Models with change-point in covariates have wide applications in cancer research with the response being the time to a certain event. A Cox model with change-point in covariate is considered at which the pattern of the change-point effects can be flexibly specified. To test for the existence of the change-point effects, three statistical tests, namely, the maximal score, maximal normalized score, and maximal Wald tests are proposed. The asymptotic properties of the test statistics are established. Monte Carlo approaches to simulate the critical values are suggested. A large-scale simulation study is carried out to study the finite sample performance of the proposed test statistics under the null hypothesis of no change-points and various alternative hypothesis settings. Each of the proposed methods provides a natural estimate for the location of the change-point, but it is found that the performance of the maximal score test can be sensitive to the true location of the change-point in some cases, while the performance of the maximal Wald test is very satisfactory in general even in cases with moderate sample size. For illustration, the proposed methods are applied to two medical datasets concerning patients with primary biliary cirrhosis and breast cancer, respectively. K E Y W O R D S asymptotic properties, change-point model, Cox regression model, Monte Carlo method, score test, Wald test

ObjectivesThe present study aimed to examine the trends and characteristics of fall-related attendance in accident and emergency department (AED) by injury type and the trend in associated average length of stay (LOS) among children and adolescents in Hong Kong.DesignA retrospective approach was adopted.SettingAED, involving all local public emergency departments from 2001 to 2012.Participants63 557 subjects aged 0–19 years with fall injury record were included in the analysis.Primary outcome measuresFall-related injury number and rates were calculated and reported. Poisson and negative binomial regression models were used to study the trends of injury incidence rate at different body regions.ResultsAED fall-related attendance rate increased significantly with an annual percentage change of 4.45 (95% CI 3.43 to 5.47%, p<0.0001). The attendance number of male subjects was persistently higher than female subjects. The standardised rate of fracture injury increased by 1.31% (95% CI 0.56 to 2.05%, p<0.0001) and that of non-fracture injury increased by 9.23% (95% CI 7.07 to 11.43%, p<0.0001) annually. Upper limb was the most frequently fractured location. It included forearm/elbow, shoulder/upper arm and wrist/hand with descending order of frequency. On the contrary, head was the most frequent non-fracture location, followed by forearm/elbow.ConclusionsThe rates of fall-related attendance have been increasing and still remain high. There were significant increases in non-fracture injuries. Fractures were most frequently found in the upper extremity of a child while the most common non-fracture location was head. It appears that more efforts should be made and preventive measures should be implemented for children and adolescents in Hong Kong.

We apply a maximal likelihood ratio test for the presence of multiple change-points in the covariate effects based on the Cox regression model. The covariate effect is assumed to change smoothly at one or more unknown change-points. The number of change-points is inferred by a sequential approach. Confidence intervals for the regression and change-point parameters are constructed by a bootstrap method based on Bernstein polynomials conditionally on the number of change-points. The methods are assessed by simulations and are applied to two datasets.

A flexible class of semiparametric partly linear frailty transformation models is considered for analyzing clustered interval‐censored data, which arise naturally in complex diseases and dental research. This class of models features two nonparametric components, resulting in a nonparametric baseline survival function and a potential nonlinear effect of a continuous covariate. The dependence among failure times within a cluster is induced by a shared, unobserved frailty term. A sieve maximum likelihood estimation method based on piecewise linear functions is proposed. The proposed estimators of the regression, dependence, and transformation parameters are shown to be strongly consistent and asymptotically normal, whereas the estimators of the two nonparametric functions are strongly consistent with optimal rates of convergence. An extensive simulation study is conducted to study the finite‐sample performance of the proposed estimators. We provide an application to a dental study for illustration.