898 resultados para least absolute deviation (LAD) fitting


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This paper aims to examine changes in common longevity and variability of the adult life span, and attempts to answer whether or not the compression of mortality continues in Switzerland in the years 1876-2005. The results show that the negative relationships between the large increase in the adult modal age at death, observed at least from the 1920s, and the decrease in the standard deviation of the ages at deaths occurring above it, illustrate a significant compression of adult mortality. Typical adult longevity increased by about 10% during the last fifty years in Switzerland, and adult heterogeneity in the age at death decreased in the same proportion. This analysis has not found any evidence suggesting that we are approaching longevity limits in term of modal or even maximum life spans. It ascertains a slowdown in the reduction of adult heterogeneity in longevity, already observed in Japan and other low mortality countries.

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The objective of this work was to evaluate a generalized response function to the atmospheric CO2 concentration [f(CO2)] by the radiation use efficiency (RUE) in rice. Experimental data on RUE at different CO2 concentrations were collected from rice trials performed in several locations around the world. RUE data were then normalized, so that all RUE at current CO2 concentration were equal to 1. The response function was obtained by fitting normalized RUE versus CO2 concentration to a Morgan-Mercer-Flodin (MMF) function, and by using Marquardt's method to estimate the model coefficients. Goodness of fit was measured by the standard deviation of the estimated coefficients, the coefficient of determination (R²), and the root mean square error (RMSE). The f(CO2) describes a nonlinear sigmoidal response of RUE in rice, in function of the atmospheric CO2 concentration, which has an ecophysiological background, and, therefore, renders a robust function that can be easily coupled to rice simulation models, besides covering the range of CO2 emissions for the next generation of climate scenarios for the 21st century.

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Tämän diplomityön tarkoituksena oli arvioida UPM-Kymmene Oyj, Kaukaan sellutehtaan havukuitulinjan uuden valkaisusäätömenetelmän, kompensoidun kappakerroinsäädön, ja vaaleusanalysaattoreiden käyttöönoton vaikutukset klooridioksidikulutukseen ja sellun laatuun. Kirjallisuusosassa esitelläänvalkaisun tärkeimpiä on-line ja in-line mittalaitteita sekä niitä hyödyntäviä säätöratkaisuja. Tiettävästi paras saatavilla oleva säätömenetelmä, kompensoitu kappakerroinsäätö määrittää klooridioksidiannoksen vaiheeseen tulevan massan kappaluvun tai vaaleuden perusteella. Valkaisukemikaaliannos optimoidaan jatkuvatoimisten vaaleus- ja jäännösmittausten sekä vaiheen jälkeisen saavutetun kappaluvuntai vaaleuden takaisinkytkennällä. Kokeellisessa osassa arvioitiin havulinjan valkaisusäätömenetelmän käyttöönoton vaikutukset klooridioksidikulutuksiin ja sellun laatuun vertailemalla uuden ja vanhan säätömenetelmän aikaisia kemikaalikulutuksia sekä välikappaluvun ja loppuvaaleuden itseisarvopoikkeamia tavoitteistaan. Lisäksi selvitettiin annossäätöön ja kompensoituun vaaleussäätöön perustuvan vanhan sekä kompensoitua kappakerroinsäätöä soveltavan uuden säätömenetelmän toimintaperiaatteet. Työssä kartoitettiin myös valkaisulinjan tarpeet uusille mittalaitteille sekä analysaattorin mittausten vertailukelpoisuus laboratorioanalyysien kanssa. Edelleen työssä arvioitiin tehtaan X koivuvalkaisulinjan uuden säätömenetelmän toimivuus. Kompensoidun kappakerroinsäädön käyttöönoton myötä valkaisun klooridioksidikulutukset pienenivät sekä välikappaluku ja loppuvaaleus saatiin pidettyä lähempänä tavoitteittaan. Säätömenetelmän toimivuuttaedisti vaaleusanalysaattoreiden mittausten korreloivuus laboratorioanalyysien kanssa. Vastaavat vaikutukset kemikaalikulutuksiin ja sellun laatuun havaittiin myös tehtaan X valkaisusäädön käyttöönotosta.

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Yleisesti tiedetään hitsin pintageometrian vaikuttavan rakenteen väsymislujuuteen. Nopean, edullisen ja luotettavan pintageometrian mittausmenetelmän kehittäminen on askel kohti tarkempaa ja varmempaa rakenteen väsymislujuuden tarkastelua. Tässä työssä on tutkittu hitsejä, joiden pinnan geometria on mitattu norjalaisen SINTEF -yrityksen kehittämällä rakenteellisen valon menetelmällä. Osana työtä kehitettiin MatLab -pohjainen ohjelma, jolla jälkikäsitellään mittauksesta saadut x-y-z -mittapisteet. Mittausdatan jälkikäsittelyssä saadaan mittauksesta määritettyähitsin reunan pyöristys, liittymäkulma, a-mitta, reunahaava ja kateettisuhde. Kehitettyä menetelmää käyttämällä mitattiin lähes 300 voimaakantamatontaristiliitoksen hitsiä. Mittaustuloksia verrattiin vastaavista kappaleista tehtyihin hiemittauksiin. Manuaalisen hieestä tehdyn mittauksen havaittiin olevan tarkempi ja pystyttiin havaitsemaan paikallisempia muotoja. Rakenteellisen valon mittauksissa tapahtunut heijastelu saatiin pienenemään käsittelemällä mitattava pinta mattavalkoisella maalilla. Rakenteellisen valon mittatarkkuudeksi saatiin noin 0,2 mm. Pohjautuen mitattuun hitsin reunan pyöristykseen ja liittymäkulmaan voidaan yksinkertaista kaavaa käyttämällä laskea hitsin jännityskonsentraatio ja näin saada alkuarvaus väsymislujuudelle. Myös muiden tekijöiden tiedetään vaikuttavan hitsin väsymislujuuteen, joten pyöristyksen ja liittymäkulman avulla tehdyt arviot eivät ole absoluuttisen oikeita. Tämä havaittiin väsytyskokeilla, joista yhdessä väsymisvaurio ei syntynyt suurimmankaan jännityskonsentraation alueella.

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BACKGROUND: While rifaximin was able to improve symptoms in patients with irritable bowel syndrome (IBS) in phase III trials, these results are yet to be repeated in phase IV studies. AIM: To evaluate the treatment response to rifaximin in IBS patients in a phase IV trial. METHODS: IBS patients underwent lactulose hydrogen breath testing (LHBT). LHBT-positive patients were treated with rifaximin for 14 days. Prior to treatment as well as at week 4 and 14 following the start of rifaximin treatment, patients completed a questionnaire assessing symptom severity on a Likert scale from 0 to 10. RESULTS: One hundred and six of 150 IBS patients (71%) were LHBT-positive and treated with rifaximin. As assessed at week 4 following commencement of the therapy, rifaximin provided significant improvement of the following IBS-associated symptoms: bloating (5.5±2.6 before the start of the treatment vs. 3.6±2.7 at week 4, P<0.001), flatulence (5.0±2.7 vs. 4.0±2.7, P=0.015), diarrhoea (2.9±2.4 vs. 2.0±2.4, P=0.005) and abdominal pain (4.8±2.7 vs. 3.3±2.5, P<0.001). Overall well-being also significantly improved (3.9 ± 2.4 vs. 2.7 ± 2.3, P < 0.001). Similar improvements in IBS symptoms were obtained at week 14. Eighty-six per cent of patients undergoing repetitive LHBT (55/64) tested negative at week 4. CONCLUSIONS: We found a high percentage of LHBT-positive IBS patients. IBS-associated symptoms (bloating, flatulence, diarrhoea, pain) were improved for a period of 3 months following 2 weeks of treatment with rifaximin. We conclude that rifaximin treatment alleviates symptoms in LHBT-positive IBS patients.

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INTRODUCTION: Preoperative scores are widely used predictors of complications after major surgery. These scores, however, are not widely used in transurethral procedures. The aim of this study was to assess the value of the Charlson Comorbidity Index (CCI), the age-adjusted CCI, the American Society of Anesthesiologist score (ASA) and the Nutritional Risk Score (NRS) in predicting early morbidity after transurethral urological procedures. METHODS: Consecutive patients undergoing transurethral resection of the bladder or the prostate were prospectively enrolled. The scores were calculated preoperatively; 30-day complications were prospectively recorded according to the Dindo-Clavien classification. Univariate logistic regression was performed to investigate the value of each score and of other factors (i.e., age, sex, body mass index, anemia, smoking habit, type of operation and anaesthesia) as predictors of complications. A multivariate model was then calculated using these predictors. RESULTS: Overall, 197 patients were included. The mean age was 72 (standard deviation ± 10). In total, 26.9% patients had at least 1 complication. Using univariate analysis, we found that each score significantly predicted complications. In multivariate analysis, only the ASA (odds ration [OR] 2.11; 95% confidence interval [CI] 1.01-4.43) and the NRS (OR 2.42; 95% CI 1.56-3.74) remained independent predictors. The best model incorporated ASA, NRS and gender, and predicted morbidity with an area under the curve of 76%. Our study's main limitations are population heterogeneity and limited sample size. CONCLUSION: The ASA and the NRS are important and independent determinants of early morbidity after transurethral procedures. The use of these indices may assist clinicians in the decision-making process to balance the possible benefits of transurethral procedures with the potential risks.

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Biological scaling analyses employing the widely used bivariate allometric model are beset by at least four interacting problems: (1) choice of an appropriate best-fit line with due attention to the influence of outliers; (2) objective recognition of divergent subsets in the data (allometric grades); (3) potential restrictions on statistical independence resulting from phylogenetic inertia; and (4) the need for extreme caution in inferring causation from correlation. A new non-parametric line-fitting technique has been developed that eliminates requirements for normality of distribution, greatly reduces the influence of outliers and permits objective recognition of grade shifts in substantial datasets. This technique is applied in scaling analyses of mammalian gestation periods and of neonatal body mass in primates. These analyses feed into a re-examination, conducted with partial correlation analysis, of the maternal energy hypothesis relating to mammalian brain evolution, which suggests links between body size and brain size in neonates and adults, gestation period and basal metabolic rate. Much has been made of the potential problem of phylogenetic inertia as a confounding factor in scaling analyses. However, this problem may be less severe than suspected earlier because nested analyses of variance conducted on residual variation (rather than on raw values) reveals that there is considerable variance at low taxonomic levels. In fact, limited divergence in body size between closely related species is one of the prime examples of phylogenetic inertia. One common approach to eliminating perceived problems of phylogenetic inertia in allometric analyses has been calculation of 'independent contrast values'. It is demonstrated that the reasoning behind this approach is flawed in several ways. Calculation of contrast values for closely related species of similar body size is, in fact, highly questionable, particularly when there are major deviations from the best-fit line for the scaling relationship under scrutiny.

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The three essays constituting this thesis focus on financing and cash management policy. The first essay aims to shed light on why firms issue debt so conservatively. In particular, it examines the effects of shareholder and creditor protection on capital structure choices. It starts by building a contingent claims model where financing policy results from a trade-off between tax benefits, contracting costs and agency costs. In this setup, controlling shareholders can divert part of the firms' cash ows as private benefits at the expense of minority share- holders. In addition, shareholders as a class can behave strategically at the time of default leading to deviations from the absolute priority rule. The analysis demonstrates that investor protection is a first order determinant of firms' financing choices and that conflicts of interests between firm claimholders may help explain the level and cross-sectional variation of observed leverage ratios. The second essay focuses on the practical relevance of agency conflicts. De- spite the theoretical development of the literature on agency conflicts and firm policy choices, the magnitude of manager-shareholder conflicts is still an open question. This essay proposes a methodology for quantifying these agency conflicts. To do so, it examines the impact of managerial entrenchment on corporate financing decisions. It builds a dynamic contingent claims model in which managers do not act in the best interest of shareholders, but rather pursue private benefits at the expense of shareholders. Managers have discretion over financing and dividend policies. However, shareholders can remove the manager at a cost. The analysis demonstrates that entrenched managers restructure less frequently and issue less debt than optimal for shareholders. I take the model to the data and use observed financing choices to provide firm-specific estimates of the degree of managerial entrenchment. Using structural econometrics, I find costs of control challenges of 2-7% on average (.8-5% at median). The estimates of the agency costs vary with variables that one expects to determine managerial incentives. In addition, these costs are sufficient to resolve the low- and zero-leverage puzzles and explain the time series of observed leverage ratios. Finally, the analysis shows that governance mechanisms significantly affect the value of control and firms' financing decisions. The third essay is concerned with the documented time trend in corporate cash holdings by Bates, Kahle and Stulz (BKS,2003). BKS find that firms' cash holdings double from 10% to 20% over the 1980 to 2005 period. This essay provides an explanation of this phenomenon by examining the effects of product market competition on firms' cash holdings in the presence of financial constraints. It develops a real options model in which cash holdings may be used to cover unexpected operating losses and avoid inefficient closure. The model generates new predictions relating cash holdings to firm and industry characteristics such as the intensity of competition, cash flow volatility, or financing constraints. The empirical examination of the model shows strong support of model's predictions. In addition, it shows that the time trend in cash holdings documented by BKS can be at least partly attributed to a competition effect.

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Gas-liquid mass transfer is an important issue in the design and operation of many chemical unit operations. Despite its importance, the evaluation of gas-liquid mass transfer is not straightforward due to the complex nature of the phenomena involved. In this thesis gas-liquid mass transfer was evaluated in three different gas-liquid reactors in a traditional way by measuring the volumetric mass transfer coefficient (kLa). The studied reactors were a bubble column with a T-junction two-phase nozzle for gas dispersion, an industrial scale bubble column reactor for the oxidation of tetrahydroanthrahydroquinone and a concurrent downflow structured bed.The main drawback of this approach is that the obtained correlations give only the average volumetric mass transfer coefficient, which is dependent on average conditions. Moreover, the obtained correlations are valid only for the studied geometry and for the chemical system used in the measurements. In principle, a more fundamental approach is to estimate the interfacial area available for mass transfer from bubble size distributions obtained by solution of population balance equations. This approach has been used in this thesis by developing a population balance model for a bubble column together with phenomenological models for bubble breakage and coalescence. The parameters of the bubble breakage rate and coalescence rate models were estimated by comparing the measured and calculated bubble sizes. The coalescence models always have at least one experimental parameter. This is because the bubble coalescence depends on liquid composition in a way which is difficult to evaluate using known physical properties. The coalescence properties of some model solutions were evaluated by measuring the time that a bubble rests at the free liquid-gas interface before coalescing (the so-calledpersistence time or rest time). The measured persistence times range from 10 msup to 15 s depending on the solution. The coalescence was never found to be instantaneous. The bubble oscillates up and down at the interface at least a coupleof times before coalescence takes place. The measured persistence times were compared to coalescence times obtained by parameter fitting using measured bubble size distributions in a bubble column and a bubble column population balance model. For short persistence times, the persistence and coalescence times are in good agreement. For longer persistence times, however, the persistence times are at least an order of magnitude longer than the corresponding coalescence times from parameter fitting. This discrepancy may be attributed to the uncertainties concerning the estimation of energy dissipation rates, collision rates and mechanisms and contact times of the bubbles.

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Thedirect torque control (DTC) has become an accepted vector control method besidethe current vector control. The DTC was first applied to asynchronous machines,and has later been applied also to synchronous machines. This thesis analyses the application of the DTC to permanent magnet synchronous machines (PMSM). In order to take the full advantage of the DTC, the PMSM has to be properly dimensioned. Therefore the effect of the motor parameters is analysed taking the control principle into account. Based on the analysis, a parameter selection procedure is presented. The analysis and the selection procedure utilize nonlinear optimization methods. The key element of a direct torque controlled drive is the estimation of the stator flux linkage. Different estimation methods - a combination of current and voltage models and improved integration methods - are analysed. The effect of an incorrect measured rotor angle in the current model is analysed andan error detection and compensation method is presented. The dynamic performance of an earlier presented sensorless flux estimation method is made better by improving the dynamic performance of the low-pass filter used and by adapting the correction of the flux linkage to torque changes. A method for the estimation ofthe initial angle of the rotor is presented. The method is based on measuring the inductance of the machine in several directions and fitting the measurements into a model. The model is nonlinear with respect to the rotor angle and therefore a nonlinear least squares optimization method is needed in the procedure. A commonly used current vector control scheme is the minimum current control. In the DTC the stator flux linkage reference is usually kept constant. Achieving the minimum current requires the control of the reference. An on-line method to perform the minimization of the current by controlling the stator flux linkage reference is presented. Also, the control of the reference above the base speed is considered. A new estimation flux linkage is introduced for the estimation of the parameters of the machine model. In order to utilize the flux linkage estimates in off-line parameter estimation, the integration methods are improved. An adaptive correction is used in the same way as in the estimation of the controller stator flux linkage. The presented parameter estimation methods are then used in aself-commissioning scheme. The proposed methods are tested with a laboratory drive, which consists of a commercial inverter hardware with a modified software and several prototype PMSMs.

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Belt-drive systems have been and still are the most commonly used power transmission form in various applications of different scale and use. The peculiar features of the dynamics of the belt-drives include highly nonlinear deformation,large rigid body motion, a dynamical contact through a dry friction interface between the belt and pulleys with sticking and slipping zones, cyclic tension of the belt during the operation and creeping of the belt against the pulleys. The life of the belt-drive is critically related on these features, and therefore, amodel which can be used to study the correlations between the initial values and the responses of the belt-drives is a valuable source of information for the development process of the belt-drives. Traditionally, the finite element models of the belt-drives consist of a large number of elements thatmay lead to computational inefficiency. In this research, the beneficial features of the absolute nodal coordinate formulation are utilized in the modeling of the belt-drives in order to fulfill the following requirements for the successful and efficient analysis of the belt-drive systems: the exact modeling of the rigid body inertia during an arbitrary rigid body motion, the consideration of theeffect of the shear deformation, the exact description of the highly nonlinear deformations and a simple and realistic description of the contact. The use of distributed contact forces and high order beam and plate elements based on the absolute nodal coordinate formulation are applied to the modeling of the belt-drives in two- and three-dimensional cases. According to the numerical results, a realistic behavior of the belt-drives can be obtained with a significantly smaller number of elements and degrees of freedom in comparison to the previously published finite element models of belt-drives. The results of theexamples demonstrate the functionality and suitability of the absolute nodal coordinate formulation for the computationally efficient and realistic modeling ofbelt-drives. This study also introduces an approach to avoid the problems related to the use of the continuum mechanics approach in the definition of elastic forces on the absolute nodal coordinate formulation. This approach is applied to a new computationally efficient two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation. The proposed beam element uses a linear displacement field neglecting higher-order terms and a reduced number of nodal coordinates, which leads to fewer degrees of freedom in a finite element.

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This paper describes a mesurement system designed to register the displacement of the legs using a two-dimensional laser range sensor with a scanning plane parallel to the ground and extract gait parameters. In the proposed methodology, the position of the legs is estimated by fitting two circles with the laser points that define their contour and the gait parameters are extracted applying a step-line model to the estimated displacement of the legs to reduce uncertainty in the determination of the stand and swing phase of the gait. Results obtained in a range up to 8 m shows that the systematic error in the location of one static leg is lower than 10 mm with and standard deviation lower than 8 mm; this deviation increases to 11 mm in the case of a moving leg. The proposed measurement system has been applied to estimate the gait parameters of six volunteers in a preliminary walking experiment.

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Transmission of drug-resistant pathogens presents an almost-universal challenge for fighting infectious diseases. Transmitted drug resistance mutations (TDRM) can persist in the absence of drugs for considerable time. It is generally believed that differential TDRM-persistence is caused, at least partially, by variations in TDRM-fitness-costs. However, in vivo epidemiological evidence for the impact of fitness costs on TDRM-persistence is rare. Here, we studied the persistence of TDRM in HIV-1 using longitudinally-sampled nucleotide sequences from the Swiss-HIV-Cohort-Study (SHCS). All treatment-naïve individuals with TDRM at baseline were included. Persistence of TDRM was quantified via reversion rates (RR) determined with interval-censored survival models. Fitness costs of TDRM were estimated in the genetic background in which they occurred using a previously published and validated machine-learning algorithm (based on in vitro replicative capacities) and were included in the survival models as explanatory variables. In 857 sequential samples from 168 treatment-naïve patients, 17 TDRM were analyzed. RR varied substantially and ranged from 174.0/100-person-years;CI=[51.4, 588.8] (for 184V) to 2.7/100-person-years;[0.7, 10.9] (for 215D). RR increased significantly with fitness cost (increase by 1.6[1.3,2.0] per standard deviation of fitness costs). When subdividing fitness costs into the average fitness cost of a given mutation and the deviation from the average fitness cost of a mutation in a given genetic background, we found that both components were significantly associated with reversion-rates. Our results show that the substantial variations of TDRM persistence in the absence of drugs are associated with fitness-cost differences both among mutations and among different genetic backgrounds for the same mutation.

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BACKGROUND: In acute respiratory failure, arterial blood gas analysis (ABG) is used to diagnose hypercapnia. Once non-invasive ventilation (NIV) is initiated, ABG should at least be repeated within 1 h to assess PaCO2 response to treatment in order to help detect NIV failure. The main aim of this study was to assess whether measuring end-tidal CO2 (EtCO2) with a dedicated naso-buccal sensor during NIV could predict PaCO2 variation and/or PaCO2 absolute values. The additional aim was to assess whether active or passive prolonged expiratory maneuvers could improve the agreement between expiratory CO2 and PaCO2. METHODS: This is a prospective study in adult patients suffering from acute hypercapnic respiratory failure (PaCO2 ≥ 45 mmHg) treated with NIV. EtCO2 and expiratory CO2 values during active and passive expiratory maneuvers were measured using a dedicated naso-buccal sensor and compared to concomitant PaCO2 values. The agreement between two consecutive values of EtCO2 (delta EtCO2) and two consecutive values of PaCO2 (delta PaCO2) and between PaCO2 and concomitant expiratory CO2 values was assessed using the Bland and Altman method adjusted for the effects of repeated measurements. RESULTS: Fifty-four datasets from a population of 11 patients (8 COPD and 3 non-COPD patients), were included in the analysis. PaCO2 values ranged from 39 to 80 mmHg, and EtCO2 from 12 to 68 mmHg. In the observed agreement between delta EtCO2 and deltaPaCO2, bias was -0.3 mmHg, and limits of agreement were -17.8 and 17.2 mmHg. In agreement between PaCO2 and EtCO2, bias was 14.7 mmHg, and limits of agreement were -6.6 and 36.1 mmHg. Adding active and passive expiration maneuvers did not improve PaCO2 prediction. CONCLUSIONS: During NIV delivered for acute hypercapnic respiratory failure, measuring EtCO2 using a dedicating naso-buccal sensor was inaccurate to predict both PaCO2 and PaCO2 variations over time. Active and passive expiration maneuvers did not improve PaCO2 prediction. TRIAL REGISTRATION: ClinicalTrials.gov: NCT01489150.

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OBJECTIVES: This is the first meta-analysis on the efficacy of composite resin restorations in anterior teeth. The objective of the present meta-analysis was to verify whether specific material classes, tooth conditioning methods and operational procedures influence the result for Class III and Class IV restorations. MATERIAL AND METHODS: The database SCOPUS and PubMed were searched for clinical trials on anterior resin composites without restricting the search to the year of publication. The inclusion criteria were: (1) prospective clinical trial with at least 2 years of observation; (2) minimal number of restorations at last recall=20; (3) report on drop-out rate; (4) report of operative technique and materials used in the trial, and (5) utilization of Ryge or modified Ryge evaluation criteria. For the statistical analysis, a linear mixed model was used with random effects to account for the heterogeneity between the studies. p-Values smaller than 0.05 were considered to be significant. RESULTS: Of the 84 clinical trials, 21 studies met the inclusion criteria, 14 of them for Class III restorations, 6 for Class IV restorations and 1 for closure of diastemata; the latter was included in the Class IV group. Twelve of the 21 studies started before 1991 and 18 before 2001. The estimated median overall success rate (without replacement) after 10 years for Class III composite resin restorations was 95% and for Class IV restorations 90%. The main reason for the replacement of Class IV restorations was bulk fractures, which occurred significantly more frequently with microfilled composites than with hybrid and macrofilled composites. Caries adjacent to restorations was infrequent in most studies and accounted only for about 2.5% of all replaced restorations after 10 years irrespective of the cavity class. Class III restorations with glass ionomer derivates suffered significantly more loss of anatomical form than did fillings with other types of material. When the enamel was acid-etched and no bonding agent was applied, significantly more restorations showed marginal staining and detectable margins compared to enamel etching with enamel bonding or the total etch technique; fillings with self-etching systems were in between of these two outcome variables. Bevelling of the enamel was associated with a significantly reduced deterioration of the anatomical form compared to no bevelling but not with less marginal staining or less detectable margins. The type of isolation (absolute/relative) had a statistically significant influence on marginal caries which, however, might be a random finding.