Research Objective:

Our primary objective is to develop and evaluate an integrated framework that combines Continuous$-$time Markov multistate models and recurrent neural networks $($RNNs$)$ for predicting the next state after k time points in Heart Transplant Monitoring Data.

Description of Data:

The dataset, available within the msm package in R$,$ comprises longitudinal records of approximately yearly angiographic examinations of heart transplant recipients. Each examination records the state of cardiac allograft vasculopathy $($CAV$),$ indicating the arterial wall's deterioration.

Methodology:

To achieve our research objective, we propose an $****$integrated framework leveraging the strengths of both Continuous$-$time Markov multistate models and RNNs$***$:

$****$Continuous$-$time Markov multistate models:

Utilizing the $\text{'}\text{'}\text{'}\text{'}$msm$\text{'}\text{'}\text{'}$ package in R$.$

This approach enables the analysis of transition probabilities between different states of CAV over time, providing insights into the disease progression dynamics.

$*****$Recurrent neural network $($RNN$)$:

Implemented to capture temporal dependencies in the data and predict the next state after k time points.

RNNs excel at learning sequential patterns in data, making them well$-$suited for time series prediction tasks.

$---$Comparison and Evaluation:

We will thoroughly compare the performance of the integrated framework against individual analyses using Continuous$-$time Markov models and RNNs$.$ Specifically, we will evaluate:

Prediction accuracy: Comparing the accuracy of predictions made by the integrated framework with those from standalone Continuous$-$time Markov models and RNNs$.$

Model interpretability: Assessing the interpretability of the integrated framework's predictions in contrast to individual model outputs.

Computational efficiency: Analyzing the computational efficiency of the integrated approach compared to separate model implementations.

Deliverables:

Kindly provide:

Detailed R codes with explanations for implementing the integrated framework, Continuous$-$time Markov models, and RNNs$.$

Comparative analysis of prediction accuracy, interpretability, and computational efficiency.

Mathematical explanations to support the methodology and results interpretation