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The use of a quantitative treatment selection marker to choose between two treatment options requires the estimate of an optimal threshold above which one of these two treatments is preferred. Herein, the optimal threshold expression is based on the definition of a utility function which aims to quantify the expected utility of the population (e.g. life expectancy, quality of life) by taking into account both efficacy (success or failure) and toxicity of each treatment option. Therefore, the optimal threshold is the marker value that maximizes the expected utility of the population. A method modelling the marker distribution in patient subgroups defined by the received treatment and the outcome is proposed to calculate the parameters of the utility function so as to estimate the optimal threshold and its 95% credible interval using the Bayesian inference. The simulation study found that the method had low bias and coverage probability close to 95% in multiple settings, but also the need of large sample size to estimate the optimal threshold in some settings. The method is then applied to the PETACC-8 trial that compares the efficacy of chemotherapy with a combined chemotherapy + anti-epidermal growth factor receptor in stage III colorectal cancer.

Background: With the increase of life expectancy, *On behalf of the REIN registry. end-stage renal disease (ESRD) is affecting a growing number of people. Simultaneously, renal replacement therapies (RRTs) have considerably improved patient survival. We investigated the way current RRT practices would affect patients' survival. Methods: We used a multi-state model to represent the transitions between RRTs and the transition to death. The concept of "crude probability of death" combined with this model allowed estimating the proportions of ESRD-related and ESRD-unrelated deaths. Estimating the ESRD-related death rate requires comparing the mortality rate between ESRD patients and the general population. Predicting patients' courses through RRTs and Death states could be obtained by solving a system of Kolmogorov differential equations. The impact of practice on patient survival was quantified using the restricted mean survival time (RMST) which was compared with that of healthy subjects with same characteristics. Results: The crude probability of ESRD-unrelated death was nearly zero in the youngest patients (18-45 years) but was a sizeable part of deaths in the oldest (≥70 years). Moreover, in the oldest patients, the proportion of expected death was higher in patient without vs. with diabetes because the former live older. In men aged 75 years at first RRT, the predicted RMSTs in patients with and without diabetes were, respectively, 61% and 69% those of comparable healthy men. Conclusion: Using the concept of "crude probability of death" with multi-state models is feasible and useful to assess the relative benefits of various treatments in ESRD and help patient long-term management.

Classifying patients according to longitudinal measures, or trajectory classification, has become frequent in clinical research. The k-means algorithm is increasingly used for this task in case of continuous variables with standard deviations that do not depend on the mean. One feature of count and binary data modeled by Poisson or logistic regression is that the variance depends on the mean; hence, the within-group variability changes from one group to another depending on the mean trajectory level. Mixture modeling could be used here for classification though its main purpose is to model the data. The results obtained may change according to the main objective. This article presents an extension of the k-means algorithm that takes into account the features of count and binary data by using the deviance as distance metric. This approach is justified by its analogy with the classification likelihood. Two applications are presented with binary and count data to show the differences between the classifications obtained with the usual Euclidean distance versus the deviance distance.

Group-based trajectory models had a rapid development in the analysis of longitudinal data in clinical research. In these models, the assumption of homoscedasticity of the residuals is frequently made but this assumption is not always met. We developed here an easy-to-perform graphical method to assess the assumption of homoscedasticity of the residuals to apply especially in group-based trajectory models. The method is based on drawing an envelope to visualize the local dispersion of the residuals around each typical trajectory. Its efficiency is demonstrated using data on CD4 lymphocyte counts in patients with human immunodeficiency virus put on antiretroviral therapy. Four distinct distributions that take into account increasing parts of the variability of the observed data are presented. Significant differences in group structures and trajectory patterns were found according to the chosen distribution. These differences might have large impacts on the final trajectories and their characteristics; thus on potential medical decisions. With a single glance, the graphical criteria allow the choice of the distribution that best capture data variability and help dealing with a potential heteroscedasticity problem., (© The Author(s) 2013.)

In Africa, HIV and feeding practices deeply affect child mortality. To prevent mother-to-child transmission, the World Health Organization recommends exclusive breastfeeding for 6 months and replacement feeding when acceptable, feasible, affordable, and sustainable. Determining the proportion and number of children saved with exclusive breastfeeding and replacement feeding is essential to design and implement crucial nationwide policies. Using data on 31 sub-Saharan countries and a decision tree for risk assessment, the authors estimated the number of children's lives potentially saved according to 6 scenarios that combine exclusive breastfeeding for 6 months or replacement feeding with 3 promotion strategies. Among all HIV-negative children born to HIV-positive mothers who die in sub-Saharan Africa per year, 52,315 (9.6%) would be saved yearly with exclusive breastfeeding versus 21,638 (4.0%) with replacement feeding. Promotion support would double these numbers (110,625 vs 45,330; ie, 20.3% vs 8.3%), and with additional prenatal group education, 132,633 versus 54,192 lives would be saved (24.3% vs 9.9%). Wherever replacement feeding is not possible, exclusive breastfeeding with promotion support and prenatal group education would save 1 of 4 exposed children.

Modelization of fecundability stepped recently from demography and population-based contexts to reproductive biology and treatment of infertility. This created a strong call for flexibility and robustness. Indeed, explained and unexplained heterogeneities are non-negligible sources of bias that result in false conclusions as to the determinants of fertility or to the success rates of reproductive techniques, among other examples. There are two main sources of heterogeneity: biological heterogeneity and heterogeneity of sexual behaviour. A uniform presentation of time-to-pregnancy and Barrett-Marshall models is proposed to enlighten their similarities and differences in modelling heterogeneity of fecundability. Mixed models for fecundability studies are presented as tools to allow for unexplained heterogeneity and to quantify heterogeneity of the effect of observed factors and variability of size of this unexplained heterogeneity between subpopulations. Some criteria for the modelling strategy in fecundability studies are suggested with emphasis on the unit-treatment additivity criterion. The strong and complex selection process resulting from heterogeneity is described as well as the selection and cross-selection processes of observed and unobserved fecundability factors. Consequences regarding data collection and statistical inference are discussed. In the current context, a consensus setting general rules for data collection and statistical analysis would be useful to compare the results and increase the reliability of these results in medical practice.

Putting a screening or a diagnostic test into everyday use requires the determination of its threshold. The authors present methods that yield a point and an interval estimation of the threshold that maximize the population utility whenever the test results are normally or log-normally distributed among healthy and among diseased subjects, with equal variances. These methods were assessed for bias, coverage probability, coverage symmetry, and confidence-interval width using simulation. They proved to be asymptotically nonbiased and to have a satisfactory coverage probability whenever the sample sizes of the healthy and the diseased subjects are equal to or greater than 50. The methods were next applied to determine an optimal threshold for the antibody load used to diagnose congenital toxoplasmosis at birth. The methods are easy to implement and impose few constraints; however, the sample sizes should be carefully determined according to the required accuracy.