2.1 Overview of the Methods

A simulation study was conducted using a published pharmacokinetic-pharmacodynamic model for allopurinol and serum urate [33]. Plasma concentrations of oxypurinol, the active metabolite of allopurinol (which contributes most of the pharmacological effect), and serum urate concentrations every 24 h were simulated for virtual individuals with gout under perfect and imperfect implementation patterns. Using these simulations, the relative forgiveness of different allopurinol implementation patterns was determined. Firstly, we determined the relative forgiveness of allopurinol under the index implementation patterns presented by Assawasuwannakit et al. [29] to enable comparison with their work. Secondly, we used observed real-life implementation patterns from a study on people with gout prescribed allopurinol where clinical outcomes were also collected [34]. Figure 1 provides a flowchart summary of the methodological approach.

Fig. 1

Flowchart summary of methodological approach showing how relative forgiveness (RF) corresponding to different implementation patterns is obtained via simulation using a pharmacokinetic–pharmacodynamic (PKPD) model (the total number of real-life study patterns is 25, only the first 3 and the last are represented in this flowchart, the remaining 21 patterns with corresponding RF values are presented in Table1)

2.2 Relative Forgiveness

The relative forgiveness of allopurinol was determined as defined previously [29]: \(RF=\frac_/\left(1-_\right)}_/\left(1-_\right)}\), where \(RF\) is the relative forgiveness, \(_\) is the probability of successful attainment of urate target under imperfect implementation, and \(_\) is the probability of successful attainment of urate target under perfect implementation. The criterion can be interpreted in the same way as an odds ratio, with values close to 1 indicating that the drug is forgiving of deviations to perfect implementation, and values closer to 0 indicating the drug is not forgiving to such deviations.

2.3 Index Implementation Patterns

Perfect implementation was defined as taking a single dose of 300 mg of allopurinol every day for 150 days. Steady-state was assumed to start on day 15 on the basis of the half-life of oxypurinol (around 24 h) and the half-life of serum urate (between 1.4 and 3.3 days) for someone with normal renal function [35]. Imperfect implementation patterns were created [29] on the basis of index implementation patterns which contained typical features of deviations from perfect implementation, including random missed doses and drug holidays. We did not assess timing variability in our study owing to the relatively long half-lives of oxypurinol [35] and urate [36] in people with gout (> 24 h) relative to the dosing interval (usually 24 h). Hence variations in time of dose within 24 h are unlikely to have a significant impact on clinical outcomes and those greater than 24 h are recorded as missed doses or drug holidays. Imperfect implementation patterns were then simulated from parametric distributions [for random missed doses: Poisson distribution (mean 13), for drug holidays (always 3 consecutive missed doses occurring 0, 1, 2 or 3 times over the 150-day period with respective likelihoods of 0.42, 0.3, 0.17 and 0.09)].

2.4 Real-Life Allopurinol Implementation Patterns

When considering the real-life implementation patterns, perfect implementation was defined as a single dose of allopurinol taken every day for 360 days (as the real-life implementation patterns covered a year). Imperfect implementation patterns corresponded to the true implementation patterns over 1 year of people with gout taking allopurinol obtained from a feasibility study [34] examining the effectiveness of point-of-care urate testing on allopurinol adherence. In brief, all study participants were prescribed allopurinol once daily and followed for 1 year. Allopurinol adherence information was collected using electronic monitoring (MEMS®) where each bottle opening was recorded by a digital device in the cap and uploaded using a mobile phone application. Medication Event Monitoring System (MEMS®) combined with the MEMS Adherence Software (MEMS AS®), AARDEX Group, Belgium, is an integrated system that is used to measure and/or to manage patient adherence to medications. Each bottle opening was assumed to indicate that the prescribed daily dose was taken by the participant. Implementation (i.e. day-to-day medication-taking) data for study participants were derived from the time and date stamp recorded by the MEMS® device. For each participant, every scheduled dose was designated either as a ‘dose missed’ or ‘dose taken’. Overall, five participants (IDs 3, 6, 12, 15 and 19) had allopurinol doses altered by their independent physician during the study so all data prior to the dose change were excluded (days 23, 272, 307, 293 and 180, respectively) to ensure the same dose was used over the whole period where implementation was studied. Only the patterns of the participants with implementation data covering at least 75% of the year and who used the electronic monitoring for the duration of the follow-up were retained (hence IDs 6, 12, 15, 19 and 32 were not included). One participant taking allopurinol every 48 h was excluded owing to difficulties reconciling the implementation data and prescribed therapy. In total, the exact implementation patterns of 25 participants over the first 360 days of the feasibility study [34] were included for the real-life implementation part of our study.

2.5 Simulation of Concentration-Time Profiles of Oxypurinol and Serum Urate

A population pharmacokinetic–pharmacodynamic (PKPD) model describing oxypurinol and serum urate concentrations developed previously [33] was used for the simulations. Briefly, this model consisted of a one-compartment first-order absorption pharmacokinetic model linked to a direct effects inhibitory Imax model with a proportional reduction from baseline serum urate. The final pharmacokinetic and pharmacodynamic parameters and corresponding between-subject-variability estimates obtained in this study [33] were used to simulate individual oxypurinol and serum urate concentrations over time by sampling from the corresponding multivariate normal distribution, however residual unexplained variability (measurement error) was set to zero. As the clinical covariates were not available in the gout study [34] from which we derived the real-life implementation patterns, we used the mean covariate values obtained in one of the six sub-studies used to build the model [37].

The simulated profile of serum urate concentrations for each virtual individual was assessed in terms of attainment of the target serum urate concentration (less than 0.36 mmol/L [6]) on each day. Only steady-state profiles were considered (data before day 15 were censored). Adequate urate control for an individual over the whole period was considered to occur when the simulated urate concentration was below 0.36 mmol/L for 90% or more of the days, as per the recommendations of the American College of Rheumatology guidelines for the management of gout [6] and considering biological variation and analytical measurement error.

Using the index implementation patterns, 1000 different imperfect implementation patterns (each with their own individual set of PKPD parameters) were simulated from the parametric distributions described above. In contrast, for the real-life implementation patterns, each of the 25 real-life implementation patterns was used to simulate 1000 individual PKPD profiles, yielding a total of 25,000 simulations. To calculate the relative forgiveness criterion of the index implementation patterns or one of the real-life implementation patterns, the achievement of adequate urate control over the whole period (yes/no, as defined above) was obtained for each simulated individual. The number of successes expressed as a fraction of the 1000 simulations corresponding to that implementation pattern provided the probability of success for either perfect implementation (PP) or imperfect implementation (PIP).

2.6 Classifying Implementation Patterns

The quartiles of the relative forgiveness values of the real-life individual implementation patterns were used to classify implementation patterns into two groups according to their forgiveness: least (first quartile) versus more forgiving (other three quartiles). The groups determined using relative forgiveness were then compared with those obtained using an exploratory cluster analysis. The cluster analysis aimed to detect similarities in implementation patterns on the basis of the frequency and duration of consecutive missed doses as well as the frequency and duration of consecutive doses on-therapy (i.e. taking the drug) for each individual standardised to 360 days. Specifically, 15 data items were included; 1, 2, 3, 4, 5 and > 5 consecutive missed doses, 1, 2, 3, 4, 5, 6, 7, 8–15 and > 15 consecutive doses on-therapy. Both hierarchical and K-means cluster analyses were performed [38]. Statistical groupings were assessed using a one-way ANOVA.

2.7 Comparison to Outcomes

The groups of implementation patterns identified using relative forgiveness and cluster analysis were then analysed in terms of clinical outcomes. Clinical outcomes reported in the feasibility study [34], such as gout flare occurrence, HRQoL and urate concentrations were also assessed. Gout flares were self-reported using the Gaffo Criteria [39]. Participants completed the EuroQoL EQ-5D-5L questionnaire [40] at baseline; at 3, 6, 9, and 12 month follow-ups; and when they experienced a gout flare to determine their health-related quality of life. A health utility score (ranging from − 0.301 to 1) was generated at each time point using an Australian value set [41]. Urate concentrations were self-monitored by each participant using a point-of-care device (HumaSens2.0plus, Human Diagnostics). Participants were asked to record their urate concentration at least once a month over the study period, although more frequent monitoring was permitted.

The final groups of implementation patterns identified using both relative forgiveness and the cluster analysis were assessed for differences in variables related to the dose of allopurinol, implementation (total number of missed doses, instances of different implementation patterns with total number of missed doses attributed to each pattern, proportion of doses taken) and observed outcomes [days below the urate target, number of gout flares, number of gout flares per person, health utility scores, EuroQoL visual analog scale (EQ-VAS) scores]. Each instance of non-implementation (defined as at least one missed dose) was defined using one of the following implementation patterns on the basis of the modified ‘rule of sixes’ proposed by Urquhart [23]: occasional missed doses (≤ 2 consecutive missed doses followed by ≥ 15 consecutive doses taken as prescribed); repeated missed doses (≤ 2 consecutive missed doses followed by < 15 consecutive doses taken as prescribed); occasional drug holidays (≥ 3 consecutive missed doses followed by ≥ 15 consecutive doses taken as prescribed); repeated drug holidays (≥ 3 consecutive missed doses followed by < 15 consecutive doses taken as prescribed). The percentage of days that the urate was < 0.36 mmol/L throughout the study period was determined for each participant using the measured urate concentrations and a linear interpolation method [42].

2.8 Software and Statistical Methods

Statistical analyses were performed using R [43], except the cluster analysis which was conducted using Statistical Package for Social Sciences (SPSS, v. 28.0.0.0, Armonk, NY: IBM Corp). The R package mrgsolve [44] was used to generate the simulated data. In the initial stages of the study, the output and results of our R code were compared with the output obtained using the Matlab code given in the Assawasuwannakit et al. [29] paper to ensure quality control. Unpaired analyses used either a two-tailed Mann–Whitney U test, a Kolmogorov–Smirnov test (for three or more groups if needed) or a χ2 test for a comparison of proportions. Odds ratios for gout flare risk between participants in dichotomous implementation groups were generated using a Fisher’s Exact test. All data were tested for normality using a Kolmogorov–Smirnov test.