Delayed kernels for longitudinal survival analysis and dynamic prediction.

Predicting patient survival probabilities based on observed covariates is an important assessment in clinical practice. These patient-specific covariates are often measured over multiple follow-up appointments. It is then of interest to predict survival based on the history of these longitudinal measurements, and to update predictions as more observations become available. The standard approaches to these so-called 'dynamic prediction' assessments are joint models and landmark analysis. Joint models involve high-dimensional parameterizations, and their computational complexity often prohibits including multiple longitudinal covariates. Landmark analysis is simpler, but discards a proportion of the available data at each 'landmark time'. In this work, we propose a 'delayed kernel' approach to dynamic prediction that sits somewhere in between the two standard methods in terms of complexity. By conditioning hazard rates directly on the covariate measurements over the observation time frame, we define a model that takes into account the full history of covariate measurements but is more practical and parsimonious than joint modelling. Time-dependent association kernels describe the impact of covariate changes at earlier times on the patient's hazard rate at later times. Under the constraints that our model (a) reduces to the standard Cox model for time-independent covariates, and (b) contains the instantaneous Cox model as a special case, we derive two natural kernel parameterizations. Upon application to three clinical data sets, we find that the predictive accuracy of the delayed kernel approach is comparable to that of the two existing standard methods.

Bayesian federated inference for estimating statistical models based on non-shared multicenter data sets.

Identifying predictive factors for an outcome of interest via a multivariable analysis is often difficult when the data set is small. Combining data from different medical centers into a single (larger) database would alleviate this problem, but is in practice challenging due to regulatory and logistic problems. Federated learning (FL) is a machine learning approach that aims to construct from local inferences in separate data centers what would have been inferred had the data sets been merged. It seeks to harvest the statistical power of larger data sets without actually creating them. The FL strategy is not always efficient and precise. Therefore, in this paper we refine and implement an alternative Bayesian federated inference (BFI) framework for multicenter data with the same aim as FL. The BFI framework is designed to cope with small data sets by inferring locally not only the optimal parameter values, but also additional features of the posterior parameter distribution, capturing information beyond what is used in FL. BFI has the additional benefit that a single inference cycle across the centers is sufficient, whereas FL needs multiple cycles. We quantify the performance of the proposed methodology on simulated and real life data.

Bayesian clinical classification from high-dimensional data: Signatures versus variability.

When data exhibit imbalance between a large number d of covariates and a small number n of samples, clinical outcome prediction is impaired by overfitting and prohibitive computation demands. Here we study two simple Bayesian prediction protocols that can be applied to data of any dimension and any number of outcome classes. Calculating Bayesian integrals and optimal hyperparameters analytically leaves only a small number of numerical integrations, and CPU demands scale as O(nd). We compare their performance on synthetic and genomic data to the mclustDA method of Fraley and Raftery. For small d they perform as well as mclustDA or better. For d = 10,000 or more mclustDA breaks down computationally, while the Bayesian methods remain efficient. This allows us to explore phenomena typical of classification in high-dimensional spaces, such as overfitting and the reduced discriminative effectiveness of signatures compared to intra-class variability.