AdhereR: Adherence to Medications

Definitions

Adherence to medications is described as a process consisting of 3 successive elements/stages: initiation, implementation, and discontinuation (Vrijens et al., 2012). After initiating treatment (first medication intake), a patient would continue with implementing the regimen for a time period, ideally equal to the recommended time necessary for achieving therapeutic benefits; the quality of implementation is commonly labelled adherence and broadly operationalized as a ratio of medication quantity used versus prescribed in a time period. If patients discontinue medication earlier than the recommended time period, the period before discontinuation is described as persistence, in contrast to the following period of non-persistence.

The ideal measurement of this process would record the prescription moment and every medication intake with an exact time-stamp. This would allow, for example, to describe adherence to a twice-daily medication prescribed for 1 year in maximum detail: how long was the delay between prescription and the moment of the first medication intake, whether each of the two prescribed administrations per day corresponded to an intake event and at what time, how much medication was taken versus prescribed on any time interval while the patient persisted with treatment, any specific implementation patterns (e.g. missing or delaying the first daily dose), and when exactly the last medication intake event took place during that year. While this level of detail can be obtained by careful use of electronic monitoring devices, electronic healthcare data usually include much less information.

Administrative claims or pharmacy databases record medication dispensation events, including patient identifier, date of event, type of medication, and quantity dispensed, and less frequently daily dosage recommended. The same information may be available for prescription events in electronic medical records used in health care organizations (e.g primary care practices, secondary care centers). In between two dispensing or prescribing events, we don’t know whether and how medication has been used. What we do know is that, if taken as prescribed, the medication supplied at the first event would have lasted a number of days. If the time interval between the two events is longer than this number it is likely that the patient ran out of medication before re-supplying or used less during that time. If the interval is substantially longer or there is no second event, then the patient has probably finished the supply at some point and then discontinued medication. Thus, EHD-based algorithms estimate medication adherence and persistence based on the availability of current supply, under four main assumptions:

• the regimen requires the use of a fixed daily dosage of medication (if medication is to be taken as needed, a ratio cannot be computed)
• all medication supplied for that patient in that period of time is recorded and the patient does not use medication from other sources (if the patient uses other medication, adherence and/or persistence will be underestimated)
• the medication supplied is used by the patient it has been supplied for (if other persons use the medication, adherence and/or persistence will be overestimated)
• medication is supposed to be supplied at least two times during that period (if all medication is supplied once at the beginning of the treatment, there are no differences between patients regarding the supply patterns and all patients would be 100% covered for the whole treatment period)

(Several other assumptions apply to individual algorithms, and will be discussed later.)

AdhereR was developed to compute adherence and persistence estimates from EHD based on the principles described above. The current version is based on a single data source, therefore an algorithm for initiation (time interval between first prescription and first dispensing event) is not implemented (it is a time difference calculation easy to implement in with basic R functions). The following terms and definitions are used:

• Adherence (implementation) = the extent to which a patient’s medication use corresponds to prescribed use,
• CMA = continuous multiple-interval measures of medication availability/gaps, representing various indicators of the quality of implementation,
• Medication event = prescribing or dispensing record of a given medication for a given patient; usually includes the patient’s unique identifier, an event date, and a duration,
• Duration = number of days the quantity of supplied medication would last if used as recommended,
• Quantity = number of doses supplied at a medication event,
• Daily dosage = number of doses recommended to be taken daily,
• Medication type = classification performed by the researcher depending on study aims, e.g. based on therapeutic use, mechanism of action, chemical molecule or pharmaceutical formulation,
• Follow-up window (FUW) = the total period for which relevant medication events are recorded for included patients,
• Observation window (OW) = the period within the FUW for which adherence or persistence is computed,
• Persistence = the length of time during which the patient continues to use medication, before discontinuing for a time period longer than a pre-specified permissible gap,
• Treatment episode = a period of active medication use, represented by the number of consecutive days between a first medication supply event and the moment when the supply of the last medication event was finished (in a row of consecutive medication events where the interval between any two consecutive events is lower than the duration of the first plus a researcher-defined permissible gap),
• Permissible gap = a researcher-defined value representing the maximum number of days between the end of the supply from one medication event and the start of the following one that can be considered as continuous medication use.

Data preparation and example dataset

AdhereR requires a dataset of medication events over a FUW of sufficient length in relation to the recommended treatment duration. To our knowledge, no research has been performed to date on the relationship between FUW length and recommended treatment duration. AdhereR offers the opportunity for answering such methodological questions, but we would hypothesize that the FUW duration also depends on the duration of medication events (shorter durations would allow shorter FUW windows to be informative).

The minimum necessary dataset includes 3 variables for each medication event: patient unique identifier, event date, and duration. Daily dosage and medication type are optional.AdhereR is thus designed to use datasets that have already been extracted from EHD and prepared for calculation. These preliminary steps depend to a large extent on the specific database used and the type of medication and research design. Several general guidelines can be consulted (Arnet et al., 2016; Peterson et al., 2007), as well as database-specific documentation. In essence, these steps should entail:

• selecting medication events applicable to the research question based on relevant time intervals and medication codes,
• coding medication type depending on clinical considerations, for example coding different therapeutic classes in polypharmacy studies,
• checking plausible values and correcting any deviations,
• handling missing data.

For demonstration purposes, we included in AdhereR a hypothetical dataset of 1080 medication events from 100 patients in a 2-year FUW. Five variables are included in this dataset:

• patient unique identifier (PATIENT_ID),
• event date (DATE; from 6 July 2030 to 3 September 2044, in the “mm/dd/yyyy” format),
• daily dosage (PERDAY; median 4, range 2-20 doses per day),
• medication type (CATEGORY; 50.8% medA and 49.2% medB), and
• duration (DURATION; median 50, range 20-150 days).

Table 1 shows the medication events of two example patients: 19 medication events related to two medication types (medA and medB). They were selected to represent two different medication histories. Patient 37 had a stable daily dosage but event duration changes with medication change. Patient 76 had a more variable pattern, including medication, daily dosage and duration changes.

# Load the AdhereR library:
library(AdhereR);

# Select the two patients with IDs 37 and 76 from the built-in dataset "med.events":
ExamplePats <- med.events[med.events$PATIENT_ID %in% c(37, 76), ];
# Display them as pretty markdown table:
knitr::kable(ExamplePats, caption = "<a name=\"Table-1\"></a>**Table 1.** Medication events for two example patients");

Visualization of patient records

A first step towards deciding which algorithm is appropriate for these data is to explore medication histories visually. We do this by creating an object of type CMA0 for the two example patients, and plotting it. This type of plots can of course be created for a much bigger subsample of patients and saved as as a JPEG, PNG, TIFF, EPS or PDF file using R’s plotting system for data exploration.

# Create an object "cma0" of the most basic CMA type, "CMA0":
cma0 <- CMA0(data=ExamplePats, # use the two selected patients
             ID.colname="PATIENT_ID", # the name of the column containing the IDs
             event.date.colname="DATE", # the name of the column containing the event date
             event.duration.colname="DURATION", # the name of the column containing the duration
             event.daily.dose.colname="PERDAY", # the name of the column containing the dosage
             medication.class.colname="CATEGORY", # the name of the column containing the category
             followup.window.start=0,  # FUW start in days since earliest event
             observation.window.start=182, # OW start in days since earliest event
             observation.window.duration=365, # OW duration in days
             date.format="%m/%d/%Y"); # date format (mm/dd/yyyy)
# Plot the object (CMA0 shows the actual event data only):
plot(cma0, # the object to plot
     align.all.patients=TRUE); # align all patients for easier comparison

Figure 1. Medication histories - two example patients

We can see that patient 76 had an interruption of more than 100 days between the second and third medB supply and several situations of new supply acquired while the previous supply was not exhausted. Patient 37 had shorter gaps between consecutive events, but very little overlap in supplies. For patient 76, the switch to medB happened while the medA supply was still available, then a switch back to medA happened later, at the end of the second year. For patient 37, there was a single medication switch (to medB) without an overlap at that point.

Sometimes it is useful to also see the daily dose:

# Same plot as above but also showing the daily doses:
plot(cma0, # the object to plot
     print.dose=TRUE, plot.dose=TRUE,
     align.all.patients=TRUE); # align all patients for easier comparison

Figure 1 (a). Same plot as in Figure 1, but also showing the daily doses as numbers and as line thickness

These observations highlight several decision points in calculating persistence and adherence, which need to be informed by the clinical context of the study:

• what OW is relevant for calculating adherence and persistence? Both patients have been on treatment during the 2 years, they had a substantial number of events of relatively short duration, and variable delays between the end of a supply and the next event. Thus, their adherence might have oscillated substantially during this period. We could compute adherence and/or persistence for the full 2-year period, or consider shorter intervals;
• is the largest interruption seen in patient 76 an indication of non-persistence, or of lower adherence over that time interval? If the medication is likely to be used rarely despite daily use recommendations, such an interval might indicate a period of low adherence. If usual adherence rates are close to 100% when used, that delay is likely to indicate a treatment gap and needs to be treated as such, and the last 2 events as reinitiation of treatment (new treatment episode);
• is the switch from medA to medB an indicator of a new treatment episode? If medA and medB are two alternative formulations of the same chemical molecule, there might be clinical arguments for considering them as part of the same treatment episode (e.g. the pharmacist provided an alternative option to a product unavailable at the moment). If they are two distinct drug classes with different mechanisms of action and recommendations of use, it may be more appropriate to consider that patient 76 has had 3 treatment episodes and patient 37 one episode;
• is it necessary to consider carry-over of oversupply from previous events? For patient 37 this seems to matter very little, as there is little overlap between event durations, but patient 76 has substantial overlaps. If available medication is not likely to be either overused or discarded at every new medication event, it is important to control for carry-over;
• it is necessary to consider carry-over also when medication changes? Patient 76 has changed from medA to medB while still having a large supply of medA available. Was the patient more likely to discard the remaining medA the moment of receiving medB or finish it before starting the medB supply? If they are two alternative formulations and medB was (for example) given because medA was not in stock at the moment, probably this came with a recommendation to finish the available supply. If they are two distinct drug classes and the switch happens usually after assessment of therapeutic versus side effects, probably this came with a recommendation to stop using medA.

These decisions therefore need to be taken based on a good understanding of the pharmacological properties of the medication studied, and the most plausible clinical decision-making in routine care. This information can be collected from an advisory committee with relevant expertise (e.g. based on consensus protocols), or (even better) qualitative or survey research on the routine practices in prescribing, dispensing and using that specific medication. Of course, this is not always possible – a second-best option (or even complementary option, if consensus is not reached) is to compare systematically the effects of different analysis choices on the hypotheses tested (e.g. as sensitivity analyses).

Persistence – treatment episodes

An essential first decision is to distinguish between persistence with treatment and quality of implementation (once the patient started treatment – which, as explained above, is assumed in situations when we have only one data source of prescribing or dispensing events). The function compute.treatment.episodes() was developed for this purpose. We provide below an example of how this function can be used.

Let’s imagine that medA and medB are two different types of medication, and clinicians in our advisory committee agree that whenever a health care professional changes the type of medication supplied this should be considered as a new treatment episode; we will specify this as setting the parameter medication.change.means.new.treatment.episode to TRUE.

They also agree that a minumum of 6 months (180 days) need to pass after the end of a medication supply (taken as prescribed) without receiving a new supply in order to be reasonably confident that the patient has discontinued/interrupted the treatment – they can conclude this for example based on an approximate calculation considering that specific medication is usually supplied for 1-2 months, daily dosage is usually 2 to 4 pills a day, and patients often use as low as 1/4 of the recommended dose in a given interval. We will specify this as maximum.permissible.gap = 180, and maximum.permissible.gap.unit = "days". (If in another scenario the clinical information we obtain suggests that the permissible gap should depend on the duration of the last supply, for example 6 times that interval should go by before a discontinuation becoming likely, we can specify this as maximum.permissible.gap = 600, and maximum.permissible.gap.unit = "percent".)

We might also have some clinical confirmation that usually people finish existing supply before starting the new one (carryover.within.obs.window = TRUE), but of course only for the same medication if medA and medB are supplied with a recommendation to start a new treatment immediately (carry.only.for.same.medication = TRUE), take the existing supply based on the new dosage recommendations if these change (consider.dosage.change = TRUE).

The rest of the parameters specify the name of the dataset (here ExamplePats), names of the variables in the dataset (here based on the demo dataset, described above), and the FUW (here the whole 2-year window).

# Compute the treatment episodes for the two patients:
TEs3<- compute.treatment.episodes(ExamplePats,
                                  ID.colname="PATIENT_ID",
                                  event.date.colname="DATE",
                                  event.duration.colname="DURATION",
                                  event.daily.dose.colname="PERDAY",
                                  medication.class.colname="CATEGORY",
                                  carryover.within.obs.window = TRUE, # carry-over into the OW
                                  carry.only.for.same.medication = TRUE, # & only for same type
                                  consider.dosage.change = TRUE, # dosage change starts new episode...
                                  medication.change.means.new.treatment.episode = TRUE, # & type change
                                  maximum.permissible.gap = 180, # & a gap longer than 180 days
                                  maximum.permissible.gap.unit = "days", # unit for the above (days)
                                  followup.window.start = 0, # 2-years FUW starts at earliest event
                                  followup.window.start.unit = "days",
                                  followup.window.duration = 365 * 2,
                                  followup.window.duration.unit = "days",
                                  date.format = "%m/%d/%Y");
knitr::kable(TEs3, 
             caption = "<a name=\"Table-2\"></a>**Table 2.** Example output `compute.treatment.episodes()` function");

The function produces a dataset as the one shown in Table 2. It includes each treatment episode for each patient (here 2 episodes for patient 37 and 3 for patient 76) and records the patient ID, episode number, date of episode start, gap days at the end of or after the treatment episode, duration of episode, and episode end date:

• the date of the episode start is taken as the first medication event for a particular medication,
• the end of the episode is taken as the day when the last supply of that medication finished (if a medication change happened, or if a period longer than the permissible gap preceded the next medication event) or the end of the FUW (if no other medication event followed until the end of the FUW),
• the number of end episode gap days represents either the number of days after the end of the treatment episode (if medication changed, or if a period longer than the permissible gap preceded the next medication event) or at the end of (and within) the episode, i.e. the number of days after the last supply finished (if no other medication event followed until the end of the FUW),
• the duration of the episode is the interval between the episode start and episode end (and may include the gap days at the end, in the latter condition described above).

Notes:

1. just the number of gap days after the end of the episode can be computed by keeping all values larger than the permissible gap and by replacing the others by 0,
2. when medication change represents a new treatment episode, the previous episode ends when the last supply is finished (irrespective of the length of gap compared to a maximum permissible gap); any days before the date of the new medication supply are considered a gap. This maintains consistence with the computation of gaps between episodes (whether they are constructed based on the maximum permissible gap rule or the medication change rule).

In some scenarios, it is important to imagine that the episodes also include the maximum permissible gap when the gap is larger than this maximum (i.e., not when a new episode is due to a change in treatment or dose before this maximum permissible gap was exceeded). To allow such scenarios, compute.treatment.episodes() has a logical parameter, maximum.permissible.gap.append.to.episode, which, when set to TRUE appends the maximum permissible gap at the end of the episodes (its default value FALSE means that the episodes end as described above).

This output can be used on its own to study causes and consequences of medication persistence (e.g. by using episode duration in time-to-event analyses). This function is also a basis for the CMA_per_episode class, which is described later in the vignette.

Adherence – continuous multiple interval measures of medication availability/gaps (CMA)

Let’s consider another scenario: medA and medB are alternative formulations of the same chemical molecule, and clinicians agree that they can be used by patients within the same treatment episode. In this case, both patients had a single treatment episode for the whole duration of the follow-up (Table 3). We can therefore compute adherence for any observation window (OW) within these 2 years without any concern that we might confuse quality of implementation with (non-)persistence.

# Compute the treatment episodes for the two patients
# but now a change in medication type does not start a new episode:
TEs4<- compute.treatment.episodes(ExamplePats,
                                  ID.colname="PATIENT_ID",
                                  event.date.colname="DATE",
                                  event.duration.colname="DURATION",
                                  event.daily.dose.colname="PERDAY",
                                  medication.class.colname="CATEGORY",
                                  carryover.within.obs.window = TRUE, 
                                  carry.only.for.same.medication = TRUE,
                                  consider.dosage.change = TRUE,
                                  medication.change.means.new.treatment.episode = FALSE, # here
                                  maximum.permissible.gap = 180,
                                  maximum.permissible.gap.unit = "days",
                                  followup.window.start = 0,
                                  followup.window.start.unit = "days",
                                  followup.window.duration = 365 * 2,
                                  followup.window.duration.unit = "days",
                                  date.format = "%m/%d/%Y");
# Pretty print the events:
knitr::kable(TEs4, 
             caption = "<a name=\"Table-3\"></a>**Table 3.** Alternative scenario output `compute.treatment.episodes()` function");

Once we clarified that we indeed measure quality of implementation and not (non)-persistence, several CMA classes can be used to compute this specific component of adherence. We will discuss first in turn the simple CMA classes, then present the more complex (or iterated) CMA_per_episode and CMA_sliding_window ones.

The simple CMAs

A first decision to consider when calculating the quality of implementation is what is the appropriate observation window – when it should start and how long it should last? We can see for example that patient 76 had some periods of regular (even overlapping) supplies, and periods when there were some large delays between consecutive medication events. Thus, estimating adherence for a whole 2-year period might be too coarse-grained to mean anything for how patients actually managed their treatment at any particular moment. As mentioned earlier in the Definitions section, EHD don’t have good granularity to start with, so we need to do the best with what we’ve got – and compressing all this information into a single estimate might not be the best solution, at least not the obvious first choice. On the other hand, due to the low granularity, we cannot target very short observation windows either because we simply don’t know what happened every day. This decision needs to be informed again by information collected from the advisory committee or qualitative/quantitative studies in the target population. It also needs to take into account the average duration of medication supply from one event, and the average time interval between two events – which can be examined in exploratory plots (Figure 1) – and the research question and design of the study. For example, if we expect that the quality of implementation reduces in time from the start of a treatment episode, medication is usually supplied for one month, and patients can take up to 4 times as much to use up their supplies, we might want to consider comparing successive 4-month OWs. If we want to examine quality of implementation 6 months before a clinical event (on the clinical assumption that how a patient takes medication in previous 6 months may impact on the probability of a health event occurring or not), we might want to consider an OW start 6 months before the event, and a 6-month duration. The posibilities here are endless, and research on the impact of different analysis choices on substantive results is still scarce. When the consensus is not reached based on the available information, one or more parametrisations can be compared – and formulated as research questions.

For demonstration purposes, let’s imagine a scenario when an adherence intervention takes place 6 months (182 days) after the start of the treatment episode, and we hypothesize that it will improve the quality of implementation in the next year (365 days) in the intervention group compared to the control group. We can specify this as followup.window.start=0, observation.window.start=182, and observation.window.duration=365 (we can of course divide this interval into shorter windows and compare the two groups in terms of longitudinal changes in adherence, as we shall see later, but for the moment let’s stick to a global 1-year estimate). We have 9 CMA classes that can produce very different estimates of the quality of implementation, the first eight have been described by Vollmer and colleagues (2012) as applied to randomized controlled trials. We implemented them in AdhereR based on the authors’ description, and in essence are defined by 4 parameters:

1. how is the OW delimited (whether time intervals before the first event and after the last event are considered),
2. whether CMA values are capped at 100%,
3. whether medication oversupply is carried over to the next event interval, and
4. whether medication available before a first event is considered in supply calculations or OW definition.

CMA1

CMA1 is the simplest method, often described in the literature as the medication possession ratio (MPR). It simply adds up the duration of all medication events within the OW, excluding the last event, and divides this by the number of days between the first and last event (multiplied by 100 to obtain a percentage). Thus, it can be higher than 1 (or 100% adherence) and, if the OW does not start and end with a medication event for all patients, it can actually refer to different lengths of time within the OW for different patients. For example, for patient 76 below CMA1 is computed for the period starting with the first event in the highlighted interval and ending at the date if the last event – thus, it considers only 4 events with considerable overlaps and results in a CMA1 of 140%, indicating overuse.

Creating an object of class CMA1 with various parameters automatically performs the estimation of CMA1 for all the patients in the dataset; moreover, the object is smart enough to allow the appropriate printing and plotting. The object includes all the parameter values with which it was created, as well as the CMA data.frame, which is the main result, with two columns: patient ID and the corresponding CMA estimate. The CMA estimates appear as ratios, but can be trivially transformed into percentages and rounded, as we did for patient 76 below (rounded to 2 decimals). The plots show the CMA as percentage rounded to 1 decimal.

# Create the CMA1 object with the given parameters:
cma1 <- CMA1(data=ExamplePats,
             ID.colname="PATIENT_ID",
             event.date.colname="DATE",
             event.duration.colname="DURATION",
             followup.window.start=0, observation.window.start=182, 
             observation.window.duration=365,
             date.format="%m/%d/%Y");
# Display the summary:
cma1

## CMA1:
##   "The ratio of days with medication available in the observation window excluding the last event; durations of all events added up and divided by number of days from first to last event, possibly resulting in a value >1.0"
##   [
##     ID.colname = PATIENT_ID
##     event.date.colname = DATE
##     event.duration.colname = DURATION
##     medication.groups = <NONE>
##     flatten.medication.groups = FALSE
##     medication.groups.colname = .MED_GROUP_ID
##     followup.window.start = 0
##     followup.window.start.unit = days
##     followup.window.start.per.medication.group = FALSE
##     followup.window.duration = 730
##     followup.window.duration.unit = days
##     observation.window.start = 182
##     observation.window.start.unit = days
##     observation.window.duration = 365
##     observation.window.duration.unit = days
##     date.format = %m/%d/%Y
##     CMA = CMA results for 2 patients
##   ]
##   DATA: 19 (rows) x 5 (columns) [2 patients].

# Display the estimated CMA table:
cma1$CMA

##   PATIENT_ID       CMA
## 1         37 0.4035874
## 2         76 1.4000000

# and equivalently using an accessor function:
getCMA(cma1);

##   PATIENT_ID       CMA
## 1         37 0.4035874
## 2         76 1.4000000

# Compute the CMA value for patient 76, as percentage rounded at 2 digits:
round(cma1$CMA[cma1$CMA$PATIENT_ID== 76, 2]*100, 2)

## [1] 140

# Plot the CMA:
# The legend shows the actual duration, the days covered and gap days, 
# the drug (medication) type, the FUW and OW, and the estimated CMA.
plot(cma1, 
     patients.to.plot=c("76"), # plot only patient 76 
     legend.x=520); # place the legend in a nice way

Figure 2. Simple CMA 1

CMA2

Thus, CMA1 assumes that there is a treatment episode within the OW (shorter or equal to the OW) when the patient used the medication, and every new medication event happened when the previous supply finished (possibly due to overuse). These assumptions rarely fit with real life use patterns. One limitation is not considering the last event – which represents almost a half of the OW in the case of patient 76.

To address this limitation, CMA2 includes the duration of the last event in the numerator and the period from the last event to the end of the OW in the denominator. Thus, the estimate Figure 3 is 77.9%, more in line with the medication history of this patient in the year after the intervention.

cma2 <- CMA2(data=ExamplePats, # we're estimating CMA2 now!
             ID.colname="PATIENT_ID",
             event.date.colname="DATE",
             event.duration.colname="DURATION",
             followup.window.start=0, observation.window.start=182, 
             observation.window.duration=365,
             date.format="%m/%d/%Y");
plot(cma2, 
     patients.to.plot=c("76"),  
     show.legend=FALSE); # don't show legend to avoid clutter (see above)

Figure 3. Simple CMA 2

CMA3 and CMA4

Both CMA1 and CMA2 can be higher that 1 (100% adherence) based on the assumption that medication supply is finished until the last event (CMA1) or the end of the OW (CMA2). But sometimes this is not plausible, because patients can refill their supply earlier (for example when going on holidays) and overuse is a less frequent behaviour for some medications (when side effects are considerable for overuse, or medications are expensive). Or it may be that it does not matter whether patients use 100% or more that 100% of their medication, the therapeutic effect is the same with no risks or side effects. Again, this is a matter of inquiry to the advisory committee or investigation in the target population.

If it is likely that implementation does not exceed 100% (or does not make a difference if it does), CMA3 and CMA4 below adjust for this by capping CMA1 and CMA2 respectively to 100%. As shown in Figures 4 and 5, CMA3 is now capped at 100%, and CMA4 remains the same as CMA2 (because it was already lower than 100%).

cma3 <- CMA3(data=ExamplePats, # we're estimating CMA3 now!
             ID.colname="PATIENT_ID",
             event.date.colname="DATE",
             event.duration.colname="DURATION",
             followup.window.start=0, observation.window.start=182, 
             observation.window.duration=365,
             date.format="%m/%d/%Y");
plot(cma3, patients.to.plot=c("76"), show.legend=FALSE);

Figure 4. Simple CMA 3

cma4 <- CMA4(data=ExamplePats, # we're estimating CMA4 now!
             ID.colname="PATIENT_ID",
             event.date.colname="DATE",
             event.duration.colname="DURATION",
             followup.window.start=0, observation.window.start=182, 
             observation.window.duration=365,
             date.format="%m/%d/%Y");
plot(cma4,patients.to.plot=c("76"), show.legend=FALSE);

Figure 5. Simple CMA 4

CMA5 and CMA6

All CMAs from 1 to 4 have a major limitation: they don’t take into account the timing of the events. But if there is a large gap between two events it is more likely that the person had used the medication less than prescribed at least in part of that interval. Just capping the values as in CMA3 and CMA4 does not account for that likely reduction in adherence – two patients with the same quantity of supply will have the same percentage of adherence even if one has had substantial delays in supply at some points and the other supplied in time.

To adjust for this, CMA5 and CMA6 provide alternative calculations to CMA1 and CMA2 respectively. Thus, we instead calculate the number of gap days, extract it from the total time interval, and divide this value by the total time interval (first to last event in CMA5, and first event to end of OW in CMA6). By considering the gaps, we now need to decide whether to control for how any remaining supply is used when a new supply is obtained. Two additional parameters are included here: carry.only.for.same.medication and consider.dosage.change. Both are set here as FALSE, to specify the fact that carry over should always happen irrespective of what medication is supplied, and that the duration of the remaining supply should be modified if the dosage recommendations are changed with a new medication event. As shown in Figures 6 and 7, these alternative calculations do not make any difference for patient 76, because there are no gaps between the 5 events in the OW highighted. There could be, however, situations in which large gaps between some events in the OW result in lower CMA estimates when considering timing of events.

cma5 <- CMA5(data=ExamplePats, # we're estimating CMA5 now!
             ID.colname="PATIENT_ID",
             event.date.colname="DATE",
             event.duration.colname="DURATION",
             event.daily.dose.colname="PERDAY",
             medication.class.colname="CATEGORY",
             carry.only.for.same.medication=FALSE, # carry-over across medication types
             consider.dosage.change=FALSE, # don't consider canges in dosage
             followup.window.start=0, observation.window.start=182, 
             observation.window.duration=365,
             date.format="%m/%d/%Y");
plot(cma5,patients.to.plot=c("76"), show.legend=FALSE);

Figure 6. Simple CMA 5

cma6 <- CMA6(data=ExamplePats, # we're estimating CMA6 now!
             ID.colname="PATIENT_ID",
             event.date.colname="DATE",
             event.duration.colname="DURATION",
             event.daily.dose.colname="PERDAY",
             medication.class.colname="CATEGORY",
             carry.only.for.same.medication=FALSE,
             consider.dosage.change=FALSE,
             followup.window.start=0, observation.window.start=182, 
             observation.window.duration=365,
             date.format="%m/%d/%Y");
plot(cma6,patients.to.plot=c("76"), show.legend=FALSE);

Figure 7. Simple CMA 6

Sometimes it is useful to also see the daily dose:

# Same plot as above but also showing the daily doses:
plot(cma6, # the object to plot
     patients.to.plot=c("76"), # plot only patient 76 
     print.dose=TRUE, plot.dose=TRUE,
     legend.x=520); # place the legend in a nice way

Figure 7 (a). Same plot as in Figure 7, but also showing the daily doses as numbers and as line thickness

CMA7

All CMAs so far have another limitation: they do not consider the interval between the start of the OW and the first event within the OW. For situations in which the OW start coincides with the treatment episode start, this limitation has no consequences. But in scenarios like ours (OW starts during the episode) this has two major drowbacks. First, the time interval for calculating CMA is not the same for all patients; this can result in biases, for example if the intervention group tends to refill sooner after the intervention moment than the control group, the control group might seem more adherent but it is because CMA is calculated on a shorter time interval within the following year. And second, if there is any medication supply left from before the OW start, this is not considered (so CMA may be underestimated).

CMA7 addresses this limitation by extending the nominator to the whole OW interval, and by considering carry over both from before and within the OW. The same paremeters are available to specify whether this depends on the type of medication and considers dosage changes (applied now to both types of carry over). Figure 8 shows how considering the period at the OW start and the prior supply reduces CMA7 to 69%, due to the gap visible in the medication history plot between the event before the OW and the first event within the OW.

cma7 <- CMA7(data=ExamplePats, # we're estimating CMA7 now!
             ID.colname="PATIENT_ID",
             event.date.colname="DATE",
             event.duration.colname="DURATION",
             event.daily.dose.colname="PERDAY",
             medication.class.colname="CATEGORY",
             carry.only.for.same.medication=FALSE,
             consider.dosage.change=FALSE,
             followup.window.start=0, observation.window.start=182, 
             observation.window.duration=365,
             date.format="%m/%d/%Y");
plot(cma7, patients.to.plot=c("76"), show.legend=FALSE);

Figure 8. Simple CMA 7

CMA8

When entering a randomized controlled trial involving a new medication, a patient on ongoing treatment may be more likely to finish the current supply before starting the trial medication. In these situations, it may be more appropriate to consider a lagged start of the OW (even if this results in a different denominator for trial participants). Let’s consider this different scenario for patient 76: at day 374, a new treatment (medB) starts and we need to estimate CMA for the next 294 days (until the next medication change). But there is still some medA left, so it is likely that the patient finished this first. Figure 9 shows how the OW is shortened with the number of days it would have taken to finish the remaining medA (assuming use as prescribed); CMA8 is quite low 36.1%, given the long gaps between medB events. In a future version, it might be interesting to implement the possibility to also move the end of OW so that its length is preserved.

cma8 <- CMA8(data=ExamplePats, # we're estimating CMA8 now!
             ID.colname="PATIENT_ID",
             event.date.colname="DATE",
             event.duration.colname="DURATION",
             event.daily.dose.colname="PERDAY",
             medication.class.colname="CATEGORY",
             carry.only.for.same.medication=FALSE,
             consider.dosage.change=FALSE,
             followup.window.start=0, observation.window.start=374, 
             observation.window.duration=294,
             date.format="%m/%d/%Y");
plot(cma8, patients.to.plot=c("76"), show.legend=FALSE);
# The value for patient 76, rounded at 2 digits
round(cma8$CMA[cma8$CMA$PATIENT_ID== 76, 2]*100, 2);

## [1] 36.14

Figure 9. Simple CMA 8

CMA9

The previous 8 CMAs were described by Vollmer and colleagues (2012) in relation to randomized controlled trials, and may apply to many observational designs as well. However, they all rely on an assumption that might not hold for longitudinal cohort studies with multiple repeated measures: the medication is used as prescribed until current supply ends. In CMA7, this may introduce additional variation in adherence estimates depending on where the start of the OW is located relative to the last event before the OW and the first event within the OW: an OW start closer to the first event in the OW generates lower estimates for the same number of gap days between the two events. To address this, CMA9 first computes a ratio of days’ supply for each event in the FUW (until the next event or FUW end), then weighs all days in the OW by their corresponding ratio to generate an average CMA value for the OW.

For the same scenario as in CMA1 to CMA7, Figure 10 shows the estimate for CMA9, which is higher than for CMA7 (70.6% versus 69%). This value would be the same no matter if the OW starts slightly earlier or later, because CMA9 considers the same intervals between events (the one starting before and the one ending after the OW). Thus, it depends less on the actual date when the OW starts.

cma9 <- CMA9(data=ExamplePats, # we're estimating CMA9 now!
             ID.colname="PATIENT_ID",
             event.date.colname="DATE",
             event.duration.colname="DURATION",
             event.daily.dose.colname="PERDAY",
             medication.class.colname="CATEGORY",
             carry.only.for.same.medication=FALSE,
             consider.dosage.change=FALSE,
             followup.window.start=0, observation.window.start=182, 
             observation.window.duration=365,
             date.format="%m/%d/%Y");
plot(cma9, patients.to.plot=c("76"), show.legend=FALSE);