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We propose two classes of nonparametric point estimators of = P (X < Y ) in the case where (X;Y ) are paired, possibly dependent, absolutely continuous random variables. The proposed estimators are based on nonparametric estimators of the joint density of (X;Y ) and the distri- bution function of Z = Y X. We explore the use of several density and distribution function estimators and characterise the convergence of the re- sulting estimators of . We consider the use of bootstrap methods to obtain condence intervals. The performance of these estimators is illustrated us- ing simulated and real data. These examples show that not accounting for pairing and dependence may lead to erroneous conclusions about the rela- tionship between X and Y.

Summary Background Despite the improvement in the prognosis of acute coronary syndrome (ACS), substantial morbidity and mortality remain. We aimed to evaluate the effect of obstructive sleep apnoea (OSA) and its treatment with continuous positive airway pressure (CPAP) on the clinical evolution of patients with ACS. Methods We designed a multicentre, open-label, parallel-group, randomised controlled trial of patients with ACS at 15 hospitals in Spain. Eligible non-sleepy patients were men and women aged 18 years and older, admitted to hospital for documented symptoms of ACS. All patients underwent respiratory polygraphy during the first 24–72 h after admission. OSA patients were randomly assigned (1:1) to CPAP treatment plus usual care (CPAP group) or usual care alone (UC group) by a computerised system available 24 h a day. A group of patients with ACS but without OSA was also included as a reference group. Because of the nature of the intervention, the trial intervention could not be masked to either investigators or patients. Patients were monitored and followed for a minimum of 1 year. Patients were examined at the time of inclusion; after 1 month, 3 months, 6 months, 12 months, 18 months, 24 months, 30 months, and 36 months; and every 12 months thereafter, if applicable, during the follow-up period. The primary endpoint was the prevalence of a composite of cardiovascular events (cardiovascular death or non-fatal events [Acute myocardial infarction, non-fatal stroke, hospital admission for heart failure, and new hospitalisations for unstable angina or transient ischaemic attack]) in patients followed up for a minimum of 1 year. The primary analysis was done according to the intention-to-treat principle. This study is registered with Clinicaltrials.gov , NCT01335087 and is now closed. Findings Between April 25, 2011, and Feb 2, 2018, a total of 2834 patients with ACS had respiratory polygraphy, of whom 2551 (90·01%) were recruited. 1264 (49·55%) patients had OSA and were randomly assigned to the CPAP group (n=633) or the UC group (n=631). 1287 (50·45%) patients did not have OSA, of whom 603 (46·85%) were randomly assigned to the reference group. Patients were followed up for a median of 3·35 years (IQR 1·50–5·31). The prevalence of cardiovascular events was similar in the CPAP and UC groups (98 events [16%] vs 108 events [17%]; hazard ratio [HR] 0·89 [95% CI 0·68–1·17]; p=0·40) during follow-up. Mean time of adherence to CPAP treatment was 2·78 h/night (SD 2·73). The prevalence of cardiovascular events was similar between patients in the reference group (90 [15%] events) and those in the UC group (102 (17%) events) during follow-up (1·01 [0·76–1·35]; p=0·93). The prevalence of cardiovascular events seem not to be related to CPAP compliance or OSA severity. 464 (74%) of 629 patients in the CPAP group had 1538 serious adverse events and 406 (65%) of 626 patients in the UC group had 1764 serious adverse events. Interpretation Among non-sleepy patients with ACS, the presence of OSA was not associated with an increased prevalence of cardiovascular events and treatment with CPAP did not significantly reduce this prevalence. Funding ResMed (Australia), Fondo de Investigacion Sanitaria (Fondo Europeo de Desarrollo Regional), the Spanish Respiratory Society, the Catalonian Cardiology Society, Esteve-Teijin, Oxigen Salud, and ALLER.

Background Large and complex population-based cancer data are becoming broadly available, thanks to purposeful linkage between cancer registry data and health electronic records. Aiming at understanding the explanatory power of factors on cancer survival, the modelling and selection of variables need to be understood and exploited properly for improving model-based estimates of cancer survival. Method We assess the performances of well-known model selection strategies developed by Royston and Sauerbrei and Wynant and Abrahamowicz that we adapt to the relative survival data setting and to test for interaction terms. Results We apply these to all male patients diagnosed with lung cancer in England in 2012 (N = 15,688), and followed-up until 31/12/2015. We model the effects of age at diagnosis, tumour stage, deprivation, comorbidity and emergency presentation, as well as interactions between age and all of the above. Given the size of the dataset, all model selection strategies favoured virtually the same model, except for a non-linear effect of age at diagnosis selected by the backward-based selection strategies (versus a linear effect selected otherwise). Conclusion The results from extensive simulations evaluating varying model complexity and sample sizes provide guidelines on a model selection strategy in the context of excess hazard modelling.

In cancer epidemiology using population-based data, regression models for the excess mortality hazard is a useful method to estimate cancer survival and to describe the association between prognosis factors and excess mortality. This method requires expected mortality rates from general population life tables: each cancer patient is assigned an expected (background) mortality rate obtained from the life tables, typically at least according to their age and sex, from the population they belong to. However, those life tables may be insufficiently stratified, as some characteristics such as deprivation, ethnicity, and comorbidities, are not available in the life tables for a number of countries. This may affect the background mortality rate allocated to each patient, and it has been shown that not including relevant information for assigning an expected mortality rate to each patient induces a bias in the estimation of the regression parameters of the excess hazard model. We propose two parametric corrections in excess hazard regression models, including a single-parameter or a random effect (frailty), to account for possible mismatches in the life table and thus misspecification of the background mortality rate. In an extensive simulation study, the good statistical performance of the proposed approach is demonstrated, and we illustrate their use on real population-based data of lung cancer patients. We present conditions and limitations of these methods, and provide some recommendations for their use in practice., to appear in Biostatistics

We introduce a numerically tractable formulation of Bayesian joint models for longitudinal and survival data. The longitudinal process is modeled using generalized linear mixed models, while the survival process is modeled using a parametric general hazard structure. The two processes are linked by sharing fixed and random effects, separating the effects that play a role at the time scale from those that affect the hazard scale. This strategy allows for the inclusion of nonlinear and time-dependent effects while avoiding the need for numerical integration, which facilitates the implementation of the proposed joint model. We explore the use of flexible parametric distributions for modeling the baseline hazard function which can capture the basic shapes of interest in practice. We discuss prior elicitation based on the interpretation of the parameters. We present an extensive simulation study, where we analyze the inferential properties of the proposed models, and illustrate the trade-off between flexibility, sample size, and censoring. We also apply our proposal to two real data applications in order to demonstrate the adaptability of our formulation both in univariate time-to-event data and in a competing risks framework. The methodology is implemented in rstan.

Bayesian variable selection often assumes normality, but the effects of model misspecification are not sufficiently understood. There are sound reasons behind this assumption, particularly for large $p$: ease of interpretation, analytical and computational convenience. More flexible frameworks exist, including semi- or non-parametric models, often at the cost of some tractability. We propose a simple extension of the Normal model that allows for skewness and thicker-than-normal tails but preserves tractability. It leads to easy interpretation and a log-concave likelihood that facilitates optimization and integration. We characterize asymptotically parameter estimation and Bayes factor rates, in particular studying the effects of model misspecification. Under suitable conditions misspecified Bayes factors are consistent and induce sparsity at the same asymptotic rates than under the correct model. However, the rates to detect signal are altered by an exponential factor, often resulting in a loss of sensitivity. These deficiencies can be ameliorated by inferring the error distribution from the data, a simple strategy that can improve inference substantially. Our work focuses on the likelihood and can thus be combined with any likelihood penalty or prior, but here we focus on non-local priors to induce extra sparsity and ameliorate finite-sample effects caused by misspecification. Our results highlight the practical importance of focusing on the likelihood rather than solely on the prior, when it comes to Bayesian variable selection. The methodology is available in R package `mombf'.

We introduce a general class of continuous univariate distributions with positive support obtained by transforming the class of two-piece distributions. We show that this class of distributions is very flexible, easy to implement, and contains members that can capture different tail behaviours and shapes, producing also a variety of hazard functions. The proposed distributions represent a flexible alternative to the classical choices such as the log-normal, Gamma, and Weibull distributions. We investigate empirically the inferential properties of the proposed models through an extensive simulation study. We present some applications using real data in the contexts of time-to-event and accelerated failure time models. In the second kind of applications, we explore the use of these models in the estimation of the distribution of the individual remaining life.

Many preclinical studies examined cue-induced relapse to heroin and cocaine seeking in animal models, but most of these studies examined only one drug at a time. In human addicts, however, polydrug use of cocaine and heroin is common. We used a polydrug self-administration relapse model in rats to determine similarities and differences in brain areas activated during cue-induced reinstatement of heroin and cocaine seeking. We trained rats to lever press for cocaine (1.0 mg/kg/infusion, 3-h/d, 18 d) or heroin (0.03 mg/kg/infusion) on alternating days (9 d for each drug); drug infusions were paired with either intermittent or continuous light cue. Next, the rats underwent extinction training followed by tests for cue-induced reinstatement where they were exposed to either heroin- or cocaine-associated cues. We observed cue-selective reinstatement of drug seeking: the heroin cue selectively reinstated heroin seeking and the cocaine cue selectively reinstated cocaine seeking. We used Fos immunohistochemistry to assess cue-induced neuronal activation in different subregions of the medial prefrontal cortex (mPFC), dorsal striatum (DS), nucleus accumbens (NAc), and amygdala. Fos expression results indicated that only the prelimbic cortex (PL) was activated by both heroin and cocaine cues; in contrast, no significant cue-induced neuronal activation was observed in other brain areas. RNA in situ hybridization indicated that the proportion of glutamatergic and GABAergic markers in PL Fos-expressing cells were similar for the heroin and cocaine cue-activated neurons. Overall the results indicate that PL may be a common brain area involved in both heroin and cocaine seeking during polydrug use.

BackgroundReducing hospital emergency admissions is a key target for all modern health systems.MethodsWe analysed colon cancer patients diagnosed in 2011–13 in England. We screened their individual Hospital Episode Statistics records in the 90 days pre-diagnosis, the 90 days post-diagnosis, and the 90 days pre-death (in the year following diagnosis), for the occurrence of hospital emergency admissions (HEAs).ResultsBetween a quarter and two thirds of patients experience HEA in the three 90-day periods examined: pre-diagnosis, post-diagnosis and before death. Patients with tumour stage I-III from more deprived backgrounds had higher proportions of HEAs than less deprived patients during all studied periods. This remains even after adjusting for differing distributions of risk factors such as age, sex, comorbidity and stage at diagnosis.CONCLUSIONSAlthough in some cases HEAs might be unavoidable or even appropriate, the proportion of HEAs varies by socioeconomic status, even after controlling for the usual patient factors, suggestive of remediable causes of excess emergency healthcare utilisation in patients belonging to higher deprivation groups. Future inquiries should address the potential role of clinical complications, sub-optimal healthcare administration, premature discharge or a lack of social support as potential explanations for these patterns of inequality.

The proportional hazards model represents the most commonly assumed hazard structure when analysing time to event data using regression models. We study a general hazard structure which contains, as particular cases, proportional hazards, accelerated hazards, and accelerated failure time structures, as well as combinations of these. We propose an approach to apply these different hazard structures, based on a flexible parametric distribution (Exponentiated Weibull) for the baseline hazard. This distribution allows us to cover the basic hazard shapes of interest in practice: constant, bathtub, increasing, decreasing, and unimodal. In an extensive simulation study, we evaluate our approach in the context of excess hazard modelling, which is the main quantity of interest in descriptive cancer epidemiology. This study exhibits good inferential properties of the proposed model, as well as good performance when using the Akaike Information Criterion for selecting the hazard structure. An application on lung cancer data illustrates the usefulness of the proposed model., Comment: To appear in Statistical Methods in Medical Research. Supplementary material and software available here: https://sites.google.com/site/fjavierrubio67/home/papers

Background Emergency presentations (EP) represent over a third of all lung cancer admissions in England. Such presentations usually reflect late stage disease and are associated with poor survival. General practitioners (GPs) act as gate-keepers to secondary care and so we sought to understand the association between GP practice characteristics and lung cancer EP. Methods Data on general practice characteristics were extracted for all practices in England from the Quality Outcomes Framework, the Health and Social Care Information Centre, the GP Patient Survey, the Cancer Commissioning Toolkit and the area deprivation score for each practice. After linking these data to lung cancer patient registrations in 2006–2013, we explored trends in three types of EP, patient-led, GP-led and ‘other’, by general practice characteristics and by socio-demographic characteristics of patients. Results Overall proportions of lung cancer EP decreased from 37.9% in 2006 to 34.3% in 2013. Proportions of GP-led EP nearly halved during this period, from 28.3 to 16.3%, whilst patient-led emergency presentations rose from 62.1 to 66.7%. When focusing on practice-specific levels of EP, 14% of general practices had higher than expected proportions of EP at least once in 2006–13, but there was no evidence of clustering of patients within practice, meaning that none of the practice characteristics examined explained differing proportions of EP by practice. Conclusion We found that the high proportion of lung cancer EP is not the result of a few practices with very abnormal patterns of EP, but of a large number of practices susceptible to reaching high proportions of EP. This suggests a system-wide issue, rather than problems with specific practices. High proportions of lung cancer EP are mainly the result of patient-initiated attendances in A&E. Our results demonstrate that interventions to encourage patients not to bypass primary care must be system wide rather than targeted at specific practices. Electronic supplementary material The online version of this article (10.1186/s12885-018-4476-5) contains supplementary material, which is available to authorized users.

Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits maximum-likelihood (or maximum-a-posteriori) inference to be conducted, approximately, using essentially the same techniques. An elementary approach to this problem which simply obtains a nonparametric approximation of the likelihood surface which is then used as a smooth proxy for the likelihood in a subsequent maximisation step is developed here and the convergence of this class of algorithms is characterised theoretically. The use of non-sufficient summary statistics in this context is considered. Applying the proposed method to four problems demonstrates good performance. The proposed approach provides an alternative for approximating the maximum likelihood estimator (MLE) in complex scenarios.