Downstream Revenue Estimator: Methods and Validation Note

Companion to: "Estimating What Follows the Mammogram: A Transparent Model of Breast Imaging Downstream Revenue"

Publisher: Mammologix (powered by I/O Trak, Inc.)

Purpose: This note documents the estimator's arithmetic in full, so that any reader can reproduce every figure the tool produces and can independently confirm the validation results described in the main article. Nothing here requires access to the source code. The formulas below are complete.

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1. Inputs and notation

For each projection year y from 1 to Y, the model uses the following inputs. Default values are shown in parentheses and are all editable.

Population and pathway:

• V = annual mammography volume in year 1 (5,000)
• s = screening share of volume, as a fraction (0.85)
• r = recall rate applied to screening volume (0.095)
• g = annual volume growth, as a fraction (0.12)
• t = patient retention, as a fraction (0.65)

Detection:

• CDR_s = screening cancer detection rate per 1,000 screened (4.5)
• CDR_d = diagnostic cancer detection rate per 1,000 diagnostic referrals (34.7)

Cascade utilization (per pathway patient):

• p_DM, n_DM = share receiving diagnostic mammography and exams per patient (0.533, 1.32)
• p_US, n_US = share receiving ultrasound and exams per patient (0.424, 1.33)
• p_BX, n_BX = share receiving biopsy and procedures per patient (0.103, 1.24)

Reimbursement:

• R_s = screening mammogram plus tomosynthesis (178.58)
• R_d = diagnostic mammogram plus tomosynthesis (165.16)
• R_us = breast ultrasound (95.00)
• R_bx = image-guided breast biopsy, by site of service (476 office default)
• m = payer blend multiplier, as a fraction of Medicare (1.00)

Treatment (optional module):

• C_0, C_12, C_3, C_4 = 24-month allowed cost by stage (71,909; 97,066; 159,442; 182,655)
• Screen-detected stage mix, as fractions summing to 1 (0.25, 0.65, 0.08, 0.02)
• Dx-detected stage mix, as fractions summing to 1 (0.12, 0.55, 0.23, 0.10)
• i = inflation adjustment, as a fraction of 2010 costs (1.00)
• k = system capture rate, as a fraction (1.00)

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2. Volume, growth, and retention

Total volume compounds on the year-1 base:

Volume(y) = V * (1 + g)^(y - 1)

Returning and new patients (year 1 has no returning cohort):

Returning(1) = 0
Returning(y) = min( Volume(y-1) * t , Volume(y) )   for y > 1
New(y)       = Volume(y) - Returning(y)

Population split within each year:

Screens(y)  = Volume(y) * s
DxRefs(y)   = Volume(y) - Screens(y)
Recalls(y)  = Screens(y) * r

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3. The three tiers

The tiers are mutually exclusive by construction. Every dollar of revenue belongs to exactly one tier, which is what allows the identity in Section 6 to hold.

Tier 1, screening base

One screening exam per screening patient:

T1(y) = Screens(y) * R_s * m

Tier 2, diagnostic referral base

One guaranteed index diagnostic mammogram per diagnostic referral. At s = 1 this term is zero:

T2(y) = DxRefs(y) * R_d * m

Tier 3, downstream cascade

Recalled screening patients flow through the full utilization pattern. Diagnostic referrals contribute only the workup beyond their Tier 2 index exam, which is the mechanism that prevents double counting. The diagnostic-mammography intensity for referrals is therefore (n_DM - 1), floored at zero.

CascadeDM(y) = Recalls(y) * p_DM * n_DM
             + DxRefs(y) * p_DM * max(0, n_DM - 1)

CascadeUS(y) = ( Recalls(y) + DxRefs(y) ) * p_US * n_US

CascadeBX(y) = ( Recalls(y) + DxRefs(y) ) * p_BX * n_BX

T3(y) = CascadeDM(y) * R_d * m
      + CascadeUS(y) * R_us * m
      + CascadeBX(y) * R_bx * m

The displayed diagnostic-mammography procedure count in the results table is DxRefs(y) + CascadeDM(y), because a facility performs the index exams plus the additional workup. The revenue for the index exams sits in Tier 2, not Tier 3, so no revenue is counted twice.

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4. Detection, by population

The two populations are scored separately, each against its own benchmark. Screening detection, by audit convention, already includes cancers found through recall workup, so no adjustment to the cascade is required.

ScreenCancers(y) = Screens(y) * CDR_s / 1000
DxCancers(y)     = DxRefs(y)  * CDR_d / 1000
Cancers(y)       = ScreenCancers(y) + DxCancers(y)

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5. Treatment (optional)

Each population's blended average per cancer is the stage-weighted mean of the per-stage costs, scaled by the inflation and capture adjustments. Let the screen-detected mix be (a_0, a_12, a_3, a_4) and the dx-detected mix be (b_0, b_12, b_3, b_4).

Adj = i * k

AvgScreen = ( a_0*C_0 + a_12*C_12 + a_3*C_3 + a_4*C_4 ) * Adj
AvgDx     = ( b_0*C_0 + b_12*C_12 + b_3*C_3 + b_4*C_4 ) * Adj

Treatment(y) = ScreenCancers(y) * AvgScreen + DxCancers(y) * AvgDx

When the module is disabled, Treatment(y) = 0. Because the dx-detected mix skews toward later stages, AvgDx exceeds AvgScreen, which the model reflects rather than averaging away.

At default settings this yields AvgScreen = $97,479 and AvgDx = $116,953 per cancer.

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6. Totals and the reconciliation identity

Per-year total and the five-year sums:

Total(y) = T1(y) + T2(y) + T3(y) + Treatment(y)

Program    = sum over y of Total(y)
Base       = sum over y of ( T1(y) + T2(y) )
Downstream = sum over y of ( T3(y) + Treatment(y) )

The load-bearing identity, which must hold on every row and on every total, is:

T1 + T2 + T3 + Treatment  ==  Total          (each year)
Base + Downstream          ==  Program        (headline)
Treatment + Workup(T3)     ==  Downstream     (middle band)

Any change to the model that breaks one of these identities is, by definition, an error.

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7. Display rounding: largest-remainder allocation

When a total is rounded for display and then split into parts (for example, total cancers into screen-detected and dx-detected), rounding each part independently can produce a breakdown that does not sum to the displayed total. The estimator avoids this with largest-remainder allocation.

Given raw parts x_1 ... x_n and decimal places d, let f = 10^d.
Target  = round( (sum of x_i) * f )
Floors  = floor(x_i * f) for each i
Deficit = Target - sum(Floors)
Distribute the Deficit by adding 1 to the Floors with the largest
fractional remainders, then divide each result by f.

This guarantees the displayed parts always sum to the displayed total, at any rounding precision.

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8. Worked example: default settings, year 1

With V = 5,000, s = 0.85, r = 0.095:

Screens  = 4,250
DxRefs   =   750
Recalls  =   403.75

Cascade counts:

CascadeDM = 403.75 * 0.533 * 1.32 + 750 * 0.533 * 0.32  =  411.98
CascadeUS = (403.75 + 750) * 0.424 * 1.33               =  650.63
CascadeBX = (403.75 + 750) * 0.103 * 1.24               =  147.36

Detection:

ScreenCancers = 4,250 * 4.5 / 1000  = 19.13
DxCancers     =   750 * 34.7 / 1000 = 26.03
Cancers                             = 45.15

Revenue at the Medicare floor (m = 1), office biopsy (R_bx = 476):

T1 = 4,250 * 178.58            = $758,965
T2 =   750 * 165.16            = $123,870
T3 = 411.98 * 165.16
   + 650.63 *  95.00
   + 147.36 * 476.00           = $199,994
Treatment (module on)          = $4,907,968
Total (year 1)                 = $5,990,797

Five-year totals at defaults, treatment enabled: Program $38,058,621; Downstream $32,450,105; Treatment $31,179,573; Workup (T3) $1,270,532.

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9. Validation matrix

The following checks were run against the model and are reproducible from the formulas above.

Band and column reconciliation (Section 6 identities). Verified across every combination of screening share from 0 to 100 percent in 5-point steps, projection horizons of 1 to 10 years, and both treatment states: 21 shares by 10 horizons by 2 states, which is 420 configurations. Zero identity failures.

Displayed-part allocation (Section 7). The cancer split was verified to sum to the displayed total across annual volumes from 1,000 to 20,000 in 250-unit steps crossed with screening shares from 0 to 100 percent in 5-point steps, which is 77 volumes by 21 shares, or 1,617 configurations. Zero allocation failures.

Edge cases. At s = 1.00, T2 = 0 exactly. Growth reproduces year-2 volume of 5,600 at g = 0.12; retention reproduces 3,250 returning at t = 0.65.

Source integrity. Every reimbursement, detection, utilization, and treatment constant traces to a primary source cited in the companion article, confirmed against the primary index (PubMed, RSNA, Dove Medical Press, or the CMS rule addenda) rather than a secondary compilation.

A reader can reproduce any of these results by implementing Sections 2 through 7 in a spreadsheet or notebook and sweeping the same parameter ranges.

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Disclaimer: The views expressed in this note are those of the author and do not constitute medical, legal, or regulatory advice. Facilities should consult their own compliance, legal, and clinical leadership before acting on anything discussed here. Patients should not rely on this content for personal health decisions and should discuss their screening, diagnostic, and follow-up care directly with their own physician or care team.

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About the Author

Richard D. Lippert Jr. is the founder of Mammologix and has supported breast imaging centers with mammography medical outcome audits, downstream revenue analysis, and operational strategy since 1995.