The volume–outcome relationship for pulmonary endarterectomy in chronic thromboembolic pulmonary hypertension
Chronic thromboembolic pulmonary hypertension (CTEPH) is diagnosed in 0.1–3.8% of pulmonary embolism survivors  and its incidence in the general population is 5.2–13.2 million per year . CTEPH is characterised by a dismal prognosis, secondary to right-sided heart-failure. Although several therapies exist, pulmonary endarterectomy (PEA) is preferred in suitable patients because it is potentially curative . Still, PEA is a complex and technically demanding procedure, during which cardiopulmonary bypass is used in combination with deep hypothermic circulatory arrest. Consequently, the PEA procedure itself is also associated with significant morbidity and mortality rates, with reported mortality rates ranging between 0.8% and 24.4% , rendering patient selection crucial . In addition, surgical expertise seems to play an important role. Given the relative infrequency of CTEPH as a disease, and PEA as a procedure, institutional volumes have historically been rather low, potentially resulting in suboptimal outcomes. However, high-volume centres have recently reported early mortality rates of <5%  and the frequency of PEA as a procedure has steadily increased during the past decade . Of note, in the absence of clear US recommendations , the 2022 European Society for Cardiology (ESC)/European Respiratory Society (ERS) guidelines for the diagnosis and treatment of pulmonary hypertension state that PEA should be performed in centres performing >50 PEA cases annually , although a substantiated recommendation was not provided in that document. Inherently, the volume–outcome (V-O) relationship is nonlinear and not absolute, because expertise is only part of the equation that determines the result . We have recently introduced a new method to determine this nonlinear V-O relationship, and to estimate the minimum required caseload to define a high-volume centre for infrequently performed surgical procedures that require centralisation . Given the call for centralisation of PEA procedures and its elective character, the current study aims to evaluate the V-O relationship in PEA procedures for CTEPH. 

Design and registration The current study was designed as a systematic review and meta-analysis, and pre-registered in PROSPERO (CRD42024548185, 28 May 2024) . We adhered to the 2020 Preferred Reporting Items for Systematic Reviews and Meta-Analyses statement . Eligibility criteria Studies published between conception of the three electronic databases and 1 May 2024 were eligible for inclusion. Inclusion criteria were studies reporting on 1) consecutive PEA patients per centre, 2) years of inclusion (to calculate the inclusion period and the subsequent annual case load) and 3) the primary outcome (early mortality). Both single- and multiple-arm studies were eligible for inclusion. The inclusion of duplicate cohorts of the same centre was prevented by including the study with the largest sample size and excluding other studies describing the same cohort. If a centre reported on separate cohorts in different timespans, these reports were both used and assessed separately. Finally, to mitigate for the risk of publication bias, we allowed conference abstracts to be eligible for inclusion, on the prerequisite of fulfilling the prespecified inclusion criteria. Information sources The search was performed in three electronic databases (PubMed, Embase and the Cochrane Library). Reference lists of included articles were screened for potentially missed articles (cross-referencing). Search strategy The first search was performed in September 2023, and was updated regularly until 1 May 2024 ( supplementary table S1 presents the full search strategy). The search was performed by one experienced author (M.J. Kawczynski). Selection process Duplicate studies were removed by automated tools, and the remaining articles were screened by title and abstract using the semi-automated web-based application Rayyan ( https://rayyan.qcri.org ) , after which a full-text screening was conducted to determine the studies eligible for final inclusion. The selection was performed by two independent reviewers (S. Heuts and A. Leus), and potential disagreement was resolved by consultation with the senior author (T. Verbelen). Data collection and items Preoperative, perioperative and postoperative data were collected using a Microsoft Excel sheet ( supplementary table S2 ) by two authors (S. Heuts and A. Leus). Outcomes and effect measures The primary outcome was early mortality in relation to annual case volume per centre. Early mortality was defined as in-hospital mortality or 30-day mortality. Secondary outcomes were the need for postoperative extracorporeal membrane oxygenation (ECMO), duration of mechanical ventilation (days), intensive care unit (ICU) length of stay (days) and long-term survival. Long-term survival was expressed in absolute risk at 10 years, and absolute risk differences and numbers needed to treat were calculated. The principal analysis focused on the statistical determination of the volume that could define a high-volume centre, using the elbow method (please see “Data synthesis” section). In addition, a 5.0% mortality rate has previously been proposed to be acceptable, and required, for this high-risk intervention . Therefore, the annual case volume corresponding to this mortality rate threshold was studied, facilitating a combination of a statistically determined and clinically indicated high-volume threshold. Finally, we calculated the early mortality rates of centres performing less and more than the previously proposed required annual case load of 50 PEA procedures. Risk of bias assessment A risk of bias assessment was performed to evaluate the quality of the included articles, using the Newcastle–Ottawa scale, which can be modified for single-arm studies by excluding one of four questions in the “Selection” section ( i.e. question 2), thereby assigning a maximal score of eight instead of nine to a study . This assessment was performed by two authors independently (S. Heuts and M.J. Kawczynski). Data synthesis All data are presented as mean± sd or n . Reported medians with interquartile range and/or minimum and maximum values were converted by Wan's method . Annual procedural volume was calculated by dividing the number of patients per centre by their total inclusion time. Studies were categorised into tertiles (T 1 , T 2 , T 3 ) according to their respective annual case volume. Early outcomes such as mortality and need for postoperative ECMO were pooled in a random-effects model (inverse variance weighting) and are presented for the overall cohort and per tertile, in n  and corresponding 95% confidence intervals. For early mortality, relative risk differences were calculated with both 10 cases per year and the threshold of a high-volume centre as a reference. The nonlinear relationship between annual case volume and early mortality was examined using restricted cubic splines (RCS) (three knots) and presented graphically in a nonlinear mixed-effect model . This outcome was studied both in unadjusted and adjusted analyses (adjusted for geographical location and median inclusion year, based on a complete case analysis, in a linear regression model, as proposed previously ). To determine the volume that determined a high-volume centre, we applied the elbow method, which was first described by A ntunes et al .  and S atopää et al .  for optimisation statistics and thereafter applied to the V-O relationship in surgical interventions by K awczynski et al .  (graphically presented in supplementary figure S1 ). For the secondary analysis of long-term survival, individual patient data derived from Kaplan–Meier curves were reconstructed as proposed by L iu et al . . The presence of an association between annual case volume as a continuous parameter and as a tertile and long-term survival was evaluated using a univariable Cox frailty model , both in unadjusted and adjusted analyses. Of note, because only 12 out of 52 studies reported on long-term survival, new tertiles were constructed for this outcome, similarly based on the distribution of centre volume (four centres per tertile). For long-term survival, absolute risk differences were calculated with T 1 as a reference, with subsequent derived numbers needed to treat. Because the third tertile encompassed centres performing more than 16 annual procedures, sensitivity analyses were performed by dividing this tertile into smaller fractions ( i.e. 16–50 procedures, 51–100 procedures and >100 procedures per year). Furthermore, sensitivity analyses were performed for studies published after 2014, and for studies only including patients after 2014 (which closely relates to the standardised introduction of balloon pulmonary angioplasty, which may have affected the patient selection for PEA from that era onwards). All analyses were conducted using the R statistics software (“metafor”, “meta”, “rms”, “mgcv”, “survival”, “survminer”, “maps”, “ggplot2”, “pathviewr” and “discfrail” packages; www.r-project.org). Publication bias assessment The presence of publication bias was assessed for the primary outcome, visualised in a funnel plot and quantified by Egger's test. Data availability All data and coding for analyses will be openly shared through https://github.com/samuelheuts/V-O_in_PEA_for_CTEPH upon publication of this study. 

The current study was designed as a systematic review and meta-analysis, and pre-registered in PROSPERO (CRD42024548185, 28 May 2024) . We adhered to the 2020 Preferred Reporting Items for Systematic Reviews and Meta-Analyses statement . 

Studies published between conception of the three electronic databases and 1 May 2024 were eligible for inclusion. Inclusion criteria were studies reporting on 1) consecutive PEA patients per centre, 2) years of inclusion (to calculate the inclusion period and the subsequent annual case load) and 3) the primary outcome (early mortality). Both single- and multiple-arm studies were eligible for inclusion. The inclusion of duplicate cohorts of the same centre was prevented by including the study with the largest sample size and excluding other studies describing the same cohort. If a centre reported on separate cohorts in different timespans, these reports were both used and assessed separately. Finally, to mitigate for the risk of publication bias, we allowed conference abstracts to be eligible for inclusion, on the prerequisite of fulfilling the prespecified inclusion criteria. 

The search was performed in three electronic databases (PubMed, Embase and the Cochrane Library). Reference lists of included articles were screened for potentially missed articles (cross-referencing). 

The first search was performed in September 2023, and was updated regularly until 1 May 2024 ( supplementary table S1 presents the full search strategy). The search was performed by one experienced author (M.J. Kawczynski). 

Duplicate studies were removed by automated tools, and the remaining articles were screened by title and abstract using the semi-automated web-based application Rayyan ( https://rayyan.qcri.org ) , after which a full-text screening was conducted to determine the studies eligible for final inclusion. The selection was performed by two independent reviewers (S. Heuts and A. Leus), and potential disagreement was resolved by consultation with the senior author (T. Verbelen). 

Preoperative, perioperative and postoperative data were collected using a Microsoft Excel sheet ( supplementary table S2 ) by two authors (S. Heuts and A. Leus). 

The primary outcome was early mortality in relation to annual case volume per centre. Early mortality was defined as in-hospital mortality or 30-day mortality. Secondary outcomes were the need for postoperative extracorporeal membrane oxygenation (ECMO), duration of mechanical ventilation (days), intensive care unit (ICU) length of stay (days) and long-term survival. Long-term survival was expressed in absolute risk at 10 years, and absolute risk differences and numbers needed to treat were calculated. The principal analysis focused on the statistical determination of the volume that could define a high-volume centre, using the elbow method (please see “Data synthesis” section). In addition, a 5.0% mortality rate has previously been proposed to be acceptable, and required, for this high-risk intervention . Therefore, the annual case volume corresponding to this mortality rate threshold was studied, facilitating a combination of a statistically determined and clinically indicated high-volume threshold. Finally, we calculated the early mortality rates of centres performing less and more than the previously proposed required annual case load of 50 PEA procedures. 

A risk of bias assessment was performed to evaluate the quality of the included articles, using the Newcastle–Ottawa scale, which can be modified for single-arm studies by excluding one of four questions in the “Selection” section ( i.e. question 2), thereby assigning a maximal score of eight instead of nine to a study . This assessment was performed by two authors independently (S. Heuts and M.J. Kawczynski). 

All data are presented as mean± sd or n . Reported medians with interquartile range and/or minimum and maximum values were converted by Wan's method . Annual procedural volume was calculated by dividing the number of patients per centre by their total inclusion time. Studies were categorised into tertiles (T 1 , T 2 , T 3 ) according to their respective annual case volume. Early outcomes such as mortality and need for postoperative ECMO were pooled in a random-effects model (inverse variance weighting) and are presented for the overall cohort and per tertile, in n  and corresponding 95% confidence intervals. For early mortality, relative risk differences were calculated with both 10 cases per year and the threshold of a high-volume centre as a reference. The nonlinear relationship between annual case volume and early mortality was examined using restricted cubic splines (RCS) (three knots) and presented graphically in a nonlinear mixed-effect model . This outcome was studied both in unadjusted and adjusted analyses (adjusted for geographical location and median inclusion year, based on a complete case analysis, in a linear regression model, as proposed previously ). To determine the volume that determined a high-volume centre, we applied the elbow method, which was first described by A ntunes et al .  and S atopää et al .  for optimisation statistics and thereafter applied to the V-O relationship in surgical interventions by K awczynski et al .  (graphically presented in supplementary figure S1 ). For the secondary analysis of long-term survival, individual patient data derived from Kaplan–Meier curves were reconstructed as proposed by L iu et al . . The presence of an association between annual case volume as a continuous parameter and as a tertile and long-term survival was evaluated using a univariable Cox frailty model , both in unadjusted and adjusted analyses. Of note, because only 12 out of 52 studies reported on long-term survival, new tertiles were constructed for this outcome, similarly based on the distribution of centre volume (four centres per tertile). For long-term survival, absolute risk differences were calculated with T 1 as a reference, with subsequent derived numbers needed to treat. Because the third tertile encompassed centres performing more than 16 annual procedures, sensitivity analyses were performed by dividing this tertile into smaller fractions ( i.e. 16–50 procedures, 51–100 procedures and >100 procedures per year). Furthermore, sensitivity analyses were performed for studies published after 2014, and for studies only including patients after 2014 (which closely relates to the standardised introduction of balloon pulmonary angioplasty, which may have affected the patient selection for PEA from that era onwards). All analyses were conducted using the R statistics software (“metafor”, “meta”, “rms”, “mgcv”, “survival”, “survminer”, “maps”, “ggplot2”, “pathviewr” and “discfrail” packages; www.r-project.org). 

The presence of publication bias was assessed for the primary outcome, visualised in a funnel plot and quantified by Egger's test. 

All data and coding for analyses will be openly shared through https://github.com/samuelheuts/V-O_in_PEA_for_CTEPH upon publication of this study. 

Study selection The predefined systematic search produced 2148 results. After eliminating 738 duplicate studies, 1410 were left for title and abstract screening. This initial screening phase resulted in the exclusion of 1168 additional articles. One article could not be retrieved and was therefore excluded as well. The remaining 241 articles underwent full-text screening, ultimately resulting in the inclusion of 52 studies for final analysis ( supplementary figure S2 ). These 52 studies originated from 51 centres, because one centre reported outcomes of two unique cohorts in two different time periods . Geography and tertiles 52 studies (51 unique centres, 52 unique consecutive cohorts) originating from 25 countries from four different continents were included. This resulted in a total number of 11 345 included patients. graphically presents the geographic distribution of centres  and their total sample sizes  and volumes . Based on the distribution of centres and centre volumes, studies/centres were evenly divided into tertiles. Tertile 1 (T 1 ) comprised 17 studies (<6 cases per year, n=673 patients), T 2 comprised 18 studies (6–15 cases per year, n=2316 patients) and T 3 comprised 17 studies (>15 cases per year, n=8356 patients, ). Centre, patient and procedural characteristics All available patient, haemodynamic, functional and procedural parameters per centre are presented in supplementary tables S3–7 , including the early mortality rates. In the overall cohort the mean age was 52.3±5.5 years, without a statistically significant difference between volume tertiles . Higher volume tertiles operated more frequently on males (T 3 : 55.2% versus T 2 : 50.4% versus T 1 : 46.5%; p<0.001) and there was an important difference in symptomatology between tertiles based on the New York Heart Association classification. Nevertheless, there were no significant differences in relevant baseline haemodynamic and functional parameters, such as mean pulmonary arterial pressure (overall: 48.1±7.8 mmHg), cardiac index (overall: 2.3±0.2 L·min −1 ·m −2 ), pulmonary vascular resistance (overall: 11.0±4.0 WU) or 6-min walking distance (overall: 346±52.3 m) between tertiles . In addition, we did not observe a statistically significant difference in circulatory arrest time, aortic cross clamping time or cardiopulmonary bypass time, although these numbers may have been affected by the wide variability in reporting . Study quality assessment A detailed quality assessment per study is presented in supplementary table S8 . Overall, risk of bias ranged from low (n=15) to intermediate (n=28) to high (n=9). Because all studies comprised consecutive patients and reported on the primary outcome of early mortality, all studies were included for this analysis. Early mortality The pooled early mortality rate for the entire cohort was 6.0% (95% CI 5.5–6.4%). Early mortality was significantly higher in the tertile containing the lowest volume centres (T 1 : 11.6% (9.4–14.2%) versus T 2 : 7.2% (6.2–8.3%) versus T 3 : 5.2% (4.7–5.7%); p<0.001) . The V-O association and the case load that defines a high-volume centre The RCS analysis identified a significant unadjusted nonlinear V-O relationship between annual case volume and early mortality (p=0.0437) . After adjusting for the predefined variables ( i.e. geographical location and median inclusion year) that were fully reported on, this significant nonlinear relationship persisted (p=0.0030) . Using the elbow method, we found that a procedural case load of 33 cases per year for both unadjusted and adjusted analyses may be used to define a high-volume centre (95% CI 29–35 cases per year for the unadjusted curves, 95% CI 31–34 cases per year for the adjusted curves) ( , d). This caseload corresponded to a modelled mean mortality rate of 5.3% (95% CI 2.4–8.1%) ( supplementary table S9 ). With 10 cases per year as a reference, this would imply a 35% relative risk reduction for early mortality in high-volume centres (relative risk 0.65, 95% CI 0.29–0.99) ( supplementary table S9 ). Of note, early mortality rates still progressively declined beyond the defined volume threshold (please see the sensitivity analyses). Previously, a 5.0% mortality threshold was advocated to define a high-volume centre . Based on our analysis and the modelled mortality curve, this mortality rate would correspond to an annual case load of 40 cases per year ( supplementary table S9 , ). Finally, the previously proposed threshold of 50 annual PEA procedures was studied as well. In a pooled analysis of studies performing less and more than this threshold, the early mortality rate was 8.2% (95% CI 6.8–9.9%, <50 PEA procedures per year) and 3.4% (95% CI 2.0–6.9%, >50 PEA procedures per year). Secondary outcomes There was a significantly increased use of postoperative ECMO in lower volume centres as compared to higher volume centres (T 1 : 16.8% versus T 2 : 8.6% versus T 3 : 4.8%; p<0.001) . Postoperative mean ventilation duration and ICU length of stay did not differ significantly between volume tertiles . Long-term survival A total of 12 centres, comprising 2198 patients, reported on long-term survival. The overall 1-year survival was 89.7% (95% CI 88.4–91.0%), with a 10-year survival of 75.9% (95% CI 73.4–78.5%) ( supplementary table S10 , ). Increased annual case volume (as a continuous variable) was associated with improved long-term survival in both unadjusted and Cox frailty-adjusted analyses (hazard ratio per case 0.98, 95% CI 0.97–0.99; unadjusted p=0.033, adjusted p=0.018) ( supplementary table S11 presents the results of the overall Cox frailty model, without residual frailty). Because only 12 studies reported on long-term survival, new tertiles of four centres per tertile were constructed (T 1 : <5 cases per year; T 2 : 5–15 cases per year; T 3 : >15 cases per year). 1-, 3-, 5- and 10-year survival per tertile is presented in supplementary table S10 and . The Cox frailty analysis demonstrated a significantly increased long-term survival in higher volume tertiles, with an unadjusted and adjusted hazard ratio per tertile of 0.77 (95% CI 0.66–0.90; p=0.001) and 0.75 (95% CI 0.63–0.89; p=0.001), respectively ( supplementary table S11 , without residual frailty). With T 1 as a reference (<5 cases per year, 10-year survival 66.0%, 95% CI 57.9–75.2%), 10-year survival was markedly increased in patients undergoing PEA in a T 3 institution (>15 cases per year, 10-year survival 79.0%, 95% CI 75.7–82.5%), resulting in a 13.0% absolute risk difference, implying a number needed to treat to save a life at 10 years of 7.7 ( supplementary table S12 ). Sensitivity analyses T 3 was subdivided into smaller fractions to further assess the V-O relationship in this highest tertile. Interestingly, the pooled mortality rate progressively decreased from 6.7% to 5.4% to 2.9% in centres performing 16–50 (13 centres), 51–100 (one centre) and >100 (three centres) procedures annually ( supplementary table S13 ). Of note, these mortality rates differed slightly from the modelled mortality rates, because the model was based on the totality of the data and these pooled rates only on the data from specific centres in this tertile. When confined to studies published in the last decade (after 2014, supplementary figure S3a ) or studies including patients in the last decade (after 2014, supplementary figure S3b ), the statistical significance of the previously observed V-O relationship persisted (p=0.040 and p=0.001, respectively). Publication bias Publication bias assessment was performed for the primary outcome (early mortality). We did not observe funnel plot asymmetry, suggesting the absence of publication bias ( supplementary figure S4 ). This was reflected statistically by the Egger's test, which showed no significant indication for publication bias (β 0.30, p=0.631). 

The predefined systematic search produced 2148 results. After eliminating 738 duplicate studies, 1410 were left for title and abstract screening. This initial screening phase resulted in the exclusion of 1168 additional articles. One article could not be retrieved and was therefore excluded as well. The remaining 241 articles underwent full-text screening, ultimately resulting in the inclusion of 52 studies for final analysis ( supplementary figure S2 ). These 52 studies originated from 51 centres, because one centre reported outcomes of two unique cohorts in two different time periods . 

52 studies (51 unique centres, 52 unique consecutive cohorts) originating from 25 countries from four different continents were included. This resulted in a total number of 11 345 included patients. graphically presents the geographic distribution of centres  and their total sample sizes  and volumes . Based on the distribution of centres and centre volumes, studies/centres were evenly divided into tertiles. Tertile 1 (T 1 ) comprised 17 studies (<6 cases per year, n=673 patients), T 2 comprised 18 studies (6–15 cases per year, n=2316 patients) and T 3 comprised 17 studies (>15 cases per year, n=8356 patients, ). 

All available patient, haemodynamic, functional and procedural parameters per centre are presented in supplementary tables S3–7 , including the early mortality rates. In the overall cohort the mean age was 52.3±5.5 years, without a statistically significant difference between volume tertiles . Higher volume tertiles operated more frequently on males (T 3 : 55.2% versus T 2 : 50.4% versus T 1 : 46.5%; p<0.001) and there was an important difference in symptomatology between tertiles based on the New York Heart Association classification. Nevertheless, there were no significant differences in relevant baseline haemodynamic and functional parameters, such as mean pulmonary arterial pressure (overall: 48.1±7.8 mmHg), cardiac index (overall: 2.3±0.2 L·min −1 ·m −2 ), pulmonary vascular resistance (overall: 11.0±4.0 WU) or 6-min walking distance (overall: 346±52.3 m) between tertiles . In addition, we did not observe a statistically significant difference in circulatory arrest time, aortic cross clamping time or cardiopulmonary bypass time, although these numbers may have been affected by the wide variability in reporting . 

A detailed quality assessment per study is presented in supplementary table S8 . Overall, risk of bias ranged from low (n=15) to intermediate (n=28) to high (n=9). Because all studies comprised consecutive patients and reported on the primary outcome of early mortality, all studies were included for this analysis. 

The pooled early mortality rate for the entire cohort was 6.0% (95% CI 5.5–6.4%). Early mortality was significantly higher in the tertile containing the lowest volume centres (T 1 : 11.6% (9.4–14.2%) versus T 2 : 7.2% (6.2–8.3%) versus T 3 : 5.2% (4.7–5.7%); p<0.001) . 

The RCS analysis identified a significant unadjusted nonlinear V-O relationship between annual case volume and early mortality (p=0.0437) . After adjusting for the predefined variables ( i.e. geographical location and median inclusion year) that were fully reported on, this significant nonlinear relationship persisted (p=0.0030) . Using the elbow method, we found that a procedural case load of 33 cases per year for both unadjusted and adjusted analyses may be used to define a high-volume centre (95% CI 29–35 cases per year for the unadjusted curves, 95% CI 31–34 cases per year for the adjusted curves) ( , d). This caseload corresponded to a modelled mean mortality rate of 5.3% (95% CI 2.4–8.1%) ( supplementary table S9 ). With 10 cases per year as a reference, this would imply a 35% relative risk reduction for early mortality in high-volume centres (relative risk 0.65, 95% CI 0.29–0.99) ( supplementary table S9 ). Of note, early mortality rates still progressively declined beyond the defined volume threshold (please see the sensitivity analyses). Previously, a 5.0% mortality threshold was advocated to define a high-volume centre . Based on our analysis and the modelled mortality curve, this mortality rate would correspond to an annual case load of 40 cases per year ( supplementary table S9 , ). Finally, the previously proposed threshold of 50 annual PEA procedures was studied as well. In a pooled analysis of studies performing less and more than this threshold, the early mortality rate was 8.2% (95% CI 6.8–9.9%, <50 PEA procedures per year) and 3.4% (95% CI 2.0–6.9%, >50 PEA procedures per year). 

There was a significantly increased use of postoperative ECMO in lower volume centres as compared to higher volume centres (T 1 : 16.8% versus T 2 : 8.6% versus T 3 : 4.8%; p<0.001) . Postoperative mean ventilation duration and ICU length of stay did not differ significantly between volume tertiles . 

A total of 12 centres, comprising 2198 patients, reported on long-term survival. The overall 1-year survival was 89.7% (95% CI 88.4–91.0%), with a 10-year survival of 75.9% (95% CI 73.4–78.5%) ( supplementary table S10 , ). Increased annual case volume (as a continuous variable) was associated with improved long-term survival in both unadjusted and Cox frailty-adjusted analyses (hazard ratio per case 0.98, 95% CI 0.97–0.99; unadjusted p=0.033, adjusted p=0.018) ( supplementary table S11 presents the results of the overall Cox frailty model, without residual frailty). Because only 12 studies reported on long-term survival, new tertiles of four centres per tertile were constructed (T 1 : <5 cases per year; T 2 : 5–15 cases per year; T 3 : >15 cases per year). 1-, 3-, 5- and 10-year survival per tertile is presented in supplementary table S10 and . The Cox frailty analysis demonstrated a significantly increased long-term survival in higher volume tertiles, with an unadjusted and adjusted hazard ratio per tertile of 0.77 (95% CI 0.66–0.90; p=0.001) and 0.75 (95% CI 0.63–0.89; p=0.001), respectively ( supplementary table S11 , without residual frailty). With T 1 as a reference (<5 cases per year, 10-year survival 66.0%, 95% CI 57.9–75.2%), 10-year survival was markedly increased in patients undergoing PEA in a T 3 institution (>15 cases per year, 10-year survival 79.0%, 95% CI 75.7–82.5%), resulting in a 13.0% absolute risk difference, implying a number needed to treat to save a life at 10 years of 7.7 ( supplementary table S12 ). 

T 3 was subdivided into smaller fractions to further assess the V-O relationship in this highest tertile. Interestingly, the pooled mortality rate progressively decreased from 6.7% to 5.4% to 2.9% in centres performing 16–50 (13 centres), 51–100 (one centre) and >100 (three centres) procedures annually ( supplementary table S13 ). Of note, these mortality rates differed slightly from the modelled mortality rates, because the model was based on the totality of the data and these pooled rates only on the data from specific centres in this tertile. When confined to studies published in the last decade (after 2014, supplementary figure S3a ) or studies including patients in the last decade (after 2014, supplementary figure S3b ), the statistical significance of the previously observed V-O relationship persisted (p=0.040 and p=0.001, respectively). 

Publication bias assessment was performed for the primary outcome (early mortality). We did not observe funnel plot asymmetry, suggesting the absence of publication bias ( supplementary figure S4 ). This was reflected statistically by the Egger's test, which showed no significant indication for publication bias (β 0.30, p=0.631). 

The current study comprised the largest accumulation of consecutive patients undergoing PEA for CTEPH in the literature and quantified the V-O association for this procedure, while objectively determining an annual case load that can define a high-volume PEA centre. Based on our findings, early mortality and long-term survival are significantly affected by procedural volume and subsequent expertise. Furthermore, operations in high-volume centres confer an important survival benefit, with a number needed to treat to save a life at 10 years of only 7.7 in a high- versus low-volume centre. Contemporary US guidelines do not provide recommendations regarding PEA as a procedure, or a volume threshold to define PEA centres of expertise . The most recent ESC/ERS guidelines for the treatment of pulmonary hypertension suggest CTEPH centres ideally perform 50 PEA procedures per year , although a formal recommendation ( i.e. class of recommendation with level of evidence) was lacking. This statement was supported by a reference to the 2011 study by M ayer et al . , who presented the results from an international multicentre registry. This commendable analysis comprised 386 surgical PEA patients from 27 centres, and primarily investigated short-term outcomes. In an exploratory analysis, M ayer et al .  observed in-hospital and 1-year mortality to be numerically lower in centres performing >50 cases per year, although this difference did not reach statistical significance (5.0% versus 8.2%, p=nonsignificant). The absence of a statistically significant relationship was also confirmed by D elcroix et al . , using longer term follow-up data from the same registry. Nevertheless, J enkins et al .  built further on these findings and stated that, in an ideal world, one CTEPH centre would serve 50 million people, while performing 75–100 PEA procedures per year. Although we firmly support the incentive to centralise CTEPH care, it is important to provide evidence-based recommendations for the required case load in high-volume centres. Based on our overview of published literature, only four centres in the world would meet the volume criterion as proposed by the ESC/ERS guidelines , which appears stringent. However, in the studies by M ayer et al .  and D elcroix et al . , annual case volume was treated as a categorical parameter , which is known to reduce the power of a statistical analysis . Moreover, the categorisation of volume disregards the nonlinear relationship between volume and outcome, a concept which is elegantly summarised by V onlanthen et al . . Also, these previous studies were based on the inclusion of 27 centres, potentially limiting the analysis’ power. Instead, the current pooled V-O analysis acknowledges the nonlinear relationship between volume and outcome by treating volume as a continuous parameter with the additional application of the RCS analysis. We were also able to include data from 51 centres (52 unique consecutive cohorts), further augmenting the statistical power of the analysis. As presented in , the modelled early mortality rate in low-volume centres (<10 cases per year) exceeds 10%, but sharply declines with the accrual of more cases, after which a deflection in the curve is observed between 20–30 cases per year. By virtue of the elbow method, a mathematical concept derived from optimisation statistics, this deflection point in the curve can be defined as the location at which the highest yield in performance is obtained, with respect to the annual volume. In this analysis, we found a “statistical threshold” of 33 cases per year, both in unadjusted and adjusted analyses, which may define a high-volume centre. Nevertheless, we also found that outcomes still improved further beyond this threshold, as presented in the sensitivity analyses. This progressive reduction in mortality was also demonstrated in studies by M adani et al .  and J enkins et al . , with commendable early mortality rates of <2%. In addition to annual institutional volume, the definition of a high-volume centre also relies on excellent outcomes. As such, a 5.0% mortality threshold was previously proposed to define such expertise . Consequently, this mortality threshold was studied as well, which corresponded to a modelled case load of 40 cases per year. Therefore, we can hypothesise that the volume threshold to define a high-volume centre may range between the statistically determined and clinically indicated volumes of 33 and 40 cases per year, notwithstanding the further progressive decline in early mortality beyond these thresholds. However, we must note that these thresholds were based on statistical analyses and assumptions, which may not be in line with clinical judgment. Therefore, it remains to be determined whether these analyses justify lowering the previously proposed thresholds. Although our findings for early mortality are also supported by the analyses of the secondary outcomes (among others, postoperative need for ECMO and long-term survival), less weight may be assigned to these findings because these parameters were incompletely reported. Still, the observed 10-year survival rate of 75.9% closely corresponds to a nationwide analysis from the UK by C annon et al .  of 72.0%. Importantly, in our analysis, the progressively diverging nature of the survival curves between volume tertiles seems to confirm a robust and durable effect of the PEA procedure in higher volume centres. Moreover, the statistically significant and clinically relevant absolute risk difference between tertiles for 10-year survival further underline these findings. Based on these analyses, a life is saved at 10 years for every 7.7 patients that are treated in a T 3 institution (>15 cases per year) as compared to a T 1 institution (<5 cases per year). Only six centres have reported annual procedural volumes exceeding the proposed threshold of 33 cases per year . In light of centralisation, PEA for CTEPH is an ideal procedure because it is performed infrequently, is associated with high morbidity and mortality rates, and has an elective character. Furthermore, CTEPH patients require a multidisciplinary approach, a thorough work-up, meticulous patient selection and dedicated peri-operative care . Still, the balance between a high case load, number of operators per centre, sufficient training and exposure, and geographical distributions of centres can be difficult. Indeed, CTEPH is a disease that can be treated in an elective setting, and can therefore be diagnosed and treated without issue as an “orphan disease” in specialised centres. Still, if centralisation is pushed to an extreme, patients will have to travel excessive distances and the accessibility to CTEPH care may be compromised. This can in turn affect and aggravate socioeconomic disparities. In addition, a lesser number of individual surgeons will be exposed to PEA procedures in this context, and fewer surgeons will be trained in this technically demanding operation. In contrast, when criteria are too lenient, patients’ outcomes may be jeopardised. Consequently, the current study provides an objective and evidence-based formulation of the threshold that could define a high-volume centre. Based on our new findings derived from objective and reproducible statistical analyses, this threshold varies between 33 and 40 procedures per year, although outcomes still further improve beyond this threshold. Keeping in mind the reported incidence and surgery rate of CTEPH , one high-volume specialised centre per 10–30 million inhabitants may eventually be justified. Such centralisation efforts would both lead to optimal outcomes while also guaranteeing CTEPH care accessibility in smaller countries. Strengths and limitations The current study provides a complete overview of the literature and included all reports of consecutive CTEPH patients treated by PEA. The need for centralisation of PEA for CTEPH is high, and substantiated recommendations to define high-volume centres are warranted. Based on a new statistical approach, the nonlinear relationship between volume and outcome was appreciated and an objective threshold for a high-volume centre was formulated. Nevertheless, several limitations should be addressed. First, we only included single-centre studies because this allowed us to calculate the annual case load per centre. This prohibited the inclusion of multicentre experiences, such as the study by M ayer et al . . Still, we believe this limitation is mitigated by the inclusion of almost all single-centre experiences from this multicentre analysis separately. In line with this, tertiles were divided based on the number of centres instead of the number of patients. Inherently, the latter is not possible in a pooled analysis. Second, volume can be measured at the institutional level or the individual operator level. Regrettably, individual operator volume was rarely reported in the included studies. Yet, CTEPH is such an exceptionally multidisciplinary disease that it may be overly simplistic to merely focus on operator volume, because institutional expertise can provide a more accurate reflection of the quality of integrated care pathways for CTEPH patients. In light of this, we should also acknowledge that the volume of PEA procedures is not the only determinant of a CTEPH centre of expertise, and other factors should be taken into account. These factors include the presence and experience of specialised cardiologists, pulmonary physicians, imagers and interventionalists with sufficient expertise in balloon pulmonary angioplasty and medical treatment (multimodality treatment ). Moreover, for PEA, expertise in cardiac anaesthesia and ICU care is equally important. Also, the training for this complex and time-sensitive surgery must be considered, because a sufficient number of cases is necessary for this aspect as well. Of note, results may be less generalisable to Asian centres and/or populations, given the geographical distribution of centres publishing on PEA. The results may therefore particularly apply to US and European centres. Finally, all literature analyses are subject to publication bias, in which suboptimal outcomes of smaller centres are usually underreported. Although we did not find an indication of a statistically significant presence of publication bias, it is intuitively there. However, the reporting of results by smaller centres with worse outcomes would inherently only further strengthen the V-O association for this procedure. Conclusion There is a significant nonlinear relationship between annual institutional PEA procedural volume and early mortality in the treatment of CTEPH by PEA. Long-term survival is also markedly influenced by procedural volume. When combining our findings with previous definitions of high-volume centres in the literature, the minimum annual required case volume that can define a high-volume centre ranges between 33 and 40 cases per year. Whether these analyses justify lowering the previously proposed thresholds remains to be determined based on clinical judgment. The application of such thresholds could optimise outcomes while guaranteeing accessibility of care. 

The current study provides a complete overview of the literature and included all reports of consecutive CTEPH patients treated by PEA. The need for centralisation of PEA for CTEPH is high, and substantiated recommendations to define high-volume centres are warranted. Based on a new statistical approach, the nonlinear relationship between volume and outcome was appreciated and an objective threshold for a high-volume centre was formulated. Nevertheless, several limitations should be addressed. First, we only included single-centre studies because this allowed us to calculate the annual case load per centre. This prohibited the inclusion of multicentre experiences, such as the study by M ayer et al . . Still, we believe this limitation is mitigated by the inclusion of almost all single-centre experiences from this multicentre analysis separately. In line with this, tertiles were divided based on the number of centres instead of the number of patients. Inherently, the latter is not possible in a pooled analysis. Second, volume can be measured at the institutional level or the individual operator level. Regrettably, individual operator volume was rarely reported in the included studies. Yet, CTEPH is such an exceptionally multidisciplinary disease that it may be overly simplistic to merely focus on operator volume, because institutional expertise can provide a more accurate reflection of the quality of integrated care pathways for CTEPH patients. In light of this, we should also acknowledge that the volume of PEA procedures is not the only determinant of a CTEPH centre of expertise, and other factors should be taken into account. These factors include the presence and experience of specialised cardiologists, pulmonary physicians, imagers and interventionalists with sufficient expertise in balloon pulmonary angioplasty and medical treatment (multimodality treatment ). Moreover, for PEA, expertise in cardiac anaesthesia and ICU care is equally important. Also, the training for this complex and time-sensitive surgery must be considered, because a sufficient number of cases is necessary for this aspect as well. Of note, results may be less generalisable to Asian centres and/or populations, given the geographical distribution of centres publishing on PEA. The results may therefore particularly apply to US and European centres. Finally, all literature analyses are subject to publication bias, in which suboptimal outcomes of smaller centres are usually underreported. Although we did not find an indication of a statistically significant presence of publication bias, it is intuitively there. However, the reporting of results by smaller centres with worse outcomes would inherently only further strengthen the V-O association for this procedure. 

There is a significant nonlinear relationship between annual institutional PEA procedural volume and early mortality in the treatment of CTEPH by PEA. Long-term survival is also markedly influenced by procedural volume. When combining our findings with previous definitions of high-volume centres in the literature, the minimum annual required case volume that can define a high-volume centre ranges between 33 and 40 cases per year. Whether these analyses justify lowering the previously proposed thresholds remains to be determined based on clinical judgment. The application of such thresholds could optimise outcomes while guaranteeing accessibility of care. 

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