Refill-interval medication possession ratio including the last fill

Divides the total days' supply from the first to the last dispensing by the days between the first and last dispensing plus the days' supply of the last fill. Sikka and colleagues describe it as an often-used definition; Raebel and colleagues list it as less common and note that it has also been called MPRm. The clock stops when the last fill's supply ends, so the ratio does not account for discontinuation, and early refilling takes it above 1.

Signature

MPR_refill = sum_(i=1)^n [S_i] / (f_n - f_1 + S_n)
Inputs
InputsDefinitionUnit
S_iDays' supply of fill i, for fills from the first to the last dispensingdays
f_nDay of the last dispensing, after f_1day number on the same scale
f_1Day of the first dispensingday number
S_nDays' supply of the last filldays
Output
MPR_refillDays' supply from the first to the last dispensing as a share of the refill interval plus the last supplyproportion, can exceed 1
  • n Number of fills from the first to the last dispensing, at least 2 (count)

Function

Medication possession ratio from summed days' supply function

Maps a patient's dispensing records for one medicine, each a fill date and a days' supply, to the medication possession ratio (MPR): the days' supply dispensed divided by a count of days. The variants differ in which fills enter the numerator and which days form the denominator: a fixed interval from the first dispensing to the end of the observation period, or a refill interval between the first and last dispensing, with or without the last fill. Because supply is summed without regard to overlap, an uncapped MPR can exceed 1, and it is often capped at 1. The records follow the notation of the Medication Possession Ratio article. The proportion of days covered, which counts unique covered days instead, is HE-FM-PDC-001.

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Implementations

  • Excel

    Refill-interval MPR from named first and last fill cells

    Excel sums the named supply range and divides by the named last dispensing day less the first, plus the named last fill's supply.

    =SUM(Supplies)/(LastFillDay-FirstFillDay+LastSupply)

Assumptions

  • Treatment ends when the last supply runs out

    The interval closes at the end of the last fill's supply, so the formula assumes nothing after it matters. A patient who stops after a fill and one who continues beyond the window can have the same ratio.

  • At least two fills on different days for the refill interval

    The refill interval needs a first and a last dispensing on different days. With one fill the ratio is that fill's supply over itself, 1 by construction, which says nothing about adherence.

Worked examples

  • Refill-interval MPR of the five-fill history

    The first and last dispensings are 169 days apart (day 1 to day 170), and adding the last fill's 30 days gives a denominator of 199, so the ratio is 210 / 199, about 1.055.

    n = 5; S_i = [30,30,30,90,30]; f_1 = 1; f_n = 170; S_n = 30; MPR_refill = 1.0553

  • Refill-interval MPR when the patient stops after the third fill

    If the patient stops after fill 3 on day 45, the denominator is 44 + 30 = 74 days and the ratio is 90 / 74, about 1.216, against 0.5 for the fixed interval, because the time after the last fill is not counted (computed here for illustration).

    n = 3; S_i = [30,30,30]; f_1 = 1; f_n = 45; S_n = 30; MPR_refill = 1.2162

Common errors

  • Using a refill-interval MPR where discontinuation matters

    A patient who stops after the third fill of the article's history scores about 1.216 on the refill interval and 0.5 on the fixed interval (computed here for illustration). Where the question includes stopping treatment, the refill interval overstates adherence.

Sources

  • Refill-interval MPR with the last fill's supply in the denominator

    Sikka R, Xia F, Aubert RE. Estimating medication persistency using administrative claims data. American Journal of Managed Care. 2005;11(7):449-457. Introduction: the MPR is often defined as the sum of the days' supply divided by the number of days between the first fill and the last refill plus the days' supply of the last refill; early refilling leads to an MPR above 1.0, often truncated at 1.0.

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  • Refill-interval MPR variation and discontinuation

    Raebel MA, Schmittdiel J, Karter AJ, Konieczny JL, Steiner JF. Standardizing terminology and definitions of medication adherence and persistence in research employing electronic databases. Medical Care. 2013;51(8 Suppl 3):S11-S21. Table 2, MPR row: variation 3 (less common, also referred to as MPRm) and the note that variations defining the interval between the first and last dispensing do not account for discontinuation.

    View source →

Canonical Identity

Persistent URI
https://healtheconomics.wiki/formula/refill-interval-medication-possession-ratio-including-the-last-fill

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