Mixed Milk Feeding: A New Approach to Describe Feeding Patterns in the First Year of Life Based on Individual Participant Data from Two Randomised Controlled Trials.

'Mixed Milk Feeding' (MMF), whereby infants are fed with both breastmilk and infant formula during the same period, is a common feeding practice. Despite its high prevalence, knowledge regarding MMF practices and their association with (health) outcomes is limited, potentially because MMF behaviours are highly variable and difficult to standardise longitudinally. In this paper, we applied a statistical clustering algorithm on individual infant feeding data collected over the first year of life from two clinical trials: 'TEMPO' (n = 855) and 'Venus' (n = 539); these studies were conducted in different years and world regions. In TEMPO, more than half of infants were MMF. Four distinct MMF clusters were identified: early exclusive formula feeding (32%), later exclusive formula feeding (25%), long-term MMF (21%), and mostly breastfeeding (22%). The same method applied to 'Venus' resulted in comparable clusters, building trust in the robustness of the cluster approach. These results demonstrate that distinct MMF patterns can be identified, which may be applicable to diverse populations. These insights could support the design of future research studying the impact of infant feeding patterns on health outcomes. To standardise this in future research, it is important to establish a unified definition of MMF.

A tutorial on frailty models.

The hazard function plays a central role in survival analysis. In a homogeneous population, the distribution of the time to event, described by the hazard, is the same for each individual. Heterogeneity in the distributions can be accounted for by including covariates in a model for the hazard, for instance a proportional hazards model. In this model, individuals with the same value of the covariates will have the same distribution. It is natural to think that not all covariates that are thought to influence the distribution of the survival outcome are included in the model. This implies that there is unobserved heterogeneity; individuals with the same value of the covariates may have different distributions. One way of accounting for this unobserved heterogeneity is to include random effects in the model. In the context of hazard models for time to event outcomes, such random effects are called frailties, and the resulting models are called frailty models. In this tutorial, we study frailty models for survival outcomes. We illustrate how frailties induce selection of healthier individuals among survivors, and show how shared frailties can be used to model positively dependent survival outcomes in clustered data. The Laplace transform of the frailty distribution plays a central role in relating the hazards, conditional on the frailty, to hazards and survival functions observed in a population. Available software, mainly in R, will be discussed, and the use of frailty models is illustrated in two different applications, one on center effects and the other on recurrent events.

The effect of treatment delay on time-to-recovery in the presence of unobserved heterogeneity.

We study the effect of delaying treatment in the presence of (unobserved) heterogeneity. In a homogeneous population and assuming a proportional treatment effect, a treatment delay period will result in notably lower cumulative recovery percentages. We show in theoretical scenarios using frailty models that if the population is heterogeneous, the effect of a delay period is much smaller. This can be explained by the selection process that is induced by the frailty. Patient groups that start treatment later have already undergone more selection. The marginal hazard ratio for the treatment will act differently in such a more homogeneous patient group. We further discuss modeling approaches for estimating the effect of treatment delay in the presence of heterogeneity, and compare their performance in a simulation study. The conventional Cox model that fails to account for heterogeneity overestimates the effect of treatment delay. Including interaction terms between treatment and starting time of treatment or between treatment and follow up time gave no improvement. Estimating a frailty term can improve the estimation, but is sensitive to misspecification of the frailty distribution. Therefore, multiple frailty distributions should be used and the results should be compared using the Akaike Information Criterion. Non-parametric estimation of the cumulative recovery percentages can be considered if the dataset contains sufficient long term follow up for each of the delay strategies. The methods are demonstrated on a motivating application evaluating the effect of delaying the start of treatment with assisted reproductive techniques on time-to-pregnancy in couples with unexplained subfertility.

Benchmarking of survival outcomes following haematopoietic stem cell transplantation: A review of existing processes and the introduction of an international system from the European Society for Blood and Marrow Transplantation (EBMT) and the Joint Accreditation Committee of ISCT and EBMT (JACIE).

In many healthcare settings, benchmarking for complex procedures has become a mandatory requirement by competent authorities, regulators, payers and patients to assure clinical performance, cost-effectiveness and safe care of patients. In several countries inside and outside Europe, benchmarking systems have been established for haematopoietic stem cell transplantation (HSCT), but access is not universal. As benchmarking is now integrated into the FACT-JACIE standards, the EBMT and JACIE established a Clinical Outcomes Group (COG) to develop and introduce a universal system accessible across EBMT members. Established systems from seven European countries (United Kingdom, Italy, Belgium, France, Germany, Spain, Switzerland), USA and Australia were appraised, revealing similarities in process, but wide variations in selection criteria and statistical methods. In tandem, the COG developed the first phase of a bespoke risk-adapted international benchmarking model for one-year survival following allogeneic and autologous HSCT based on current capabilities within the EBMT registry core dataset. Data completeness, which has a critical impact on validity of centre comparisons, is also assessed. Ongoing development will include further scientific validation of the model, incorporation of further variables (when appropriate) alongside implementation of systems for clinically meaningful interpretation and governance aiming to maximise acceptance to centres, clinicians, payers and patients across EBMT.

Correction: Benchmarking of survival outcomes following haematopoietic stem cell transplantation: A review of existing processes and the introduction of an international system from the European Society for Blood and Marrow Transplantation (EBMT) and the Joint Accreditation Committee of ISCT and EBMT (JACIE).

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Models with interactions overestimated heterogeneity of treatment effects and were prone to treatment mistargeting.

OBJECTIVES: We aimed to compare the performance of different regression modeling approaches for the prediction of heterogeneous treatment effects. STUDY DESIGN AND SETTING: We simulated trial samples (n = 3,600; 80% power for a treatment odds ratio of 0.8) from a superpopulation (N = 1,000,000) with 12 binary risk predictors, both without and with six true treatment interactions. We assessed predictions of treatment benefit for four regression models: a "risk model" (with a constant effect of treatment assignment) and three "effect models" (including interactions of risk predictors with treatment assignment). Three novel performance measures were evaluated: calibration for benefit (i.e., observed vs. predicted risk difference in treated vs. untreated), discrimination for benefit, and prediction error for benefit. RESULTS: The risk modeling approach was well-calibrated for benefit, whereas effect models were consistently overfit, even with doubled sample sizes. Penalized regression reduced miscalibration of the effect models considerably. In terms of discrimination and prediction error, the risk modeling approach was superior in the absence of true treatment effect interactions, whereas penalized regression was optimal in the presence of true treatment interactions. CONCLUSION: A risk modeling approach yields models consistently well calibrated for benefit. Effect modeling may improve discrimination for benefit in the presence of true interactions but is prone to overfitting. Hence, effect models-including only plausible interactions-should be fitted using penalized regression.

Nonproportional hazards and unobserved heterogeneity in clustered survival data: When can we tell the difference?

Multivariate survival data are frequently encountered in biomedical applications in the form of clustered failures (or recurrent events data). A popular way of analyzing such data is by using shared frailty models, which assume that the proportional hazards assumption holds conditional on an unobserved cluster-specific random effect. Such models are often incorporated in more complicated joint models in survival analysis. If the random effect distribution has finite expectation, then the conditional proportional hazards assumption does not carry over to the marginal models. It has been shown that, for univariate data, this makes it impossible to distinguish between the presence of unobserved heterogeneity (eg, due to missing covariates) and marginal nonproportional hazards. We show that time-dependent covariate effects may falsely appear as evidence in favor of a frailty model also in the case of clustered failures or recurrent events data, when the cluster size or number of recurrent events is small. When true unobserved heterogeneity is present, the presence of nonproportional hazards leads to overestimating the frailty effect. We show that this phenomenon is somewhat mitigated as the cluster size grows. We carry out a simulation study to assess the behavior of test statistics and estimators for frailty models in such contexts. The gamma, inverse Gaussian, and positive stable shared frailty models are contrasted using a novel software implementation for estimating semiparametric shared frailty models. Two main questions are addressed in the contexts of clustered failures and recurrent events: whether covariates with a time-dependent effect may appear as indication of unobserved heterogeneity and whether the additional presence of unobserved heterogeneity can be detected in this case. Finally, the practical implications are illustrated in a real-world data analysis example.

Ascertainment correction in frailty models for recurrent events data.

In retrospective studies involving recurrent events, it is common to select individuals based on their event history up to the time of selection. In this case, the ascertained subjects might not be representative for the target population, and the analysis should take the selection mechanism into account. The purpose of this paper is two-fold. First, to study what happens when the data analysis is not adjusted for the selection and second, to propose a corrected analysis. Under the Andersen-Gill and shared frailty regression models, we show that the estimators of covariate effects, incidence, and frailty variance can be biased if the ascertainment is ignored, and we show that with a simple adjustment of the likelihood, unbiased and consistent estimators are obtained. The proposed method is assessed by a simulation study and is illustrated on a data set comprising recurrent pneumothoraces. Copyright © 2016 John Wiley & Sons, Ltd.

Score test for association between recurrent events and a terminal event.

The statistical analysis of recurrent events relies on the assumption of independent censoring. When random effects are used, this means, in addition, that the censoring cannot depend on the random effect. Whenever the recurrent event process is terminated by death, this assumption might not be satisfied. Because joint models arising from such situations are more difficult to fit and interpret, clinicians rarely check whether joint modeling is preferred. In this paper, we propose and compare simple, yet efficient methods for testing whether the terminal event and the recurrent events are associated or not. The performance of the proposed methods is evaluated in a simulation study, and the sensitivity to misspecification of the model is assessed. Finally, the methods are illustrated on a data set comprising repeated observations of skin tumors on T-cell lymphoma patients. Copyright © 2016 John Wiley & Sons, Ltd.