Nonparametric change point estimation for survival distributions with a partially constant hazard rate

Abstract

We present a new method for estimating a change point in the hazard function of a survival distribution assuming a constant hazard rate after the change point and a decreasing hazard rate before the change point. Our method is based on fitting a stump regression to p values for testing hazard rates in small time intervals. We present three real data examples describing survival patterns of severely ill patients, whose excess mortality rates are known to persist far beyond hospital discharge. For designing survival studies in these patients and for the definition of hospital performance metrics (e.g. mortality), it is essential to define adequate and objective end points. The reliable estimation of a change point will help researchers to identify such end points. By precisely knowing this change point, clinicians can distinguish between the acute phase with high hazard (time elapsed after admission and before the change point was reached), and the chronic phase (time elapsed after the change point) in which hazard is fairly constant. We show in an extensive simulation study that maximum likelihood estimation is not robust in this setting, and we evaluate our new estimation strategy including bootstrap confidence intervals and finite sample bias correction.

Non-parametric treatment time-lag effect estimation

“…While there has been much research into change point analysis, there has been little research on time-lag effects. Some authors have used change point methods to find the time point of change in one group, 12,19,20 but there have been few non-parametric methods considering two groups. It should also be noted that non-parametric and semi-parametric methods that have already been proposed for survival analysis applications do not seem to be readily extendable to either identifying the time point of change between two groups, or to identify the time point of change non-parametrically.…”

“…More recently, Brazzale et al. 19 proposed a non-parametric method to estimate the time point of change in a single group, based on fitting a stump regression to p values for testing hazards rates over small time intervals.…”

“…-since it can be crucial to not only know if two groups differ but also at what point in time some treatment begins to take effect. In methods such as the non-parametric estimation proposed by Brazzale et al 19 and the semi-parametric approach suggested by Chen and Baron 20 that find the change point in distribution of one survival curve, the lag effect could be found by finding the estimate for each group separately. However, it may be preferential in the case of a treatment time-lag effect when a treatment group is begin compared to a control group (for example) to use information from both groups to see when the treatment group changes in distribution from the control group.…”

“…Chen and Baron 20 reviewed some MLE methods as well as introducing some least-square estimation of the Cox proportional hazard model. More recently, Brazzale et al 19 proposed a non-parametric method to estimate the time point of change in a single group, based on fitting a stump regression to p values for testing hazards rates over small time intervals.…”

Efficient estimation of Cox model with random change point

“…8,[17][18][19] Instead of focusing on testing, of course, an alternative approach is to directly make inference about the assumed models and to predict disease risks for different subgroups. [20][21][22][23][24][25] For example, Pons developed a maximum partial likelihood estimation method under a non-regular Cox model with a change-point. 20 And Kosorok and Song proposed a nonparametric maximum likelihood method under the linear transformation model with a change-point to estimate both the threshold and the risk function.…”