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.

Influence of weather, rank, and home advantage on football outcomes in the gulf region.

PURPOSE: The objective of this study was to investigate the effects of weather, rank, and home advantage on international football match results and scores in the Gulf Cooperation Council (GCC) region. METHODS: Football matches (n = 2008) in six GCC countries were analyzed. To determine the weather influence on the likelihood of favorable outcome and goal difference, generalized linear model with a logit link function and multiple regression analysis were performed. RESULTS: In the GCC region, home teams tend to have greater likelihood of a favorable outcome (P < 0.001) and higher goal difference (P < 0.001). Temperature difference was identified as a significant explanatory variable when used independently (P < 0.001) or after adjustment for home advantage and team ranking (P < 0.001). The likelihood of favorable outcome for GCC teams increases by 3% for every 1-unit increase in temperature difference. After inclusion of interaction with opposition, this advantage remains significant only when playing against non-GCC opponents. While home advantage increased the odds of favorable outcome (P < 0.001) and goal difference (P < 0.001) after inclusion of interaction term, the likelihood of favorable outcome for a GCC team decreased (P < 0.001) when playing against a stronger opponent. Finally, the temperature and wet bulb globe temperature approximation were found as better indicators of the effect of environmental conditions than absolute and relative humidity or heat index on match outcomes. CONCLUSIONS: In GCC region, higher temperature increased the likelihood of a favorable outcome when playing against non-GCC teams. However, international ranking should be considered because an opponent with a higher rank reduced, but did not eliminate, the likelihood of a favorable outcome.

The use of the likelihood ratio for evaluative and investigative purposes in comparative forensic handwriting examination

This paper extends previous research and discussion on the use of multivariate continuous data, which are about to become more prevalent in forensic science. As an illustrative example, attention is drawn here on the area of comparative handwriting examinations. Multivariate continuous data can be obtained in this field by analysing the contour shape of loop characters through Fourier analysis. This methodology, based on existing research in this area, allows one describe in detail the morphology of character contours throughout a set of variables. This paper uses data collected from female and male writers to conduct a comparative analysis of likelihood ratio based evidence assessment procedures in both, evaluative and investigative proceedings. While the use of likelihood ratios in the former situation is now rather well established (typically, in order to discriminate between propositions of authorship of a given individual versus another, unknown individual), focus on the investigative setting still remains rather beyond considerations in practice. This paper seeks to highlight that investigative settings, too, can represent an area of application for which the likelihood ratio can offer a logical support. As an example, the inference of gender of the writer of an incriminated handwritten text is forwarded, analysed and discussed in this paper. The more general viewpoint according to which likelihood ratio analyses can be helpful for investigative proceedings is supported here through various simulations. These offer a characterisation of the robustness of the proposed likelihood ratio methodology.

The use of classification and regression trees to predict the likelihood of seasonal influenza.

Background Individual signs and symptoms are of limited value for the diagnosis of influenza. Objective To develop a decision tree for the diagnosis of influenza based on a classification and regression tree (CART) analysis. Methods Data from two previous similar cohort studies were assembled into a single dataset. The data were randomly divided into a development set (70%) and a validation set (30%). We used CART analysis to develop three models that maximize the number of patients who do not require diagnostic testing prior to treatment decisions. The validation set was used to evaluate overfitting of the model to the training set. Results Model 1 has seven terminal nodes based on temperature, the onset of symptoms and the presence of chills, cough and myalgia. Model 2 was a simpler tree with only two splits based on temperature and the presence of chills. Model 3 was developed with temperature as a dichotomous variable (≥38°C) and had only two splits based on the presence of fever and myalgia. The area under the receiver operating characteristic curves (AUROCC) for the development and validation sets, respectively, were 0.82 and 0.80 for Model 1, 0.75 and 0.76 for Model 2 and 0.76 and 0.77 for Model 3. Model 2 classified 67% of patients in the validation group into a high- or low-risk group compared with only 38% for Model 1 and 54% for Model 3. Conclusions A simple decision tree (Model 2) classified two-thirds of patients as low or high risk and had an AUROCC of 0.76. After further validation in an independent population, this CART model could support clinical decision making regarding influenza, with low-risk patients requiring no further evaluation for influenza and high-risk patients being candidates for empiric symptomatic or drug therapy.

The likelihood approach to compare populations : a study on DNA evidence and pitfalls of intuitions

The paper follows on from earlier work [Taroni F and Aitken CGG. Probabilistic reasoning in the law, Part 1: assessment of probabilities and explanation of the value of DNA evidence. Science & Justice 1998; 38: 165-177]. Different explanations of the value of DNA evidence were presented to students from two schools of forensic science and to members of fifteen laboratories all around the world. The responses were divided into two groups; those which came from a school or laboratory identified as Bayesian and those which came from a school or laboratory identified as non-Bayesian. The paper analyses these responses using a likelihood approach. This approach is more consistent with a Bayesian analysis than one based on a frequentist approach, as was reported by Taroni F and Aitken CGG. [Probabilistic reasoning in the law, Part 1: assessment of probabilities and explanation of the value of DNA evidence] in Science & Justice 1998.

The Rank Lecture: Has imaging told us anything new about human visual organisation?

The functional architecture of the occipital cortex is being studied with increasing detail. Functional and structural MR based imaging are altering views about the organisation of the human visual system. Recent advances have ranged from comparative studies with non-human primates to predictive scanning. The latter multivariate technique describes with sub-voxel resolution patterns of activity that are characteristic of specific visual experiences. One can deduce what a subject experienced visually from the pattern of cortical activity recorded. The challenge for the future is to understand visual functions in terms of cerebral computations at a mesoscopic level of description and to relate this information to electrophysiology. The principal medical application of this new knowledge has focused to a large extent on plasticity and the capacity for functional reorganisation. Crossmodality visual-sensory interactions and cross-correlations between visual and other cerebral areas in the resting state are areas of considerable current interest. The lecture will review findings over the last two decades and reflect on possible roles for imaging studies in the future.

Predictors of HIV-protection behaviour in HIV-positive men who have sex with casual male partners: a test of the explanatory power of an extended Information-Motivation-Behavioural Skills model.

This prospective study applies an extended Information-Motivation-Behavioural Skills (IMB) model to establish predictors of HIV-protection behaviour among HIV-positive men who have sex with men (MSM) during sex with casual partners. Data have been collected from anonymous, self-administered questionnaires and analysed by using descriptive and backward elimination regression analyses. In a sample of 165 HIV-positive MSM, 82 participants between the ages of 23 and 78 (M=46.4, SD=9.0) had sex with casual partners during the three-month period under investigation. About 62% (n=51) have always used a condom when having sex with casual partners. From the original IMB model, only subjective norm predicted condom use. More important predictors that increased condom use were low consumption of psychotropics, high satisfaction with sexuality, numerous changes in sexual behaviour after diagnosis, low social support from friends, alcohol use before sex and habitualised condom use with casual partner(s). The explanatory power of the calculated regression model was 49% (p<0.001). The study reveals the importance of personal and social resources and of routines for condom use, and provides information for the research-based conceptualisation of prevention offers addressing especially people living with HIV ("positive prevention").

Serum anticholinergic activity and postoperative cognitive dysfunction in elderly patients.

BACKGROUND: Cerebral cholinergic transmission plays a key role in cognitive function, and anticholinergic drugs administered during the perioperative phase are a hypothetical cause of postoperative cognitive dysfunction (POCD). We hypothesized that a perioperative increase in serum anticholinergic activity (SAA) is associated with POCD in elderly patients. METHODS: Seventy-nine patients aged >65 years undergoing elective major surgery under standardized general anesthesia (thiopental, sevoflurane, fentanyl, and atracurium) were investigated. Cognitive functions were assessed preoperatively and 7 days postoperatively using the extended version of the CERAD-Neuropsychological Assessment Battery. POCD was defined as a postoperative decline >1 z-score in at least 2 test variables. SAA was measured preoperatively and 7 days postoperatively at the time of cognitive testing. Hodges-Lehmann median differences and their 95% confidence intervals were calculated for between-group comparisons. RESULTS: Of the patients who completed the study, 46% developed POCD. Patients with POCD were slightly older and less educated than patients without POCD. There were no relevant differences between patients with and without POCD regarding gender, demographically corrected baseline cognitive functions, and duration of anesthesia. There were no large differences between patients with and without POCD regarding SAA preoperatively (pmol/mL, median [interquartile range]/median difference [95% CI], P; 1.14 [0.72, 2.37] vs 1.13 [0.68, 1.68]/0.12 [-0.31, 0.57], P = 0.56), SAA 7 days postoperatively (1.32 [0.68, 2.59] vs 0.97 [0.65, 1.83]/0.25 [-0.26, 0.81], P = 0.37), or changes in SAA (0.08 [-0.50, 0.70] vs -0.02 [-0.53, 0.41]/0.1 [-0.31, 0.52], P = 0.62). There was no significant relationship between changes in SAA and changes in cognitive function (Spearman rank correlation coefficient preoperatively of 0.03 [95% CI, -0.21, 0.26] and postoperatively of -0.002 [95% CI, -0.24, 0.23]). CONCLUSIONS: In this panel of patients with low baseline SAA and clinically insignificant perioperative anticholinergic burden, although a relationship cannot be excluded in some patients, our analysis suggests that POCD is probably not a substantial consequence of anticholinergic medications administered perioperatively but rather due to other mechanisms.

European collaborative study of early-onset bipolar disorder: Evidence for genetic heterogeneity on 2q14 according to age at onset.

Bipolar disorder has a genetic component, but the mode of inheritance remains unclear. A previous genome scan conducted in 70 European families led to detect eight regions linked to bipolar disease. Here, we present an investigation of whether the phenotypic heterogeneity of the disorder corresponds to genetic heterogeneity in these regions using additional markers and an extended sample of families. The MLS statistic was used for linkage analyses. The predivided sample test and the maximum likelihood binomial methods were used to test genetic homogeneity between early-onset bipolar type I (cut-off of 22 years) and other types of the disorder (later onset of bipolar type I and early-onset bipolar type II), using a total of 138 independent bipolar-affected sib-pairs. Analysis of the extended sample of families supports linkage in four regions (2q14, 3p14, 16p23, and 20p12) of the eight regions of linkage suggested by our previous genome scan. Heterogeneity testing revealed genetic heterogeneity between early and late-onset bipolar type I in the 2q14 region (P = 0.0001). Only the early form of the bipolar disorder but not the late form appeared to be linked to this region. This region may therefore include a genetic factor either specifically involved in the early-onset bipolar type I or only influencing the age at onset (AAO). Our findings illustrate that stratification according to AAO may be valuable for the identification of genetic vulnerability polymorphisms.

Fourth order pseudo maximum likelihood methods

We extend PML theory to account for information on the conditional moments up to order four, but without assuming a parametric model, to avoid a risk of misspecification of the conditional distribution. The key statistical tool is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in Gourieroux et al. (1984) to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed. The key numerical tool that we use is the Gauss-Freud integration scheme that solves a computational problem that has previously been raised in several fields. Simulation exercises demonstrate the feasibility and robustness of the methods [Authors]

Real-time dual-wavelength digital holographic microscopy for extended measurement range with enhanced axial resolution

We report on advanced dual-wavelength digital holographic microscopy (DHM) methods, enabling single-acquisition real-time micron-range measurements while maintaining single-wavelength interferometric resolution in the nanometer regime. In top of the unique real-time capability of our technique, it is shown that axial resolution can be further increased compared to single-wavelength operation thanks to the uncorrelated nature of both recorded wavefronts. It is experimentally demonstrated that DHM topographic investigation within 3 decades measurement range can be achieved with our arrangement, opening new applications possibilities for this interferometric technique. ©2008 COPYRIGHT SPIE

Uncertainty about the true source. A note on the likelihood ratio at the activity level.

This paper focuses on likelihood ratio based evaluations of fibre evidence in cases in which there is uncertainty about whether or not the reference item available for analysis - that is, an item typically taken from the suspect or seized at his home - is the item actually worn at the time of the offence. A likelihood ratio approach is proposed that, for situations in which certain categorical assumptions can be made about additionally introduced parameters, converges to formula described in existing literature. The properties of the proposed likelihood ratio approach are analysed through sensitivity analyses and discussed with respect to possible argumentative implications that arise in practice.

Simultaneous biliary drainage and portal vein embolization before extended hepatectomy for hilar cholangiocarcinoma: preliminary experience.

BACKGROUND: Patients with resectable hilar cholangiocarcinoma often present obstructive jaundice and a small future remnant liver (FRL) ratio. A sequential approach comprising preoperative biliary drainage followed by portal vein embolization (PVE) is usually performed but leads to long preoperative management (6-12 weeks) before patients can undergo resection. To simplify and shorten this phase of liver preparation, we developed a new preoperative approach that involves percutaneous biliary drainage and PVE during the same procedure. We report the outcomes of this combined procedure. METHODS: During 1 year, four patients underwent simultaneous biliary drainage and PVE followed 1 month later by surgical resection of hilar cholangiocarcinoma. Liver volumes were assessed by CT before, and 1, and 3 months after the combined procedure. Serum liver enzymes were assessed before and 1 month after the combined procedure. RESULTS: The combined procedure was feasible in all cases, with no related complications. After the combined procedure, transaminases remained stable or decreased, whereas gamma-glutamyl-transpeptidase, alkaline phosphatase, and bilirubin decreased. During the first month, the left lobe volume increased by +27.9 % (range 19-40.9 %). The FRL ratio increased from 24.9 to 33.2 %. All patients underwent R0 liver resection with a favorable postoperative outcome. The remnant liver volume increased by +132 % (range 78-245 %) between 1 and 3 months. CONCLUSIONS: Simultaneous percutaneous biliary drainage and PVE is feasible. This all-in-one preoperative approach greatly decreases waiting time until surgical resection. These encouraging results warrant further investigation to confirm the safety and to evaluate the reduction in the dropout rate for liver resection in this tumor with poor prognosis.

Complete longitudinal analyses of the randomized, placebo-controlled, phase III trial of sunitinib in patients with gastrointestinal stromal tumor following imatinib failure.

PURPOSE: To analyze final long-term survival and clinical outcomes from the randomized phase III study of sunitinib in gastrointestinal stromal tumor patients after imatinib failure; to assess correlative angiogenesis biomarkers with patient outcomes. EXPERIMENTAL DESIGN: Blinded sunitinib or placebo was given daily on a 4-week-on/2-week-off treatment schedule. Placebo-assigned patients could cross over to sunitinib at disease progression/study unblinding. Overall survival (OS) was analyzed using conventional statistical methods and the rank-preserving structural failure time (RPSFT) method to explore cross-over impact. Circulating levels of angiogenesis biomarkers were analyzed. RESULTS: In total, 243 patients were randomized to receive sunitinib and 118 to placebo, 103 of whom crossed over to open-label sunitinib. Conventional statistical analysis showed that OS converged in the sunitinib and placebo arms (median 72.7 vs. 64.9 weeks; HR, 0.876; P = 0.306) as expected, given the cross-over design. RPSFT analysis estimated median OS for placebo of 39.0 weeks (HR, 0.505, 95% CI, 0.262-1.134; P = 0.306). No new safety concerns emerged with extended sunitinib treatment. No consistent associations were found between the pharmacodynamics of angiogenesis-related plasma proteins during sunitinib treatment and clinical outcome. CONCLUSIONS: The cross-over design provided evidence of sunitinib clinical benefit based on prolonged time to tumor progression during the double-blind phase of this trial. As expected, following cross-over, there was no statistical difference in OS. RPSFT analysis modeled the absence of cross-over, estimating a substantial sunitinib OS benefit relative to placebo. Long-term sunitinib treatment was tolerated without new adverse events.