Objective Central blood pressure (CBP) and carotid intima-media thickness (CIMT) are surrogate measures of cardiovascular risk. Allopurinol reduces serum uric acid and oxidative stress and improves endothelial function and may therefore reduce CBP and CIMT progression. This study sought to ascertain whether allopurinol reduces CBP, arterial stiffness and CIMT progression in patients with ischaemic stroke or transient ischaemic attack (TIA).
Methods We performed a randomised, double-blind, placebo-controlled study, examining the effect of 1-year treatment with allopurinol (300 mg daily), on change in CBP, arterial stiffness and CIMT progression at 1 year and change in endothelial function and circulating inflammatory markers at 6 months. Patients aged over 18 years with recent ischaemic stroke or TIA were eligible.
Results Eighty participants were recruited, mean age 67.8 years (SD 9.4). Systolic CBP [−6.6 mm Hg (95% CI −13.0 to −0.3), p=0.042] and augmentation index [−4.4% (95% CI −7.9 to −1.0), p=0.013] were each lower following allopurinol treatment compared with placebo at 12 months. Progression in mean common CIMT at 1 year was less in allopurinol-treated patients compared with placebo [between-group difference [−0.097 mm (95% CI −0.175 to −0.019), p=0.015]. No difference was observed for measures of endothelial function.
Conclusions Allopurinol lowered CBP and reduced CIMT progression at 1 year compared with placebo in patients with recent ischaemic stroke and TIA. This extends the evidence of sustained beneficial effects of allopurinol to these prognostically significant outcomes and to the stroke population, highlighting the potential for reduction in cardiovascular events with this treatment strategy.
Trial registration number ISRCTN11970568.
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Despite secondary preventative measures, recurrent stroke events remain common; approximately 13% of participants suffered recurrent stroke in recent secondary preventative trials,1 and 40% of those with transient ischaemic attack (TIA) experienced recurrent cardiovascular events during long-term follow-up.2 Novel strategies are needed to reduce this burden.
Elevated serum uric acid (UA) is associated with increased risk of cardiovascular disease3 and adverse outcomes following ischaemic stroke.4 Allopurinol reduces serum UA through inhibition of the xanthine oxidoreductase (XO) enzymatic system, which is responsible for the final steps in purine metabolism. Further, XO inhibition reduces the reactive oxygen species formed through action of the enzyme and may thus reduce vascular oxidative stress, which is implicated in atherogenesis.5 Allopurinol may therefore provide benefits in addition to or independent of its effects on UA.6
Systematic review and meta-analysis of studies examining XO inhibition has demonstrated beneficial effects on endothelial function and other surrogate measures of cardiovascular function.7 Further, following stroke, allopurinol has been reported to reduce both arterial stiffness8 and markers of inflammation9 and also increases nitric oxide bioavailability in patients with type 2 diabetes.10 More recently, treatment with high-dose allopurinol was found to induce regression in left ventricular hypertrophy (LVH)11 and improve exercise capacity in patients with coronary artery disease.12 However, studies examining XO inhibition have typically been of limited duration and there are no prolonged studies in the stroke patient population, or on measures of atherosclerosis.
We sought to address this evidence gap by performing a randomised, double-blind, placebo-controlled study with a 1-year treatment duration, which examined the effect of allopurinol 300 mg daily on change in central blood pressure (BP), arterial stiffness, endothelial function and circulating markers of low-grade inflammation and also provided pilot data concerning the effect of allopurinol on carotid intima-media thickness (CIMT) progression.
We performed a randomised, double-blind, placebo-controlled trial, comparing allopurinol 300 mg once daily with matched placebo in an adult population with recent ischaemic stroke or TIA. Patients were followed up for 12 months and underwent repeated measurement of CIMT, arterial haemodynamics and endothelial function.
Patients aged over 18 years with ischaemic stroke or TIA, within the past year, were eligible for inclusion. Principal exclusion criteria were >70% extra-cranial internal carotid artery stenosis, significant comorbidity likely to cause death within 12 months and either indication for, or contraindication to (including estimated glomerular filtration rate <50 mL/min), administration of allopurinol. Exclusion criteria were chosen to minimise the potential risks of allopurinol treatment and to ensure CIMT measurements were not affected by intrinsic carotid disease. Full details of inclusion and exclusion criteria are detailed in online supplementary table S1.
Patients were identified during admission or outpatient attendance at the Acute Stroke Unit at the Western Infirmary, Glasgow. All participants were provided with a study patient information sheet, given the opportunity to ask questions and provided written informed consent to participate. The study was approved by the West Medical research ethics committee and was registered in the ISRCTN database (ISRCTN 11970568).
We studied a sample size of 40 participants per group. The primary study endpoint was change in CIMT at 12 months. Based on a mean annualised CIMT progression rate of 0.0176 mm (95% CI 0.0149 to 0.023, SD 0.05), mean baseline CIMT of approximately 1 mm13 ,14 and a treatment effect approximately half that observed with Statin therapy,14 253 participants in each treatment group, followed for 2 years, would provide 80% power to detect a 0.03 mm difference in IMT progression (α of 0.05). This study lacked power to exclude a potentially meaningful treatment effect for this endpoint and was designed to allow us to confirm these assumptions for a larger CIMT trial and provide preliminary data while specifically addressing important prespecified secondary endpoints. This sample provided 80% power to detect a 6 mm Hg difference in central BP (assumed SD 10 mm Hg) and 90% power to replicate, in prolonged follow-up, previously reported change in augmentation index (AI)8 and circulating markers of vascular inflammation9 following allopurinol therapy after stroke.
Randomisation, study intervention and masking
Enrolled participants were randomised, via an interactive voice response system (Robertson Centre for Biostatistics, University of Glasgow), to receive either 300 mg of allopurinol orally once daily or matched placebo, on a 1:1 basis. Investigators and patients were blinded to treatment allocation. Allopurinol tablets were manufactured and over encapsulated by Bilcare Ltd. Dosing began on the day following baseline assessment and continued for 1 year. Concordance with therapy was assessed by questioning and pill counts. Investigators were blinded to serum UA levels to avoid potential inference of study group allocation. The randomisation code was not broken until all follow-up was complete and all data were prepared for analysis.
Study follow-up and endpoint data collection
All study procedures were performed in the Western Infirmary. Patients attended study visits at baseline (randomisation), 1, 3, 6 and 12 months. Patients attended following an overnight fast and were asked to avoid caffeine, tobacco and alcohol for the preceding 12 h. At each visit a clinical examination, blood sampling, adverse event review and brachial artery BP measurement (using a semiautomated sphygmomanometer (Critikon DINAMAP)) were performed. Following 15 min supine rest, three BP measurements were taken at 1 min intervals and the mean of these was recorded. CIMT and BP-pulse wave analysis (BP-PWA) were measured at baseline, 6 and 12 months. Peripheral arterial tonometry (PAT) and circulating markers of endothelial function were measured at baseline and 6 months. An outline of study procedures is included in online supplementary figure S1.
BP-PWA was performed using the non-invasive technique of applanation tonometry. High-fidelity radial artery BP pulse waveforms were recorded using the Sphygmocor software platform (PWV Medical, Sydney, Australia) and a hand-held piezo tonomoter (Millar instruments). Application of a validated generalised transfer function to the obtained radial waveforms was automatically performed with the Sphygmocor software, generating a derived central aortic BP pulse wave form, calculation of AI and central aortic BP (calibrated using brachial artery BP measurements), as previously described.15 AI was calculated as the ratio of difference between the early and late central systolic pressure peaks to the central pulse pressure. For each patient study visit, the mean of three 10 s recordings of radial waveforms were used for statistical analysis.
Blood was sampled at baseline and 6-month follow-up for measurement of circulating levels of Von Willebrand factor (vWF), soluble intercellular adhesion molecule 1 (s-ICAM-1), e-selectin and s-thrombomodulin. Highly sensitive ELISA techniques were used.9 Laboratory analysis was performed by DH.
PAT measurements were added following a protocol amendment after the first 15 participants were enrolled. Recordings were performed using the EndoPAT 2000 device (Itamar medical, Caesarea, Israel) following 15 min supine rest in a room with controlled temperature (23°C). Pneumatic PAT probes placed on the index finger of each hand measured change in finger tip blood volume associated with arterial pulsation prior to and following a 5 min brachial artery occlusion. Thereafter, calculation of the PAT reactive hyperaemia index (RHI, an index of endothelial function) was performed in an automated, operator-independent fashion, with the EndoPAT proprietary software.
We measured mean maximum CIMT and mean common CIMT in keeping with guidelines at the time of the study protocol approval.13 ,16 B mode ultrasonography using a 7.5 MHz annular array ultrasound system (Zonare, California, USA) was used. Still images were captured during ventricular systole at each of three carotid artery segments (distal 1 cm of common carotid, carotid bulb and proximal 1 cm of internal carotid). Far and near-wall images were acquired from the optimal angle for image acquisition and two further predefined angles (using a Meijer carotid arc), at each of the right and left carotid arteries. Thus, a complete study comprised 18 images and 36 points of CIMT measurement. All scans were performed by an experienced and certified sonographer (KS). Image-Pro Plus software (Media Cybernetics, USA) was used for offline CIMT image analysis. Blood-intima and media-adventitia boundaries were marked with a calliper, and semiautomated analysis of the CIMT was then performed using the leading edge principle. Batch reading (in groups of 10 and in randomised order) was employed.
The mean maximum IMT was derived as the arithmetic mean of the maximum CIMT value measured at each of the potential 36 points of measurement.16 The mean common carotid (far wall) CIMT was based on the mean CIMT measurement for the carotid artery far wall within the common segment. It was calculated as a weighted mean, according to the length of the common arterial wall for which the CIMT measurements were obtained for each of the three measurement angles.16
All CIMT image analysis, BP-PWA and PAT-RHI measurements were performed by PH. Full details of the CIMT scanning protocol and image analysis, BP-PWA and PAT-RHI methodology are detailed in online supplementary appendix S1.
All analyses were performed on an intention-to-treat basis based on complete data available at baseline and final follow-up for each endpoint. Study comparisons on continuous measurements were performed with analysis of covariance adjusted for baseline value and treatment allocation and results are expressed as the change in allopurinol group value minus the change in placebo group value. Sensitivity analysis was performed for all efficacy endpoints to assess sensitivity to extreme values. Comparisons on categorical variables were performed with difference in proportions. A p value of <0.05 was considered statistically significant. All statistical analyses were performed by the Robertson Centre for Biostatistics (HM and AM), University of Glasgow.
Study endpoints included change in BP-PWA derived parameters (AI, central BP) at 1 year, the difference in change in CIMT between treatment groups over a 1-year period (CIMT progression, for both mean common (far wall) CIMT and mean maximum CIMT) and change in endothelial function (PAT-derived RHI and circulating levels of vWF, s-ICAM-1, e-selectin and s-thrombomodulin) at 6 months. The distribution of s-ICAM-1 and s-thrombomodulin was positively skewed and therefore a natural logarithmic transformation was used before performing analysis. Our safety analysis included the number of serious adverse events attributable to therapy and the number of all serious adverse events and all adverse events.
Eighty participants were recruited between September 2009 and November 2010 (mean (SD) age 67.8 (9.4) years). Twelve-month follow-up visits were completed in November 2011. Baseline characteristics and outcome parameter values are shown in table 1. Groups were generally well balanced, although the placebo group contained a greater proportion of participants with index event of stroke (rather than TIA) and diabetes while fewer had documented hypertension, atrial fibrillation or treatment with ACE-I/angiotensin receptor blocker (ARB) agents.
In total, 72 participants (90%) completed 6-month follow-up and 69 (86%) completed 12-month follow-up. Vital status was ascertained for all participants except one who left the country and was lost to follow-up. Of the 10 patients with incomplete 12-month follow-up, three withdrew following adverse events respectively of brain tumour, pancreatic carcinoma and depressive psychosis; five chose to withdraw and two did not attend for the final visit despite repeated attempts to schedule appointments. A CONSORT diagram detailing recruitment and withdrawals is shown in figure 1. Ninety-one per cent of patients took at least 80% of their prescribed study medication doses. One patient (who subsequently withdrew) received no study medication, as renal function had deteriorated subsequent to initial screening by the time of randomisation.
Serum UA level fell with allopurinol compared with placebo by 0.07 mmol/L (95% CI 0.04 to 0.10, p<0.0001) at 6 months and 0.08 mmol/L (95% CI 0.05 to 0.10, p<0.0001) at 12 months.
Two patients developed neutropenia at 1-month follow-up (one attributed to intercurrent viral infection, the other potentially to study medication). One patient developed an urticarial rash within 1 week (likely due to concomitant nicotine replacement patches). Study medication was immediately discontinued without rechallenge in all three patients. All three patients were in the placebo group. No other treatment study related serious adverse events or adverse reactions were reported.
Changes in AI, mean central systolic BP and brachial artery systolic BP were all reduced with allopurinol compared with placebo at 12 months (table 2). AI (standardised for heart rate of 75 bpm) was non-significantly reduced with allopurinol compared with placebo. The change in central systolic BP was not independent of the change in brachial BP (p=0.60 when adjusted for change in brachial BP).
Endothelial function analysis
No significant difference between groups was observed for circulating markers of endothelial function or PAT RHI at 6 months (table 2).
Mean common CIMT progression was reduced following allopurinol treatment compared with placebo at 12 months (table 2). This treatment effect persisted on sensitivity analysis with exclusion of extreme values. Mean maximum CIMT progression was not significantly different between treatment groups. There was satisfactory intraobserver agreement for CIMT image analysis. The within observer intraclass correlation coefficient for mean common CIMT was 0.87 (95% CI 0.77 to 0.93) and for mean maximum CIMT was 0.91 (95% CI 0.79 to 0.96).
There was no difference between groups for recurrent stroke, TIA, myocardial infarction or any combination of these clinical endpoints (table 2).
We found that 1 year of treatment with allopurinol reduced both central BP and arterial stiffness, determined as AI. In addition, we found evidence of reduced CIMT progression in association with allopurinol treatment. We found no difference in measures of endothelial function. This study extends the evidence of beneficial effects of allopurinol on vascular health to these prognostically significant surrogate outcome measures, with sustained treatment effect and to the stroke patient population. In addition to recent studies showing a positive effect of allopurinol on LVH regression11 and exercise capacity in patients with angina,12 our findings highlight the potential for this therapeutic strategy in reducing cardiovascular events and support the conduct of large clinical endpoint studies.
Central BP is an independent predictor of cardiovascular events and may be more powerful in predicting risk than brachial BP measurements.17 Differential cardiovascular outcomes for equivalent reductions in brachial BP have been attributed to differing central BP-lowering treatment properties18 and central BP reduction has been proposed as a therapeutic target in the prevention of cardiovascular disease.19
While reduction in brachial BP has been noted previously with allopurinol treatment (in a young hypertensive population following 2-month treatment),20 no studies have previously identified any significant reduction in central BP.8 Recently published studies have reported that allopurinol use lowers left ventricular mass in patients with LVH, independently of peripheral BP effects.11 Our findings offer evidence for a potential mechanistic basis for both these results and for the reduction in CIMT progression observed in the current study.
In addition, we observed a fall in brachial systolic BP with allopurinol during study follow-up, though this was partly attributable to a rise BP in the placebo group that exceeded that which would usually be expected in a clinical trial population. It is apparent that antihypertensive agents exert differing effects on central BP despite similar brachial artery BP effects.18 In a small study with 3-month follow-up, allopurinol treatment was previously associated with a reduction in AI.8 Our results confirm this finding in a larger sample and provide evidence of a sustained treatment benefit. The reduction in central BP appears likely to be attributable to this accompanying observed reduction in arterial stiffness, which represents the key determinant of central BP.15
In turn, endothelial function is a determinant of arterial stiffness.21 In patients with cardiovascular disease, large artery endothelial function is improved with allopurinol therapy,7 which also improves endothelial nitric oxide bioavailability,10 offering a potential mechanism for reduced arterial stiffness following allopurinol treatment.
However, no significant benefit on endothelial function was observed in the current study. This was somewhat unexpected and at odds with the otherwise beneficial effects observed. Our study may have lacked statistical power as the PAT RHI outcome measurement was included only after the study commenced, limiting the number of participants available for analysis of this endpoint. Second, PAT RHI represents a composite of both large and small arterial function. Reported as an index of pulse wave amplitude, lack of benefit in this measurement could potentially reflect reduced vascular tone in the context of improved endothelial function overall. However, our study lacked control measures to further evaluate this hypothesis.
Beyond effects on endothelial function, reduction in UA with allopurinol has effects that could favourably modify vascular structural determinants of arterial stiffness and that may attenuate atherosclerosis and IMT progression. UA has previously been demonstrated to increase smooth muscle cell proliferation22 and low-density lipoprotein oxidation.23 Further, allopurinol inhibits xanthine oxidase and reduces oxidative stress in the vasculature.6 ,7
CIMT is an independent risk factor for the development of stroke and CHD events.24 Further, temporal change in CIMT progression is also independently predictive of CV risk.25 Incorporation of CIMT measurements to the Framingham cardiovascular risk stratification model refines its predictive power, and CIMT progression has been recommended as a suitable biomarker for atherosclerotic disease; it has become an established surrogate endpoint in large clinical trials evaluating preventative therapeutic strategies for CV disease.26 However, there remains debate as to whether therapeutic reduction in CIMT necessarily translates to a reduction in clinical endpoints.27
Regardless, the observed reduction in CIMT progression is encouraging. We observed benefit only on mean common CIMT and not on mean maximum CIMT progression. This may be accounted for by the observation that mean maximum CIMT incorporates CIMT measurements at multiple carotid segment levels and represents an inherently more variable measurement parameter (coefficient of variation in our study population was 26% for mean maximum CIMT compared with 18% for mean common CIMT), making it a less powerful outcome measure.16 It is now accepted that mean common CIMT is the recommended standard for measurement and reporting in both clinical practice and research studies.16
Although the observation that CIMT progression and systolic BP were each significantly reduced with allopurinol was in keeping with the study hypothesis and with positive findings for other surrogate markers reported elsewhere, interpretation of these findings requires caution. This was a small study with insufficient power to exclude a potentially important treatment effect with respect to CIMT. Despite this, a statistically significant treatment effect in favour of allopurinol was observed. While the annualised CIMT progression rate in the placebo group exceeded that included in our power calculation, it was within 95% CIs based on population statistics. Similarly, the increase in systolic BP observed during follow-up in the placebo group was higher than expected (although CIs extended to negligible change from baseline). A clinical trial of the effect of allopurinol on 24 h ambulatory BP measures should be performed to confirm the effect on BP.
Despite randomisation, there were minor imbalances between treatment groups. These included a greater proportion of participants in the placebo group with index event of stroke (rather than TIA), diabetes and β-blocker treatment, while fewer had documented hypertension, atrial fibrillation or treatment with ACE-I/ARB agents. The difference in the proportion of patients treated with ACE-I or ARB between treatment groups was significant and potentially favoured the observation of a treatment effect in favour of allopurinol. We therefore repeated statistical analysis with adjustment for this imbalance and found the results to be unchanged from the intention-to-treat analysis. No significant differences in concomitant medications arose between groups during the period of study follow-up. Patient withdrawals were unrelated to the study intervention and incomplete availability of final follow-up endpoint data was balanced between the two treatment groups. It is feasible that other unidentified confounding factors could have influenced our results.
Although AI reduced significantly with allopurinol, this did not reach statistical significance when standardised for a heart rate of 75 bpm. This may in part reflect some loss of power due to patient withdrawals during study follow-up, but it is feasible that a non-significant rise in heart rate (p=0.09) observed in the allopurinol group compared with placebo (potentially reflecting the higher use of β-blocker therapy in the placebo group at baseline, which remained constant during study follow-up). It has been suggested that the heart rate standardised parameter may represent a better parameter for reporting; however, the epidemiological association with risk of cardiovascular events is established for uncorrected AI.
Previous studies in patients with heart failure suggest the beneficial effects of allopurinol are not related to a reduction in UA.6 Conversely, in adolescents with pre-hypertension, UA reduction per se appears beneficial in the form of BP reduction.20 In post hoc analysis, we identified no correlation between the observed change in UA and change in either mean common CIMT or central BP, potentially indicating a UA-independent treatment effect. Statistical analysis with adjustment for the observed change in UA did not affect the observed results. Our study used only one UA-lowering strategy and was therefore not designed to further differentiate the mechanism of benefit in terms of UA-lowering versus reduced vascular oxidative stress.
Our study enrolled participants irrespective of their baseline UA level. Consequently, although highly statistically significant, the observed therapeutic reduction in UA level (0.08 mmol/L) was relatively modest, and from a lower baseline level (0.31 mmol/L), compared with studies that selected patients based on elevated serum UA. Post hoc analysis of the largest trial of XO inhibition to date, the OPT-CHF study, suggested benefit of XO inhibition may be limited to those with baseline hyperuricaemia,28 with no difference observed between active treatment and placebo groups in the trial as a whole. Conversely, improved endothelial function has been reported with XO inhibition in patients with increased cardiovascular risk despite apparently normal levels of UA.29 While it is feasible that patient subgroups may exist who would experience differential benefit, according to their baseline UA level, through inclusion of patients regardless of baseline UA level, our results provide evidence of treatment benefit in a general population with normal range uricemia.
It is feasible that greater magnitude of benefit than that observed in the current study could be achieved with allopurinol therapy; a dose-dependent improvement in endothelial function has been reported with allopurinol6 and regression in LVH was achieved with higher doses than we studied.11 The allopurinol treatment dose was well tolerated during the study, with high concordance documented through pill counts and confirmed with the observed reduction in serum UA. No serious adverse reactions attributable to active study medication were observed.
In conclusion, this randomised, placebo-controlled double-blind study extends the evidence of beneficial effects of allopurinol treatment on the vasculature to include the stroke patient population, with sustained effects including central BP reduction and reduced CIMT progression. This therapeutic strategy holds the potential to reduce cardiovascular events and merits evaluation in definitive clinical endpoint studies.
What is already known on this subject?
Allopurinol, through either uric acid reduction or reduced production of reactive oxygen species by the xanthine oxidase enzymatic system, has been shown to improve various surrogate markers of cardiovascular health: improved endothelial function in a variety of populations, reduced left ventricular mass in both hypertensive and diabetic patients and improved exercise capacity in coronary artery disease patients.
What might this study add?
These data extend the evidence of sustained benefit of allopurinol therapy to include effects on carotid intima-media thickness progression, reduced central blood pressure and reduced arterial stiffness. They provide a potential mechanistic explanation for the observed benefits in left ventricular hypertrophy regression observed with treatment in other populations and extend evidence of benefit to patients with cerebrovascular disease.
How might this impact on clinical practice?
Despite available primary and secondary preventative measures, the incidence of cardiovascular disease remains high. Novel preventative strategies are required to reduce this burden. These data support for the hypothesis that xanthine oxidase inhibition represents a strategy with the potential to reduce the incidence of cardiovascular disease and provide support for the conduct of definite clinical trials.
We are grateful to our research nurses (Elizabeth Colquhoun, Lesley MacDonald, Belinda Manak), our sonographer (Karen Shields, KS), our trials manager (Pamela MacKenzie), laboratory lead (David Hughes, DH) and staff at the Robertson Centre for Biostatistics (Sharon Kean, Lorna Gillespie, Gill Wilson) for their hard work on this study. We also thank all stroke unit staff at Glasgow Western Infirmary and especially the patients who participated in the study.
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PH and MRW are co-first authors.
Contributors All authors contributed to the design and conduct of the study and to the approval of the manuscript.
Funding This study was competitively funded by a grant from The Stroke Association, UK (TSA 2007/10) and supported by the Scottish Stroke Research Network. The funder did not contribute to study design, study conduct, report preparation or submission.
Competing interests JD has received honoraria and speaker fees from Boehringer Ingelheim, Pfizer and Bayer for lectures on anticoagulation treatment for the prevention of cardioembolic stroke. KRL has held the following positions: chairman of independent data monitoring committee for DIAS trials (Lundbeck); Plasmin (GRIFOLS); ECASS-IV (Boehringer Ingelheim); ICTUS (Ferrer); NEST-3 (Photothera); ATTEST (University of Glasgow); member of independent data monitoring committee for REVASCAT (Covidien); WAKE-UP (EU FP7). He has received speaker fees from Boehringer Ingelheim. He is director for the NIHR Stroke Research Network. MRW has held the following positions: steering committees of FAST (Mennarini); SCOT (Pfizer); TICH-2 (Stroke Association); IDMC for TARDIS (Stroke Association, UK); CEC roles for Roche, GSK and Astellas Pharma; global advisory board work for Lundbeck; Scottish Stroke Research Network directorship.
Patient consent Obtained.
Ethics approval West Medical research ethics committee and was registered in the ISRCTN database (ISRCTN 11970568).
Provenance and peer review Not commissioned; externally peer reviewed.
Data sharing statement Data from this study would be made available to collaborators for meta-analysis.