Marius Ooms

Vitamin D supplementation and fracture incidence in elderly persons. A randomized, placebo-controlled clinical trial

Vitamin D deficiency is common in elderly persons, especially those with hip fracture [1, 2]. It is caused by low exposure to sunshine, decreased synthesis of vitamin D3 in the aging skin, and a diet low in vitamin D [3, 4]. The mean vitamin D intake in elderly persons in the Netherlands is about 100 IU/d, half that of elderly persons in the United States [5]. Most of this vitamin D comes from margarine, which is the only vitamin D-supplemented food in the Netherlands (3 IU/g). In vitamin D deficiency, the low serum concentration of 25-hydroxyvitamin D [25(OH)D] leads to a low 1,25-dihydroxyvitamin D [1,25(OH)2D] concentration and then to a higher serum parathyroid hormone concentration, especially in the winter [6-10]. Histologically, the increased parathyroid activity is associated with high bone turnover, leading to cortical bone loss and low density bone [5, 11], which may lead to hip fracture. We previously studied the effects of vitamin D supplementation in residents of a home for the elderly and residents of a nursing home [10]. Vitamin D3, 400 IU/d, led to an adequate increase of the serum 25(OH)D concentration, to a small but significant increase of the serum 1,25(OH)2D concentration, and to a decrease of the serum concentration of intact parathyroid hormone. It was recently observed [12, 13] that bone mineral density at the hip is positively related to serum 25(OH)D concentration in postmenopausal and elderly women. Therefore, it might be expected that vitamin D supplementation would increase bone mineral density in elderly persons deficient in vitamin D. In line with this expectation, it was shown that vitamin D supplementation prevented bone loss from the spine during the winter in postmenopausal women [14]. These results suggest that vitamin D supplementation may reduce the incidence of hip fractures, because bone strength shows a strong correlation with bone mineral density [15]. However, increasing bone mineral density through a therapeutic intervention does not necessarily lead to increased bone strength, as has been shown with sodium fluoride [16]. Bone structure and bone quality are also determinants of bone strength [17], and falls are a risk factor for hip fractures [18]. Therefore, hip fracture should be the outcome criterion in studies on the effect of vitamin D supplementation. Intervention studies on the prevention of osteoporotic fractures necessitate large numbers of patients, because the outcome has an annual incidence of 0.5% to 4% in the elderly population [19]. We report the results of a large-scale, prospective study on the effect of vitamin D supplementation on the incidence of hip and other osteoporotic fractures. Methods Participants The study included 2578 persons (1916 women and 662 men) 70 years of age and older (mean age SD, 80 6 years; range, 70 to 97 years). Participants were recruited from general practitioners, from apartment houses for elderly persons, and from homes for elderly persons in Amsterdam and its vicinity. Persons recruited from practitioners were living independently; those recruited from apartment houses and homes were receiving some care, but less than they would have received in a nursing home. Participants had to be reasonably healthy and able to give informed consent. Persons with a history of hip fracture or total hip arthroplasty, known hypercalcemia, sarcoidosis, or recent urolithiasis (< 5 years earlier) were excluded. Patients who had diseases or who used medications that influence bone metabolism (such as thyroid disease or glucocorticoid medication) were not excluded. The spontaneous use of vitamin D supplements and multivitamins was discouraged, but the prescription practices of the general practitioners were not altered. All vitamin use was carefully documented. The study was approved by the Ethical Review Board of the Vrije Universiteit Hospital, and all participants gave informed consent. Study Design After checking the inclusion and exclusion criteria and obtaining informed consent, the participants were randomly assigned to receive either active treatment with vitamin D3 or placebo. The study was double-blind, and randomization was done in blocks of 10 per general practice, apartment house, or home. Randomization lists were made using a computerized random-number generator. Lists in sealed envelopes were sent to the hospital pharmacy for assignment. Each participant took either one tablet per day that contained vitamin D3, 400 IU, or one placebo tablet per day that was identical in appearance and taste to the vitamin tablet. After enrollment, the participants received the first container of tablets (210 tablets). The container was replaced every 6 months with a full container. All participants were also advised in writing to consume at least three servings of dairy products per day (for example, 1 glass of milk, 1 cup of yogurt, and 1 slice of cheese) to ensure a calcium intake of at least 800 to 1000 mg/d. The study was started in August 1988. The last participant was enrolled in December 1990, and all participants had stopped using study medication by December 1993. The follow-up period had been planned to last no more than 3 years, but because the number of hip fractures during the study was lower than expected, a 6-month extension was planned. The study participants thus received medication for 3 to 3.5 years; those who received it for 3.5 years were those who consented to the 6-month extension. Total follow-up was to a maximum of 4 years. Data collected at baseline included an outdoor activity score (1 equals going outdoors less than once a week; 2 equals going outdoors 1 or 2 times per week; and 3 equals going outdoors 3 times per week or more) and a score for sunshine exposure (when outside: 1 equals in the shade as much as possible; 2 equals sometimes in sunshine; 3 equals much exposure to sunshine). These scores show a positive relation with serum 25(OH)D concentration [3]. Mobility was estimated by a walking score that ranged from 1 (unable to walk) to 5 (walks independently a fair distance on any surface) [20]. The dietary calcium intake from dairy products was estimated in a subset of 348 women by using a questionnaire, as described previously [21]. The participants were evaluated annually with a questionnaire on hip fractures, other peripheral fractures, outdoor score, sunshine exposure score, use of vitamin supplements, and walking score. Each general practitioner or caretaker was asked to immediately report change of address, hip fracture, or death. Hip fracture and death were verified by the general practitioner. All participants were followed for the maximal period of 4 years if possible, even if they had stopped using the trial medication, had sustained a fracture, or had moved to another city. To investigate possible selection bias, 267 potential participants in a home for the elderly and its adjunct apartments (all residents of the institution) were studied for baseline characteristics, including age, sex, sunshine exposure score, outdoor score, walking score, and reasons for nonparticipation. Compliance was checked when the tablet containers were replaced (every 6 months), by questionnaire (every year), and by measurement of the serum 25(OH)D concentration. Serum 25(OH)D concentration was measured at baseline and after 1 year in 270 persons who participated in a substudy investigating the effect of vitamin D supplementation on bone mineral density and bone turnover variables. This substudy included a nonrandom sample of participants from several apartment houses and homes for the elderly and is described in detail elsewhere [21]. In the same substudy, dietary calcium intake from diary products was assessed. Serum 25(OH)D concentration was also estimated during the third year of the study in February and March in a random sample of 96 participants drawn from the remaining study population. These participants received a letter giving them an appointment within 10 days; the blood samples were drawn at home. Serum 25(OH)D concentration was measured by competitive protein binding assay after being purified by gradient high-pressure liquid chromatography. The intra- and interassay coefficients of variation were 5% and 6%, respectively [22]. Statistical Analysis Baseline data of the vitamin D group and the placebo group were compared using t-tests (age, calcium intake), chi-square tests (sex, residence), and Wilcoxon rank-sum tests (scores). The serum 25(OH)D concentrations of both groups were compared using t-tests. Data on fractures and mortality were analyzed by survival analysis using log-rank tests, Cox proportional-hazards regression, and hazard rate ratios [23]. Hip fractures are presented using the Kaplan-Meier method. All participants were kept in the study as long as possible. The data were analyzed in two ways. The intention-to-treat analysis included all randomly assigned participants for either the total follow-up period or until fracture, death, or loss to follow-up. The active treatment analysis included the participants as long as they stated that they were using the trial medication. Thus, the participants were included in the active treatment analysis until they stopped using the trial medication, regardless of whether a fracture occurred after they had stopped. Age, sex, and residence were added in both analyses as covariates to the Cox regression model. Because outdoor score, sunshine score, and walking score were interrelated (correlation coefficients ranging from 0.21 to 0.59) and were likely to indicate general health or mobility, they were averaged over the years and added up to a sum score. For this purpose, the walking score was simplified (1, 2, or 3 equals 1; 4 equals 2; 5 equals 3), because the lower walking scores applied to a few participants only. The resulting total score, ranging from 3 to 9, was entered as a covariate in the model. The level of compliance (weekly intake as reported on the

Periodic Seasonal Reg-ARFIMA-GARCH Models for Daily Electricity Spot Prices

Novel periodic extensions of dynamic long-memory regression models with autoregressive conditional heteroscedastic errors are considered for the analysis of daily electricity spot prices. The parameters of the model with mean and variance specifications are estimated simultaneously by the method of approximate maximum likelihood. The methods are implemented for time series of 1,200–4,400 daily price observations in four European power markets. Apart from persistence, heteroscedasticity, and extreme observations in prices, a novel empirical finding is the importance of day-of-the-week periodicity in the autocovariance function of electricity spot prices. In particular, the very persistent daily log prices from the Nord Pool power exchange of Norway are effectively modeled by our framework, which is also extended with explanatory variables to capture supply-and-demand effects. The daily log prices of the other three electricity markets—EEX in Germany, Powernext in France, and APX in The Netherlands—are less persistent, but periodicity is also highly significant. The dynamic behavior differs from market to market and depends primarily on the method of power generation: hydro power, power generated from fossil fuels, or nuclear power. The article improves on existing models in capturing the memory characteristics, which are important in derivative pricing and real option analysis.

Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models

Computational aspects of likelihood-based estimation of univariate ARFIMA(p,d,q) models are addressed. Particular issues are the numerically stable evaluation of the autocovariances and efficient handling of the variance matrix which has dimension equal to the sample size. It is shown how efficient computation and simulation are feasible, even for large samples. Implementation of analytical bias corrections in ARFIMA regression models is also discussed.

Inflation, forecast intervals and long memory regression models

We examine recursive out-of-sample forecasting of monthly postwarU.S. core inflation and log price levels. We use theautoregressive fractionally integrated moving average model withexplanatory variables (ARFIMAX). Our analysis suggests asignificant explanatory power of leading indicators associatedwith macroeconomic activity and monetary conditions forforecasting horizons up to two years. Even after correcting forthe effect of explanatory variables, there is conclusive evidenceof both fractional integration and structural breaks in the meanand variance of inflation in the 1970s and 1980s and weincorporate these breaks in the forecasting model for the 1980sand 1990s. We compare the results of the fractionally integratedARFIMA(0,d,0) model with those for ARIMA(1,d,1) models withfixed order of d=0 and d=1 for inflation. Comparing meansquared forecast errors, we find that the ARMA(1,1) model performsworse than the other models over our evaluation period 1984-1999.The ARIMA(1,1,1) model provides the best forecasts, but itsmulti-step forecast intervals are too large.

Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation

Practical aspects of likelihood-based inference and forecasting of series with long memory are considered, based on the arfima(p; d; q) model with deterministic regressors. Sampling characteristics of approximate and exact first-order asymptotic methods are compared. The analysis is extended using modified profile likelihood analysis, which is a higher-order asymptotic method suggested by Cox and Reid (1987). The relevance of the differences between the methods is investigated for models and forecasts of monthly core consumer price inflation in the US and quarterly overall consumer price inflation in the UK.

A periodic long-memory model for quarterly UK inflation

We consider an extension of the fractionally integrated ARIMA(0, d, 0) model for quarterly UK inflation, where we allow the fractional integration parameter d to vary with the season s. This periodic ARFIMA(0, d, 0) model does not only provide an informative in-sample description, it may also be useful for out-of-sample forecasting. The main result is that the integration parameter in the first two quarters is significantly larger than that in the last two quarters.

Dynamic factors in periodic time-varying regressions with an application to hourly electricity load modelling

A dynamic multivariate periodic regression model for hourly data is considered. The dependent hourly univariate time series is represented as a daily multivariate time series model with 24 regression equations. The regression coefficients differ across equations (or hours) and vary stochastically over days. Since an unrestricted model contains many unknown parameters, an effective methodology is developed within the state-space framework that imposes common dynamic factors for the parameters that drive the dynamics across different equations. The factor model approach leads to more precise estimates of the coefficients. A simulation study for a basic version of the model illustrates the increased precision against a set of univariate benchmark models. The empirical study is for a long time series of French national hourly electricity loads with weather variables and calendar variables as regressors. The empirical results are discussed from both a signal extraction and a forecasting standpoint.

Forecasting daily time series using periodic unobserved components time series models

A periodic time series analysis is explored in the context of unobserved components time series models that include stochastic time functions for trend, seasonal and irregular effects. Periodic time series models allow dynamic characteristics (autocovariances) to depend on the period of the year, month, week or day. In the standard multivariate approach one can interpret a periodic time series analysis as a simultaneous treatment of typically yearly time series where each series is related to a particular season. Here, the periodic analysis applies to a vector of monthly time series related to each day of the month. Particular focus is on the forecasting performance and therefore on the underlying periodic forecast function, defined by the in-sample observation weights for producing (multi-step) forecasts. These weight patterns facilitate the interpretation of periodic model extensions. A statistical state space approach is used to estimate the model and allows for irregularly spaced observations in daily time series. Recent algorithms are adopted for the computation of observation weights for forecasting based on state space models with regressor variables. The methodology is illustrated for daily Dutch tax revenues that appear to have periodic dynamic properties. The dimension of our periodic unobserved components model is relatively large as we allow each element (day) of the vector of monthly time series to have a changing seasonal pattern. Nevertheless, even with only five years of data we find that the increased periodic flexibility can help in out-of-sample forecasting for two extra years of data.

On the effect of seasonal adjustment on the log-periodogram regression

Abstract We discuss how prior regression on seasonal dummies leads to singularities in log-periodogram regression procedures for the detection of long memory. We suggest a modified procedure. We illustrate the problems using monthly inflation data from [ Hassler and Wolters, 1995 , Long Memory in Inflation Rates: International Evidence, Journal of Business and Economic Statistics 13, 37–46]. Our new estimates reconfirm their basic finding.

Long memory with stochastic variance model: A recursive analysis for US inflation

The time series characteristics of postwar US inflation have been found to vary over time. The changes are investigated in a model-based analysis where the time series of inflation is specified by a long memory autoregressive fractionally integrated moving average process with its variance modelled by a stochastic volatility process. Estimates of the parameters are obtained by a Monte Carlo maximum likelihood method. A long sample of monthly core inflation is considered in the analysis as well as subsamples of varying length. The empirical results reveal major changes in the variance, in the order of integration, in the short memory characteristics, and in the volatility of volatility. The findings provide further evidence that the time series properties of inflation are not stable over time.