Dynamic Pseudo-Observations: A Robust Approach to Dynamic Prediction in Competing Risks

Abstract

In this article, we propose a new approach to the problem of dynamic prediction of survival data in the presence of competing risks as an extension of the landmark model for ordinary survival data. The key feature of our method is the introduction of dynamic pseudo-observations constructed from the prediction probabilities at different landmark prediction times. They specifically address the issue of estimating covariate effects directly on the cumulative incidence scale in competing risks. A flexible generalized linear model based on these dynamic pseudo-observations and a generalized estimation equations approach to estimate the baseline and covariate effects will result in the desired dynamic predictions and robust standard errors. Our approach has a number of attractive features. It focuses directly on the prediction probabilities of interest, avoiding in this way complex modeling of cause-specific hazards or subdistribution hazards. As a result, it is robust against departures from these omnibus models. From a computational point of view an advantage of our approach is that it can be fitted with existing statistical software and that a variety of link functions and regression models can be considered, once the dynamic pseudo-observations have been estimated. We illustrate our approach on a real data set of chronic myeloid leukemia patients after bone marrow transplantation.

Dynamic prediction of cumulative incidence functions by direct binomial regression

“…This is a continuation of the work by Nicolaie et al. (, ), where the cause‐specific and pseudo‐observation approach was combined with landmarking. The three approaches differ in a number of ways.…”

“…The same data were also analyzed using cause‐specific hazards (Nicolaie et al., ) and dynamic pseudo‐observations (Nicolaie et al., ), where the focus was on dynamic prediction of the cumulative incidence function at 5 years for s between 0 and 1 year. We have taken it a step further by also allowing t to vary.…”

Prediction errors for state occupation and transition probabilities in multi‐state models

“…Aalen–Johansen) estimates of the state occupation probabilities based on subjects at risk at the prediction time s (Putter and Spitoni, ). This idea of dynamic pseudo‐observations has been used previously in for instance Nicolaie, van Houwelingen, de Witte, and Putter ().…”

Dynamic prediction of mortality among patients in intensive care using the sequential organ failure assessment (SOFA) score: a joint competing risk survival and longitudinal modeling approach

“…Another popular approach for calculating dynamically updated predictions of survival probabilities with time‐dependent covariates is by landmarking (HOUWELINGEN, ; YINGYE and HEAGERTY, ; HOUWELINGEN and PUTTER, ). This approach has also been applied to data with competing risks (NICOLAIE et al , ; ; CORTESE and ANDERSEN, ). Here, at every landmark time point t s , a survival model is fitted using data of individuals who are at risk at landmark s .…”