Covered days in the PDC observation period from shifted same-drug fills

Adds, over the n fills of one drug after shifting, the days of each fill's supply that fall on or before the last day of the period. Shifting leaves the fills without overlap, so the sum counts each day once; a fill that starts after the end day adds nothing, and supply running past the end day is ignored. Day numbers run from the index date as day 1, so every fill starts on or after day 1 and the end day E equals the number of days in the period. Each comparison in parentheses inside the bracket equals 1 when it is true and 0 otherwise, so a fill adds its full supply when the supply ends on or before the end day, only the days up to the end day when it runs past it, and nothing when it starts after the end day.

Signature

C = sum_(i=1)^n [(E - a_i + 1) * (E - a_i + 1 > 0) * (E - a_i + 1 < S_i) + S_i * (E - a_i + 1 >= S_i)]
Inputs
InputsDefinitionUnit
ELast day of the observation period on the same day scaleday number
a_iShifted start day of fill i from HE-FM-PDC-002day number, with the index date as day 1
S_iDays' supply of fill idays, above zero
Output
CNumber of days within the period covered by the shifted fills, each day counted oncedays
  • n Number of fills of the drug from the index date onwards (count)

Function

Proportion of days covered from pharmacy fill dates and days' supply function

Maps a patient's dispensing records, each a fill date and a days' supply, and an observation period to the proportion of days covered (PDC), the share of days in the period on which at least one fill provides medicine, each day counted once. Same-drug refills collected before the previous supply runs out are shifted to start the day after it ends, overlaps between different drugs in a class are not shifted, supply running past the end of the period is ignored, and the CMS method removes inpatient and skilled nursing facility stay days. The records follow the notation of the Proportion of Days Covered article. The medication possession ratio, which sums days' supply instead, is HE-FM-MPR-001.

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Implementations

  • Excel

    Covered days from ranges of shifted starts and supplies

    With the shifted start days in a range named ShiftedStarts, the matching days' supply in a range named Supplies and the last day of the period in a cell named EndDay, the formula adds each fill's supply up to the end day and nothing for a fill starting after it. It works as entered in Excel 365 and as an array formula in earlier versions.

    =SUM(IF(EndDay-ShiftedStarts+1<Supplies,IF(EndDay-ShiftedStarts+1>0,EndDay-ShiftedStarts+1,0),Supplies))

Assumptions

  • Shifted fills of one drug do not overlap

    The fills belong to one drug and have been shifted, so no two of them cover the same day and their days can be added. For a class measure with different drugs the covered days are the union of the arrays, each day counted once, which the sum does not give.

  • Index date as day 1 of the PDC period

    The first fill falls on day 1, the index date, and no fill starts before it, so every covered day counted is inside the period.

Worked examples

  • Covered days in the 180-day period from the five shifted fills

    With shifted starts on days 1, 31, 61, 121 and 211, fills 1 to 3 add 30 days each, fill 4 adds the 60 days from day 121 to day 180 and fill 5 adds none, 150 covered days in all. The other 60 days of supply fall after day 180.

    n = 5; S_i = [30,30,30,90,30]; a_i = [1,31,61,121,211]; E = 180; C = 150

  • Covered days over a 240-day period from the same shifted fills

    Extending the period to day 240 lets fills 4 and 5 count in full, so all 210 days of supply are covered and only the 30-day gap from day 91 to day 120 is uncovered, a PDC of 0.875 (computed here for illustration).

    n = 5; S_i = [30,30,30,90,30]; a_i = [1,31,61,121,211]; E = 240; C = 210

Common errors

  • Counting supply that runs past the PDC end date

    Adding the full days' supply of every fill gives 210 days for the article's history and a ratio of about 1.167, which is the fixed-interval medication possession ratio (HE-FM-MPR-001), instead of 150 covered days and a PDC of about 0.833. The 60 days of supply after day 180 hide the 30-day gap.

  • Summing covered days across different drugs in a PDC class measure

    Two drugs in a class taken together, each covering days 1 to 90 of a 180-day period, give 180 summed days and a PDC of 1, against 90 covered days and a PDC of 0.5 when a day counts once if at least one drug is available (computed here for illustration).

Sources

  • PQA time arrays and days covered by at least one array

    Nau DP. Proportion of Days Covered (PDC) as a Preferred Method of Measuring Medication Adherence. Pharmacy Quality Alliance; undated, cited as 2011 by Raebel and colleagues (2013); archived copy of 27 July 2018. Page 2: rather than summing the days' supply, the analyst creates time arrays of the dates covered by each fill and determines how many of the days in the denominator period were covered by at least one array.

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Canonical Identity

Persistent URI
https://healtheconomics.wiki/formula/covered-days-in-the-pdc-observation-period-from-shifted-same-drug-fills

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