Long Run Confidence: Estimating Confidence Intervals when using Long Run Multipliers

The recent exchange on Error Correction Models in Political Analysis and elsewhere dealt with several important issues involved in time series analysis. While there was much disagreement in the symposium, one common theme was the lack of power due to the few number of observations for much of this work. In this paper we highlight two well known but rarely discussed problems this has for inferences from standard time series techniques. First, one result of low power is inflated standard errors. One issue low powered time series can face is that the confidence interval on a lagged dependent variable, even when the series is stationary, includes values ≥ 1. This is particularly problematic when calculating the confidence interval of the long run multiplier. If the confidence interval of the lagged dependent variable includes 1, the standard error of the long run multiplier will be explosive. Second, the calculation of the long run multiplier is the ratio of coefficients, which makes the calculation of the uncertainty slightly more complicated. Unfortunately, the two standard approaches to calculating the uncertainty in the long run multiplier, the delta method and the Bewley transformation, are asymptotically accurate, but may have difficulties in small samples. As a solution, we suggest using a Bayesian approach. For autoregressive distributed lag models, the Bayesian approach can formalizes the stationarity assumption by using a beta prior that is strictly less than 1. With error correction models, the researcher can easily calculate the credible region of the long run multiplier from the posterior distribution of the ratio of the coefficients. As a result, we obtain theoretically informed estimates of the confidence regions for the distribution of the long run multiplier

IL-6 Linkage To Exercise-Induced Shifts In Lipid-Related Metabolites: A Metabolomics-Based Analysis

Metabolomics profiling and bioinformatics technologies were Substantial increase In used to determine the relationship between exercise-induced increases in IL-6 and lipid-related metabolites 6 and lipid-related metabolites. Twenty-four male runners (age 36.5 +/- 1.8 y) ran on treadmills to exhaustion (2.26 +/- 0.01 h, 24.9 +/- 1.3km, 69.7 +/- 1.9% Vastus lateralis muscle biopsy and blood samples were collected before and immediately after running and showed a 33.7 +/- 4.2% decrease in muscle glycogen, 39.0 +/- 8.8-, 2.4 +/- 0.3-, and 1.4 +/- 0.1-fold increases in plasma IL-6, IL-8, and MCP-1, respectively, and 95.0 +/- 18.9 and 158 20.6% increases in cortisol and epinephrine, respectively (all, P < 0.001). The metabolomics analysis revealed changes in 209 metabolites, especially long- and medium-chain fatty acids, fatty acid oxidation products (dicarboxylate and monohydroxy fatty acids, acylcarnitines), and ketone bodies. OPLS-DA modeling supported a strong separation in pre- and post-exercise samples (R2Y = 0.964, Q2Y = 0.902). OPLSR analysis failed to produce a viable model for the relationship between IL-6 and all lipid-related metabolites (R2Y = 0.76, Q2Y = -0.0748). Multiple structure equation models were evaluated based on IL-6, with the best-fit pathway model showing a linkage of exercise time to IL-6, then camitine, and 13-methylmyristic acid (a marker for adipose tissue lipolysis) and sebacate. These metabolomics-based data indicate that the increase in plasma IL-6 after long endurance running has a minor relationship to increases in lipid related metabolites

Carbohydrate Ingestion Influences Skeletal Muscle Cytokine mRNA And Plasma Cytokine Levels After A 3 Hour Run

Sixteen experienced marathoners ran on treadmills for 3 h at ~ 70% maximal oxygen consumption (Vo2 max) on two occasions while receiving 1 l/h carbohydrate (CHO) or placebo (Pla) beverages. Blood and vastus lateralis muscle biopsy samples were collected before and after exercise. Plasma was analyzed for IL-6, IL-10, IL-1 receptor agonist (IL-1ra), IL-8, cortisol, glucose, and insulin. Muscle was analyzed for glycogen content and relative gene expression of 13 cytokines by using real-time quantitative RT-PCR. Plasma glucose and insulin were higher, and cortisol, IL-6, IL-10, and IL-1ra, but not IL-8, were significantly lower postexercise in CHO vs. Pla. Change in muscle glycogen content did not differ between CHO and Pla (P = 0.246). Muscle cytokine mRNA content was detected preexercise for seven cytokines in this order (highest to lowest): IL-15, TNF-a, IL-8, IL-1ß, IL-12p35, IL-6, and IFN-y. After subjects ran for 3 h, gene expression above prerun levels was measured for five of these cytokines: IL-1ß, IL-6, and IL-8 (large increases), and IL-10 and TNF-a (small increases). The increase in mRNA (fold difference from preexercise) was attenuated in CHO (15.9-fold) compared with Pla (35.2-fold) for IL-6 (P = 0.071) and IL-8 (CHO, 7.8-fold; Pla, 23.3-fold; P = 0.063). CHO compared with Pla beverage ingestion attenuates the increase in plasma IL-6, IL-10, and IL-1ra and gene expression for IL-6 and IL-8 in athletes running 3 h at 70% Vo2 max despite no differences in muscle glycogen content

Immune And Oxidative Changes During And Following The Western States Endurance Run

Changes in immune and oxidative stress parameters were measured in ultramarathon runners competing in the 160-km Western States Endurance Run. Forty-five runners agreed to provide blood and saliva samples the morning before the race event, at the 90-km aid station, and 5 - 10 min post-race. Upper respiratory tract infection (URTI) during the two-week period post-race was assessed retrospectively by telephone interviews. Forty subjects completed 90-km (race time, 13.1 ± 0.3 h), and 31 completed the 160-km race event (27.0 ± 0.4 h). The blood neutrophil and monocyte counts rose 249 % and 214 %, respectively, in the 31 finishers. Salivary IgA (sIgA) secretion rate decreased significantly from 508 ± 40 µg/min pre-race, to 287 ± 39 µg/min at 90-km, and 254 ± 30 µg/min post-race (50 % decrease). Significant increases were measured in cytokines at 90-km and post-race, with post-race IL-10 increasing 9.5-fold, IL-1ra 6.1-fold, IL-6 50.2-fold, and IL-8 2.5-fold over pre-race levels. Post-race indicators of oxidative stress, F2-isoprostane and lipid hydroperoxides, increased 33 % and 88 %, respectively. Pearson product-moment correlations revealed positive correlations at 90-km between F2-isoprostane and IL-6 (r = 0.31, p = 0.048), IL-10 (r = 0.31, p = 0.050), and IL-8 (r = 0.43, p = 0.005), but no other significant relationships between immune and oxidative stress indicators at 90-km and post-race. In the group of runners completing at least 90 km of the race, 26 % reported an URTI episode during the two-week period post-race. A low sIgA secretion rate at 90-km was the best predictor of post-race URTI (173 ± 34 µg/min in those who later acquired URTI compared to 325 ± 40 µg/min in those without URTI, p = 0.007). In conclusion, a modest correlation was found between cytokines and F2-isoprostane at 90-km when the greatest oxidative stress occurred, but no other significant correlations in immune and oxidative stress indicators during and following a 160-km ultramarathon race event were noted. About one in four ultramarathoners reported URTI during the two-week period post-race, and a low sIgA secretion rate mid-race best predicted URTI occurrence

Influence Of Vitamin C Supplementation On Oxidative And Immune Changes After An Ultramarathon

The purpose of this randomized study was to measure the influence of vitamin C (n = 15 runners) compared with placebo (n = 13 runners) supplementation on oxidative and immune changes in runners competing in an ultramarathon race. During the 7-day period before the race and on race day, subjects ingested in randomized, double-blind fashion 1,500 mg/day vitamin C or placebo. On race day, blood samples were collected 1 h before race, after 32 km of running, and then again immediately after race. Subjects in both groups maintained an intensity of 75% maximal heart rate throughout the ultramarathon race and ran a mean of 69 km (range: 48– 80 km) in 9.8 h (range: 5–12 h). Plasma ascorbic acid was markedly higher in the vitamin C compared with placebo group prerace and rose more strongly in the vitamin C group during the race (postrace: 3.21 ± 0.29 and 1.28 ± 0.12 µg/100 µl, respectively, P < 0.001). No significant group or interaction effects were measured for lipid hydroperoxide, F2-isoprostane, immune cell counts, plasma interleukin (IL)-6, IL-10, IL-1-receptor antagonist, or IL-8 concentrations, or mitogen-stimulated lymphocyte proliferation and IL-2 and IFN-y production. These data indicate that vitamin C supplementation in carbohydrate-fed runners does not serve as a countermeasure to oxidative and immune changes during or after a competitive ultramarathon race

Influence Of Vitamin C Supplementation On Oxidative And Salivary IgA Changes Following An Ultramarathon

This randomized study measured the influence of vitamin C (N=15) compared to placebo (N=13) supplementation on oxidative and salivary immunoglobulin A (sIgA) changes in runners competing in an ultramarathon race. Seven days prior to the race, subjects ingested in randomized, double-blind fashion three 500-mg tablets of vitamin C or placebo each day. On race day, blood and saliva samples were collected 1 h pre-race, after 32 km of running, and then again immediately post-race. During the race, runners received 1 l/h carbohydrate beverages (60 g/l) with vitamin C (150 mg/l) or without in a double-blinded fashion. The runners also ingested two to three carbohydrate gel packs per hour (25 g each). Subjects in both groups ran a mean of 69 km (range 48–80 km) in 9.8 h (range 5–12 h) and maintained an intensity of approximately 75% maximal heart rate (HRmax) throughout the ultramarathon race. Plasma ascorbic acid was higher in the vitamin C compared to placebo group pre-race, and increased significantly in the vitamin C group during the race [post-race, 3.21 (0.29) and 1.28 (0.12) µg/100 µl, respectively, P<0.001]. No significant group or interaction effects were measured for lipid hydroperoxide and F2-isoprostane, but both oxidative measures rose significantly during the ultramarathon race. Saliva volume, sIgA concentration, sIgA secretion and sIgA:saliva protein ratio all decreased significantly (P<0.001) during the race, but the pattern of change in all saliva measures did not differ significantly between groups. No significant correlations were found between post-race plasma vitamin C, oxidative, and saliva measures, except for a positive correlation between post-race serum cortisol and serum vitamin C (r=0.50, P=0.006). These data indicate that vitamin C supplementation in carbohydrate-fed runners does not serve as a countermeasure to oxidative and sIgA changes during or following a competitive ultramarathon race

n-3 Polyunsaturated Fatty Acids Do Not Alter Immune And Inflammation Measures In Endurance Athletes

The purpose of this study was to test the influence of 2.4 g/d fish oil n-3 polyunsaturated fatty acids (n-3 PUFA) over 6 wk on exercise performance, inflammation, and immune measures in 23 trained cyclists before and after a 3-d period of intense exercise. Participants were randomized to n-3 PUFA (n = 11; 2,000 mg eicosapentaenoic acid [EPA], 400 mg docosahexaenoic acid [DHA]) or placebo (n = 12) groups. They ingested supplements under double-blind methods for 6 wk before and during a 3-d period in which they cycled for 3 hr/d at ~57% Wmax with 10-km time trials inserted during the final 15 min of each 3-hr bout. Blood and saliva samples were collected before and after the 6-wk supplementation period, immediately after the 3-hr exercise bout on the third day, and 14 hr postexercise and analyzed for various immune-function and inflammation parameters. Supplementation with n-3 PUFA resulted in a significant increase in plasma EPA and DHA but had no effect on 10-km time-trial performance; preexercise outcome measures; exercise-induced increases in plasma cytokines, myeloperoxidase, blood total leukocytes, serum C-reactive protein, and creatine kinase; or the decrease in the salivary IgA:protein ratio. In conclusion, 6 wk supplementation with a large daily dose of n-3 PUFAs increased plasma EPA and DHA but had no effect on exercise performance or in countering measures of inflammation and immunity before or after a 3-d period of 9 hr of heavy exertion

Infuence Of 2-Weeks Ingestion Of High Chlorogenic Acid Coffee On Mood State, Performance, And Postexercise Inflammation And Oxidative Stress: A Randomized, Placebo-Controlled Trial

This study measured the influence of 2-weeks ingestion of high chlorogenic acid (CQA) coffee on postexercise inflammation and oxidative stress, with secondary outcomes including performance and mood state. Cyclists (N = 15) were randomized to CQA coffee or placebo (300 ml/day) for 2 weeks, participated in a 50-km cycling time trial, and then crossed over to the opposite condition with a 2-week washout period. Blood samples were collected pre- and postsupplementation, and immediately postexercise. CQA coffee was prepared using the Turkish method with 30 g lightly roasted, highly ground Hambela coffee beans in 300 ml boiling water, and provided 1,066 mg CQA and 474 mg caffeine versus 187 mg CQA and 33 mg caffeine for placebo. Plasma caffeine was higher with CQA coffee versus placebo after 2-weeks (3.3-fold) and postexercise (21.0-fold) (interaction effect, p < .001). Higher ferric reducing ability of plasma (FRAP) levels were measured after exercise with CQA coffee versus placebo (p = .01). No differences between CQA coffee and placebo were found for postexercise increases in plasma IL-6 (p = .74) and hydroxyoctadecadienoic acids (9 + 13 HODEs) (p = .99). Total mood disturbance (TMD) scores were lower with CQA coffee versus placebo (p = .04). 50-km cycling time performance and power did not differ between trials, with heart rate and ventilation higher with CQA coffee, especially after 30 min. In summary, despite more favorable TMD scores with CQA coffee, these data do not support the chronic use of coffee highly concentrated with chlorogenic acids and caffeine in mitigating postexercise inflammation or oxidative stress or improving 50-km cycling performance

A commercialized dietary supplement alleviates joint pain in community adults: a double-blind, placebo-controlled community trial

Background-The purpose of this study was to assess the effect of 8-weeks ingestion of a commercialized joint pain dietarysupplement (InstaflexTM Joint Support, Direct Digital, Charlotte, NC) compared to placebo on joint pain, stiffness, and function in adults with self-reported joint pain. InstaflexTM is a joint pain supplement containing glucosamine sulfate, methylsufonlylmethane (MSM), white willow bark extract (15% salicin), ginger root concentrate, boswella serrata extract(65% boswellic acid), turmeric root extract, cayenne, and hyaluronic acid.Methods- Subjects included 100 men and women, ages 50-75 years, with a history (>3 months) of joint pain, and were randomized to Instaflex™ or placebo (3 colored gel capsules per day for 8 weeks, double-blind administration). Subjectsagreed to avoid the use of non-steroidal anti-inflammatory drugs (NSAID) and all other medications and supplementsmtargeted for joint pain. Primary outcome measures were obtained pre- and post-study and included joint pain severity,stiffness, and function (Western Ontario and McMaster Universities [WOMAC]), and secondary outcome measures included health-related quality of life (Short Form 36 or SF-36), systemic inflammation (serum C-reactive protein and 9plasma cytokines), and physical function (6-minute walk test). Joint pain symptom severity was assessed bi-weekly using a12-point Likert visual scale (12-VS).Results- Joint pain severity was significantly reduced in Instaflex™ compared to placebo (8-week WOMAC, ?37% versus?16%, respectively, interaction effect P=0.025), with group differences using the 12-VS emerging by week 4 of the study(interaction effect, P=0.0125). Improvements in ability to perform daily activities and stiffness scores in Instaflex™ comparedto placebo were most evident for the 74% of subjects reporting knee pain (8-week WOMAC function score, ?39% versus?14%, respectively, interaction effect P=0.027; stiffness score, ?30% versus ?12%, respectively, interaction effect P=0.081). Patterns of change in SF-36, systemic inflammation biomarkers, and the 6-minute walk test did not differ significantly between groups during the 8-week studyConclusions-Results from this randomized, double blind, placebo-controlled community trial support the use of the Instaflex™ dietary supplement in alleviating joint pain severity in middle-aged and older adults, with mitigation of difficultyperforming daily activities most apparent in subjects with knee pain

Influence Of Pistachios On Performance And Exercise-Induced Inflammation, Oxidative Stress, Immune Dysfunction, And Metabolite Shifts In Cyclists: A Randomized, Crossover Trial

Objectives: Pistachio nut ingestion (3 oz./d, two weeks) was tested for effects on exercise performance and 21-h post-exercise recovery from inflammation, oxidative stress, immune dysfunction, and metabolite shifts. Methods: Using a randomized, crossover approach, cyclists (N = 19) engaged in two 75-km time trials after 2-weeks pistachio or no pistachio supplementation, with a 2-week washout period. Subjects came to the lab in an overnight fasted state, and ingested water only or 3 oz. pistachios with water before and during exercise. Blood samples were collected 45 min pre-exercise, and immediately post-, 1.5-h post-, and 21-h post-exercise, and analyzed for plasma cytokines, C-reactive protein (CRP), F2-isoprostanes (F2-IsoP), granulocyte phagocytosis (GPHAG) and oxidative burst activity (GOBA), and shifts in metabolites. Results: Performance time for the 75-km time trial was 4.8% slower under pistachio conditions (2.8460.11 and 2.7160.07 h, respectively, P = 0.034). Significant time effects were shown for plasma cytokines, CRP, F2-IsoP, GPHAG, and GOBA, with few group differences. Metabolomics analysis revealed 423 detectable compounds of known identity, with significant interaction effects for 19 metabolites, especially raffinose, (12Z)-9,10-Dihydroxyoctadec-12-enoate (9,10-DiHOME), and sucrose. Dietary intake of raffinose was 2.1960.15 and 0.3560.08 mg/d during the pistachio and no pistachio periods, and metabolomics revealed that colon raffinose and sucrose translocated to the circulation during exercise due to increased gut permeability. The post-exercise increase in plasma raffinose correlated significantly with 9,10-DiHOME and other oxidative stress metabolites.Conclusions: In summary, 2-weeks pistachio nut ingestion was associated with reduced 75-km cycling time trial performance and increased post-exercise plasma levels of raffinose, sucrose, and metabolites related to leukotoxic effects and oxidative stress