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.

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.

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.