This paper deals with fitting piecewise terms in regression models where one or more break-points are true parameters of the model. For estimation, a simple linearization technique is called for, taking advantage of the linear formulation of the problem. As a result, the method is suitable for any regression model with linear predictor and so current software can be used; threshold modelling as function of explanatory variables is also allowed. Differences between the other procedures available are shown and relative merits discussed. Simulations and two examples are presented to illustrate the method.

Summary This paper is concerned with interval estimation for the breakpoint parameter in segmented regression. We present score‐type confidence intervals derived from the score statistic itself and from the recently proposed gradient statistic. Due to lack of regularity conditions of the score, non‐smoothness and non‐monotonicity, naive application of the score‐based statistics is unfeasible and we propose to exploit the smoothed score obtained via induced smoothing. We compare our proposals with the traditional methods based on the Wald and the likelihood ratio statistics via simulations and an analysis of a real dataset: results show that the smoothed score‐like statistics perform in practice somewhat better than competitors, even when the model is not correctly specified.

The methods described in this article are implemented in the new R package cumSeg available from the Comprehensive R Archive Network at http://CRAN.R-project.org/package=cumSeg.

We present a simple and effective iterative procedure to estimate segmented mixed models\ud in a likelihood based framework. Random effects and covariates are allowed for each model parameter,\ud including the changepoint. The method is practical and avoids the computational burdens related\ud to estimation of nonlinear mixed effects models. A conventional linear mixed model with proper\ud covariates that account for the changepoints is the key to our estimating algorithm. We illustrate\ud the method via simulations and using data from a randomized clinical trial focused on change in\ud depressive symptoms over time which characteristically show two separate phases of change

We present a model for estimation of temperature effects on mortality that is able to capture jointly the typical features of every temperature-death relationship, that is, nonlinearity and delayed effect of cold and heat over a few days. Using a segmented approximation along with a doubly penalized spline-based distributed lag parameterization, estimates and relevant standard errors of the cold- and heat-related risks and the heat tolerance are provided. The model is applied to data from Milano, Italy.

Our approach provides a flexible and precise method to quantify health effects of both heat and cold exposure at individual lags and to model the overall pattern of the delayed effect.

In this article we propose a parsimonious parameterisation to model the so-called erosion of the covariate effect in the Cox model, namely a covariate effect approaching to zero as the follow-up time increases. The proposed parameterisation is based on the segmented relationship where proper constraints are set to accomodate for the erosion. Relevant hypothesis testing is discussed. The approach is illustrated on two historical datasets in the survival analysis literature, and some simulation studies are presented to show how the proposed framework leads to a test for a global effect with good power as compared with alternative procedures. Finally, possible generalisations are also presented for future research.

Exhaled nitric oxide (eNO) levels are correlated with several markers of atopy and inflammatory activity in the airways, but the relationship between eNO and total serum IgE has not been fully elucidated in the context of allergic sensitization. The aim of this study was to investigate the relationship between eNO, total serum IgE and allergic sensitization in childhood asthma and allergic rhinitis. eNO levels, lung function, skin prick tests and total serum IgE were determined in 109 children (mean age, 10.4 yr) with mild intermittent asthma and in 41 children (mean age, 10.1 yr) with allergic rhinitis; 25 healthy non-atopic children were recruited as controls. eNO levels (median) were significantly higher in patients with asthma (22.7 p.p.b.) and in those with allergic rhinitis (15.3 p.p.b.) than in healthy controls (5.9 p.p.b.). Children with allergic asthma had higher eNO levels than children with allergic rhinitis. A significant positive correlation was found between eNO and total serum IgE (asthma, r = 0.42, p < 0.0001; allergic rhinitis, r = 0.31, p < 0.01), and between eNO and the number of positive skin prick tests (asthma, r = 0.31, p < 0.0001; allergic rhinitis, r = 0.39, p < 0.01). eNO levels were better correlated with total IgE than with the number of positive skin prick tests. This correlation was independent of allergic sensitization. High total serum IgE represents a specific and predictive marker of eNO increase in children with asthma or allergic rhinitis. This finding adds further support to the hypothesis that increased serum IgE could be a marker itself of airway inflammation in patients with allergic disease.