Robust prediction of t-year survival with data from multiple studies

Assessment of heterogeneity in an individual participant data meta-analysis of prediction models: An overview and illustration

Clinical prediction models aim to provide estimates of absolute risk for a diagnostic or prognostic endpoint. Such models may be derived from data from various studies in the context of a meta‐analysis. We describe and propose approaches for assessing heterogeneity in predictor effects and predictions arising from models based on data from different sources. These methods are illustrated in a case study with patients suffering from traumatic brain injury, where we aim to predict 6‐month mortality based on individual patient data using meta‐analytic techniques (15 studies, n = 11 022 patients). The insights into various aspects of heterogeneity are important to develop better models and understand problems with the transportability of absolute risk predictions.

The use of prognostic scores for causal inference with general treatment regimes

In nonrandomised studies, inferring causal effects requires appropriate methods for addressing confounding bias. Although it is common to adopt propensity score analysis to this purpose, prognostic score analysis has recently been proposed as an alternative strategy. While both approaches were originally introduced to estimate causal effects for binary interventions, the theory of propensity score has since been extended to the case of general treatment regimes. Indeed, many treatments are not assigned in a binary fashion and require a certain extent of dosing. Hence, researchers may often be interested in estimating treatment effects across multiple exposures. To the best of our knowledge, the prognostic score analysis has not been yet generalised to this case. In this article, we describe the theory of prognostic scores for causal inference with general treatment regimes. Our methods can be applied to compare multiple treatments using nonrandomised data, a topic of great relevance in contemporary evaluations of clinical interventions. We propose estimators for the average treatment effects in different populations of interest, the validity of which is assessed through a series of simulations. Finally, we present an illustrative case in which we estimate the effect of the delay to Aspirin administration on a composite outcome of death or dependence at 6 months in stroke patients.

Causal mediation analysis on failure time outcome without sequential ignorability

Mediation analysis is an important topic as it helps researchers to understand why an intervention works. Most previous mediation analyses define effects in the mean scale and require a binary or continuous outcome. Recently, possible ways to define direct and indirect effects for causal mediation analysis with survival outcome were proposed. However, these methods mainly rely on the assumption of sequential ignorability, which implies no unmeasured confounding. To handle the potential confounding between the mediator and the outcome, in this article, we proposed a structural additive hazard model for mediation analysis with failure time outcome and derived estimators for controlled direct effects and controlled mediator effects. Our methods allow time-varying effects. Simulations showed that our proposed estimator is consistent in the presence of unmeasured confounding while the traditional additive hazard regression ignoring unmeasured confounding produces biased results. We applied our method to the Women's Health Initiative data to study whether the dietary intervention affects breast cancer risk through changing body weight.

Time-dependent ROC curve analysis in medical research: current methods and applications

BACKGROUND

ROC (receiver operating characteristic) curve analysis is well established for assessing how well a marker is capable of discriminating between individuals who experience disease onset and individuals who do not. The classical (standard) approach of ROC curve analysis considers event (disease) status and marker value for an individual as fixed over time, however in practice, both the disease status and marker value change over time. Individuals who are disease-free earlier may develop the disease later due to longer study follow-up, and also their marker value may change from baseline during follow-up. Thus, an ROC curve as a function of time is more appropriate. However, many researchers still use the standard ROC curve approach to determine the marker capability ignoring the time dependency of the disease status or the marker.

METHODS

We comprehensively review currently proposed methodologies of time-dependent ROC curves which use single or longitudinal marker measurements, aiming to provide clarity in each methodology, identify software tools to carry out such analysis in practice and illustrate several applications of the methodology. We have also extended some methods to incorporate a longitudinal marker and illustrated the methodologies using a sequential dataset from the Mayo Clinic trial in primary biliary cirrhosis (PBC) of the liver.

RESULTS

From our methodological review, we have identified 18 estimation methods of time-dependent ROC curve analyses for censored event times and three other methods can only deal with non-censored event times. Despite the considerable numbers of estimation methods, applications of the methodology in clinical studies are still lacking.

CONCLUSIONS

The value of time-dependent ROC curve methods has been re-established. We have illustrated the methods in practice using currently available software and made some recommendations for future research.

Retrospective likelihood-based methods for analyzing case-cohort genetic association studies

The case cohort (CCH) design is a cost-effective design for assessing genetic susceptibility with time-to-event data especially when the event rate is low. In this work, we propose a powerful pseudo-score test for assessing the association between a single nucleotide polymorphism (SNP) and the event time under the CCH design. The pseudo-score is derived from a pseudo-likelihood which is an estimated retrospective likelihood that treats the SNP genotype as the dependent variable and time-to-event outcome and other covariates as independent variables. It exploits the fact that the genetic variable is often distributed independent of covariates or only related to a low-dimensional subset. Estimates of hazard ratio parameters for association can be obtained by maximizing the pseudo-likelihood. A unique advantage of our method is that it allows the censoring distribution to depend on covariates that are only measured for the CCH sample while not requiring the knowledge of follow-up or covariate information on subjects not selected into the CCH sample. In addition to these flexibilities, the proposed method has high relative efficiency compared with commonly used alternative approaches. We study large sample properties of this method and assess its finite sample performance using both simulated and real data examples.

Explained variation for recurrent event data

Although there are many suggested measures of explained variation for single-event survival data, there has been little attention to explained variation for recurrent event data. We describe an existing rank-based measure and we investigate a new statistic based on observed and expected event count processes. Both methods can be used for all models. Adjustments for missing data are proposed and demonstrated through simulation to be effective. We compare the population values of the two statistics and illustrate their use in comparing an array of non-nested models for data on recurrent episodes of infant diarrhoea.