",
#showPageSizeOptions = TRUE,
columnGroups = list(
colGroup("Time Period", columns = c("Month", "NDiP")),
colGroup("Financials", columns = c("GCt", "EARB", "ADC", "DAR")),
colGroup("DAR Ratio", columns = c("Actual", "Ideal", "Difference"))
),
defaultPageSize = 12,
defaultColDef = colDef(
header = function(value) gsub(".", " ", value, fixed = TRUE),
minWidth = 75,
headerStyle = list(background = "#f7f7f8")
),
columns = list(
Month = colDef(align = "left"),
NDiP = colDef(align = "left"),
GCt = colDef(format = colFormat(prefix = "$", separators = TRUE, digits = 0), align = "left"),
EARB = colDef(format = colFormat(prefix = "$", separators = TRUE, digits = 0), align = "left"),
ADC = colDef(format = colFormat(prefix = "$", separators = TRUE, digits = 0), align = "left"),
DAR = colDef(align = "left"),
Actual = colDef(align = "left"),
Ideal = colDef(align = "left"),
Difference = colDef(align = "left")
),
resizable = TRUE,
wrap = FALSE,
bordered = TRUE,
highlight = TRUE,
striped = TRUE
)
\[\\[3pt]\]
The immediate takeaway from the data is that if the difference between the Actual and Ideal Ratio is positive, DAR is over the threshold set by the Ideal Ratio (39.445, in this case) and is failing. If the difference is negative, DAR is under the threshold or passing.
Remember, DAR would meet the desired threshold (39.445) if the difference was zero, but, as you’ll find, this will never be the case, as the GCt and EARB will never be the exact same number.
\[\\[3pt]\]
EARB & GCt 12-Month Comparison.
library(tidyverse)
library(plotly)
DAR_Month_Min <- read.csv("data/DAR_Month_Min2.csv")
DAR_Month_Min <- DAR_Month_Min %>%
janitor::clean_names()
DAR_Month_Min$month = factor(DAR_Month_Min$month, levels = month.abb)
options(scipen = 999)
line.month_1 = DAR_Month_Min %>%
mutate(color = case_when(type == "GCt" ~ "#013369", TRUE ~ "#d50a0a")) %>%
ggplot(aes(month, amount, group = type, shape = type, linetype = type,
text = paste(type,
"<br>Month: ", month,
"<br>Amount: $", round(amount/1000, digits = 0), "k",
"<br>DAR: ", dar, "days",
"<br>NDiP: ", ndip, "days"))) +
scale_y_continuous(labels = scales::dollar_format(prefix="$"))+
geom_line(aes(color = color),size = 1.2) +
geom_point(aes(color = color), size = 4, fill = "white") +
scale_shape_manual(values = c(22,21)) +
scale_color_identity() +
theme(legend.position = "none", axis.title.x = element_blank(), axis.title.y = element_blank(), panel.grid.minor = element_blank())
# PLOTLY LINE PLOT
ggplotly(line.month_1, tooltip = "text")Data from Table 4.2.
\[\\[3pt]\]
Figure 4.1 illustrates that when GCt falls too far below EARB, DAR exceeds the 39.445 threshold. Looking at the data for the months where DAR failed, the results of this disparity are plainly apparent:
| Month | GCt | EARB | DAR |
|---|---|---|---|
| March | $198,655 | $253,977 | 39.63 days |
| April | $86,047 | $183,685 | 64.04 days |
| May | $123,654 | $204,228 | 51.20 days |
| June | $131,440 | $203,460 | 46.44 days |
Figure 4.2. EARB & GCt 12-Month Comparison.
library(tidyverse)
library(plotly)
library(scales)
library(mdthemes)
library(hrbrthemes)
library(viridis)
library(ggsci)
DAR_Month_Min <- read.csv("data/DAR_Month_Min2.csv")
DAR_Month_Min <- DAR_Month_Min %>%
janitor::clean_names()
DAR_Month_Min$month = factor(DAR_Month_Min$month, levels = month.abb)
options(scipen = 999)
bar1.month = DAR_Month_Min %>%
ggplot(aes(month, amount, fill = type, text = paste(type, ": $", round(amount/1000, digits = 0), "k", "<br>DAR: ", dar))) +
geom_bar(position = "fill", stat = "identity") +
coord_flip() +
scale_x_discrete(limits = rev) +
scale_y_continuous(labels = scales::percent) +
scale_fill_viridis(discrete = TRUE, option = "viridis") +
#scale_color_identity() +
#geom_text(aes(label = amount), size = 3, color = "white", stat = "identity", position = position_fill(vjust = 0.5)) +
#mdthemes::md_theme_few() +
theme_ipsum_rc(grid="Y", axis="XY") +
#scale_fill_futurama() +
theme(axis.line.x = element_blank(),
axis.ticks.x = element_blank()) +
theme(legend.position = "none", axis.title.x = element_blank(), axis.title.y = element_blank(), panel.grid.minor = element_blank())
# PLOTLY LINE PLOT
ggplotly(bar1.month, tooltip = "text")Data from Table 4.2.
So, we now have an indicator of DAR that, although dependent upon the number of days, is independent of dollar amounts. It would be nice to know if we could find an optimal dollar amount for both the GCt and EARB to achieve the desired DAR threshold. For this, we will need a proportion.
Figure 4.3. EARB & GCt 12-Month Comparison.
library(tidyverse)
library(plotly)
library(scales)
library(mdthemes)
library(hrbrthemes)
library(viridis)
DAR_Month_Min_Id_Fail <- read.csv("data/DAR_Month_Min_Id_Fail.csv")
#DAR_Month_Min_Id_Fail <- DAR_Month_Min_Id_Fail %>%
#janitor::clean_names()
DAR_Month_Min_Id_Fail$Month = factor(DAR_Month_Min_Id_Fail$Month, levels = month.abb)
options(scipen = 999)
bar3.month = DAR_Month_Min_Id_Fail %>%
ggplot(aes(Act_Idl, Amount, fill = Type, text = paste(Type, ": $", round(Amount/1000, digits = 0), "k", "<br>DAR: ", DAR))) +
geom_bar(position = "fill", stat = "identity") +
facet_grid(~Month) +
#coord_flip() +
scale_x_discrete(limits = rev) +
scale_y_continuous(labels = scales::percent) +
#scale_color_identity() +
#geom_text(aes(label = Amount), size = 3, color = "white", stat = "identity", position = position_fill(vjust = 0.5)) +
scale_fill_viridis(discrete = TRUE) +
theme_ipsum() +
#mdthemes::md_theme_classic(base_size = 14) +
theme(axis.line.x = element_blank(),
axis.ticks.x = element_blank()) +
theme(legend.position = "none", axis.title.x = element_blank(), axis.title.y = element_blank(), panel.grid.minor = element_blank())
# PLOTLY BAR PLOT
ggplotly(bar3.month, tooltip = "text")Data from Table 4.2.
Optimal Proportion of GCt and EARB for \(x\) DAR
In this section, I’ll demonstrate the calculation for the optimal proportions (as percentages) of GCt and EARB needed for \(x\) DAR. One of the main takeaways you will come to find is just how incredibly sensitive DAR is to the Number of Days in the Period that you are measuring. We will look at monthly, bimonthly, and quarterly data to show this sensitivity.
The following is a table of sample data wherein each row contains a 31-day month’s financial activity, sorted by DAR in descending order. In addition to the DAR Ratio measurements, there are several new figures included.
Under the Percentages spanner, the first two figures represent the individual proportions of Gross Charges and Ending AR to the whole of those two figures added together. The Difference percentage is that of the difference between the Gross Charges and Ending AR in relation to the whole figure as well.
\[\\[3pt]\]
Table 4.5. Sample Financial Data for for 31-Day Months.
NDIP_31 <- read.csv("data/NDIP_31.csv")
NDIP_31 <- NDIP_31 %>%
janitor::clean_names()
library(gt)
head(NDIP_31) %>%
gt() %>%
cols_hide(columns = c(i_ndip, g_ct_earb)) %>%
tab_header(title =NULL) %>%
cols_align(align = "left",columns = 1) %>%
cols_align(align = "left",columns = 2) %>%
cols_align(align = "left",columns = 3) %>%
cols_align(align = "left",columns = 4) %>%
cols_align(align = "left",columns = 5) %>%
cols_align(align = "left",columns = 6) %>%
cols_align(align = "left",columns = 7) %>%
cols_align(align = "left",columns = 8) %>%
cols_align(align = "left",columns = 9) %>%
cols_align(align = "left",columns = 10) %>%
cols_align(align = "left",columns = 11) %>%
cols_align(align = "left",columns = 12) %>%
cols_label("i_ndip" = md("**NDiP**"),
`gct` = md("**GCt**"),
`earb` = md("**EARB**"),
`difference` = md("**Diff**"),
`g_ct_earb` = md("**GCt+EARB**"),
`gct_2` = md("**GCt (%)**"),
`earb_2` = md("**EARB (%)**"),
`difference_2` = md("**Diff (%)**"),
`dar` = md("**DAR**"),
`actual` = md("**Actual**"),
`ideal` = md("**Ideal**"),
`difference_1` = md("**Diff**")) %>%
tab_spanner(label = md("**Percentages**"),columns = c(gct_2, earb_2, difference_2)) %>%
tab_spanner(label = md("**DAR Ratio**"),columns = c(actual, ideal, difference_1)) %>%
tab_footnote(footnote = "Ideal Ratio for 39.445 DAR.", locations = cells_column_labels(columns = c(ideal))
) %>%
tab_footnote(footnote = "USD($), rounded to whole numbers.", locations = cells_column_labels(columns = c(gct, earb, difference, g_ct_earb))
) %>%
data_color(
columns = c(gct, earb, dar),
colors = scales::col_numeric(paletteer::paletteer_d(palette = "ggsci::red_material") %>% as.character(),domain = NULL)) %>%
opt_row_striping(row_striping = TRUE)| GCt1 | EARB1 | Diff1 | Percentages | DAR | DAR Ratio | ||||
|---|---|---|---|---|---|---|---|---|---|
| GCt (%) | EARB (%) | Diff (%) | Actual | Ideal2 | Diff | ||||
| 127758 | 542242 | 414484 | 19.07% | 80.93% | 61.86% | 131.57 | 4.2443 | 1.2723 | 2.9720 |
| 125033 | 529108 | 404075 | 19.11% | 80.89% | 61.77% | 131.18 | 4.2317 | 1.2723 | 2.9595 |
| 1381 | 5277 | 3896 | 20.74% | 79.26% | 58.52% | 118.45 | 3.8211 | 1.2723 | 2.5489 |
| 43901 | 154765 | 110865 | 22.10% | 77.90% | 55.80% | 109.29 | 3.5253 | 1.2723 | 2.2531 |
| 28908 | 82995 | 54087 | 25.83% | 74.17% | 48.33% | 89.00 | 2.8710 | 1.2723 | 1.5988 |
| 32946 | 89013 | 56066 | 27.01% | 72.99% | 45.97% | 83.75 | 2.7017 | 1.2723 | 1.4295 |
|
1
USD($), rounded to whole numbers.
2
Ideal Ratio for 39.445 DAR.
|
|||||||||
\[\\[3pt]\]
As you can see, these percentages are independent of the GCt and EARB dollar amounts. And, from looking through the data to just where the DAR crosses from passing to failing, we can see that, for an NDiP of 31, the optimal percentage for GCt is approximately 44.01%, while EARB’s optimal percentage is 55.99%.
The optimal difference between the two amounts is 11.99%. If GCt falls below 44.01%, the DAR is failing. If EARB rises above 55.99%, the DAR is failing. If the difference between the two rises above 11.99%, the DAR is failing.
\[\\[3pt]\]
The DAR Fails IF:
GCtfalls below 44.01%EARBrises above 55.99%the Difference between
GCtandEARBrises above 11.99%
\[\\[3pt]\]
Figure 4.2. EARB & GCt for DAR PASSING or FAILING the 39.445 Threshold.
library(tidyverse)
library(plotly)
NDIP_31_DAR <- read.csv("data/NDIP_31_DAR.csv")
NDIP_31_DAR <- NDIP_31_DAR %>%
janitor::clean_names()
options(scipen = 999)
scatter.ndip_31 = NDIP_31_DAR %>%
mutate(color = case_when(dar < 39.445 ~ "#013369",TRUE ~ "#D50A0A")) %>%
ggplot(aes(gct, earb, text = paste("GCt: $", round(gct/1000, digits = 0), "k (", gct_2, ")",
"<br>EARB: $", round(earb/1000, digits = 0), "k (", earb_2, ")",
"<br>Difference: $", round(difference/1000, digits = 0), "k (", difference_2, ")",
"<br>DAR: ", dar))) +
geom_point(aes(color = color), size = 3, alpha = 0.6) +
#geom_smooth() +
geom_abline(intercept = 0, slope = 1.2724193548, linetype = 5, size = 0.8, alpha = 1, color = "black") +
scale_y_continuous(labels = scales::dollar_format(prefix="$"), breaks = seq(0, 800000, by = 100000)) +
scale_x_continuous(labels = scales::dollar_format(prefix="$"), breaks = seq(0, 800000, by = 100000)) +
scale_color_identity() +
labs(x = "Total Gross Charges", y = "Ending AR Balance") +
theme(legend.position = "none")
# PLOTLY LINE PLOT
#ggplotly(scatter.ndip_31, tooltip = "text")
ggp <- ggplotly(scatter.ndip_31, tooltip = "text") %>% layout(dragmode = "select2d")
ggp %>% config(displayModeBar = "static", collaborate = F, displaylogo = FALSE, modeBarButtonsToRemove = list("sendDataToCloud", "toImage", "autoScale2d", "resetScale2d", "hoverClosestCartesian", "hoverCompareCartesian", "select2d", "lasso2d", "zoomIn2d", "zoomOut2d", "toggleSpikelines")
)Data from Table 4.5. Dashed Line = Optimal Pct for GCt (44.01%) and EARB (55.99%) for NDiP of 31.
library(tidyverse)
ggplot(NDIP_31_DAR, aes(gct, earb)) +
geom_point() +
geom_smooth(method = lm, se = FALSE) +
geom_abline(intercept = 0, slope = 1.2724193548, linetype = 5, size = 0.8, alpha = 1, color = "black")## Warning: Generic CSS font families (e.g. '-apple-system') aren't supported.
## Consider using a Google Font family instead https://fonts.google.com/## Warning: Generic CSS font families (e.g. 'BlinkMacSystemFont') aren't supported.
## Consider using a Google Font family instead https://fonts.google.com/## Warning: The font family 'Segoe UI' doesn't appear to be available as a Google
## Font. Try manually downloading and installing it on your system. For more info,
## visit https://github.com/rstudio/thematic#fonts## Warning: It seems the current graphics device 'png' is unable to render the
## requested font family ''. To render custom fonts, either use a ragg device or
## install the showtext package## `geom_smooth()` using formula 'y ~ x'
Key Performance Indicator↩︎
Percentage of AR Beyond \(x\) Days↩︎
A list of fees physicians establish as the fair price for the services they provide. Keep in mind that it is not the same as a payment schedule.↩︎
The term rate is often used loosely to refer to rate, proportion, percentage, and ratio. For this reason, it is important to be aware of how any measure being reported has actually been defined and calculated.↩︎