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.

An accurate estimator of the real-time fatality rate is warranted to monitor the progress of ongoing epidemics, hence facilitating the policy-making process. However, most of the existing estimators fail to capture the time-varying nature of the fatality rate and are often biased in practice. A simple real-time fatality rate estimator with adjustment for reporting delays is proposed in this paper using the fused lasso technique. This approach is easy to use and can be broadly applied to public health practice as only basic epidemiological data are required. A large-scale simulation study suggests that the proposed estimator is a reliable benchmark for formulating public health policies during an epidemic with high accuracy and sensitivity in capturing the changes in the fatality rate over time, while the other two commonly-used case fatality rate estimators may convey delayed or even misleading signals of the true situation. The application to the COVID-19 data in Germany between January 2020 and January 2022 demonstrates the importance of the social restrictions in the early phase of the pandemic when vaccines were not available, and the beneficial effects of vaccination in suppressing the fatality rate to a low level since August 2021 irrespective of the rebound in infections driven by the more infectious Delta and Omicron variants during the fourth wave.

This research is motivated by a periodontal disease dataset that possesses certain special features. The dataset consists of clustered current status time‐to‐event observations with large and varying cluster sizes, where the cluster size is associated with the disease outcome. Also, heavy censoring is present in the data even with long follow‐up time, suggesting the presence of a cured subpopulation. In this paper, we propose a computationally efficient marginal approach, namely the cluster‐weighted generalized estimating equation approach, to analyze the data based on a class of semiparametric transformation cure models. The parametric and nonparametric components of the model are estimated using a Bernstein‐polynomial based sieve maximum pseudo‐likelihood approach. The asymptotic properties of the proposed estimators are studied. Simulation studies are conducted to evaluate the performance of the proposed estimators in scenarios with different degree of informative clustering and within‐cluster dependence. The proposed method is applied to the motivating periodontal disease data for illustration.

The area under the receiver operating characteristic curve (AUC) is one of the most popular measures for evaluating the performance of a predictive model. In nested models, the change in AUC (ΔAUC) can be a discriminatory measure of whether the newly added predictors provide significant improvement in terms of predictive accuracy. Recently, several authors have shown rigorously that ΔAUC can be degenerate and its asymptotic distribution is no longer normal when the reduced model is true, but it could be the distribution of a linear combination of some [Formula: see text] random variables [ 1 , 2 ]. Hence, the normality assumption and existing variance estimate cannot be applied directly for developing a statistical test under the nested models. In this paper, we first provide a brief review on the use of ΔAUC for comparing nested logistic models and the difficulty of retrieving the reference distribution behind. Then, we present a special case of the nested logistic regression models that the newly added predictor to the reduced model contains a change-point in its effects. A new test statistic based on ΔAUC is proposed in this setting. A simple resampling scheme is proposed to approximate the critical values for the test statistic. The inference of the change-point parameter is done via m-out-of- n bootstrap. Large-scale simulation is conducted to evaluate the finite-sample performance of the ΔAUC test for the change-point model. The proposed method is applied to two real-life datasets for illustration.

Infectious diseases, such as the ongoing COVID-19 pandemic, pose a significant threat to public health globally. Fatality rate serves as a key indicator for the effectiveness of potential treatments or interventions. With limited time and understanding of novel emerging epidemics, comparisons of the fatality rates in real-time among different groups, say, divided by treatment, age, or area, have an important role to play in informing public health strategies. We propose a statistical test for the null hypothesis of equal real-time fatality rates across multiple groups during an ongoing epidemic. An elegant property of the proposed test statistic is that it converges to a Brownian motion under the null hypothesis, which allows one to develop a sequential testing approach for rejecting the null hypothesis at the earliest possible time when statistical evidence accumulates. This property is particularly important as scientists and clinicians are competing with time to identify possible treatments or effective interventions to combat the emerging epidemic. The method is widely applicable as it only requires the cumulative number of confirmed cases, deaths, and recoveries. A large-scale simulation study shows that the finite-sample performance of the proposed test is highly satisfactory. The proposed test is applied to compare the difference in disease severity among Wuhan, Hubei province (exclude Wuhan) and mainland China (exclude Hubei) from February to March 2020. The result suggests that the disease severity is potentially associated with the health care resource availability during the early phase of the COVID-19 pandemic in mainland China.