Threshold estimation based on a p-value framework in dose-response and regression settings

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

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.

Thirty-day mortality leads to underestimation of postoperative death after liver resection: A novel method to define the acute postoperative period

BACKGROUND

Postoperative mortality commonly is defined as death occurring within 30 days of surgery or during hospitalization. After resection for liver malignancies, this definition may result in underreporting, because mortality caused by postoperative complications can be delayed as the result of improved critical care. The aim of this study was to estimate statistically the acute postoperative period (APP) after partial hepatectomy and to compare mortality within this phase to standard timestamps.

METHODS

From a prospective database, 784 patients undergoing resection for primary and secondary hepatic malignancies between 2003 and 2013 were reviewed. For estimation of APP, a novel statistical method applying tests for a constant postoperative hazard was implemented. Multivariable mortality analysis was performed.

RESULTS

The APP was determined to last for 80 postoperative days (95% confidence interval 40-100 days). Within this period, 55 patients died (7.0%; 80-day mortality). In comparison, 30-day mortality (N = 32, 4.0%) and in-hospital death (N = 39, 5.0%) were relevantly less. No patient died between postoperative days 80 and 90. The causes of mortality within 30 days and from days 30-80 did not greatly differ, especially regarding posthepatectomy liver failure (44% vs 39%, P = .787). Septic complications, however, tended to cause late deaths more frequently (43% vs 25%, P = .255). Comorbidities (Charlson comorbidity index ≥ 3; P = .046), increased preoperative alanine aminotransferase activity (P = .030), and major liver resection (P = .035) were independent risk factors of 80-day mortality.

CONCLUSION

After liver resection for primary and secondary malignancies, 90-day rather than 30-day or in-hospital mortality should be used to avoid underreporting of deaths.

Change point testing in logistic regression models with interaction term

A threshold effect takes place in situations where the relationship between an outcome variable and a predictor variable changes as the predictor value crosses a certain threshold/change point. Threshold effects are often plausible in a complex biological system, especially in defining immune responses that are protective against infections such as HIV-1, which motivates the current work. We study two hypothesis testing problems in change point models. We first compare three different approaches to obtaining a p-value for the maximum of scores test in a logistic regression model with change point variable as a main effect. Next, we study the testing problem in a logistic regression model with the change point variable both as a main effect and as part of an interaction term. We propose a test based on the maximum of likelihood ratios test statistic and obtain its reference distribution through a Monte Carlo method. We also propose a maximum of weighted scores test that can be more powerful than the maximum of likelihood ratios test when we know the direction of the interaction effect. In simulation studies, we show that the proposed tests have a correct type I error and higher power than several existing methods. We illustrate the application of change point model-based testing methods in a recent study of immune responses that are associated with the risk of mother to child transmission of HIV-1.