Saddlepoint approximations

The saddlepoint method provides accurate approximations for the distributions of many test statistics, estimators and for important probabilities arising in various stochastic models. The saddlepoint approximation is a large deviations technique which is substantially more accurate than limiting normal or Edgeworth approximations, especially in presence of very small sample sizes or very small probabilities. The outstanding accuracy of the saddlepoint approximation can be explained by the fact that it has bounded relative error.

Stochastic simulation of rare events

Stochastic simulation is an important and practical technique for computing probabilities of rare events, like the payoff probability of a financial option, the probability that a queue exceeds a certain level or the probability of ruin of the insurer's risk process. Rare events occur so infrequently, that they cannot be reasonably recorded during a standard simulation procedure: specifc simulation algorithms which thwart the rarity of the event to simulate are required. An important algorithm in this context is based on changing the sampling distribution and it is called importance sampling. Optimal Monte Carlo algorithms for computing rare event probabilities are either logarithmic eficient or possess bounded relative error.

Diagnostic value of immunoassays for heparin-induced thrombocytopenia: a systematic review and meta-analysis.

Immunoassays are essential in the workup of patients with suspected heparin-induced thrombocytopenia. However, the diagnostic accuracy is uncertain with regard to different classes of assays, antibody specificities, thresholds, test variations, and manufacturers. We aimed to assess diagnostic accuracy measures of available immunoassays and to explore sources of heterogeneity. We performed comprehensive literature searches and applied strict inclusion criteria. Finally, 49 publications comprising 128 test evaluations in 15 199 patients were included in the analysis. Methodological quality according to the revised tool for quality assessment of diagnostic accuracy studies was moderate. Diagnostic accuracy measures were calculated with the unified model (comprising a bivariate random-effects model and a hierarchical summary receiver operating characteristics model). Important differences were observed between classes of immunoassays, type of antibody specificity, thresholds, application of confirmation step, and manufacturers. Combination of high sensitivity (>95%) and high specificity (>90%) was found in 5 tests only: polyspecific enzyme-linked immunosorbent assay (ELISA) with intermediate threshold (Genetic Testing Institute, Asserachrom), particle gel immunoassay, lateral flow immunoassay, polyspecific chemiluminescent immunoassay (CLIA) with a high threshold, and immunoglobulin G (IgG)-specific CLIA with low threshold. Borderline results (sensitivity, 99.6%; specificity, 89.9%) were observed for IgG-specific Genetic Testing Institute-ELISA with low threshold. Diagnostic accuracy appears to be inadequate in tests with high thresholds (ELISA; IgG-specific CLIA), combination of IgG specificity and intermediate thresholds (ELISA, CLIA), high-dose heparin confirmation step (ELISA), and particle immunofiltration assay. When making treatment decisions, clinicians should be a aware of diagnostic characteristics of the tests used and it is recommended they estimate posttest probabilities according to likelihood ratios as well as pretest probabilities using clinical scoring tools.

Long-term outcome of patients with newly diagnosed chronic myeloid leukemia: a randomized comparison of stem cell transplantation with drug treatment.

Tyrosine kinase inhibitors represent today's treatment of choice in chronic myeloid leukemia (CML). Allogeneic hematopoietic stem cell transplantation (HSCT) is regarded as salvage therapy. This prospective randomized CML-study IIIA recruited 669 patients with newly diagnosed CML between July 1997 and January 2004 from 143 centers. Of these, 427 patients were considered eligible for HSCT and were randomized by availability of a matched family donor between primary HSCT (group A; N=166 patients) and best available drug treatment (group B; N=261). Primary end point was long-term survival. Survival probabilities were not different between groups A and B (10-year survival: 0.76 (95% confidence interval (CI): 0.69-0.82) vs 0.69 (95% CI: 0.61-0.76)), but influenced by disease and transplant risk. Patients with a low transplant risk showed superior survival compared with patients with high- (P<0.001) and non-high-risk disease (P=0.047) in group B; after entering blast crisis, survival was not different with or without HSCT. Significantly more patients in group A were in molecular remission (56% vs 39%; P=0.005) and free of drug treatment (56% vs 6%; P<0.001). Differences in symptoms and Karnofsky score were not significant. In the era of tyrosine kinase inhibitors, HSCT remains a valid option when both disease and transplant risk are considered.Leukemia advance online publication, 20 November 2015; doi:10.1038/leu.2015.281.

Impact of comorbidities on overall survival in patients with chronic myeloid leukemia: results of the randomized CML study IV.

We studied the influence of comorbidities on remission rate and overall survival (OS) in patients with chronic myeloid leukemia (CML). Participants of the CML Study IV, a randomized 5-arm trial designed to optimize imatinib therapy, were analyzed for comorbidities at diagnosis using the Charlson Comorbidity Index (CCI); 511 indexed comorbidities were reported in 1519 CML patients. Age was an additional risk factor in 863 patients. Resulting CCI scores were as follows: CCI 2, n = 589; CCI 3 or 4, n = 599; CCI 5 or 6, n = 229; and CCI ≥ 7, n = 102. No differences in cumulative incidences of accelerated phase, blast crisis, or remission rates were observed between patients in the different CCI groups. Higher CCI was significantly associated with lower OS probabilities. The 8-year OS probabilities were 93.6%, 89.4%, 77.6%, and 46.4% for patients with CCI 2, 3 to 4, 5 to 6, and ≥7, respectively. In multivariate analysis, CCI was the most powerful predictor of OS, which was still valid after removal of its age-related components. Comorbidities have no impact on treatment success but do have a negative effect on OS, indicating that survival of patients with CML is determined more by comorbidities than by CML itself. OS may therefore be inappropriate as an outcome measure for specific CML treatments. The trial was registered at www.clinicaltrials.gov as #NCT00055874.

Tuberculosis-related mortality in people living with HIV in Europe and Latin America: an international cohort study

BACKGROUND Management of tuberculosis in patients with HIV in eastern Europe is complicated by the high prevalence of multidrug-resistant tuberculosis, low rates of drug susceptibility testing, and poor access to antiretroviral therapy (ART). We report 1 year mortality estimates from a multiregional (eastern Europe, western Europe, and Latin America) prospective cohort study: the TB:HIV study. METHODS Consecutive HIV-positive patients aged 16 years or older with a diagnosis of tuberculosis between Jan 1, 2011, and Dec 31, 2013, were enrolled from 62 HIV and tuberculosis clinics in 19 countries in eastern Europe, western Europe, and Latin America. The primary endpoint was death within 12 months after starting tuberculosis treatment; all deaths were classified according to whether or not they were tuberculosis related. Follow-up was either until death, the final visit, or 12 months after baseline, whichever occurred first. Risk factors for all-cause and tuberculosis-related deaths were assessed using Kaplan-Meier estimates and Cox models. FINDINGS Of 1406 patients (834 in eastern Europe, 317 in western Europe, and 255 in Latin America), 264 (19%) died within 12 months. 188 (71%) of these deaths were tuberculosis related. The probability of all-cause death was 29% (95% CI 26-32) in eastern Europe, 4% (3-7) in western Europe, and 11% (8-16) in Latin America (p<0·0001) and the corresponding probabilities of tuberculosis-related death were 23% (20-26), 1% (0-3), and 4% (2-8), respectively (p<0·0001). Patients receiving care outside eastern Europe had a 77% decreased risk of death: adjusted hazard ratio (aHR) 0·23 (95% CI 0·16-0·31). In eastern Europe, compared with patients who started a regimen with at least three active antituberculosis drugs, those who started fewer than three active antituberculosis drugs were at a higher risk of tuberculosis-related death (aHR 3·17; 95% CI 1·83-5·49) as were those who did not have baseline drug-susceptibility tests (2·24; 1·31-3·83). Other prognostic factors for increased tuberculosis-related mortality were disseminated tuberculosis and a low CD4 cell count. 18% of patients were receiving ART at tuberculosis diagnosis in eastern Europe compared with 44% in western Europe and 39% in Latin America (p<0·0001); 12 months later the proportions were 67% in eastern Europe, 92% in western Europe, and 85% in Latin America (p<0·0001). INTERPRETATION Patients with HIV and tuberculosis in eastern Europe have a risk of death nearly four-times higher than that in patients from western Europe and Latin America. This increased mortality rate is associated with modifiable risk factors such as lack of drug susceptibility testing and suboptimal initial antituberculosis treatment in settings with a high prevalence of drug resistance. Urgent action is needed to improve tuberculosis care for patients living with HIV in eastern Europe. FUNDING EU Seventh Framework Programme.

Retention in care during the first 3 years of antiretroviral therapy for women in Malawi's option B+ programme: an observational cohort study

Background Studies of Malawi's option B+ programme for HIV-positive pregnant and breastfeeding women have reported high loss to follow-up during pregnancy and at the start of antiretroviral therapy (ART), but few data exist about retention during breastfeeding and after weaning. We examined loss to follow-up and retention in care in patients in the option B+ programme during their first 3 years on ART. Methods We analysed two data sources: aggregated facility-level data about patients in option B+ who started ART between Oct 1, 2011, and June 30, 2012, at 546 health facilities; and patient-level data from 20 large facilities with electronic medical record system for HIV-positive women who started ART between Sept 1, 2011, and Dec 31, 2013, under option B+ or because they had WHO clinical stages 3 or 4 disease or had CD4 counts of less than 350 cells per μL. We used facility-level data to calculate representative estimates of retention and loss to follow-up. We used patient-level data to study temporal trends in retention, timing of loss to follow-up, and predictors of no follow-up and loss to follow-up. We defined patients who were more than 60 days late for their first follow-up visit as having no follow-up and patients who were more than 60 days late for a subsequent visit as being lost to follow-up. We calculated proportions and cumulative probabilities of patients who had died, stopped ART, had no follow-up, were lost to follow-up, or were retained alive on ART for 36 months. We calculated odds ratios and hazard ratios to examine predictors of no follow-up and loss to follow-up. Findings Analysis of facility-level data about patients in option B+ who had not transferred to a different facility showed retention in care to be 76·8% (20 475 of 26 658 patients) after 12 months, 70·8% (18 306 of 25 849 patients) after 24 months, and 69·7% (17 787 of 25 535 patients) after 36 months. Patient-level data included 29 145 patients. 14 630 (50·2%) began treatment under option B+. Patients in option B+ had a higher risk of having no follow-up and, for the first 2 years of ART, higher risk of loss to follow-up than did patients who started ART because they had CD4 counts less than 350 cells per μL or WHO clinical stage 3 or 4 disease. Risk of loss to follow-up during the third year was low and similar for patients retained for 2 years. Retention rates did not change as the option B+ programme matured. Interpretation Our data suggest that pregnant and breastfeeding women who start ART immediately after they are diagnosed with HIV can be retained on ART through the option B+ programme, even after many have stopped breastfeeding. Interventions might be needed to improve retention in the first year on ART in option B+. Funding Bill & Melinda Gates Foundation, Partnerships for Enhanced Engagement in Research Health, and National Institute of Allergy and Infectious Diseases.

Zonal playfield attributes – A stochastic approach to subjective passing affordances in football

Introduction: According to the ecological view, coordination establishes byvirtueof social context. Affordances thought of as situational opportunities to interact are assumed to represent the guiding principles underlying decisions involved in interpersonal coordination. It’s generally agreed that affordances are not an objective part of the (social) environment but that they depend on the constructive perception of involved subjects. Theory and empirical data hold that cognitive operations enabling domain-specific efficacy beliefs are involved in the perception of affordances. The aim of the present study was to test the effects of these cognitive concepts in the subjective construction of local affordances and their influence on decision making in football. Methods: 71 football players (M = 24.3 years, SD = 3.3, 21 % women) from different divisions participated in the study. Participants were presented scenarios of offensive game situations. They were asked to take the perspective of the person on the ball and to indicate where they would pass the ball from within each situation. The participants stated their decisions in two conditions with different game score (1:0 vs. 0:1). The playing fields of all scenarios were then divided into ten zones. For each zone, participants were asked to rate their confidence in being able to pass the ball there (self-efficacy), the likelihood of the group staying in ball possession if the ball were passed into the zone (group-efficacy I), the likelihood of the ball being covered safely by a team member (pass control / group-efficacy II), and whether a pass would establish a better initial position to attack the opponents’ goal (offensive convenience). Answers were reported on visual analog scales ranging from 1 to 10. Data were analyzed specifying general linear models for binomially distributed data (Mplus). Maximum likelihood with non-normality robust standard errors was chosen to estimate parameters. Results: Analyses showed that zone- and domain-specific efficacy beliefs significantly affected passing decisions. Because of collinearity with self-efficacy and group-efficacy I, group-efficacy II was excluded from the models to ease interpretation of the results. Generally, zones with high values in the subjective ratings had a higher probability to be chosen as passing destination (βself-efficacy = 0.133, p < .001, OR = 1.142; βgroup-efficacy I = 0.128, p < .001, OR = 1.137; βoffensive convenience = 0.057, p < .01, OR = 1.059). There were, however, characteristic differences in the two score conditions. While group-efficacy I was the only significant predictor in condition 1 (βgroup-efficacy I = 0.379, p < .001), only self-efficacy and offensive convenience contributed to passing decisions in condition 2 (βself-efficacy = 0.135, p < .01; βoffensive convenience = 0.120, p < .001). Discussion: The results indicate that subjectively distinct attributes projected to playfield zones affect passing decisions. The study proposes a probabilistic alternative to Lewin’s (1951) hodological and deterministic field theory and enables insight into how dimensions of the psychological landscape afford passing behavior. Being part of a team, this psychological landscape is not only constituted by probabilities that refer to the potential and consequences of individual behavior, but also to that of the group system of which individuals are part of. Hence, in regulating action decisions in group settings, informers are extended to aspects referring to the group-level. References: Lewin, K. (1951). In D. Cartwright (Ed.), Field theory in social sciences: Selected theoretical papers by Kurt Lewin. New York: Harper & Brothers.

Incidence and predictors of cutaneous manifestations during the early course of systemic sclerosis: a 10-year longitudinal study from the EUSTAR database.

OBJECTIVES To longitudinally map the onset and identify risk factors for skin sclerosis and digital ulcers (DUs) in patients with systemic sclerosis (SSc) from an early time point after the onset of Raynaud's phenomenon (RP) in the European Scleroderma Trials and Research (EUSTAR) cohort. METHODS 695 patients with SSc with a baseline visit within 1 year after RP onset were followed in the prospective multinational EUSTAR database. During the 10-year observation period, cumulative probabilities of cutaneous lesions were assessed with the Kaplan-Meier method. Cox proportional hazards regression analysis was used to evaluate risk factors. RESULTS The median modified Rodnan skin score (mRSS) peaked 1 year after RP onset, and was 15 points. The 1-year probability to develop an mRSS ≥2 in at least one area of the arms and legs was 69% and 25%, respectively. Twenty-five per cent of patients developed diffuse cutaneous involvement in the first year after RP onset. This probability increased to 36% during the subsequent 2 years. Only 6% of patients developed diffuse cutaneous SSc thereafter. The probability to develop DUs increased to a maximum of 70% at the end of the 10-year observation. The main factors associated with diffuse cutaneous SSc were the presence of anti-RNA polymerase III autoantibodies, followed by antitopoisomerase autoantibodies and male sex. The main factor associated with incident DUs was the presence of antitopoisomerase autoantibodies. CONCLUSION Early after RP onset, cutaneous manifestations exhibit rapid kinetics in SSc. This should be accounted for in clinical trials aiming to prevent skin worsening.

Focal Epilepsy: MR Imaging of Nonhemodynamic Field Effects by Using a Phase-cycled Stimulus-induced Rotary Saturation Approach with Spin-Lock Preparation.

Purpose To investigate whether nonhemodynamic resonant saturation effects can be detected in patients with focal epilepsy by using a phase-cycled stimulus-induced rotary saturation (PC-SIRS) approach with spin-lock (SL) preparation and whether they colocalize with the seizure onset zone and surface interictal epileptiform discharges (IED). Materials and Methods The study was approved by the local ethics committee, and all subjects gave written informed consent. Eight patients with focal epilepsy undergoing presurgical surface and intracranial electroencephalography (EEG) underwent magnetic resonance (MR) imaging at 3 T with a whole-brain PC-SIRS imaging sequence with alternating SL-on and SL-off and two-dimensional echo-planar readout. The power of the SL radiofrequency pulse was set to 120 Hz to sensitize the sequence to high gamma oscillations present in epileptogenic tissue. Phase cycling was applied to capture distributed current orientations. Voxel-wise subtraction of SL-off from SL-on images enabled the separation of T2* effects from rotary saturation effects. The topography of PC-SIRS effects was compared with the seizure onset zone at intracranial EEG and with surface IED-related potentials. Bayesian statistics were used to test whether prior PC-SIRS information could improve IED source reconstruction. Results Nonhemodynamic resonant saturation effects ipsilateral to the seizure onset zone were detected in six of eight patients (concordance rate, 0.75; 95% confidence interval: 0.40, 0.94) by means of the PC-SIRS technique. They were concordant with IED surface negativity in seven of eight patients (0.88; 95% confidence interval: 0.51, 1.00). Including PC-SIRS as prior information improved the evidence of the standard EEG source models compared with the use of uninformed reconstructions (exceedance probability, 0.77 vs 0.12; Wilcoxon test of model evidence, P < .05). Nonhemodynamic resonant saturation effects resolved in patients with favorable postsurgical outcomes, but persisted in patients with postsurgical seizure recurrence. Conclusion Nonhemodynamic resonant saturation effects are detectable during interictal periods with the PC-SIRS approach in patients with epilepsy. The method may be useful for MR imaging-based detection of neuronal currents in a clinical environment. (©) RSNA, 2016 Online supplemental material is available for this article.

An analysis of two methods for the classification of stage of readiness to obtain repeat mammography screening

Background and purpose: Breast cancer continues to be a health problem for women, representing 28 percent of all female cancers and remaining one of the leading causes of death for women. Breast cancer incidence rates become substantial before the age of 50. After menopause, breast cancer incidence rates continue to increase with age creating a long-lasting source of concern (Harris et al., 1992). Mammography, a technique for the detection of breast tumors in their nonpalpable stage when they are most curable, has taken on considerable importance as a public health measure. The lifetime risk of breast cancer is approximately 1 in 9 and occurs over many decades. Recommendations are that screening be periodic in order to detect cancer at early stages. These recommendations, largely, are not followed. Not only are most women not getting regular mammograms, but this circumstance is particularly the case among older women where regular mammography has been proven to reduce mortality by approximately 30 percent. The purpose of this project was to increase our understanding of factors that are associated with stage of readiness to obtain subsequent mammograms. A secondary purpose of this research was to suggest further conceptual considerations toward the extension of the Transtheoretical Model (TTM) of behavior change to repeat screening mammography. ^ Methods. A sample (n = 1,222) of women 50 years and older in a large multi-specialty clinic in Houston, Texas was surveyed by mail questionnaire regarding their previous screening experience and stage of readiness to obtain repeat screening. A computerized database, maintained on all women who undergo mammography at the clinic, was used to identify women who are eligible for the project. The major statistical technique employed to select the significant variables and to examine the man and interaction effects of independent variables on dependent variables was polychotomous stepwise, logistic regression. A prediction model for each stage of readiness definition was estimated. The expected probabilities for stage of readiness were calculated to assess the magnitude and direction of significant predictors. ^ Results. Analysis showed that both ways of defining stage of readiness for obtaining a screening mammogram were associated with specific constructs, including decisional balance and processes of the change. ^ Conclusions. The results of the present study demonstrate that the TTM appears to translate to repeat mammography screening. Findings in the current study also support finding of previous studies that suggest that stage of readiness is associated with respondent decisional balance and the processes of change. ^

Prophylactic mastectomy and oophorectomy for women at risk of breast and ovarian cancer: Incorporating preferences in a decision analysis

The discoveries of the BRCA1 and BRCA2 genes have made it possible for women of families with hereditary breast/ovarian cancer to determine if they carry cancer-predisposing genetic mutations. Women with germline mutations have significantly higher probabilities of developing both cancers than the general population. Since the presence of a BRCA1 or BRCA2 mutation does not guarantee future cancer development, the appropriate course of action remains uncertain for these women. Prophylactic mastectomy and oophorectomy remain controversial since the underlying premise for surgical intervention is based more upon reduction in the estimated risk of cancer than on actual evidence of clinical benefit. Issues that are incorporated in a woman's decision making process include quality of life without breasts, ovaries, attitudes toward possible surgical morbidity as well as a remaining risk of future development of breast/ovarian cancer despite prophylactic surgery. The incorporation of patient preferences into decision analysis models can determine the quality-adjusted survival of different prophylactic approaches to breast/ovarian cancer prevention. Monte Carlo simulation was conducted on 4 separate decision models representing prophylactic oophorectomy, prophylactic mastectomy, prophylactic oophorectomy/mastectomy and screening. The use of 3 separate preference assessment methods across different populations of women allows researchers to determine how quality adjusted survival varies according to clinical strategy, method of preference assessment and the population from which preferences are assessed. ^

Penalty Enhancement for Hate Crimes: An Economic Analysis

The issue of bias-motivated crimes has attracted consderable attention in recent years. In this paper, we develop an economic framework to analyze penalty enhancements for bias-motivated crimes. We extend the standard model by introducing two different groups of potential victims of crime, and assume that a potential offender's benefits from a crime depend on the group to which the victim belongs. We begin with the assumption that the harm to an individual victim from a bias-motivated crime is identical to that from an equivalent non-hate crime. Nonetheless, we derive the result that a pattern of crimes disproportionately targeting an identifiable group leads to greater social harm. This conclusion follows both from a model where disparities in groups' victimization probabilities lead to social losses due to fairness concerns, as well as a model where potential victims have the opportunity to undertake socially costly victimization avoidance activities. In particular, penalty enhancements can reduce the incentives for avoidance activity, and thereby protect the networks of profitable interactions that link members of different groups. We also argue that those groups that are covered by hate crime statutes tend to be those whose characteristics make it especially likely that penalty enhancement is socially optimal. Finally, we consider a number of other issues related to hate crimes, including teh choice of sanctions from behind a Rawlsian 'veil of ignorance' concerning group identity.

Polytomies and bayesian phylogenetic inference

Bayesian phylogenetic analyses are now very popular in systematics and molecular evolution because they allow the use of much more realistic models than currently possible with maximum likelihood methods. There are, however, a growing number of examples in which large Bayesian posterior clade probabilities are associated with very short edge lengths and low values for non-Bayesian measures of support such as nonparametric bootstrapping. For the four-taxon case when the true tree is the star phylogeny, Bayesian analyses become increasingly unpredictable in their preference for one of the three possible resolved tree topologies as data set size increases. This leads to the prediction that hard (or near-hard) polytomies in nature will cause unpredictable behavior in Bayesian analyses, with arbitrary resolutions of the polytomy receiving very high posterior probabilities in some cases. We present a simple solution to this problem involving a reversible-jump Markov chain Monte Carlo (MCMC) algorithm that allows exploration of all of tree space, including unresolved tree topologies with one or more polytomies. The reversible-jump MCMC approach allows prior distributions to place some weight on less-resolved tree topologies, which eliminates misleadingly high posteriors associated with arbitrary resolutions of hard polytomies. Fortunately, assigning some prior probability to polytomous tree topologies does not appear to come with a significant cost in terms of the ability to assess the level of support for edges that do exist in the true tree. Methods are discussed for applying arbitrary prior distributions to tree topologies of varying resolution, and an empirical example showing evidence of polytomies is analyzed and discussed.

Extracting more out of relocation data: building movement models as mixtures of random walks

We present a framework for fitting multiple random walks to animal movement paths consisting of ordered sets of step lengths and turning angles. Each step and turn is assigned to one of a number of random walks, each characteristic of a different behavioral state. Behavioral state assignments may be inferred purely from movement data or may include the habitat type in which the animals are located. Switching between different behavioral states may be modeled explicitly using a state transition matrix estimated directly from data, or switching probabilities may take into account the proximity of animals to landscape features. Model fitting is undertaken within a Bayesian framework using the WinBUGS software. These methods allow for identification of different movement states using several properties of observed paths and lead naturally to the formulation of movement models. Analysis of relocation data from elk released in east-central Ontario, Canada, suggests a biphasic movement behavior: elk are either in an "encamped" state in which step lengths are small and turning angles are high, or in an "exploratory" state, in which daily step lengths are several kilometers and turning angles are small. Animals encamp in open habitat (agricultural fields and opened forest), but the exploratory state is not associated with any particular habitat type.