Aurélien Latouche

A competing risks analysis should report results on all cause-specific hazards and cumulative incidence functions.

Competing risks endpoints are frequently encountered in hematopoietic stem cell transplantation where patients are exposed to relapse and treatment-related mortality. Both cause-specific hazards and direct models for the cumulative incidence functions have been used for analyzing such competing risks endpoints. For both approaches, the popular models are of a proportional hazards type. Such models have been used for studying prognostic factors in acute and chronic leukemias. We argue that a complete understanding of the event dynamics requires that both hazards and cumulative incidence be analyzed side by side, and that this is generally the most rigorous scientific approach to analyzing competing risks data. That is, understanding the effects of covariates on cause-specific hazards and cumulative incidence functions go hand in hand. A case study illustrates our proposal.

Effectiveness of two year balance training programme on prevention of fall induced injuries in at risk women aged 75-85 living in community: Ossébo randomised controlled trial

Objective To assess the effectiveness of a two year exercise programme of progressive balance retraining in reducing injurious falls among women aged 75-85 at increased risk of falls and injuries and living in the community. Design Pragmatic multicentre, two arm, parallel group, randomised controlled trial. Setting 20 study sites in 16 medium to large cities throughout France. Participants 706 women aged 75-85, living in their own home, and with diminished balance and gait capacities, randomly allocated to the experimental intervention group (exercise programme, n=352) or the control group (no intervention, n=354). Intervention Weekly supervised group sessions of progressive balance training offered in community based premises for two years, supplemented by individually prescribed home exercises. Outcome measures A geriatrician blinded to group assignment classified falls into one of three categories (no consequence, moderate, severe) based on physical damage and medical care. The primary outcome was the rate of injurious falls (moderate and severe). The two groups were compared for rates of injurious falls with a “shared frailty” model. Other outcomes included the rates of all falls, physical functional capacities (balance and motor function test results), fear of falling (FES-I), physical activity level, and perceived health related quality of life (SF-36). Analysis was by intention to treat. Results There were 305 injurious falls in the intervention group and 397 in the control group (hazard ratio 0.81, 95% confidence interval 0.67 to 0.99). The difference in severe injuries (68 in intervention group v 87 in control group) was of the same order of magnitude (0.83, 0.60 to 1.16). At two years, women in the intervention group performed significantly better on all physical tests and had significantly better perception of their overall physical function than women in the control group. Among women who started the intervention (n=294), the median number of group sessions attended was 53 (interquartile range 16-71). Five injurious falls related to the intervention were recorded. Conclusion A two year progressive balance retraining programme combining weekly group and individual sessions was effective in reducing injurious falls and in improving measured and perceived physical function in women aged 75-85 at risk of falling. Trial registration ClinicalTrials.gov (NCT00545350).

Competing Risks Regression for Stratified Data

For competing risks data, the Fine-Gray proportional hazards model for subdistribution has gained popularity for its convenience in directly assessing the effect of covariates on the cumulative incidence function. However, in many important applications, proportional hazards may not be satisfied, including multicenter clinical trials, where the baseline subdistribution hazards may not be common due to varying patient populations. In this article, we consider a stratified competing risks regression, to allow the baseline hazard to vary across levels of the stratification covariate. According to the relative size of the number of strata and strata sizes, two stratification regimes are considered. Using partial likelihood and weighting techniques, we obtain consistent estimators of regression parameters. The corresponding asymptotic properties and resulting inferences are provided for the two regimes separately. Data from a breast cancer clinical trial and from a bone marrow transplantation registry illustrate the potential utility of the stratified Fine-Gray model.

Competing risks regression for clustered data

A population average regression model is proposed to assess the marginal effects of covariates on the cumulative incidence function when there is dependence across individuals within a cluster in the competing risks setting. This method extends the Fine-Gray proportional hazards model for the subdistribution to situations, where individuals within a cluster may be correlated due to unobserved shared factors. Estimators of the regression parameters in the marginal model are developed under an independence working assumption where the correlation across individuals within a cluster is completely unspecified. The estimators are consistent and asymptotically normal, and variance estimation may be achieved without specifying the form of the dependence across individuals. A simulation study evidences that the inferential procedures perform well with realistic sample sizes. The practical utility of the methods is illustrated with data from the European Bone Marrow Transplant Registry.

On the Benefit of Intensive Care for Very Old Patients

A lthough intensive care unit (ICU) admission of very old patients has been discussed for almost 20 years, the overall benefit of ICU admission for very old patients remains unknown. The best design to address the benefits of ICU admission, a randomized trial, was claimed to be infeasible on ethical grounds. Observational studies generally report lower crude mortality rates for patients admitted to an ICU than in those refused, yet studies of very old patients find similar crude mortality rates. A few studies have reported adjusted results using binary outcome models, but they did not focus on elderly patients and had contradictory conclusions. Comparisons of survival in admitted and nonadmitted patients is seldom published. Wunsh et al showed that elderly ICU survivors had a lower longterm survival than hospital discharge survivors who did not receive ICU care, matched on age, sex, race, and whether they had surgery. Survival curve comparisons require adjustment on more confounding factors such as comorbidities and initial severity. To analyze the effect of ICU admission on midor long-term outcome, it is mandatory to target the “atrisk” population. All but 1 study on ICU admission failed to take into account pre-triage made by physicians from other specialties. The Intensive Care Elderly CUB-Réa (ICE-CUB) study, which focused on patients older than 80 years presenting to the emergency department (ED) with a condition potentially warranting ICU admission, reported the pre-triage made by ED physicians. Herein, we compare the survival between ICU admitted and nonadmitted patients from the ICE-CUB study with adjusted Cox model and adjusted survival curves using inverse probability weights (IPW) for confounder control.

Relative index of inequality and slope index of inequality: a structured regression framework for estimation.

Background: The relative index of inequality and the slope index of inequality are the two major indices used in epidemiologic studies for the measurement of socioeconomic inequalities in health. Yet the current definitions of these indices are not adapted to their main purpose, which is to provide summary measures of the linear association between socioeconomic status and health in a way that enables valid between-population comparisons. The lack of appropriate definitions has dissuaded the application of suitable regression methods for estimating the slope index of inequality. Methods: We suggest formally defining the relative and slope indices of inequality as so-called least false parameters, or more precisely, as the parameters that provide the best approximation of the relation between socioeconomic status and the health outcome by log-linear and linear models, respectively. From this standpoint, we establish a structured regression framework for inference on these indices. Guidelines for implementation of the methods, including R and SAS codes, are provided. Results: The new definitions yield appropriate summary measures of the linear association across the entire socioeconomic scale, suitable for comparative studies in epidemiology. Our regression-based approach for estimation of the slope index of inequality contributes to an advancement of the current methodology, which mainly consists of a heuristic formula relying on restrictive assumptions. A study of the educational inequalities in all-cause and cause-specific mortality in France is used for illustration. Conclusion: The proposed definitions and methods should guide the use and estimation of these indices in future studies.

Guidelines for time-to-event end-point definitions in trials for pancreatic cancer. Results of the DATECAN initiative (Definition for the Assessment of Time-to-event End-points in CANcer trials) ☆

BACKGROUND Using potential surrogate end-points for overall survival (OS) such as Disease-Free- (DFS) or Progression-Free Survival (PFS) is increasingly common in randomised controlled trials (RCTs). However, end-points are too often imprecisely defined which largely contributes to a lack of homogeneity across trials, hampering comparison between them. The aim of the DATECAN (Definition for the Assessment of Time-to-event End-points in CANcer trials)-Pancreas project is to provide guidelines for standardised definition of time-to-event end-points in RCTs for pancreatic cancer. METHODS Time-to-event end-points currently used were identified from a literature review of pancreatic RCT trials (2006-2009). Academic research groups were contacted for participation in order to select clinicians and methodologists to participate in the pilot and scoring groups (>30 experts). A consensus was built after 2 rounds of the modified Delphi formal consensus approach with the Rand scoring methodology (range: 1-9). RESULTS For pancreatic cancer, 14 time to event end-points and 25 distinct event types applied to two settings (detectable disease and/or no detectable disease) were considered relevant and included in the questionnaire sent to 52 selected experts. Thirty experts answered both scoring rounds. A total of 204 events distributed over the 14 end-points were scored. After the first round, consensus was reached for 25 items; after the second consensus was reached for 156 items; and after the face-to-face meeting for 203 items. CONCLUSION The formal consensus approach reached the elaboration of guidelines for standardised definitions of time-to-event end-points allowing cross-comparison of RCTs in pancreatic cancer.

Predictiveness curves in virtual screening

BackgroundIn the present work, we aim to transfer to the field of virtual screening the predictiveness curve, a metric that has been advocated in clinical epidemiology. The literature describes the use of predictiveness curves to evaluate the performances of biological markers to formulate diagnoses, prognoses and assess disease risks, assess the fit of risk models, and estimate the clinical utility of a model when applied to a population. Similarly, we use logistic regression models to calculate activity probabilities related to the scores that the compounds obtained in virtual screening experiments. The predictiveness curve can provide an intuitive and graphical tool to compare the predictive power of virtual screening methods.ResultsSimilarly to ROC curves, predictiveness curves are functions of the distribution of the scores and provide a common scale for the evaluation of virtual screening methods. Contrarily to ROC curves, the dispersion of the scores is well described by predictiveness curves. This property allows the quantification of the predictive performance of virtual screening methods on a fraction of a given molecular dataset and makes the predictiveness curve an efficient tool to address the early recognition problem. To this last end, we introduce the use of the total gain and partial total gain to quantify recognition and early recognition of active compounds attributed to the variations of the scores obtained with virtual screening methods. Additionally to its usefulness in the evaluation of virtual screening methods, predictiveness curves can be used to define optimal score thresholds for the selection of compounds to be tested experimentally in a drug discovery program. We illustrate the use of predictiveness curves as a complement to ROC on the results of a virtual screening of the Directory of Useful Decoys datasets using three different methods (Surflex-dock, ICM, Autodock Vina).ConclusionThe predictiveness curves cover different aspects of the predictive power of the scores, allowing a detailed evaluation of the performance of virtual screening methods. We believe predictiveness curves efficiently complete the set of tools available for the analysis of virtual screening results.

A competing risks approach for nonparametric estimation of transition probabilities in a non-Markov illness-death model

Competing risks model time to first event and type of first event. An example from hospital epidemiology is the incidence of hospital-acquired infection, which has to account for hospital discharge of non-infected patients as a competing risk. An illness-death model would allow to further study hospital outcomes of infected patients. Such a model typically relies on a Markov assumption. However, it is conceivable that the future course of an infected patient does not only depend on the time since hospital admission and current infection status but also on the time since infection. We demonstrate how a modified competing risks model can be used for nonparametric estimation of transition probabilities when the Markov assumption is violated.

Discrimination measures for survival outcomes: Connection between the AUC and the predictiveness curve

Finding out biomarkers and building risk scores to predict the occurrence of survival outcomes is a major concern of clinical epidemiology, and so is the evaluation of prognostic models. In this paper, we are concerned with the estimation of the time-dependent AUC--area under the receiver-operating curve--which naturally extends standard AUC to the setting of survival outcomes and enables to evaluate the discriminative power of prognostic models. We establish a simple and useful relation between the predictiveness curve and the time-dependent AUC--AUC(t). This relation confirms that the predictiveness curve is the key concept for evaluating calibration and discrimination of prognostic models. It also highlights that accurate estimates of the conditional absolute risk function should yield accurate estimates for AUC(t). From this observation, we derive several estimators for AUC(t) relying on distinct estimators of the conditional absolute risk function. An empirical study was conducted to compare our estimators with the existing ones and assess the effect of model misspecification--when estimating the conditional absolute risk function--on the AUC(t) estimation. We further illustrate the methodology on the Mayo PBC and the VA lung cancer data sets.