Impact of treatment discontinuation definitions on comparative retention studies: a simulation-based case study in spondyloarthritis

doi:10.21203/rs.3.rs-5124443/v1

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Research Article

Impact of treatment discontinuation definitions on comparative retention studies: a simulation-based case study in spondyloarthritis

https://doi.org/10.21203/rs.3.rs-5124443/v1

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Background:

In comparative effectiveness research, treatment retention - i.e., the time from treatment start to treatment discontinuation - is an important indicator of treatment effectiveness for chronic illnesses. There is no agreement on the event that defines discontinuation. Commonly used are “last dose received”, “decision to discontinue”, or “first dose missed”, as well as mixtures of these in multi-source studies. For drugs administered less frequently than once daily as is the case for many disease-modifying anti-rheumatic drugs (DMARDs) used for the treatment of spondyloarthritis, retention as determined by these events can vary considerably. Our goal was to quantify the impact of the different definitions of discontinuation on conclusions drawn from treatment comparisons and to recommend a standardised definition.

Methods:

We utilised model-based simulations and real-world data from spondyloarthritis patients treated with tumour necrosis factor (TNF) inhibitors, DMARDs with a wide range of dosing intervals, in Europe. We compared the estimation of the hazard ratio of discontinuation between treatments with varying differences in dosing intervals for the different definitions of discontinuation. To accommodate interval-censored events we used linear transformation models.

Results:

The simulation revealed increasing differences in the estimated treatment hazard ratio based on time to “last dose received” or “first dose missed” compared to “decision to discontinue” with increasing differences in the dosing interval (up to 55 days). These differences were, however, small and further diminished with mixed events. No bias was observed when the time to “decision to discontinue” was analysed as interval-censored between the times to “last dose received” and “first dose missed” instead of as exactly observed. No clinically meaningful differences in estimated hazard ratios between TNF inhibitors with different dosing intervals (56 versus 7 days) were observed in the real-world data.

Conclusions:

The impact of the different treatment discontinuation definitions on comparative retention were found to be negligible. Nonetheless, we recommend to define retention as the time from treatment start to the decision to discontinue treatment. Is the timing of the decision unknown, retention can be analysed as interval-censored between the last dose received and the first dose missed using transformation models.

Trial registration:

Not applicable.

treatment retention

time-to-event

interval-censoring

linear transformation models

spondyloarthritis

The time from treatment start to treatment discontinuation, known as treatment retention (also termed treatment survival, drug retention, or drug survival), is a frequently utilised example of time-to-event data. This metric serves as a key indicator of treatment effectiveness for chronic illnesses such as the inflammatory rheumatic diseases and plays a significant role in comparative effectiveness research (1–19). Basically, the longer a treatment for a chronic condition can be retained, the more beneficial it is.

There is no agreement on the actual event that marks treatment discontinuation. Commonly adopted events include the last dose received (16), the decision to discontinue treatment (17, 19), or the first dose missed (10). In most cases, however, the event is not clearly defined (1–4, 6–9, 11, 12, 14, 15). For drugs administered less frequently than on a daily basis as is the case for many disease-modifying anti-rheumatic drugs (DMARDs) used for the treatment of spondyloarthritis, a family of inflammatory rheumatic diseases, retention as determined by these events can vary considerably (Fig. 1).

Given its vital role in the assessment of treatment effectiveness, a standardised definition of treatment retention seemed important. All the more so because the definition could, in our view, significantly impact the conclusions drawn from comparative retention studies of treatments with differing dosing intervals. Therefore, our goal was to quantify the impact of the different definitions of treatment discontinuation by utilising model-based simulations and real-world data on patients diagnosed with spondyloarthritis, either axial spondyloarthritis (axSpA) or psoriatic arthritis (PsA), from European patient registries and to provide a well-founded recommendation for a standardised definition.

Model-based simulations

We compared the performance of different analyses in estimating the ratio of discontinuation hazards between treatments with varying dosing intervals - as observed for biologic and targeted-synthetic DMARDs (b/tsDMARDs) used in the treatment of axSpA and PsA - by means of model-based simulations. Hereby the analyses differed with respect to the event considered for discontinuation, “last dose received”, “decision to discontinue”, or “first dose missed”. Several properties of the simulation were informed by the real-world data (introduced in a later section).

Simulation set-up

We assumed either an exponential or a Weibull distribution with decreasing hazard for the time to the date it was decided to discontinue treatment. For the reference drug A, the values of the distributional parameters were guided by a probability of 80% to stay on treatment beyond twelve months and a median retention of eight years (for the Weibull distribution only) as roughly observed in the data used for the application example. For details on the derivations see Additional file 1. The distribution for the test drug B was assumed to be either the same as for the reference drug A or different to such an extent that it led to a proportional hazard ratio (HR) of B versus A equal to two. For each randomly drawn time to the discontinuation decision, the time to the last dose received and the time to the first dose missed were calculated based on the dosing interval chosen for the drug, as shown in the schematic in Fig. 1. For detailed calculations see Additional file 1. Data generation aligned with the causal structure shown in Figure S1, Additional file 1.

The follow-up period per patient from start of the treatment was set to three years leading to right-censoring of times as explained in the following section. The choice was guided by the average follow-up time of patients by their registries of 2.8 years as observed in the data used for the application.

For each of the 104 scenarios defined by the combination of the two underlying distributions (exponential and Weibull), sample sizes per drug (500 and 1000), true HRs (one and two), and the dosing intervals in days for each drug, as described in detail in Table 1, we ran 2000 simulation repetitions.

Table 1

List of simulation scenarios.
Distribution	Exponential or Weibull
Sample size per drug	500 or 1000
True HR B vs A	1				2
Drug A interval (days)	1	7	14	56	1	7	14	56
Drug B interval (days)	1	1, 7	1, 7, 14	1, 7, 14, 56	1, 7, 14, 56	1, 7, 14, 56	1, 7, 14, 56	1, 7, 14, 56
All 104 vertical combinations of distribution, sample size per drug, true HR, drug A dosing interval, and drug B dosing interval were assessed.

Estimand and analysis methods

The estimand of interest was the (natural log-transformed) ratio of the hazards for deciding to discontinue between the test drug B and the reference drug A.

For each simulation repetition, we performed the following analyses (denominated simulation methods, SM for short) and estimated the treatment HR from a Cox proportional hazards regression:

SM1: Time to discontinuation decision as an exactly observed event subject to right-censoring at the end of follow-up in case the decision to discontinue occurred thereafter.
SM2: Time to discontinuation decision as an interval-censored event, with the interval bounded by the time to the last dose received on the left and the time to the minimum of the date of the first dose missed and the end of follow-up on the right, subject to right-censoring at the end of follow-up in case the decision to discontinue occurred thereafter.
SM3: Time to last dose received as an exactly observed event subject to right-censoring at the end of follow-up in case the decision to discontinue occurred thereafter.
SM4: Time to first dose missed as an exactly observed event subject to right-censoring at the end of follow-up in case the decision to discontinue occurred after the last dose received prior to end of follow-up.
SM5: A mixture of time to discontinuation decision, time to last dose received, and time to first dose missed, all considered as exactly observed, as collected by ten notional registries. For this purpose, 50% of the observations per drug were attributed randomly in equal proportions to five notional registries collecting the date of the last dose received as the treatment stop, 30% to three notional registries collecting the date of the decision to discontinue, and 20% to two registries collecting the date of the first dose missed. This partitioning was guided by the application example.

All analyses included drug as covariate. In addition, the last analysis, SM5, was stratified by registry. The common reference was the first analysis, SM1, as it provides a consistent estimator of the estimand of interest in this case (20).

Performance assessment

For each analysis listed above we assessed its performance in estimating the true HR by means of bias, variance (empirical and model-based), coverage, and type I error / power of their treatment HR estimate as well as some therefrom derived measures such as the percent relative error of the model-based versus the empirical variance and, for comparisons of analyses, the percent precision gain of analyses compared to the reference analysis. For an overview and further explanation of the performance measures used please refer to the Additional file 1 as well as to reference (21) for further details. The initial choice of 2000 simulation repetitions seemed appropriate as assessed during the simulation work based on the Monte Carlo standard errors for the estimates of the performance measures (21). To accommodate the estimation uncertainty, we report the performance measures as estimates and two-sided 95% Wald-type confidence intervals (CIs).

Application: Retention of TNFi in axSpA and PsA

We used real-world data from patients diagnosed with either axSpA or PsA to assess the differences arising from analyses of tumour necrosis factor inhibitor (TNFi, a class of bDMARDs) retention using “last dose received”, “decision to discontinue”, or “first dose missed” to mark treatment discontinuation.

Study design and data provenance

A retrospective study based on data from European patient registries consolidated by the EuroSpA Research Collaboration Network (RCN), a registry-based initiative to collaboratively investigate observational data from axSpA and PsA patients throughout Europe (22). For the present study, we used data collected by nine registries (BIOBADASAR (Spain, ES), Biorx.si (Slovenia, SI), BSRBR-AS (United Kingdom, UK), ERS Biologic Therapy Register (Estonia, EE), ICEBIO (Iceland, IS), NOR-DMARD (Norway, NO), Reuma.pt (Portugal, PT), Romanian Registry of Rheumatic Diseases (Romania, RO), and SCQM (Switzerland, CH)) who confirmed to collect the date of the first dose as the treatment start date and either the date of the last dose received, the date it was decided to discontinue the treatment, or the date of the first dose missed as the treatment stop date. Of interest were b/tsDMARD-naive axSpA and PsA patients diagnosed at the age of 18 years or older who initiated a TNFi therapy between January 1st 2015 and June 30th 2021. Patients were followed up until the earlier of discontinuation of the TNFi treatment or last clinical visit recorded prior to the time of data extraction from the registry databases. The last registry’s data extraction occurred on April 1st 2022.

Outcomes and exposure of interest

The outcomes of interest were the time from treatment start to the date of the last dose received, the date of the first dose missed, or the date of the discontinuation decision.

For registries collecting the date of the last dose received or first dose missed the times to all three events were derived with the help of the dosing interval. The date of the decision to discontinue was interval-censored between the date of the last dose received and the minimum of the date of the first dose missed or the end of the patient’s follow-up. Any event, had it not or was it not known to have occurred until the end of the patient’s follow-up, was right-censored at that time.

For registries collecting the date of the discontinuation decision the time to that event was the only one available. It was observed exactly and right-censored at the end of the patient’s follow-up had it not occurred before.

The different TNFi treatments were the exposure of interest. The standard dosing intervals (after possible initial uptitration phases) were once every two weeks for adalimumab and certolizumab pegol, once every week for etanercept, once every four weeks for golimumab, and once every eight weeks for infliximab.

Exclusion from analysis

Patients who discontinued or possibly discontinued their TNFi treatment but had incomplete, missing, or conflicting information on the treatment stop date were excluded from the analyses.

For patients missing information on the dosing interval, the dosing interval was imputed by the most frequent interval among the enrolled patients from the same country, diagnosis, type of TNFi, and dose. Patients from registries collecting the date of the last dose received or the first dose missed for whom the dosing interval could not be imputed by this procedure were excluded from the analyses to keep the sample of patients the same for all compared analyses. Lastly, patients missing information on at least one of the patient characteristics assessed at start of treatment used as covariates in the analyses were also excluded.

We assumed conditional independence between the time to treatment discontinuation and missing information on dosing interval or covariates given the covariates in the model. Conditional independence ensures that an analysis restricted to the patients not excluded for missing information is unbiased. However, since patients who discontinued or possibly discontinued their treatment but had incomplete, missing, or conflicting information on the treatment stop date were excluded as well, the estimated HRs are likely biased and should not be interpreted apart from the intended comparison between analyses.

Statistical methods

Apart from adequate descriptions of the data, summaries by diagnosis and type of TNFi of patient characteristics at the start of treatment of all patients enrolled were derived.

Analogously to the simulation, we applied Cox proportional hazards regression models to estimate the ratios of discontinuation hazards for different treatments. The ratios for infliximab versus etanercept (largest difference in standard dosing intervals, 56 versus 7 days, respectively) and certolizumab pegol versus adalimumab (same standard dosing interval of 14 days) were of main interest. In addition, we compared the hazards of males and females for reference. In accordance with the simulation, we performed the following analyses (denominated application methods, AM for short, with numerals corresponding to the respective simulation methods) and compared their results with respect to the hazard ratios of interest.

Based on the registries collecting either the date of the last dose received or the date of the first dose missed as treatment stop date we analysed:

AM2: Time to discontinuation decision as an interval-censored event subject to right-censoring at the end of patients’ follow-up.
AM3: Time to last dose received as an exactly observed event subject to right-censoring at the end of patients’ follow-up.
AM4: Time to first dose missed as an exactly observed event subject to right-censoring at the end of patients’ follow-up.
AM5: A mixture of last dose received and first dose missed, all exactly observed. Registries provided information on either the time to last dose received or the time to first dose missed depending on what they collect as treatment stop date.

Based on all registries we analysed:

AM’2: Time to discontinuation decision as an interval-censored or exactly observed event (the latter applying to registries collecting the date of the discontinuation decision as treatment stop date) subject to right-censoring at the end of patients’ follow-up.
AM’5: A mixture of events, all considered as exactly observed. Registries provided information on either the time to the discontinuation decision, the time to last dose received, or the time to first dose missed depending on what they collect as treatment stop date.

No analyses were performed based on data from only the registries collecting the discontinuation decision. This explains the absence of an AM1 analysis.

The first analysis listed (AM2) was the reference analysis for the second (AM3), third (AM4), and fourth (AM5). The fifth analysis (AM’2) was the reference analysis for the last one (AM’5).

We performed the analyses separately for the two diagnoses axSpA and PsA and adjusted them for some variables considered to possibly affect treatment choice and treatment retention, such as country (by stratification), calendar year, concomitant csDMARD therapy, sex, and age. However, we assume that the intended comparison of analyses is not affected by the conditioning of the association of treatment and treatment retention.

Linear transformation models and software

For a short description of linear transformation models please refer to Additional file 1. For an introduction to transformation models please refer to references (23) and (24).

All analyses were performed in R (25), version 4.2.2, and the manuscript was written with Rmarkdown (26), version 2.20, within the RStudio IDE (27), server version 2022.02.2 + 485. Times to exactly observed events were analysed with Cox proportional hazards models using the function coxph from the R package survival (28), version 3.5.0, with the Efron approximation for tied event times. Times to interval-censored or mixed censored events were analysed with linear transformation models using the function Coxph from the R package tram (29), version 0.8.3, with the log_first argument set to true. While times to exactly observed events could be analysed with tram’s Coxph function, survival’s coxph was considerably faster and therefore chosen. Figures were mainly produced using the ggplot2 package (30), version 3.4.0.

Model-based simulations

Figure 2 shows the results obtained for bias with a true ratio of hazards for the discontinuation decision of drug B versus drug A of one. In scenarios with equal dosing intervals we essentially observed no indication for a bias for any analysis. For SM1 and SM2 no indication of a bias was also observed with different dosing intervals. However, as the dosing intervals started to increasingly differ, longer for drug A and shorter for drug B, we observed increasing biases for SM3, SM4, and SM5. The estimated biases of SM3 and SM4 were of comparable extent (slightly larger for SM4) but opposite sign, negative for SM3 and positive for SM4. The estimated bias for SM5 was generally smaller in extent than for SM3 and SM4 and closer to SM3 than SM4. There was no difference in the behaviour between an exponential and a Weibull distribution for the time to the discontinuation decision apart from slightly smaller biases and wider CIs for the latter. The respective plot of estimated biases with a true HR of drug B versus drug A of two is included as Figure S2 in Additional file 2. The findings were very similar to a true HR of one.

Figure 3 shows the results obtained for the square root of the empirical variance of the natural log-transformed HR estimate for a true HR of drug B versus drug A of one. As expected, the empirical variance estimate was smaller with the larger sample size. Estimated empirical variances were very similar among the different analyses for a given scenario, while there were some minor differences across scenarios for a given distribution. For the Weibull distribution the estimated empirical variances were consistently larger than for the exponential distribution. The respective plot of the square root of the estimated empirical variance for a true HR of drug B versus drug A of two is included as Figure S3 in Additional file 2. The findings were essentially the same as for a true HR of one apart from consistently slightly smaller variances.

Figure 4 allows a closer look at the empirical variance estimate of different analyses by showing the estimated gain in precision compared to SM1. As indicated already by the estimated empirical variances, the gains/losses compared to SM1 were negligible. However, though hardly discernible in Fig. 3, there was an indication of a minuscule loss in precision of SM2 to a larger extent for the Weibull compared to the exponential distribution. If anything, SM3 and SM4 tended to gain or loose, respectively, a small amount of precision compared to SM1. For SM5, the changes in precision were generally intermediate. There was notable variation in the simulation uncertainty within and across scenarios driven by the differences in the correlation between the HR estimates of each type of analysis and SM1, which was used to calculate the Monte Carlo standard error. The respective plot of estimated gains in precision for a true HR of drug B versus drug A of two is included as Figure S4 in Additional file 2. The findings were similar to a true HR of one.

Figure 5 shows the results obtained for the relative error, i.e., the comparison of the model-based variance to the empirical variance of the natural log-transformed HR estimate for a true HR of drug B versus drug A of one. There was essentially no indication for a non-performance of the model-based variance estimation. The different analyses for a given scenario were hardly different. There was some variation in the estimated relative error between scenarios. The respective plot of estimated relative errors for a true HR of drug B versus drug A of two is included as Figure S5 in Additional file 2. The findings were very similar to a true HR of one.

As expected given the results for the bias and the model-based variance, there was no indication of undercoverage (Fig. 6) with SM1 and SM2 for any setting and for SM3, SM4 and SM5 when the dosing intervals were the same for both drugs. Indication for undercoverage was observed for SM3 and SM4 only once the difference in dosing intervals was larger. In presence of a bias, undercoverage is expected to worsen with increasing sample size and our results support that. Undercoverage seemed somewhat more pronounced for the exponential distribution, which is in line with the findings for the bias. The respective plot of estimated coverages for a true HR of drug B versus drug A of two is included as Figure S6 in Additional file 2. The findings were comparable to a true HR of one but with somewhat more pronounced undercoverage.

Lastly, we assessed the type I error (Fig. 7), which is expected to mirror the behaviour for coverage, which it did. For a true HR of drug B versus drug A equal to two, the respective performance measure is power. Power reached one for all scenarios, i.e., none of the 64*2000 simulation repetitions failed to reject the null hypthesis of no difference between drug B and drug A (Figure S7, Additional file 2).

For all scenarios and repetitions, estimates of the (natural log-transformed) treatment HR for all analyses were obtained. Figures S8 to S11 in Additional file 3 and S12 to S13 in Additional file 4, display the estimates data (scatter plots, normal quantile-quantile plots, zip plots showing the individual CIs, and pairs plot contrasting different analyses). Natural log-transformed estimates of the treatment HRs were approximately normally distributed (Figure S10, Additional file 3). For all scenarios and repetitions, the absolute difference between SM2 and SM1 estimates on the log scale was smaller than 0.01 (see also Figure S12, Additional file 4).

Application: Retention of TNFi in axSpA and PsA

A total of 4606 eligible axSpA and 2109 eligible PsA patients were retrieved from the EuroSpA RCN data server and enrolled. Figures S14 to S23 in Additional file 5 provide an overview of patient study entry, time at risk, and occurrence of treatment discontinuation as a function of calendar time by diagnosis and TNFi. Tables 2 and 3 provide a summary of characteristics of enrolled patients by TNFi received for axSpA and PsA, respectively. Of note, there was considerable variation in dosing intervals (either at time of discontinuation or as last known) of different extent and direction depending on the TNFi. For example, the dosing interval of infliximab tended to be shorter than the standard whereas for etanercept it tended to be longer. Of the nine contributing registries, five collected the date of the last dose received (CH, PT, RO, SI, UK), two the date of the decision (ES, NO), and two the date of the first dose missed (EE, IS). The median follow-up time from start of the TNFi to the earlier of treatment discontinuation or last clinical visit was 20 months for axSpA and 18.2 months for PsA patients. Dated discontinuation of the TNFi therapy was reported for 1561 axSpA and 890 PsA patients, 73 and 67 of which missed a reason. Remission was reported as the reason for discontinuation the least often, for 37 axSpA and 11 PsA patients. We did not differentiate between remission and other reasons for discontinuation in our analyses.

Table 2

Summary of enrolled axSpA patient characteristics at start of first TNFi by TNFi.
	Adalimumab (n = 1932)	Certolizumab (n = 305)	Etanercept (n = 1078)	Golimumab (n = 690)	Infliximab (n = 601)
Male sex, n (%)	1196 (61.9)	151 (49.5)	693 (64.3)	416 (60.3)	377 (62.7)
Age in yrs^a, median [IQR]^b	37.0 [28.0, 46.0]	33.0 [26.0, 40.0]	36.0 [28.0, 46.0]	36.0 [28.0, 45.0]	36.0 [28.0, 47.0]
Disease duration in yrs^a, median [IQR]^b	3.0 [1.0, 9.0]	2.0 [1.0, 6.0]	3.0 [1.0, 9.0]	2.0 [1.0, 8.0]	2.0 [1.0, 9.0]
HLA-B27 positive, n (%)	1183 (77.7) (n = 1523)	197 (76.1) (n = 259)	615 (76.6) (n = 803)	433 (76.6) (n = 565)	349 (83.7) (n = 417)
BMI, median [IQR]^b	26.1 [23.3, 29.4] (n = 1533)	25.5 [23.4, 29.7] (n = 193)	25.9 [23.3, 29.4] (n = 884)	25.7 [23.1, 29.3] (n = 582)	26.1 [23.1, 29.8] (n = 457)
BASDAI, median [IQR]^b	63.6 [49.0, 75.0] (n = 1253)	57.0 [40.0, 73.0] (n = 208)	66.0 [53.4, 78.0] (n = 689)	64.0 [49.0, 76.0] (n = 399)	62.4 [48.0, 74.8] (n = 378)
ASDAS-CRP, median [IQR]^b	3.9 [3.1, 4.6] (n = 826)	3.4 [2.5, 4.1] (n = 146)	4.1 [3.3, 4.8] (n = 513)	3.7 [2.9, 4.5] (n = 276)	3.6 [2.8, 4.5] (n = 228)
Concomitant csDMARDs, n (%)	563 (34.8) (n = 1620)	55 (20.8) (n = 265)	265 (28.8) (n = 920)	165 (28.9) (n = 571)	209 (46.1) (n = 453)
Dosing interval, n (%)^c	n = 1921	n = 304	n = 1073	n = 677	n = 503
standard	1536 (80.0)	249 (81.9)	980 (91.3)	517 (76.4)	363 (72.2)
shorter	40 ( 2.1)	4 ( 1.3)	7 ( 0.7)	2 ( 0.3)	130 (25.8)
longer	345 (18.0)	51 (16.8)	86 ( 8.0)	158 (23.3)	10 ( 2.0)
Calendar year, n (%)
2015/2016	608 (31.5)	157 (51.5)	321 (29.8)	291 (42.2)	250 (41.6)
2017/2018	485 (25.1)	74 (24.3)	457 (42.4)	262 (38.0)	263 (43.8)
2019/2020/2021	839 (43.4)	74 (24.3)	300 (27.8)	137 (19.9)	88 (14.6)
Country, n (%)
CH	173 ( 9.0)	48 (15.7)	83 ( 7.7)	178 (25.8)	55 ( 9.2)
EE	124 ( 6.4)	0 ( 0.0)	25 ( 2.3)	1 ( 0.1)	98 (16.3)
ES	262 (13.6)	43 (14.1)	163 (15.1)	111 (16.1)	51 ( 8.5)
IS	18 ( 0.9)	0 ( 0.0)	10 ( 0.9)	8 ( 1.2)	100 (16.6)
NO	79 ( 4.1)	56 (18.4)	34 ( 3.2)	4 ( 0.6)	73 (12.1)
PT	305 (15.8)	34 (11.1)	178 (16.5)	127 (18.4)	56 ( 9.3)
RO	489 (25.3)	31 (10.2)	370 (34.3)	192 (27.8)	145 (24.1)
SI	106 ( 5.5)	19 ( 6.2)	32 ( 3.0)	56 ( 8.1)	20 ( 3.3)
UK	376 (19.5)	74 (24.3)	183 (17.0)	13 ( 1.9)	3 ( 0.5)
a: yrs = years.
b: IQR = inter-quartile range.
c: Recorded at time of discontinuation or as last known, not at start of first TNFi.
Unless specified otherwise, the numbers of observations equal the number of patients indicated in the column headers.

Table 3

Summary of enrolled PsA patient characteristics at start of first TNFi by TNFi.
	Adalimumab (n = 801)	Certolizumab (n = 168)	Etanercept (n = 552)	Golimumab (n = 307)	Infliximab (n = 281)
Male sex, n (%)	395 (49.3)	68 (40.5)	256 (46.4)	154 (50.2)	132 (47.0)
Age in yrs^a, median [IQR]^b	45.0 [35.0, 52.0]	42.0 [33.0, 51.2]	46.0 [36.0, 55.0]	45.0 [36.0, 54.0]	43.0 [35.0, 53.0]
Disease duration in yrs^a, median [IQR]^b	3.0 [1.0, 8.0]	3.0 [1.0, 7.0]	3.0 [1.0, 7.0]	3.0 [1.0, 7.0]	5.0 [1.0, 9.0]
HLA-B27 positive, n (%)	90 (20.0) (n = 449)	21 (21.2) (n = 99)	50 (15.6) (n = 320)	35 (18.7) (n = 187)	19 (22.6) (n = 84)
BMI, median [IQR]^b	26.9 [24.0, 30.9] (n = 579)	26.3 [24.0, 31.8] (n = 101)	27.3 [24.0, 31.1] (n = 417)	26.8 [24.2, 30.8] (n = 248)	28.1 [25.1, 32.4] (n = 177)
DAS28-CRP, median [IQR]^b	4.2 [3.5, 5.0] (n = 498)	4.2 [3.2, 4.9] (n = 128)	4.2 [3.4, 5.1] (n = 357)	4.0 [3.0, 5.0] (n = 176)	4.4 [3.7, 5.1] (n = 146)
CDAI, median [IQR]^b	21.0 [14.0, 27.9] (n = 348)	17.7 [11.8, 26.0] (n = 82)	20.0 [13.5, 30.0] (n = 208)	19.4 [13.0, 27.0] (n = 132)	21.0 [14.3, 26.8] (n = 107)
Concomitant csDMARDs, n (%)	568 (84.4) (n = 673)	99 (72.3) (n = 137)	381 (83.2) (n = 458)	208 (77.0) (n = 270)	195 (91.5) (n = 213)
Dosing interval, n (%)^c	n = 797	n = 166	n = 532		n = 236
standard	589 (73.9)	140 (84.3)	511 (96.1)	210 (68.4)	156 (66.1)
shorter	10 ( 1.3)	1 ( 0.6)	2 ( 0.4)	3 ( 1.0)	80 (33.9)
longer	198 (24.8)	25 (15.1)	19 ( 3.6)	94 (30.6)	0 ( 0.0)
Calendar year, n (%)
2015/2016	181 (22.6)	83 (49.4)	169 (30.6)	136 (44.3)	137 (48.8)
2017/2018	171 (21.3)	55 (32.7)	217 (39.3)	116 (37.8)	105 (37.4)
2019/2020/2021	449 (56.1)	30 (17.9)	166 (30.1)	55 (17.9)	39 (13.9)
Country, n (%)
CH	84 (10.5)	17 (10.1)	43 ( 7.8)	85 (27.7)	9 ( 3.2)
EE	77 ( 9.6)	0 ( 0.0)	20 ( 3.6)	0 ( 0.0)	58 (20.6)
ES	217 (27.1)	48 (28.6)	191 (34.6)	63 (20.5)	32 (11.4)
IS	31 ( 3.9)	0 ( 0.0)	29 ( 5.3)	13 ( 4.2)	86 (30.6)
NO	42 ( 5.2)	53 (31.5)	30 ( 5.4)	1 ( 0.3)	51 (18.1)
PT	174 (21.7)	12 ( 7.1)	133 (24.1)	74 (24.1)	17 ( 6.0)
RO	82 (10.2)	2 ( 1.2)	69 (12.5)	38 (12.4)	14 ( 5.0)
SI	94 (11.7)	36 (21.4)	37 ( 6.7)	33 (10.7)	14 ( 5.0)
UK	0 ( 0.0)	0 ( 0.0)	0 ( 0.0)	0 ( 0.0)	0 ( 0.0)
a: yrs = years.
b: IQR = inter-quartile range.
c: Recorded at time of discontinuation or as last known, not at start of first TNFi.
Unless specified otherwise, the numbers of observations equal the number of patients indicated in the column headers.

Of the patients enrolled, 971 for axSpA and 507 for PsA were excluded from the analyses; among them 188 axSpA and 147 PsA for incomplete, missing, or conflicting information on the treatment stop date, 83 axSpA and 39 PsA for missing information on dosing interval, and another 700 axSpA and 321 PsA for missing information on the concomitant csDMARD status at TNFi start. Therefore, the analysis data set consisted of 3635 patients and 1127 discontinuations for axSpA and 1602 patients and 591 discontinuations for PsA. Of note, for “first dose missed” the number of events was reduced by 61 for axSpA and 16 for PsA compared to “last dose received” and “decision to discontinue” as the first dose was missed only after the end of the patient’s follow-up.

In contrast to the simulation, times to “last dose received” and “first dose missed” were not obviously discrete and their Kaplan-Meier estimates almost indistinguishable (see Figures S24 to S27, Additional file 5). Median retention times as read from the Kaplan-Meier estimates by disease and TNFi were all longer than three years, possibly substantially so.

Estimated HRs for infliximab versus etanercept, adalimumab versus certolizumab, and males versus females from the different analyses are shown in Fig. 8. More detailed information on fitted models is available from Additional file 5. The treatment HR estimates and CIs for the three comparisons were very similar across the different analyses within diagnoses and sets of registries considered. For infliximab versus etanercept, the difference in the log-transformed HR estimate between AM3 and AM4 was − 0.00187 for axSpA and − 0.000959 for PsA. Compared to the range of differences between SM3 and SM4 with a sample size of 500 and dosing intervals of 7 and 56 days for drug A and B of 0.0188 to 0.109 (based on 4000 simulation repetitions), these differences are unexpected. For simulation scenarios with a difference in dosing intervals of 7 or less days, negative differences between SM3 and SM4 were observed. For adalimumab versus certolizumab, the respective difference between AM3 and AM4 was 0.039 for axSpA and − 0.0328 for PsA, which were more in line with the range of -0.0362 to 0.0333 obtained from the simulation of a sample size of 500 and equal dosing intervals of 14 days (based on 8000 simulation repetitions). The difference between AM3 and AM4 with respect to the sex comparison was 0.00632 for axSpA and − 0.0238 for PsA.

According to the target trial emulation framework (31, 32), a retrospective study should be designed to emulate the ideal prospective trial. If we were to perform a randomised prospective trial to compare retention of treatments, then patients would be followed up until either the event of interest (i.e., discontinuation of treatment), death, or the end of study has occurred. It seems obvious that discontinuation in such a trial would be understood as the decision to discontinue: a patient’s follow-up cannot be stopped at the time of the dose to be received last, as this dose can only be identified in hindsight once the decision to discontinue was made and observed. Furthermore, if we have followed up the patient until the decision to discontinue was taken, the timing of the first dose missed is known and there is nothing to gain from observing the patient for longer in this respect. Hence, treatment retention in comparative effectiveness research should also focus on the decision event.

The simulation work confirmed that estimated treatment HRs differ depending on the event considered as discontinuation, “last dose received”, “decision to discontinue”, or “first dose missed”, when the drugs compared differ in their dosing interval. As the dosing interval increased, the hazard of “last dose received” grew progressively larger compared to the hazard of “decision to discontinue”, while the hazard of “first dose missed” decreased progressively. Consequently, in terms of longer retention, treatments with shorter dosing intervals were favoured with “last dose received”, whereas treatments with longer dosing intervals were favoured with “first dose missed”. When events were mixed according to the notional registries’ data collection, differences in the estimated treatment HRs compared to “decision to discontinue” were diminished but closer to those with “last dose received”, which was the most frequent event. On the other hand, and in line with findings presented elsewhere (33), applying a Cox proportional hazards model with a suitable correction for tied event times (34) to the discrete times to last dose received or first dose missed when dosing intervals were the same, performed well for all dosing intervals assessed despite the mis-specified model (proportional hazards do not apply to discrete event times). With respect to the variance of the treatment HR estimate differences between events and their analyses were slight and irrelevant yet to be expected. Due to the uncertainty in occurrence, the interval-censored SM2 was expected to provide a more variable estimate than SM1, which was confirmed. The variance of an exponential or Weibull time-to-event variable decreases as the hazard or the inverse of the scale parameter (with shape remaining constant), respectively, increases. We suppose that the reason why SM3 tended to gain and SM4 to loose some precision compared to SM1 was because the hazard with time to last dose received (first dose missed) tended to be larger (smaller) compared to the time to the discontinuation decision.

The reasons underlying the differences between “last dose received” or “first dose missed” and “decision to discontinue” are of a causal nature. Undeniably, the time to the last dose received is defined by the time to the discontinuation decision and the dosing interval. This means that treatments can impact the time to the last dose received through two different pathways; by their impact on the time to the discontinuation decision and by their impact on the dosing interval (please refer to Figure S1, Additional file 1, for a depiction of the presumed causal structure). For effectiveness, the decisive cause-effect relationship seems to be between treatment and the time to the discontinuation decision, not between treatment and the time to the last dose received. After all, given the time to the discontinuation decision, treatment adds nothing to the time to the last dose received except through the dosing interval. Therefore, unless an effect of the dosing interval on our assessment of retention is wanted, which we doubt, we should not analyse the time to the last dose received. The same reasoning applies to the time to the first dose missed. Hence, we consider “last dose received” and “first dose missed” but unqualified surrogates.

The simulated biases in estimated treatment HRs for “last dose received” and “first dose missed” compared to the decision to discontinue were, however, small. Assessing whether a treatment with a long dosing interval is retained differently than a treatment with a short dosing interval is very likely resulting in the same conclusions regardless of the event used as discontinuation if the true HR for deciding to discontinue is of clinical relevance. With true HRs close to one, conclusions are more likely to differ, especially as the sample size increases and the estimation becomes more precise. On the other hand, large sample sizes allow one to conclude that small, statistically significant differences are not clinically relevant making inconsistent results less worrisome.

In line with the simulation results, we found no relevant differences in HR estimates and CIs even when comparing TNFi treatments with a standard dosing interval of 56 and 7 days, respectively, in the data from the spondyloarthritis patients across Europe. At first glance, there seemed to be subtle disagreement with the results obtained from the simulation. However, these differences could be explained by the fact that the actual dosing intervals tended to differ from the standard dosing intervals in different ways for the different types of TNFi (e.g., shorter than standard for infliximab and longer than standard for etanercept). Surprisingly, the discrete nature of the times to last dose received and first dose missed seen in the simulation, was not obvious in the EuroSpA RCN spondyloarthritis data. We presume that this is mostly due to differences in the dosing interval of a given TNFi across patients (Tables 2 and 3), as well as possibly due to changes of the dosing interval within patients over time or recording errors. Recording errors due to recollection of wrong dates or recording of the wrong type of date are probably not so rare. Together, these circumstances will also attenuate the impact of treatments on the time to the last dose received or first dose missed through differences in dosing intervals. Overall, the differences in treatment HR estimates between analyses were similar to the differences in estimates observed between analyses for the comparison of males and females for which we did not expect any meaningful differences (in line with the causal structure in Figure S1, Additional file 1).

As expected, an interval-censored approach for the decision to discontinue using a linear transformation model (23) performed well in estimating the treatment HRs. Linear transformation models and interval censoring based on the last dose received or first dose missed offer thus a possibility to analyse the time to the decision event for drugs not tapered even when the decision is not recorded as is the case in seven out of the nine registries whose data was considered in this study.

We believe that our simulation results are robust and that biases as those found are to be expected generally when dosing intervals and retention times are similar to those observed in our spondyloarthritis data. The simulation was based on two different distributions for the time to the discontinuation decision exhibiting either a constant or a decreasing hazard function, two sample sizes, and two true HRs. The observed differences between different events and dosing intervals were remarkably similar across the two distributions and true HRs and varied as expected with sample size. Issues with coverage and type I error would obviously aggravate with even larger sample sizes. Whether or not there could be situations in which the biases would, contrary to the findings in this study, actually matter is, however, not known.

Limitations

Drug tapering implies that the decision to discontinue treatment precedes the last dose received and invalidates the interval-censored approach for the discontinuation decision discussed here. Fortunately, tapering of b/tsDMARDs in the treatment of spondyloarthritis patients is commonly considered only in response to the achievement of sustained remission (or low activity) of the disease under their use (35). Disease remission is distinctly different from other reasons for discontinuation; instead of treatment failure or inadequacy it indicates treatment success and should be treated differently. Developing an approach to appropriately handle discontinuation due to remission was beyond the scope of this study. However, we are confident that it can be integrated without problems into a revised approach for comparative effectiveness in terms of treatment retention.

Apart from differences in the event collected as treatment stop date, registries also differ with respect to the event collected as the treatment start date. Three of the 16 patient registries participating in the EuroSpA RCN at the time of data collection for this study confirmed that they record the date of the decision to initiate treatment as the treatment start date. Similarly, in randomised clinical trials the clock usually starts at the time of randomisation. However, contrary to the end of treatment, these initialising events are not expected to be affected by treatment characteristics such as the dosing interval, which we do not want to affect our assessment of effectiveness. Hence, differences in the event defining the treatment start, which tend to lie close to each other in time, should be negligible. Nevertheless, the event considered as start of treatment should also be clearly defined.

Finally, due to the exclusion of patients who discontinued or possibly discontinued their treatment but had missing, incomplete, or conflicting information on the treatment stop date, the estimated HRs obtained for the application should not be interpreted due to the likely possibility of bias. While we excluded patients with missing information on their terminal dosing interval for comparability of the different analyses, they can be included in an actual study given appropriate consideration and handling of the additional uncertainty.

Clinically relevant differences in conclusions drawn from comparative analyses of treatment retention as a result of using different events to mark treatment discontinuation are unlikely. Nonetheless, we recommend to define retention as the time from treatment start to the decision to discontinue treatment. Is information on the timing of the decision unavailable, retention can be analysed as interval-censored between the last dose received and the first dose missed using transformation models.

ASDAS-CRP	Ankylosing Spondylitis Disease Activity Score based on CRP
axSpA	Axial SpondyloArthritis
b/tsDMARD	biologic or targeted-synthetic Disease Modifying Anti-Rheumatic Drug
BASDAI	Bath Ankylosing Spondylitis Disease Activity Index
BMI	Body Mass Index
CDAI	Clinical Disease Activity Index
CI	Confidence Interval
CRP	C-Reactive Protein
DAS28-CRP	Disease Activity Score based on 28 joints and CRP
HLA-B27	Human Leukocyte Antigen-B, variant 27
HR	Hazard Ratio
PsA	Psoriatic Arthritis
RCN	Research Collaboration Network
TNFi	Tumour Necrosis Factor inhibitor

Ethics approval and consent to participate

All patient data were collected in accordance with national legal and regulatory requirements in the different countries. The study was approved by the respective national Data Protection Agencies or Ethical Committees according to legal regulatory requirements in the participating countries.

Consent for publication

Not applicable

Availability of data and materials

The real-world data in this article was collected in the individual patient registries and made available for secondary use through the EuroSpA Research Collaboration Network [https://eurospa.eu/#registries]. Relevant patient level data may be made available on reasonable request to the corresponding author but will require approval from all contributing registries.

Competing interests

The authors declare that they have no competing interests.

Funding

This EuroSpA study was financially supported by Novartis Pharma AG. No financial sponsor had any influence on the data collection, statistical analyses, abstract/manuscript preparation, or decision to submit.

Authors’ contributions

Conceptualisation	MR, SK, AC, LMØ, MØ, MLH, BrM, BG, DDG
Methodology	MR, SK, CP, BT
Software	CP, MR, SHR
Validation	CP, MR
Formal analysis	CP, MR
Investigation	CC, IC, MB, PAR, AC, BM, MJN, GJM, GTJ, ZR, KPP, BrM, GB, KL, SV, BjG
Resources	MLH, MØ, JH, CC, IC, MB, PAR, AC, BM, MJN, GJM, GTJ, ZR, KPP, BrM, GB, KL, SV, BjG
Data curation	JH, SHR, LMØ, SG
Writing (original draft)	MR, CP
Writing (review and editing)	All authors
Visualisation	CP, MR
Supervision	MR, BT, MØ, MLH
Project administration	MR
Funding acquisition	MLH, MØ

Acknowledgements

We thank all the patients and health care professionals who collected the data for the individual patient registries participating in this study.

A special thank goes to Almut Scherer and Torsten Hothorn for valuable input during the planning of the study or writing of the manuscript.

The EuroSpA collaboration has been supported by Novartis Pharma AG since 2017 and UCB Biopharma SRL since 2022. This EuroSpA study was financially supported by Novartis. No financial sponsor had any influence on the data collection, statistical analyses, abstract/manuscript preparation, or decision to submit.

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No competing interests reported.

Additionalfile1.docx
Additional file 1.docx: Supplementary methods. Description: Additional information with respect to methods like mathematical derivations, detailed descriptions of performance measures, and a description of linear transformation models.
Additionalfile2.docx
Additional file 2.docx: Supplementary results I related to the simulation. Description: Additional plots of estimated performance measures from simulations.
Additionalfile3.docx
Additional file 3.docx: Supplementary results II related to the simulation. Description: Plots of estimates data from simulations: scatter plots, normal quantile-quantile plots, and zip plots showing the individual CIs.
Additionalfile4.docx
Additional file 4.docx: Supplementary results III related to the simulation. Description: Plots of estimates data from simulations: pairs plot contrasting different analyses.
Additionalfile5.docx
Additional file 5.docx: Supplementary results related to the EuroSpA RCN spondyloarthritis data. Description: Additional information on patient recruitment, time at risk, and discontinuation, Kaplan-Meier plots for TNFi retention, and fitted model outputs.

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Impact of treatment discontinuation definitions on comparative retention studies: a simulation-based case study in spondyloarthritis

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Abstract

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BACKGROUND

METHODS

Model-based simulations

Application: Retention of TNFi in axSpA and PsA

Linear transformation models and software

RESULTS

Model-based simulations

Application: Retention of TNFi in axSpA and PsA

DISCUSSION

Limitations

CONCLUSIONS

Abbreviations

Declarations

Ethics approval and consent to participate

Consent for publication

Availability of data and materials

Competing interests

Funding

Authors’ contributions

Acknowledgements

References

Additional Declarations

Supplementary Files

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