Testing for change‐point in the covariate effects based on the Cox regression model

Abstract

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

On the association between COVID-19 vaccination levels and incidence and lethality rates at a regional scale in Spain

“…This leads to models with change points in the covariates, which can be adapted to multiple contexts, including survival analyses (Lee et al. 2020 ) and exposure-outcome epidemiological studies (Sarnaglia et al. 2021 ).…”

Survival analysis with change-points in covariate effects

“…13,14 Unlike the maximal normalized score and Wald tests, evaluation of the maximal likelihood ratio test statistic does not involve an estimate of the variance–covariance matrix. 15…”

“…13,14 Unlike the maximal normalized score and Wald tests, evaluation of the maximal likelihood ratio test statistic does not involve an estimate of the variance-covariance matrix. 15 If H ð0Þ 0 is rejected, we proceed to test for the presence of two or more change-points in the model. The maximal likelihood ratio test statistic considered in step m for the hypotheses H ðmÞ 0 against H ðmÞ 1 for m !…”

On the association between COVID-19 vaccination levels and incidence and lethality rates at a regional scale in Spain

“…The basis behind change point analysis can be extended to account for the effect of a temporallyvarying covariate potentially associated with a variation in the values of a time series of interest. This leads to models with change points in the covariates, which can be adapted to multiple contexts, including survival analyses (Lee et al, 2020) and exposure-outcome epidemiological studies (Sarnaglia et al, 2021). In general, segmented regression models (Muggeo, 2003) are the natural framework for dealing with this type of covariate effects.…”