Technical One-Pager

This section serves to define concepts with precision to ensure data scientists are working with consistent logic and definitions.

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1. Defining the Rate Object Space

Let $\Omega$ be the set of all Rate Objects. Each Rate Object $O \in \Omega$ is defined as:

$$O = \bigl(o,\, n,\, g,\, c,\, \tau,\, \{\,v_s\}\bigr),$$

where:

• $o$: A unique Rate Object ID.
• $n \in N$: Network ID (unique payer-network identifier).
• $g \in G$: Provider Group ID (unique set of providers sharing identical rates).
• $c \in C$: Code Object ID (e.g., HCPCS, MS-DRG, code-version, place of service, plus any relevant modifiers).
• $\tau \in T$: Time (month).
• $\{v_s\}$: A set of rate values, each indexed by a methodology key $s$.

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Defining the Methodology Key $s$

A methodology key $s$ (sometimes called a source for simplicity) represents a combination of:

1. Data source (e.g., "Hospital MRF","Payer MRF", "Komodo")
2. Contract methodology (e.g., "case rate", "per diem")
3. Rate type (e.g., "dollar", "percent").

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2. Rate Values

Inside each Rate Object $O$, the rate values are:

$$v_s = \quad \text{for each methodology key } s \in S.$$

For example:

• $v_{\text{hospital-mrf-case-rate-percent}}$ is the hospital’s percentage case rate for a given procedure.
• $v_{\text{komodo-allowed-amount}}$ is Komodo’s allowed amount for a given procedure or code.

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Multiple Source Entries

In the raw source data, there can be multiple entries for a specific methodology key $\{r_1, r_2, \ldots, r_k\}$. To produce a single rate value $v_s$, define an aggregation function

$$v_s = \text{Agg}(r_1,\, r_2,\, \ldots,\, r_k).$$

This ensures that although data may come from multiple records, it is ultimately consolidated into a single numerical rate value $v_s$ associated with each methodology key $s$.

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3a. Transformations

Define transformations as functions acting on individual rate values:

$$t: v_s \;\to\; v_s'$$

e.g. APR-DRG crosswalk, percent -> dollar, per diem * expected days, ...

3b. Imputations

An imputation function is used to generate alternate sources for rate values:

$$v_{i} = \text{Impute}\bigl(\{v_s\};\,\theta\bigr),$$

where:

• $\{v_s\}$ may be missing or partially observed.
• $\theta$ represents covariates/parameters (e.g., provisions, payer-specific trends, geographic-trends etc.).

For instance, consider a provider-payer-network with inpatient (IP) rates for 25 DRG codes. Suppose 18 of these codes have rates that, when normalized by CMS weights, yield the same base value $X$:

$$\frac{v_s^{(1)}}{w_1} \approx \frac{v_s^{(2)}}{w_2} \approx \cdots \approx \frac{v_s^{(18)}}{w_{18}} \approx X$$

This suggests a base rate structure: the observed IP rates are proportionally scaled by CMS DRG weights.

Thus, for the missing DRG codes, we can impute their rate values using:

$$v_i = X \cdot w_i$$

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4. Accuracy Metrics

$$A(v) = f\bigl(\text{data quality},\, \text{benchmarks},\, \text{historical fit},\, \ldots\bigr).$$

This score assesses reliability and validity of the rate value, taking into account various factors such as data lineage, plausibility, benchmarks, or alignment with trends.

Compute for each $v$ in {${v_s, v_s', v_i}$} $\forall \left( s,i \right)$

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5. Canonical Rate Selection within Sub-Version

$$v_{\text{best}} = \arg\max_{v \,\in\, \{v_s,\, v_s',\, v_i\}} \, A(v).$$

Ties are broken with the following hierarchy.

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6. Canonical Rates Across Sub-Versions (Recent Historic with Threshold)

Let $T$ be array of recent sub-versions (e.g. ["2024_11", "2024_10", ...], where current sub-version is "2024_12")

Select the current or historic rate with the highest score.

$$v_{\text{best}}' = \arg\max_{v \,\in\, \{v_{\text{best},t}\},\forall t \in T} \, A(v).$$

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Output:

Then, the CLD is $\Omega'$: the rate object space, enhanced with analysis columns. So each Rate Object $O' \in \Omega'$ is defined as:

$$O' = \bigl(o, n, g, c, \tau, v_{\text{best}}'\bigr)$$