Adaptively weighted maximum likelihood estimation of discrete distributions

SummaryDiscrete data arise in various research fields, typically when the observations are count data.I propose a robust and efficient parametric procedure for estimation of discrete distributions. The estimation is done in two phases. First, a very robust, but possibly inefficient, estimate of the model parameters is computed and used to indentify outliers. Then the outliers are either removed from the sample or given low weights, and a weighted maximum likelihood estimate (WML) is computed.The weights are determined via an adaptive process such that if the data follow the model, then asymptotically no observation is downweighted.I prove that the final estimator inherits the breakdown point of the initial one, and that its influence function at the model is the same as the influence function of the maximum likelihood estimator, which strongly suggests that it is asymptotically fully efficient.The initial estimator is a minimum disparity estimator (MDE). MDEs can be shown to have full asymptotic efficiency, and some MDEs have very high breakdown points and very low bias under contamination. Several initial estimators are considered, and the performances of the WMLs based on each of them are studied.It results that in a great variety of situations the WML substantially improves the initial estimator, both in terms of finite sample mean square error and in terms of bias under contamination. Besides, the performances of the WML are rather stable under a change of the MDE even if the MDEs have very different behaviors.Two examples of application of the WML to real data are considered. In both of them, the necessity for a robust estimator is clear: the maximum likelihood estimator is badly corrupted by the presence of a few outliers.This procedure is particularly natural in the discrete distribution setting, but could be extended to the continuous case, for which a possible procedure is sketched.RésuméLes données discrètes sont présentes dans différents domaines de recherche, en particulier lorsque les observations sont des comptages.Je propose une méthode paramétrique robuste et efficace pour l'estimation de distributions discrètes. L'estimation est faite en deux phases. Tout d'abord, un estimateur très robuste des paramètres du modèle est calculé, et utilisé pour la détection des données aberrantes (outliers). Cet estimateur n'est pas nécessairement efficace. Ensuite, soit les outliers sont retirés de l'échantillon, soit des faibles poids leur sont attribués, et un estimateur du maximum de vraisemblance pondéré (WML) est calculé.Les poids sont déterminés via un processus adaptif, tel qu'asymptotiquement, si les données suivent le modèle, aucune observation n'est dépondérée.Je prouve que le point de rupture de l'estimateur final est au moins aussi élevé que celui de l'estimateur initial, et que sa fonction d'influence au modèle est la même que celle du maximum de vraisemblance, ce qui suggère que cet estimateur est pleinement efficace asymptotiquement.L'estimateur initial est un estimateur de disparité minimale (MDE). Les MDE sont asymptotiquement pleinement efficaces, et certains d'entre eux ont un point de rupture très élevé et un très faible biais sous contamination. J'étudie les performances du WML basé sur différents MDEs.Le résultat est que dans une grande variété de situations le WML améliore largement les performances de l'estimateur initial, autant en terme du carré moyen de l'erreur que du biais sous contamination. De plus, les performances du WML restent assez stables lorsqu'on change l'estimateur initial, même si les différents MDEs ont des comportements très différents.Je considère deux exemples d'application du WML à des données réelles, où la nécessité d'un estimateur robuste est manifeste : l'estimateur du maximum de vraisemblance est fortement corrompu par la présence de quelques outliers.La méthode proposée est particulièrement naturelle dans le cadre des distributions discrètes, mais pourrait être étendue au cas continu.

The Effect Of Induced Intraocular Straylight (cataract Simulation) On Sensitivity Measures Of Standard Automated Perimetry, Pulsar Perimetry And Moorfields Motion Displacement Test

Purpose: To investigate the effect of incremental increases in intraocular straylight on threshold measurements made by three modern forms of perimetry: Standard Automated Perimetry (SAP) using Octopus (Dynamic, G-Pattern), Pulsar Perimetry (PP) (TOP, 66 points) and the Moorfields Motion Displacement Test (MDT) (WEBS, 32 points).Methods: Four healthy young observers were recruited (mean age 26yrs [25yrs, 28yrs]), refractive correction [+2 D, -4.25D]). Five white opacity filters (WOF), each scattering light by different amounts were used to create incremental increases in intraocular straylight (IS). Resultant IS values were measured with each WOF and at baseline (no WOF) for each subject using a C-Quant Straylight Meter (Oculus, Wetzlar, Germany). A 25 yr old has an IS value of ~0.85 log(s). An increase of 40% in IS to 1.2log(s) corresponds to the physiological value of a 70yr old. Each WOFs created an increase in IS between 10-150% from baseline, ranging from effects similar to normal aging to those found with considerable cataract. Each subject underwent 6 test sessions over a 2-week period; each session consisted of the 3 perimetric tests using one of the five WOFs and baseline (both instrument and filter were randomised).Results: The reduction in sensitivity from baseline was calculated. A two-way ANOVA on mean change in threshold (where subjects were treated as rows in the block and each increment in fog filters was treated as column) was used to examine the effect of incremental increases in straylight. Both SAP (p<0.001) and Pulsar (p<0.001) were significantly affected by increases in straylight. The MDT (p=0.35) remained comparatively robust to increases in straylight.Conclusions: The Moorfields MDT measurement of threshold is robust to effects of additional straylight as compared to SAP and PP.

Evolution of a debris flow channel monitored using a 3D terrestrial laser scanner

Like numerous torrents in mountainous regions, the Illgraben creek (canton of Wallis, SW Switzerland) produces almost every year several debris flows. The total area of the active catchment is only 4.7 km², but large events ranging from 50'000 to 400'000 m³ are common (Zimmermann 2000). Consequently, the pathway of the main channel often changes suddenly. One single event can for instance fill the whole river bed and dig new several-meters-deep channels somewhere else (Bardou et al. 2003). The quantification of both, the rhythm and the magnitude of these changes, is very important to assess the variability of the bed's cross section and long profile. These parameters are indispensable for numerical modelling, as they should be considered as initial conditions. To monitor the channel evolution an Optech ILRIS 3D terrestrial laser scanner (LIDAR) was used. LIDAR permits to make a complete high precision 3D model of the channel and its surroundings by scanning it from different view points. The 3D data are treated and interpreted with the software Polyworks from Innovmetric Software Inc. Sequential 3D models allow for the determination of the variation in the bed's cross section and long profile. These data will afterwards be used to quantify the erosion and the deposition in the torrent reaches. To complete the chronological evolution of the landforms, precise digital terrain models, obtained by high resolution photogrammetry based on old aerial photographs, will be used. A 500 m long section of the Illgraben channel was scanned on 18th of August 2005 and on 7th of April 2006. These two data sets permit identifying the changes of the channel that occurred during the winter season. An upcoming scanning campaign in September 2006 will allow for the determination of the changes during this summer. Preliminary results show huge variations in the pathway of the Illgraben channel, as well as important vertical and lateral erosion of the river bed. Here we present the results of a river bank on the left (north-western) flank of the channel (Figure 1). For the August 2005 model the scans from 3 viewpoints were superposed, whereas the April 2006 3D image was obtained by combining 5 separate scans. The bank was eroded. The bank got eroded essentially on its left part (up to 6.3 m), where it is hit by the river and the debris flows (Figures 2 and 3). A debris cone has also formed (Figure 3), which suggests that a part of the bank erosion is due to shallow landslides. They probably occur when the river erosion creates an undercut slope. These geometrical data allow for the monitoring of the alluvial dynamics (i.e. aggradation and degradation) on different time scales and the influence of debris flows occurrence on these changes. Finally, the resistance against erosion of the bed's cross section and long profile will be analysed to assess the variability of these two key parameters. This information may then be used in debris flow simulation.

Rates and pattern of evolution among Cretaceous radiolarians: relations with global paleoceanographic events

We present a new approach for analyzing the turnover rates of Cretaceous radiolarians recorded in pelagic sequences of western Tethys, The analysis of major extinction-radiation events and the fluctuation of diversity are compared with major paleoceanographic events and variation of diversity in dinoflagellates, calcareous nannoplankton and ammonites. There is an extraordinary correlation between biotic changes and sea level changes, temperatures, O, C and Sr isotopes, phosphorus accumulation rates and anoxic episodes. This reveals a predominantly abiotic control on the evolution of radiolarians. The rate of turnover and the diversity through time of two major orders of radiolarians (nassellarians and spumellarians) exhibits (1) the quasi-parallelism of their diversity curves, excluding a direct competition between them, (2) greater resistance of spumellarians to extinction during the early stage of extinction intervals and (3) a stronger post-extinction recovery of nassellarians. Evolutionary rates of radiolarians can be a good means of monitoring global environmental changes and allowing us to understand more clearly the relationship between plankton evolution, climate and pale oceanographic processes.

Adverse life events among community-dwelling persons aged 65-70 years: gender differences in occurrence and perceived psychological consequences.

OBJECTIVES: To describe the occurrence of selected adverse life events in young-old men and women, as well as their perceived psychological consequences. METHODS: In 2005, 1,422 participants in the Lausanne Cohort 65+ study, born in 1934-1938, self-reported whether they experienced any of 26 life events during the preceding year. Most participants (N = 1,309, 92%) completed the geriatric adverse life events scale during a face-to-face interview, by rating the level of stress associated with each event, as well as its impact on their psychological well-being. RESULTS: Overall, 72% of the participants experienced at least one of the 26 events in the preceding year (range 1-9). Disease affecting the respondent (N = 525) or a close relative (N = 276) was most frequent, as well as the death of a friend or non-close relative (N = 274). Women indicated a higher frequency of events (mean 2.1 vs. 1.7 events, P < 0.001), as well as a higher level of stress and a stronger negative impact on well-being than men. In multivariate analyses adjusting for self-rated health, depressive symptoms and comorbidity, female gender remained significantly associated with the level of stress and negative impact on psychological well-being. CONCLUSION: This exploratory study shows that several types of adverse life events frequently occur at age 65-70, with gender differences both in the frequency of reporting and consequences of these events. However, information on this topic is limited and studies based on different populations and designs are needed to better understand the impact of such events.

Subclinical thyroid dysfunction and the risk of heart failure events: an individual participant data analysis from 6 prospective cohorts.

BACKGROUND: American College of Cardiology/American Heart Association guidelines for the diagnosis and management of heart failure recommend investigating exacerbating conditions such as thyroid dysfunction, but without specifying the impact of different thyroid-stimulation hormone (TSH) levels. Limited prospective data exist on the association between subclinical thyroid dysfunction and heart failure events. METHODS AND RESULTS: We performed a pooled analysis of individual participant data using all available prospective cohorts with thyroid function tests and subsequent follow-up of heart failure events. Individual data on 25 390 participants with 216 248 person-years of follow-up were supplied from 6 prospective cohorts in the United States and Europe. Euthyroidism was defined as TSH of 0.45 to 4.49 mIU/L, subclinical hypothyroidism as TSH of 4.5 to 19.9 mIU/L, and subclinical hyperthyroidism as TSH <0.45 mIU/L, the last two with normal free thyroxine levels. Among 25 390 participants, 2068 (8.1%) had subclinical hypothyroidism and 648 (2.6%) had subclinical hyperthyroidism. In age- and sex-adjusted analyses, risks of heart failure events were increased with both higher and lower TSH levels (P for quadratic pattern <0.01); the hazard ratio was 1.01 (95% confidence interval, 0.81-1.26) for TSH of 4.5 to 6.9 mIU/L, 1.65 (95% confidence interval, 0.84-3.23) for TSH of 7.0 to 9.9 mIU/L, 1.86 (95% confidence interval, 1.27-2.72) for TSH of 10.0 to 19.9 mIU/L (P for trend <0.01) and 1.31 (95% confidence interval, 0.88-1.95) for TSH of 0.10 to 0.44 mIU/L and 1.94 (95% confidence interval, 1.01-3.72) for TSH <0.10 mIU/L (P for trend=0.047). Risks remained similar after adjustment for cardiovascular risk factors. CONCLUSION: Risks of heart failure events were increased with both higher and lower TSH levels, particularly for TSH ≥10 and <0.10 mIU/L.

Orthotropic active strain models for the numerical simulation of cardiac biomechanics

An active strain formulation for orthotropic constitutive laws arising in cardiac mechanics modeling is introduced and studied. The passive mechanical properties of the tissue are described by the Holzapfel-Ogden relation. In the active strain formulation, the Euler-Lagrange equations for minimizing the total energy are written in terms of active and passive deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiac cells. The well-posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed and different mechanical activation functions are considered. In addition, the active strain formulation is compared with the classical active stress formulation from both numerical and modeling perspectives. Taylor-Hood and MINI finite elements are employed to discretize the mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main key features of the phenomenon, while allowing savings in computational costs.

Bridging the Faraoni and Selli oceanic anoxic events: late Hauterivian to early Aptian dysaerobic to anaerobic phases in the Tethys

A detailed geochemical analysis was performed on the upper part of the Maiolica Formation in the Breggia (southern Switzerland) and Capriolo sections (northern Italy). The analysed sediments consist of well-bedded, partly siliceous, pelagic carbonate, which lodges numerous thin, dark and organic-rich layers. Stable-isotope, phosphorus, organic-carbon and a suite of redox-sensitive trace-element contents (RSTE: Mo, U, Co, V and As) were measured. The RSTE pattern and C-org:P-tot ratios indicate that most organic-rich layers were deposited under dysaerobic rather than anaerobic conditions and that latter conditions were likely restricted to short intervals in the latest Hauterivian, the early Barremian and the pre-Selli early Aptian. Correlations are both possible with organic-rich intervals in central Italy (the Gorgo a Cerbara section) and the Boreal Lower Saxony Basin, as well as with the facies and drowning pattern in the Helvetic segment of the northern Tethyan carbonate platform. Our data and correlations suggest that the latest Hauterivian witnessed the progressive installation of dysaerobic conditions in the Tethys, which went along with the onset in sediment condensation, phosphogenesis and platform drowning on the northern Tethyan margin, and which culminated in the Faraoni anoxic episode. This episode is followed by further episodes of dysaerobic conditions in the Tethys and the Lower Saxony Basin, which became more frequent and progressively stronger in the late early Barremian. Platform drowning persisted and did not halt before the latest early Barremian. The late Barremian witnessed diminishing frequencies and intensities in dysaerobic conditions, which went along with the progressive installation of the Urgonian carbonate platform. Near the Barremian-Aptian boundary, the increasing density in dysaerobic episodes in the Tethyan and Lower Saxony Basins is paralleled by a change towards heterozoan carbonate production on the northern Tethyan shelf. The following return to more oxygenated conditions is correlated with the second phase of Urgonian platform growth and the period immediately preceding and corresponding to the Selli anoxic episode is characterised by renewed platform drowning and the change to heterozoan carbonate production. Changes towards more humid climate conditions were the likely cause for the repetitive installation of dys- to anaerobic conditions in the Tethyan and Boreal basins and the accompanying changes in the evolution of the carbonate platform towards heterozoan carbonate-producing ecosystems and platform drowning.

Population PK-guided simulation study in children exposed to drugs in human milk

Risks of significant infant drug exposure through human milk arepoorly defined due to lack of large-scale PK data. We propose to useBayesian approach based on population PK (popPK)-guided modelingand simulation for risk prediction. As a proof-of-principle study, weexploited fluoxetine milk concentration data from 25 women. popPKparameters including milk-to-plasma ratio (MP ratio) were estimatedfrom the best model. The dose of fluoxetine the breastfed infant wouldreceive through mother's milk, and infant plasma concentrations wereestimated from 1000 simulated mother-infant pairs, using randomassignment of feeding times and milk volume. A conservative estimateof CYP2D6 activity of 20% of the allometrically-adjusted adult valuewas assumed. Derived model parameters, including MP ratio were consistentwith those reported in the literature. Visual predictive check andother model diagnostics showed no signs of model misspecifications.The model simulation predicted that infant exposure levels to fluoxetinevia mother's milk were below 10% of weight-adjusted maternal therapeuticdoses in >99% of simulated infants. Predicted median ratio ofinfant-mother serum levels at steady state was 0.093 (range 0.033-0.31),consistent with literature reported values (mean=0.07; range 0-0.59).Predicted incidence of relatively high infant-mother ratio (>0.2) ofsteady-state serum fluoxetine concentrations was <1.3%. Overall, ourpredictions are consistent with clinical observations. Our approach maybe valid for other drugs, allowing in silico prediction of infant drugexposure risks through human milk. We will discuss application of thisapproach to another drug used in lactating women.

The Toarcian in the Subbetic basin (southern Spain): Bio-events (ammonite and calcareous nannofossils) and carbon-isotope stratigraphy

A detailed carbon-isotope stratigraphic study for the uppermost Pliensbachian lowermost Aalenian interval in the Median Subbetic palaeogeographic domain (External zones of the Betic Cordillera, southern Spain) has been carried out. During the Early Jurassic, the Median Subbetic, which represents a typical basin of the Hispanic Corridor connecting the Tethys and the Eastern Pacific, was located in the westernmost Tethys. The analyzed sections encompass the entire Toarcian stage as represented in the southern Iberian palaeomargin. Rocks are mainly rhythmic sequences of grey marls and marly limestones containing a rich ammonite fauna, nannofossils, and benthic foraminifers-all these provide an accurate biostratigraphic control. The lower and upper Toarcian boundaries are well represented in some of these sections and therefore represent optimal sites to link the carbon-isotope curves to ammonite zones, and to nannofossil events. delta C-13 values of bulk carbonates from the different localities of the Subbetic basin have similar variations from the uppermost Pliensbachian to the lowermost Aalenian, suggesting changes in the original DIC carbon isotope composition along the Hispanic corridor. The transition from Pliensbachian to Toarcian is marked by increasing delta C-13 values from similar to 12 to 2.0 parts per thousand, interrupted in the Serpentinum Zone by a negative shift concomitant with the Toarcian oceanic anoxic event (T-OAE), with the major ammonite extinction event of the Toarcian, and an important turnover of calcareous nannoplankton. The negative shift observed in the Serpentinum Zone confirms the global perturbation of the carbon cycling documented along the Tethys and the palaeo-Pacific in organic material and in marine carbonates. However, the amplitude of the negative excursion (similar to - 1.5 parts per thousand) is not compatible with an isotopic homogeneous seawater DIC and/or CO2 atmospheric reservoirs. The interval from the middle to the top of the Toarcian delta C-13 shows relatively constant values, minor ammonite turnovers, and is associated with increasing diversity of calcareous nannoplankton. (c) 2012 Elsevier B.V. All rights reserved.

Prediction of infant drug exposure through breastfeeding: population PK modeling and simulation of fluoxetine

BACKGROUND: Risks of significant infant drug exposurethrough breastmilk are poorly defined for many drugs, and largescalepopulation data are lacking. We used population pharmacokinetics(PK) modeling to predict fluoxetine exposure levels ofinfants via mother's milk in a simulated population of 1000 motherinfantpairs.METHODS: Using our original data on fluoxetine PK of 25breastfeeding women, a population PK model was developed withNONMEM and parameters, including milk concentrations, wereestimated. An exponential distribution model was used to account forindividual variation. Simulation random and distribution-constrainedassignment of doses, dosing time, feeding intervals and milk volumewas conducted to generate 1000 mother-infant pairs with characteristicssuch as the steady-state serum concentrations (Css) and infantdose relative to the maternal weight-adjusted dose (relative infantdose: RID). Full bioavailability and a conservative point estimate of1-month-old infant CYP2D6 activity to be 20% of the adult value(adjusted by weigth) according to a recent study, were assumed forinfant Css calculations.RESULTS: A linear 2-compartment model was selected as thebest model. Derived parameters, including milk-to-plasma ratios(mean: 0.66; SD: 0.34; range, 0 - 1.1) were consistent with the valuesreported in the literature. The estimated RID was below 10% in >95%of infants. The model predicted median infant-mother Css ratio was0.096 (range 0.035 - 0.25); literature reported mean was 0.07 (range0-0.59). Moreover, the predicted incidence of infant-mother Css ratioof >0.2 was less than 1%.CONCLUSION: Our in silico model prediction is consistent withclinical observations, suggesting that substantial systemic fluoxetineexposure in infants through human milk is rare, but further analysisshould include active metabolites. Our approach may be valid forother drugs. [supported by CIHR and Swiss National Science Foundation(SNSF)]

The risk of subsequent cancer and arterial cardiovascular events in patients with superficial vein thrombosis in the legs.

Although it has been clearly demonstrated that venous thromboembolism is associated with an increased risk of subsequent overt cancer and arterial cardiovascular events in comparison with control populations, whether this association also applies to patients with isolated (ie, without concomitant involvement of the deep vein system) superficial vein thrombosis (SVT) in the legs is unknown. In 737 consecutive patients with isolated SVT not involving the sapheno-femoral junction, we conducted a retrospective investigation to assess the rate of cancer and that of arterial cardiovascular events occurring during follow-up. The event rates were compared with those occurring in 1438 controls having comparable characteristics. Both cases and controls were followed-up for an average period of 26 ± 8 months (range, 3-45). Malignancy was diagnosed in 26 cases (3.5%) and 56 controls (3.9%), leading to a hazard ratio of 0.86 (95% confidence interval, 0.55%-1.35%). Arterial cardiovascular events occurred in 32 cases (4.3%) and 63 controls (4.4%), leading to a hazard ratio of 0.97 (95% confidence interval, 0.63%-1.50%). We conclude that the occurrence of isolated SVT in the legs does not place patients at an increased risk of malignancies or arterial cardiovascular events. Whether this conclusion also applies to patients whose thrombosis involves the sapheno-femoral junction remains to be demonstrated.