Medication Possession Ratio

Medication Possession Ratio Formula, Variants, Values Above 1 and How It Differs from PDC

The medication possession ratio (MPR) turns pharmacy dispensing or claims records into a single number for how much of a prescribed medicine a patient obtained, and it is one of the most widely reported refill-based measures of medication adherence. The name covers several formulas that differ in their denominator and in whether the result is capped, so two studies can both report "the MPR" and mean different things. An uncapped MPR can exceed 1 (100%). The measure differs from the proportion of days covered (PDC), and an 80% cut-off is often applied when MPR-based adherence is used in economic evaluation.

Days' supply as evidence of possession

Refill measures rest on a simple inference. If a pharmacy dispensed 30 days of tablets, the patient had the means to take 30 days of treatment. The ISPOR Medication Compliance and Persistence Work Group defines compliance (with adherence as a synonym) as the extent to which a patient acts in accordance with the prescribed interval and dose of a dosing regimen. In retrospective studies, the group notes, this definition is operationalised as the number of doses dispensed in relation to the dispensing period, often called the medication possession ratio, and compliance with the prescription is assumed once the medicine is dispensed.

In a review of 136 studies using automated dispensing data, Andrade and colleagues found the MPR and related measures of medication availability in 77, more than any other type of measure. The ISPOR group treats persistence, the duration of time from initiation to discontinuation of therapy, as a separate construct. Sikka and colleagues show that two patients with very different refill timing, one refilling every other month and one stopping for six months, can have identical MPRs.

The basic calculation

Every version of the MPR divides a sum of dispensed supply by a count of days. For one medicine and one patient, the general form is as follows.

$$MPR = \frac{\sum_{i=1}^{n} S_i}{D}$$

where $S_i$ is the days' supply recorded for fill $i$, $n$ is the number of fills counted, and $D$ is the number of days in the denominator period. The result is reported as a proportion or multiplied by 100 as a percentage.

Variants by fixed interval, refill interval and capping

What changes between versions is which fills enter the numerator and which days make up $D$. A 2013 review by Raebel and colleagues lists confusion due to multiple calculation methods as a weakness of the MPR, and describes it as the share of days' supply obtained either during a specified time period or over a period of refill intervals, with four variations.

Fixed-interval versions count the time after the last refill, so stopping treatment lowers the result, although a fixed-interval MPR cannot tell stopping apart from scattered missed refills. Refill-interval versions stop the clock at the last dispensing, and Raebel and colleagues note that they do not account for discontinuation.

Capping is a separate decision. Sikka and colleagues note that early refilling can push the MPR above 1.0 and that it is then often truncated at 1.0. A capped MPR is written as follows.

$$MPR_{capped} = \min(MPR, 1)$$

where $MPR$ is the uncapped ratio from any of the variants above. In a claims study of 358,418 commercially insured people filling prescriptions for antihypertensive medicines, Bjarnadottir and colleagues found that two modelling decisions, whether to use interval-based or prescription-based study periods and how to handle overlapping prescription claims, each moved the MPR by more than 25 percentage points from the base case. Bjarnadottir and colleagues call for standard approaches to study period length and overlapping claims, and for transparent reporting of modelling decisions to make results comparable across studies.

Why the ratio can exceed 1

The MPR sums supply without asking whether one fill overlaps another, so supply that arrives before the previous supply would have run out adds to the numerator without adding days to the denominator. Raebel and colleagues list early refills that produce an extra fill within the measurement interval, switching between drugs in the same class with an overlap, and taking more than one drug from the same class at once as reasons the MPR can overstate adherence. A large supply dispensed near the end of a fixed window has the same effect, because supply running past the window end still counts unless the analyst truncates it.

Real data show how far the uncapped ratio can go, and how it distorts averages. Among adults with asthma using inhaled corticosteroids, Vollmer and colleagues found 95th percentiles of 1.24 and 1.33 for the two uncapped measures that authors often call the MPR, with maximum values of 50 and 100. The mean was 0.61 and 0.63 for those measures and 0.55 and 0.52 once each was capped at 1, in line with the warning from Raebel and colleagues that uncapped averages are skewed upwards. Vollmer and colleagues concluded that the uncapped measures should not be used where the aim is to describe adherence.

Worked example of five fills over 180 days

The fill history is hypothetical and illustrative, and matches the PDC worked example on this wiki. A patient starts a once-daily medicine on day 1 and is followed for 180 days (days 1 to 180). The patient refills early twice, has no fill until a 90-day supply on day 121, and refills early again on day 170.

1. Total days' supply. The five fills sum to 30 + 30 + 30 + 90 + 30 = 210 days.

2. Fixed-interval MPR. The window runs from the first dispensing to day 180 and gives the ratio below.

$$MPR_{fixed} = \frac{210}{180} = 1.167$$

where 210 is the total days' supply and 180 is the number of days in the window. Capped at 1, it is 1.000, which reads as perfect adherence.

3. Refill-interval MPR. The first and last dispensings are 169 days apart (day 1 to day 170). Including the last fill, with its supply added to the denominator, the ratio is as follows.

$$MPR_{refill} = \frac{210}{199} = 1.055$$

where 199 is the 169 days plus the 30-day supply of the last fill.

4. Days actually covered. With each early refill starting only when the previous supply runs out, fills 1 to 3 cover days 1 to 90 and fill 4 starts on day 121. Days 91 to 120 have no medicine, a gap of 30 days, and 150 of the 180 days are covered, as shown below.

$$PDC = \frac{150}{180} = 0.833$$

where 150 is the number of covered days in the window and 180 is the window length. The other 60 days of supply (30 from fill 4 and all 30 from fill 5) fall after day 180, which is why the MPR exceeds 1.

What the numbers show. The same five fills give an MPR of 1.167, 1.055 or 1.000 depending on the variant, while 16.7% of the days in the window had no medicine on hand. Every version passes an 80% threshold, so a dichotomised MPR hides the gap.

How the MPR differs from the proportion of days covered

The MPR and the PDC are related but not the same measure. Raebel and colleagues define the PDC with the same fixed denominator as the most common MPR, capped at 1, and recommend building time arrays of the dates each dispensing covers instead of summing days' supply across drugs. The PDC in the example counts covered calendar days, with early refills shifted forward, as in the Pharmacy Quality Alliance method; agreement between the two measures is typical across populations, not guaranteed for each patient.

For a single drug, Raebel and colleagues report that the two give nearly identical results, and in Hess and colleagues' comparison of 11 refill measures on one study's data the MPR was 63.5% and the PDC 63.0%. The PDC gives a more conservative estimate where patients switch between drugs or take several drugs in the same class. A capped MPR and the PDC can still differ, because the MPR credits surplus supply against days without medicine wherever it falls, while the PDC counts only days actually covered within the window.

The 80% cut-off and the evidence behind it

Raebel and colleagues list an MPR of at least 80% as the cut-point commonly used for adequate adherence, adding that it is used by convention and only rarely with supporting evidence. The ISPOR terminology paper found that categories of good and poor compliance, often set at 80%, were usually unsupported by research showing the cut-off suited the medicine class or disease. In Medicaid claims for five chronic conditions, Karve and colleagues found that the MPR and PDC cut-offs that best predicted any-cause hospitalisation ranged from 0.63 to 0.89, which they presented as an initial empirical basis for 0.80.

Uses in health economics

The ISPOR terminology paper calls factoring in actual compliance central to an accurate assessment of the effectiveness and cost-effectiveness of therapy. Refill measures such as the MPR are a common source of that adherence evidence in economic evaluation.

Adherence as a model input. Hughes and colleagues observed that decision-analytic models rarely allowed for the difference between compliance in trials and in routine practice, and recommended a clear definition of compliance and sensitivity analysis of its effect on cost-effectiveness. The MPR variant and cut-off are obvious candidates for that analysis.

Cost-effectiveness of adherence interventions. A cost-effectiveness analysis of an intervention to improve adherence needs a link from adherence to outcomes. Huo and colleagues built a probabilistic cohort Markov model of difficult-to-control asthma, taking the effect of adherence on exacerbations from a meta-analysis in which adherence was defined mainly by the MPR and prescription refill data. In their model, raising an individual's adherence from 50% to 70%, for example through an educational intervention, was expected to reduce exacerbations by 1.75 over 20 years, add 0.20 discounted QALYs and lower discounted healthcare costs by GBP 989; the intervention's own cost was not modelled. The authors noted that other definitions of adherence could give different effect estimates.

Limitations and common misreadings

Most errors with the MPR come from treating a measure of medicine acquisition as a measure of medicine taking, or from comparing results that used different formulas. The points below concern the MPR as used in claims and dispensing studies.

• Possession is not ingestion. The MPR assumes dispensed medicine is taken as directed. Sikka and colleagues note that patients may give medicine to others, discard it before refilling or stockpile it.
• The most non-adherent patients are missing. The MPR cannot be calculated for people who never fill a first prescription, and Raebel and colleagues note that it therefore systematically excludes the most non-adherent patients. Measures requiring one or two dispensings could not be calculated for 17% to 32% of participants in Vollmer's study.
• Short windows inflate the result. Because measurement starts with a dispensing, Vollmer and colleagues found the upward bias was most pronounced over periods shorter than about 9 months in their asthma cohort, where fills typically lasted 2 to 3 months.
• Not every gap is non-adherence. Sikka and colleagues note that gaps may follow clinical decisions such as dose titration or a response to side effects.

Sources

• Andrade SE, Kahler KH, Frech F, Chan KA. Methods for evaluation of medication adherence and persistence using automated databases. Pharmacoepidemiology and Drug Safety. 2006;15(8):565-574. doi:10.1002/pds.1230
• Bjarnadottir MV, Czerwinski D, Onukwugha E. Sensitivity of the medication possession ratio to modelling decisions in large claims databases. PharmacoEconomics. 2018;36(3):369-380. doi:10.1007/s40273-017-0597-y
• Cramer JA, Roy A, Burrell A, Fairchild CJ, Fuldeore MJ, Ollendorf DA, Wong PK. Medication compliance and persistence: terminology and definitions. Value in Health. 2008;11(1):44-47. doi:10.1111/j.1524-4733.2007.00213.x
• Hess LM, Raebel MA, Conner DA, Malone DC. Measurement of adherence in pharmacy administrative databases: a proposal for standard definitions and preferred measures. Annals of Pharmacotherapy. 2006;40(7-8):1280-1288. doi:10.1345/aph.1H018
• Hughes DA, Bagust A, Haycox A, Walley T. Accounting for noncompliance in pharmacoeconomic evaluations. PharmacoEconomics. 2001;19(12):1185-1197. doi:10.2165/00019053-200119120-00001
• Huo D, Hinde S, Smith H, Linden D, Jones L. Modelling the case for cost-effectiveness of interventions to improve medication adherence in patients with difficult to control asthma. NIHR Open Research. 2025;5:8 (version 2). doi:10.3310/nihropenres.13775.2
• Karve S, Cleves MA, Helm M, Hudson TJ, West DS, Martin BC. Good and poor adherence: optimal cut-point for adherence measures using administrative claims data. Current Medical Research and Opinion. 2009;25(9):2303-2310. doi:10.1185/03007990903126833
• Nau DP. Proportion of Days Covered (PDC) as a Preferred Method of Measuring Medication Adherence. Pharmacy Quality Alliance; undated, cited as 2011 by Raebel et al. (2013). Archived copy of 27 July 2018, accessed 3 October 2026.
• 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. doi:10.1097/MLR.0b013e31829b1d2a
• Sikka R, Xia F, Aubert RE. Estimating medication persistency using administrative claims data. American Journal of Managed Care. 2005;11(7):449-457.
• Vollmer WM, Xu M, Feldstein A, Smith D, Waterbury A, Rand C. Comparison of pharmacy-based measures of medication adherence. BMC Health Services Research. 2012;12:155. doi:10.1186/1472-6963-12-155