A new innovations state space modeling framework, incorporating Box-Cox transformations, Fourier series with time varying coefficients and ARMA error correction, is introduced for forecasting complex seasonal time series that cannot be handled using existing forecasting models. Such complex time series include time series with multiple seasonal periods, high frequency seasonality, non-integer seasonality and dual-calendar effects. Our new modelling framework provides an alternative to existing exponential smoothing models, and is shown to have many advantages. The methods for initialization and estimation, including likelihood evaluation, are presented, and analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors are derived, leading to a simple, comprehensible approach to forecasting complex seasonal time series. Our trigonometric formulation is also presented as a means of decomposing complex seasonal time series, which cannot be decomposed using any of the existing decomposition methods. The approach is useful in a broad range of applications, and we illustrate its versatility in three empirical studies where it demonstrates excellent forecasting performance over a range of prediction horizons. In addition, we show that our trigonometric decomposition leads to the identification and extraction of seasonal components, which are otherwise not apparent in the time series plot itself.

AimsGenetics plays an important role in coronary heart disease (CHD) but the clinical utility of genomic risk scores (GRSs) relative to clinical risk scores, such as the Framingham Risk Score (FRS), is unclear. Our aim was to construct and externally validate a CHD GRS, in terms of lifetime CHD risk and relative to traditional clinical risk scores.Methods and resultsWe generated a GRS of 49 310 SNPs based on a CARDIoGRAMplusC4D Consortium meta-analysis of CHD, then independently tested it using five prospective population cohorts (three FINRISK cohorts, combined n = 12 676, 757 incident CHD events; two Framingham Heart Study cohorts (FHS), combined n = 3406, 587 incident CHD events). The GRS was associated with incident CHD (FINRISK HR = 1.74, 95% confidence interval (CI) 1.61–1.86 per S.D. of GRS; Framingham HR = 1.28, 95% CI 1.18–1.38), and was largely unchanged by adjustment for known risk factors, including family history. Integration of the GRS with the FRS or ACC/AHA13 scores improved the 10 years risk prediction (meta-analysis C-index: +1.5–1.6%, P < 0.001), particularly for individuals ≥60 years old (meta-analysis C-index: +4.6–5.1%, P < 0.001). Importantly, the GRS captured substantially different trajectories of absolute risk, with men in the top 20% of attaining 10% cumulative CHD risk 12–18 y earlier than those in the bottom 20%. High genomic risk was partially compensated for by low systolic blood pressure, low cholesterol level, and non-smoking.ConclusionsA GRS based on a large number of SNPs improves CHD risk prediction and encodes different trajectories of lifetime risk not captured by traditional clinical risk scores.

Metabolomics research often requires the use of multiple analytical platforms, batches of samples, and laboratories, any of which can introduce a component of unwanted variation. In addition, every experiment is subject to within-platform and other experimental variation, which often includes unwanted biological variation. Such variation must be removed in order to focus on the biological information of interest. We present a broadly applicable method for the removal of unwanted variation arising from various sources for the identification of differentially abundant metabolites and, hence, for the systematic integration of data on the same quantities from different sources. We illustrate the versatility and the performance of the approach in four applications, and we show that it has several advantages over the existing normalization methods.

Metabolomics experiments are inevitably subject to a component of unwanted variation, due to factors such as batch effects, long runs of samples, and confounding biological variation. Although the removal of this unwanted variation is a vital step in the analysis of metabolomics data, it is considered a gray area in which there is a recognised need to develop a better understanding of the procedures and statistical methods required to achieve statistically relevant optimal biological outcomes. In this paper, we discuss the causes of unwanted variation in metabolomics experiments, review commonly used metabolomics approaches for handling this unwanted variation, and present a statistical approach for the removal of unwanted variation to obtain normalized metabolomics data. The advantages and performance of the approach relative to several widely-used metabolomics normalization approaches are illustrated through two metabolomics studies, and recommendations are provided for choosing and assessing the most suitable normalization method for a given metabolomics experiment. Software for the approach is made freely available online.

Background Genetics plays an important role in coronary heart disease (CHD) but the clinical utility of a genomic risk score (GRS) relative to clinical risk scores, such as the Framingham Risk Score (FRS), is unclear. Methods We generated a GRS of 49,310 SNPs based on a CARDIoGRAMplusC4D Consortium meta-analysis of CHD, then independently tested this using five prospective population cohorts (three FINRISK cohorts, combined n=12,676, 757 incident CHD events; two Framingham Heart Study cohorts (FHS), combined n=3,406, 587 incident CHD events). Results The GRS was strongly associated with time to CHD event (FINRISK HR=1.74, 95% CI 1.61-1.86 per S.D. of GRS; Framingham HR=1.28, 95% CI 1.18-1.38), and was largely unchanged by adjustment for clinical risk scores or individual risk factors, including family history. Integration of the GRS with clinical risk scores (FRS and ACC/AHA13 score) improved prediction of CHD events within 10 years (meta-analysis C-index: +1.5-1.6%, P<0.001), particularly for individuals ≥60 years old (meta-analysis C-index: +4.6-5.1%, P<0.001). Men in the top 20% of the GRS had 3-fold higher risk of CHD by age 75 in FINRISK and 2-fold in FHS, and attaining 10% cumulative CHD risk 18y earlier in FINRISK and 12y earlier in FHS than those in the bottom 20%. Furthermore, high genomic risk was partially compensated for by low systolic blood pressure, low cholesterol level, and non-smoking. Conclusions A GRS based on a large number of SNPs substantially improves CHD risk prediction and encodes decades of variation in CHD risk not captured by traditional clinical risk scores.

BackgroundSexual dysfunction (SD) is very common in people with multiple sclerosis (PwMS) and contributes a significant burden of disease, particularly for young people. SD has direct neurological contributions from depression and fatigue, which occur commonly in PwMS. Modifiable factors may represent potential targets for treatment and prevention of SD. We aimed to assess the prevalence of SD and explore associations between SD and demographic and modifiable risk factors, as well as depression and fatigue in a large cohort of PwMS.MethodsWe analysed self-reported data from a large, international sample of PwMS recruited via Web 2.0 platforms, including demographic, lifestyle and disease characteristics. Specific sexual function questions included 4 items from the sexual function scale and 1 item regarding satisfaction with sexual function, part of the MS Quality of Life-54 instrument.Results2062 PwMS from 54 countries completed questions on sexual function. 81.1 % were women, mean age was 45 years, most (62.8 %) reported having relapsing-remitting MS. The majority (54.5 %) reported one or more problems with sexual function and were classified as having SD. Lack of sexual interest (41.8 % of women), and difficulty with erection (40.7 % of men) were most common. The median total sexual function score was 75.0 out of 100, and 43.7 % were satisfied with their sexual function. Regression modeling revealed independent associations between sexual function and satisfaction and a range of demographic factors, including age, as well as depression risk, antidepressant use, and fatigue in PwMS.ConclusionThis cross-sectional study shows that SD and lack of satisfaction with sexual function are associated with depression risk and fatigue, as well as modifiable lifestyle factors diet and physical activity (after adjusting for depression and fatigue). Planned longitudinal follow-up of this sample may help clarify these associations and the underlying mechanisms. There is potential to prevent and treat SD in PwMS by addressing depression and fatigue and their determinants. Clinicians and PwMS should be aware of SD and associated factors as part of a comprehensive preventive approach to managing MS.

BackgroundPeople with multiple sclerosis (MS) often experience pain, which can interfere with mobility, employment, and quality of life (QOL).MethodsThis cross-sectional study explored associations between pain, demographic, disease, and modifiable lifestyle factors in an international sample of people with MS recruited online.ResultsSubstantial pain, of moderate/severe intensity and interfering at least moderately with work/household or enjoyment of life in the past 4 weeks, was reported by 682/2,362 (28.9%). Substantial pain was associated with fatigue (odds ratio (OR): 6.7, 95% confidence interval (CI): 4.9,9.3), depression (OR:4.0, 95% CI:3.2,5.1), anxiety (OR:2.4, 95% CI:1.9,2.9), and lower mental health QOL (Mean Difference: −14.7, 95% CI:−16.6,−12.8). Regression analyses showed that smoking (OR: 2.0, 95% CI:1.35,2.87) and obesity (OR:2.1, 95% CI: 1.5,2.8), moderate alcohol use (OR: 0.7, 95% CI:0.5,0.9), moderate (OR 0.7, 95% CI: 0.55,0.98) or high (OR 0.6, 95% CI: 0.4,0.8) physical activity level, and healthy diet (OR 0.8, 95% CI: 0.75,0.95, per 10 points) were associated with substantial pain.ConclusionOur results show clear associations with modifiable lifestyle factors and substantial pain in MS. These factors are already considered in the prevention and management of pain in other populations but have not previously been considered in MS. Conversely, pain and associated common MS comorbidities, such as depression, anxiety, and fatigue, may hamper efforts to start or maintain healthy behaviors. Strategies to overcome these barriers need to be considered. Further research should clarify the direction of these associations.

BackgroundModifiable risk factors such as smoking and sedentary lifestyle adversely affect multiple sclerosis (MS) progression. Few multimodal behavioural interventions have been conducted for people with MS, and follow-up beyond 1 year is rare for lifestyle interventions. This study assessed adoption and adherence to healthy lifestyle behaviours and health outcomes 3 years after a lifestyle modification intervention, using generalized estimating equation models to account for within-participant correlation over time.Methods95 people with MS completed baseline surveys before participating in 5-day MS lifestyle risk-factor modification workshops. 76 and 78 participants completed the 1-year and 3-year follow-up surveys respectively. Mean age at 3-year follow-up was 47 years, 72% were female, most (62.8%) had MS for 5 years or less, and 73% had relapsing remitting MS (RRMS).ResultsCompared to baseline, participants reported clinically meaningful increases in physical (mean difference (MD): 8.0, 95% Confidence Interval (CI): 5.2–10.8) and mental health (MD: 9.2, CI: 5.8–12.6) quality of life (QOL) at 1-year, and physical (MD: 8.7, CI: 5.3–12.2) and mental health (MD: 8.0, CI: 4.2–11.8) QOL at 3-year follow-up. There was a small decrease in disability from baseline to 1-year follow-up (MD: 0.9, CI: 0.9,1.0) and to 3-year follow-up (MD: 1.0, CI: 0.9,1.0), which was not clinically meaningful. Of those with RRMS, compared to baseline, fewer had a relapse during the year before 1-year follow-up (OR: 0.1, CI 0.0–0.2) and 3-year follow-up (OR: 0.15, CI 0.06–0.33). Participants’ healthy diet score, the proportion meditating ≥1 hours a week, supplementing with ≥ 5000IU vitamin D daily, and supplementing with omega-3 flaxseed oil increased at 1-year follow-up and was sustained, although slightly lower at 3-year follow-up. However, there was no evidence for a change in physical activity and not enough smokers to make meaningful comparisons. Medication use increased at 1-year follow-up and at 3-year follow-up.ConclusionThe results provide evidence that lifestyle risk factor modification is feasible and sustainable over time, in a small self-selected and motivated sample of people with MS. Furthermore, participation in a lifestyle intervention is not associated with a decrease in MS medication use.