International Journal of Cardiology 184 (2015) 159–162
Contents lists available at ScienceDirect
International Journal of Cardiology journal homepage: www.elsevier.com/locate/ijcard
Vitamin D deﬁciency and atrial ﬁbrillation Joseph Thompson a, Rynda Nitiahpapand a, Prashan Bhatti a, Antonios Kourliouros b,⁎ a b
GKT School of Medical Education, Strand, King's College London, WC2R 2LS, UK Department of Cardiac Surgery, Hareﬁeld Hospital, Hill End Road, Hareﬁeld, UB9 6JH, UK
a r t i c l e
i n f o
Article history: Received 3 December 2014 Received in revised form 4 February 2015 Accepted 8 February 2015 Available online 10 February 2015 Keywords: Vitamin D deﬁciency Atrial ﬁbrillation Antioxidants Oxidative stress Cardiac arrhythmias
a b s t r a c t Vitamin D deﬁciency has been linked with hypertension, coronary artery disease, and stroke, but there is no consensus regarding the possible association between vitamin D deﬁciency and atrial ﬁbrillation (AF). Vitamin D negatively regulates the renin–angiotensin–aldosterone-system (RAAS), mediates calcium homeostasis, binds to vitamin D receptors on cardiac myocytes, and has antioxidant properties that may reduce levels of reactive oxygen species (ROS) in the atria, which contribute to inﬂammation and proarrhythmic substrate formation. As vitamin D status is a readily modiﬁable risk factor this association has potential clinical implications. An extensive search of the literature identiﬁed six studies that speciﬁcally investigated vitamin D status and AF. Results were equivocal with three studies identifying a positive association between vitamin D deﬁciency and AF, whilst two studies suggested there may be no association. Additionally, one study indicated that elevated vitamin D levels are associated with AF. Whilst the weight of the evidence suggests that there may be an association between vitamin D deﬁciency and AF, incomparable study designs and methodological limitations hinder interpretation of the current body of evidence. Further work taking into account considerations raised within this paper is required to better understand the relationship between vitamin D status and AF. © 2015 Elsevier Ireland Ltd. All rights reserved.
1. Introduction Atrial ﬁbrillation (AF) is the most common cardiac arrhythmia, both in the general population, and in the ﬁrst days following cardiac surgery. Between 1994 and 2003 the prevalence of AF in the UK rose from 0.78% to 1.31% , reﬂecting the ageing nature of the population, with estimates suggesting that there will be a 3-fold increase in prevalence over the next 50 years . AF is associated with signiﬁcant morbidity and mortality due to its impact on cardiac function and predisposition to thromboembolic events. The exact pathogenesis of AF is not yet well understood, although structural and electrophysiological remodelling in the atria have been identiﬁed as key components, with inﬂammation as a potential driver for these changes. Inﬂammation in the atria is often caused by oxidative stress, which results from the excessive production of reactive oxygen species (ROS). AF itself promotes further remodelling, causing selfperpetuation of the arrhythmia. Currently, medications available for the treatment of AF are limited by poor efﬁcacy and pro-arrhythmic complications. Within the context Abbreviations: 25[OH]D, 25-hydroxyvitamin D; 1,25[OH]D, 1,25-dihydroxyvitamin D; AP, action potential; APA, action potential amplitude; APD, action potential duration POAF; POAF, post-operative atrial ﬁbrillation; RAAS, renin–angiotensin/aldosterone system; RAP, rapid atrial pacing; RMP, resting membrane potential; ROS, reactive oxygen species; VDR, vitamin D receptor. ⁎ Corresponding author. E-mail address: [email protected]
http://dx.doi.org/10.1016/j.ijcard.2015.02.012 0167-5273/© 2015 Elsevier Ireland Ltd. All rights reserved.
of “upstream therapies”, the impact of prophylactic antioxidant therapy on the incidence of postoperative atrial ﬁbrillation (POAF) has been investigated, and a meta-analysis of randomised controlled trials (RCT's) concluded that prophylaxis with the antioxidants vitamin C and vitamin E signiﬁcantly reduces the incidence of POAF (odds ratio (OR) 0.43, 95% conﬁdence interval [CI] 0.21 to 0.89) and all causes of arrhythmia (OR 0.54, 95% CI 0.29 to 0.99) following cardiac surgery . Vitamin D deﬁciency has been linked with hypertension , coronary artery disease , myocardial infarction , and stroke . Due to its antioxidant properties, it has been hypothesised that vitamin D levels may impact on the production of ROS in the atria, and subsequently the formation of the proarrhythmic substrate. In addition to this direct antiﬁbrillatory mechanism, vitamin D negatively regulates the renin–angiotensin–aldosterone system (RAAS), contributing to the maintenance of blood pressure at levels that minimise the atrial structural remodelling observed in AF . Furthermore, vitamin D receptors (VDR's) are found in myocytes and ﬁbroblasts in the heart . A number of animal studies conﬁrm that VDR's are important in mediating cardiac hypertrophy, whilst the association between VDR's and mediation of ﬁbrosis is less clear [9–11]. This multifaceted mechanism of action suggests that vitamin D may be protective against AF. Large population studies in Scotland  and Denmark  have shown that the incidence of AF is at its highest in winter months and lowest in summer months, which correlates with the sinusoidal seasonal variation seen in 25-hydroxyvitamin D (25[OH]D) levels . The mechanism behind this association is unclear, and whilst sunlight
25[OH]D levels were similar in patients with valvular AF (mitral valve disease) and the control group 300
Case control study
Case control study
Chen et al., 2013, 
Demir et al., 2014, 
Three cohorts of Turkish participants; non-valvular AF patients, valvular AF patients, and controls
25[OH]D measured at single time point
Low 25[OH]D associated with non-valvular AF, increased LA diameter, increased pulmonary systolic pressure, increased high sensitivity C-reactive protein Low 25[OH]D associated with non-valvular AF 25[OH]D measured at single time point
Retrospective cohort study Qayyum et al., 2012, 
Two cohorts of Chinese participants; patients with non-valvular AF, and controls 322
Prospective cohort study Smith et al., 2011, 
One cohort of Danish patients with either paroxysmal, persistent, or permanent AF
25[OH]D measured at single time point
No association between 25[OH]D levels and type of AF, or between 25[OH]D levels and IHD, CVA or MI.
Excess 25[OH]D is an independent risk factor for promoting the development of AF, whereas 25[OH]D deﬁciency does not. Comorbidities (hypertension, heart failure, diabetes, renal failure) were more prevalent in the latter group Study reports result incorrectly in ng/dl, instead of ng/ml Lifetime prevalence of vitamin D deﬁciency in Denmark is estimated at 30–70% No control subjects included, making it difﬁcult to analyse results regarding whether there is a link between 25[OH]D and AF Two-fold difference in AF prevalence between subjects with the lowest and highest levels of 25[OH]D 25[OH]D levels greater than 100 ng/ml associated with AF. No association seen between 25[OH]D less than 20 mg/ml and AF. One cohort of patients without previous episode of prevalent AF, with prior 25[OH]D measurements
Rienstra et al., 2011, 
Participants Study design
Prospective cohort study
Table 1 Observational studies.
The electromechanical effects of the active form of vitamin D, 1,25dihydroxyvitamin D (1,25[OH]2D) on isolated rabbit left atria, and in heart failure (HF) rabbits that had undergone left coronary artery ligation, were examined by Hanafy et al. . An electrical stimulus was used to trigger action potentials (APs) in isolated left atria, with control specimens pre-treated with 0.1 μM ryanodine, an antagonist of the ryanodine receptor responsible for calcium induced calcium release and subsequent contraction of the myocardium. 1,25[OH]2D was infused into the tissue at concentrations of 0.01, 0.1, and 1 nM, and microelectrodes were used to measure the resting membrane potential (RMP), AP amplitude (APA), and AP duration (APD). When ryanodine was not present, the presence of 1,25[OH]2D exhibited a dose dependent increase in the APD, but did not affect the RMP or APA, electromechanically stabilising the substrate. In contrast, when ryanodine was present, 1,25[OH]2D had no effect on APD, RMP, or APA, but did decrease contractility. These results suggest that 1,25[OH]2D may have an effect on calcium regulation. Rapid atrial pacing  in combination with acetylcholine infusion was used to test AF inducibility in the isolated atria, both in the presence and absence of 1,25[OH]2D. AF developed in 64.3% of atria (n = 14) treated with 1,25[OH]2D, compared to 100% of controls (n = 14) (p b 0.05), with longer APD's observed in the 1,25[OH]2D group. In addition to this, slower rates were noted in the atria treated with 1,25[OH]2D that did develop AF (p b 0.05). In HF rabbits (n = 5), 1,25[OH]2D had a protective effect against AF, with AF only inducible with RAP and acetylcholine infusion in 11.9%, vs. 100% of controls (p b 0.001). Furthermore, APD was prolonged in the 1,25[OH]2D group (p b 0.05). Effects were atria speciﬁc, with 1,25[OH]2D having no effect on QT interval or APD in isolated rabbit Purkinje ﬁbres. This study demonstrates that 1,25[OH]2D has a direct and atrialspeciﬁc antiarrhythmic effect, due to its prolongation of the APD. Furthermore, results were reproducible in an in vivo model at clinically relevant doses. Despite promising results, the authors admit that the low number of animals in the study may limit its power. Additionally, only male rabbits were used, although it is not clear whether gender differences impact upon the effects of 1,25[OH]2D.
3.1. Experimental studies
No association between 25[OH]D and AF development
We conducted an extensive search of MEDLINE and EMBASE (1966, November 2014) using the MeSH terms: “atrial ﬁbrillation,” “arrhythmia*,” “vitamin D,” “cholecalciferol,” and “ergocalciferol”. A search of the Cochrane Library using the same terms in “Titles, Abstracts and Keywords” was also conducted. The search was limited to English language papers. Additional papers were identiﬁed by searching for ‘related articles’ in MEDLINE, as well as through examining the references of identiﬁed articles. Only articles that studied the relationship between vitamin D and AF were included in our review. Our search of the literature identiﬁed one experimental study  and ﬁve observational studies [17–21] that speciﬁcally investigated the relationship between vitamin D and AF (Table 1).
25[OH]D measured at biennial or quadrennial intervals with a mean f ollow-up time of 9.9 years. Participants monitored for episodes of AF Patients monitored for the ﬁrst episode of AF
Two American community cohorts without prevalent AF
exposure and vitamin D levels may contribute, other factors such as air temperature , atmospheric pressure , and seasonal variation in respiratory infections are also hypothesised to be causative . Despite the established link between vitamin D deﬁciency and cardiovascular disease, and the strong mechanistic basis for the formation of a proarrhythmic substrate in those who are vitamin D deﬁcient, few studies have examined the relationship between vitamin D and AF. The aim of this review is to critically appraise the relevant studies in this area.
In the community setting the development of AF was not related to vitamin D status
J. Thompson et al. / International Journal of Cardiology 184 (2015) 159–162
J. Thompson et al. / International Journal of Cardiology 184 (2015) 159–162
Whilst it is evident from these ﬁndings that 1,25[OH]2D has a direct effect on the atria, the mechanism remains unclear. The authors note that increased calcium release in the presence of 1,25[OH]2D is unlikely to explain the prolongation of APD's as ryanodine alone exerts no significant effect upon APD. In the context of isolated atria the potential role of oxidative stress is difﬁcult to examine as this model allows only local, and not systemic inﬂammatory response to be assessed. Additionally, this study only investigated acute changes in the atria in response to vitamin D, and does not examine chronic changes that occur over time within the atria, such as hypertrophy and ﬁbrosis, which are key to the pathogenesis of AF. These results provide a foundation for further in vivo studies, and further work could be undertaken to establish whether there is a correlation between ROS levels in isolated atria and the prolongation of the APD seen with increasing concentrations of 1,25[OH]2D. 3.2. Observational studies To date, large population studies have been unable to conﬁrm the relationship between vitamin D and AF demonstrated in Hanafy et al.'s electrophysiology study. Clinically, 25[OH]D is used as a surrogate marker for vitamin D levels. It has a half-life of approximately 3 weeks, compared to 1,25[OH]2D, which has a half-life of just 4–6 h, allowing for more accurate assessment of vitamin D stores. The relationship between vitamin D status and the development of prevalent AF in two large community cohorts of the Framingham Heart Study participants was examined by Rienstra et al. . No association was found between 25[OH]D levels and AF in those who had biennial 25[OH]D measurement (original cohort), or in those who had quadrennial 25[OH]D measurement (offspring cohort). 15% of participants (n = 425) developed AF during follow-up, with a hazard ratio of 0.99 per SD increment in 25[OH]D (95% CI: 0.88–1.10 p = 0.81) after adjustment for independent risk factors for AF (hypertension, myocardial infarction, HF), as well as for winter season. Further analysis showed that there was no difference in the prevalence of AF in participants whose 25[OH]D levels fell below the 20th percentile, when compared to the remainder of the study participants (p = 0.59). Post-hoc power analysis suggested that the study had 80% power to detect an adjusted hazard ratio of 1.15 per SD increment in 25[OH]D levels. Despite the large sample size and mean follow-up of 9.9 years, more subtle associations between 25[OH]D levels and the development of AF may have been obscured by the lack of participants with low 25[OH]D levels. This was most evident in the original cohort of older participants (76.6 years ± 6 years) who due to their age are more likely to develop AF, where mean 25[OH]D levels were 29.2 ng/ml ± 12.6 ng/ml; well above the 20 ng/ml that the Institute of Medicine suggests is required for 97.5% of the adult population . Despite the relatively long half-life of 25[OH]D, measurements at biennial and quadrennial intervals cannot accurately account for changes in vitamin D status over such long time periods. Additionally, whilst studies that have found an association between vitamin D levels and AF have been carried out during the winter, when vitamin D deﬁciency is more common (10, 14), Rienstra et al. do not report whether blood samples were taken at a speciﬁc time of the year. No association was found between 25[OH]D levels and whether patients had paroxysmal, persistent, or permanent AF by Qayyum et al. , suggesting that vitamin D levels may not impact upon AF burden. Additionally, no association was found between 25[OH]D levels and ischaemic heart disease, stroke, or acute myocardial infarction despite previous studies that have shown vitamin D deﬁciency to be associated with increased incidence of these conditions (4, 5, 6). The inclusion of patients without AF in this study would have provided useful information on whether vitamin D status is associated with AF at all, and not just the type and chronicity of AF. Two observational studies to date have shown a relationship between vitamin D deﬁciency and AF. Demir et al.  suggested that
vitamin D deﬁciency may be associated with the development of AF in those without concurrent valve disease. Patients with non-valvular AF were found to have both lower serum 25[OH]D levels, and higher parathyroid hormone levels than age matched patients in sinus rhythm or with mitral valve disease and AF (p b .001), suggesting that vitamin D status may impact upon the development and maintenance of AF. Patients were excluded from the study if they had conditions that could have an effect on vitamin D levels or the development of AF, except for hypertension and diabetes mellitus. The study was carried out in Turkey, during winter, when vitamin D levels are at their lowest. All patients with vitamin D levels within 2SDs of the mean in each of the three groups studied were vitamin D deﬁcient according to the established Institute of Medicine criteria. Whilst this ensured that the study was well powered, caution must be exercised in extrapolating these results to populations with higher mean vitamin D levels. Chen et al.  found 25(OH)D levels to be signiﬁcantly lower in patients with persistent non-valvular AF than in age matched controls in sinus rhythm (18.5 ± 10.3 vs. 21.4 ± 10.7 ng/ml, p b 0.05). Low serum 25[OH]D was associated with increased high sensitivity Creactive protein levels, supporting the hypothesis that inﬂammation may be linked to AF. Patients with vitamin D levels below 20 ng/ml were twice as likely to have AF as those with a 25[OH]D level greater than 30 ng/ml. Mean vitamin D levels in the control group were approximately twice as high as the mean vitamin D levels in Demir et al.'s study , and almost three times as high in the AF group compared to the corresponding group in Demir's study, highlighting how important the consideration of local environmental factors such as climate and diet is in designing studies to investigate the effects of vitamin D. One study abstract identiﬁed vitamin D excess as a risk factor for the development of AF in those without prior AF . The conclusion that 25[OH]D levels above 100 ng/dl increases AF risk by 2.5 times is initially rather concerning, until the authors assert that normal vitamin D level is 20–40 ng/dl, and it becomes apparent that they possibly have mistakenly used ng/dl throughout instead of ng/ml. This potential error aside, the study conﬁrms that very high levels of vitamin D are a risk factor for AF, as explained by the well understood effects of vitamin D on calcium levels, and the proarrhythmic effect of hypercalcaemia. 4. Discussion The current evidence regarding whether vitamin D status impacts upon the development of AF is equivocal, and is hindered by small sample sizes and methodological limitations. Hanafy et al. offer compelling experimental evidence that vitamin D acts directly within the atria, and is protective against AF in in vivo models. Proof of a direct mechanism of action adds weight to the hypothesis that the antiﬁbrillatory effect of vitamin D extends beyond indirect effects mediated by the RAAS. However, it is unclear if, and how, oxidative stress and vitamin D mediated calcium homeostasis within myocytes contribute to this effect. VDR's found in myocytes and ﬁbroblasts in the heart may also play a role in the antiarrhythmic action of vitamin D, but are thought to be responsible for mediating long term structural changes in the pathogenesis of AF such as cardiac hypertrophy and ﬁbrosis. 4.1. Study design Of the ﬁve observational studies that examined the relationship between vitamin D and AF, only two are of comparable designs, with both studies taking place in winter, with well-deﬁned exclusion criteria [17, 21]. They both suggest an association between vitamin D deﬁciency and AF, but the minimal overlap in terms of 25[OH]D levels observed in their populations hinders comparison of these results. Concerns regarding adequate power were raised in both Rienstra et al.  and Qayyum et al.'s  studies, and the failure to include control subjects in the later means that its results offer no evidence to suggest that vitamin D does not have an effect on the initial development of AF. Future
J. Thompson et al. / International Journal of Cardiology 184 (2015) 159–162
prospective cohort studies should measure 25[OH]D at frequent intervals to ensure that an association with AF is not overlooked, and, as well as being of sufﬁcient size, would ideally take place in populations where vitamin D deﬁciency is more common, in order to be powered to detect more subtle association. Although 25[OH]D is commonly used to clinically assess vitamin D status, it may not be sufﬁcient as a marker for research purposes due to variation in results from different assays. In particular, liquid chromatography–mass spectrometry assays have been found to give relatively high results compared to radioimmunoassays . Future studies should ensure assay monitoring with a proﬁciency testing scheme, and consider analysing additional biomarkers related to vitamin D and calcium to more accurately assess vitamin D status. Of the studies reviewed, Hanafy et al. measured 1,25[OH]2D whilst the ﬁve observational studies measured 25[OH]D, either independently [19,20] or with additional biomarkers [17,18,21]. 4.2. Seasonal variation in vitamin D levels A signiﬁcant inverse relationship between daylight hours and AF incidence has been observed in several population wide studies, leading to a marked increase in hospital admissions for paroxysmal AF and AF associated stroke during winter months. [12,25,26] Shoben et al.  illustrated a sinusoidal pattern for mean monthly 25[OH]D concentration, with low levels throughout winter corresponding to the seasonal increase in AF incidence, suggesting that vitamin D levels may be responsible. As such, the seasonal variation in vitamin D levels due to changes in ultraviolet exposure must be taken in to account when designing and interpreting studies investigating vitamin D and AF. In the studies directly investigating vitamin D and atrial ﬁbrillation, Qayyum et al.  observed signiﬁcant seasonal variation in 25[OH]D with mean levels in summer twice those of mean levels in winter (66 nmol/l vs. 33.5 nmol/l, p = 0.0001), whilst Chen et al.  and Demir et al.  conducted their studies only during the winter season, maximising power to detect a signiﬁcant association between vitamin D status and AF. Rienstra et al.  do not state at what time of the year the data was collected throughout their study, but adjusted statistical models for the season. It has been suggested that using season or month speciﬁc cut off points to assign exposure categories is preferable in statistically adjusting for the date of sample collection for avoidance of potential bias , and future studies should consider this method. 4.3. Future work Studies into the effects of other antioxidants on the initiation of AF have focused around the post-operative setting, where AF is very common compared to community and outpatient populations. Additionally, the measurement of local and systemic ROS, inﬂammatory cytokines, and other acute phase proteins is possible both peri- and postoperatively, allowing for mechanisms of action to be explored. Similar studies examining the relationship between vitamin D status and POAF would expand our current knowledge. The post-operative setting could also provide a platform for undertaking RCTs in this area, where prophylactic vitamin D supplementation in deﬁcient individuals could be studied. In conclusion, the evidence currently available regarding whether vitamin D deﬁciency is a risk factor for AF presents mixed results with no clear consensus regarding association between low levels and the development of arrhythmia. Despite compelling experimental data, observational studies have been marred by small sample sizes and poor study design. Large, well designed prospective studies, as well as RCT's
in the context of POAF, are required to further investigate the hypothesised link between vitamin D deﬁciency and AF.
Conﬂict of interest The authors report no relationships that could be construed as a conﬂict of interest.
References  S. DeWilde, et al., Trends in the prevalence of diagnosed atrial ﬁbrillation, its treatment with anticoagulation and predictors of such treatment in UK primary care, Heart 92 (8) (2006) 1064–1070.  Y. Miyasaka, et al., Secular trends in incidence of atrial ﬁbrillation in Olmsted County, Minnesota, 1980 to 2000, and implications on the projections for future prevalence, Circulation 114 (2) (2006) 119–125.  L. Harling, et al., Do antioxidant vitamins have an anti-arrhythmic effect following cardiac surgery? A meta-analysis of randomised controlled trials, Heart 97 (20) (2011) 1636–1642.  J.P. Forman, et al., Plasma 25-hydroxyvitamin D levels and risk of incident hypertension, Hypertension 49 (5) (2007) 1063–1069.  P. Brondum-Jacobsen, et al., 25-hydroxyvitamin d levels and risk of ischemic heart disease, myocardial infarction, and early death: population-based study and metaanalyses of 18 and 17 studies, Arterioscler. Thromb. Vasc. Biol. 32 (11) (2012) 2794–2802.  K.E. Poole, et al., Reduced vitamin D in acute stroke, Stroke 37 (1) (2006) 243–245.  Y.C. Li, Vitamin D regulation of the renin–angiotensin system, J. Cell. Biochem. 88 (2) (2003) 327–331.  D.G. Gardner, S. Chen, D.J. Glenn, Vitamin D and the heart, Am. J. Physiol. Regul. Integr. Comp. Physiol. 305 (9) (2013) R969–R977.  S. Chen, et al., Cardiomyocyte-speciﬁc deletion of the vitamin D receptor gene results in cardiac hypertrophy, Circulation 124 (17) (2011) 1838–1847.  W. Xiang, et al., Cardiac hypertrophy in vitamin D receptor knockout mice: role of the systemic and cardiac renin–angiotensin systems, Am. J. Physiol. Endocrinol. Metab. 288 (1) (2005) E125–E132.  P. Mancuso, et al., 1,25-Dihydroxyvitamin-D3 treatment reduces cardiac hypertrophy and left ventricular diameter in spontaneously hypertensive heart failureprone (cp/+) rats independent of changes in serum leptin, J. Cardiovasc. Pharmacol. 51 (6) (2008) 559–564.  N.F. Murphy, et al., Seasonal variation in morbidity and mortality related to atrial ﬁbrillation, Int. J. Cardiol. 97 (2) (2004) 283–288.  L. Frost, et al., Seasonal variation in hospital discharge diagnosis of atrial ﬁbrillation: a population-based study, Epidemiology 13 (2) (2002) 211–215.  A.B. Shoben, et al., Seasonal variation in 25-hydroxyvitamin D concentrations in the cardiovascular health study, Am. J. Epidemiol. 174 (12) (2011) 1363–1372.  A. Gluszak, et al., Episodes of atrial ﬁbrillation and meteorological conditions, Kardiol. Pol. 66 (9) (2008) 958–963 (discussion 964–5).  D.A. Hanafy, et al., Electromechanical effects of 1,25-dihydroxyvitamin d with antiatrial ﬁbrillation activities, J. Cardiovasc. Electrophysiol. 25 (3) (2014) 317–323.  M. Demir, U. Uyan, M. Melek, The effects of vitamin D deﬁciency on atrial ﬁbrillation, Clin. Appl. Thromb. Hemost. 20 (1) (2014) 98–103.  F. Qayyum, et al., Vitamin D deﬁciency is unrelated to type of atrial ﬁbrillation and its complications, Dan. Med. J. 59 (9) (2012) A4505.  M. Rienstra, et al., Vitamin D status is not related to development of atrial ﬁbrillation in the community, Am. Heart J. 162 (3) (2011) 538–541.  M.B. Smith, et al., Abstract 14699: vitamin D excess is signiﬁcantly associated with risk of atrial ﬁbrillation, Circulation 124 (2011) A14699.  W.R. Chen, et al., Relation of Low vitamin D to nonvalvular persistent atrial ﬁbrillation in Chinese patients, Ann Noninvasive Electrocardiol 19 (2) (2014) 166–173.  D. Pickar, et al., Clinical and biologic response to clozapine in patients with schizophrenia. Crossover comparison with ﬂuphenazine, Arch. Gen. Psychiatry 49 (5) (1992) 345–353.  A.C. Ross, The 2011 report on dietary reference intakes for calcium and vitamin D, Public Health Nutr. 14 (5) (2011) 938–939.  G.D. Carter, Accuracy of 25-hydroxyvitamin D assays: confronting the issues, Curr. Drug Targets 12 (1) (2011) 19–28.  A.L. Christensen, et al., Seasonality, incidence and prognosis in atrial ﬁbrillation and stroke in Denmark and New Zealand, BMJ Open 2 (4) (2012).  A. Gluszak, et al., May sunshine protect women against paroxysms of atrial ﬁbrillation? Tohoku J. Exp. Med. 219 (4) (2009) 303–306.  Y. Wang, et al., Comparing methods for accounting for seasonal variability in a biomarker when only a single sample is available: insights from simulations based on serum 25-hydroxyvitamin d, Am. J. Epidemiol. 170 (1) (2009) 88–94.