Signature
MPR_m = (sum_(i=1)^n [S_i] - S_n) / (f_n - f_1)
| Inputs | Definition | Unit |
|---|---|---|
S_i | Days' supply of fill i, for fills from the first to the last dispensing | days |
S_n | Days' supply of the last fill, subtracted from the total | days |
f_n | Day of the last dispensing, after f_1 | day number on the same scale |
f_1 | Day of the first dispensing | day number |
MPR_m | Days' supply before the last dispensing as a share of the days between the first and last dispensing | proportion, can exceed 1 |
|---|
nNumber 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
MPRm from a supply range and named first and last fill cells
Excel subtracts the named last fill's supply from the summed supply range and divides by the named last dispensing day less the first.
=(SUM(Supplies)-LastSupply)/(LastFillDay-FirstFillDay)
Assumptions
Refilling between first and last dispensing describes adherence
The ratio takes the pattern of refills up to the last dispensing as the measure of adherence and does not account for discontinuation after it. It needs at least two fills on different days.
Worked examples
MPRm of the five-fill history
Leaving out fill 5's 30 days gives 180 days of supply over the 169 days from day 1 to day 170, a ratio of about 1.065 (computed here for illustration).
n = 5; S_i = [30,30,30,90,30]; S_n = 30; f_1 = 1; f_n = 170; MPR_m = 1.0651
MPRm when the patient stops after the third fill
With fills 1 to 3 only, 60 days of supply over the 44 days from day 1 to day 45 give about 1.364 (computed here for illustration).
n = 3; S_i = [30,30,30]; S_n = 30; f_1 = 1; f_n = 45; MPR_m = 1.3636
Common errors
Mixing the two variants both called MPRm
Raebel and colleagues note that the variant including the last fill has also been referred to as MPRm. On the article's fills, the version excluding the last fill gives about 1.065 and the version including it about 1.055, so the definition, not the label, has to be reported (computed here for illustration).
Sources
MPR modified excluding the last refill
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 2, also known as MPR modified (MPRm), the days' supply excluding the last refill divided by the days between the first and last dispensing, which does not account for discontinuation.
Canonical Identity
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