Joint modeling of survival time and longitudinal outcomes with flexible random effects

Modelling the patient accrual with truncated Gaussian mixture distribution for the accurate estimation of sample size in survival trials

In survival trials with fixed trial length, the patient accrual rate has a significant impact on the sample size estimation or equivalently, on the power of trials. A larger sample size is required for the staggered patient entry. During enrollment, the patient accrual rate changes with the recruitment publicity effect, disease incidence and many other factors and fluctuations of the accrual rate occur frequently. However, the existing accrual models are either over-simplified for the constant rate assumption or complicated in calculation for the subdivision of the accrual period. A more flexible accrual model is required to represent the fluctuant patient accrual rate for accurate sample size estimation. In this paper, inspired by the flexibility of the Gaussian mixture distribution in approximating continuous densities, we propose the truncated Gaussian mixture distribution accrual model to represent different variations of accrual rate by different parameter configurations. The sample size calculation formula and the parameter setting of the proposed accrual model are discussed further.

A Multi-Objective INLP Model of Sustainable Resource Allocation for Long-Range Maritime Search and Rescue

Maritime search and rescue (SAR) operations play a crucial role in reducing fatalities and mitigating human suffering. Compared to short-range maritime SAR, long-range maritime SAR (LRMSAR) is more challenging due to the far distance from the shore, changeful weather, and less available resources. Such an operation put high requirements on decision makers to timely assign multiple resources, such as aircraft and vessels to deal with the emergency. However, most current researches pay attention to assign only one kind of resource, while practically, multiple resources are necessary for LRMSAR. Thus, a method is proposed to provide support for decision makers to allocate multiple resources in dealing with LRMSAR problem; to ensure the sustainable use of resources. First, by analyzing the factors involved in the whole process, we formulated the problem as a multi-objective optimization problem, the objective of which was to maximize both the probability of completing the tasks and the utilities of allocated resources. Based on the theory of search, an integer nonlinear programming (INLP) model was built for different tasks. Second, in order to solve the non-deterministic polynomial-time hardness (NP-hard) model, by constructing a rule base, candidate solutions can be found to improve the calculation efficiency. Furthermore, in order to obtain the optimal scheme, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was applied to the candidate solution sets to approximate Pareto fronts. Finally, an emergency case of Chinese Bohai Sea was used to demonstrate the effectiveness of the proposed model. In the study, 11 resource allocation schemes were obtained to respond to the emergency, and calculation processes of schemes were further analyzed to demonstrate our model’s rationality. Results showed that the proposed models provide decision-makers with scientific decision support on different emergency tasks.

joineRML: a joint model and software package for time-to-event and multivariate longitudinal outcomes

BACKGROUND

Joint modelling of longitudinal and time-to-event outcomes has received considerable attention over recent years. Commensurate with this has been a rise in statistical software options for fitting these models. However, these tools have generally been limited to a single longitudinal outcome. Here, we describe the classical joint model to the case of multiple longitudinal outcomes, propose a practical algorithm for fitting the models, and demonstrate how to fit the models using a new package for the statistical software platform R, joineRML.

RESULTS

A multivariate linear mixed sub-model is specified for the longitudinal outcomes, and a Cox proportional hazards regression model with time-varying covariates is specified for the event time sub-model. The association between models is captured through a zero-mean multivariate latent Gaussian process. The models are fitted using a Monte Carlo Expectation-Maximisation algorithm, and inferences are based on approximate standard errors from the empirical profile information matrix, which are contrasted to an alternative bootstrap estimation approach. We illustrate the model and software on a real data example for patients with primary biliary cirrhosis with three repeatedly measured biomarkers.

CONCLUSIONS

An open-source software package capable of fitting multivariate joint models is available. The underlying algorithm and source code makes use of several methods to increase computational speed.