Disease Progression Modeling

Module: Healthcare AI | Difficulty: Advanced

Linear Mixed-Effects Model

where and .

Joint Model

where is the longitudinal marker value at time .

Disease Progression Models

import torch
import torch.nn as nn
import numpy as np

class RecurrentProgressionModel(nn.Module):
    def __init__(self, input_dim=50, hidden_dim=64, num_layers=2):
        super().__init__()
        self.input_proj = nn.Linear(input_dim, hidden_dim)
        self.rnn = nn.LSTM(hidden_dim, hidden_dim, num_layers,
                          batch_first=True, dropout=0.2)
        self.attention = nn.MultiheadAttention(hidden_dim, num_heads=4,
                                              batch_first=True)
        self.progression_head = nn.Linear(hidden_dim, 1)

    def forward(self, x, lengths=None):
        x = torch.relu(self.input_proj(x))
        if lengths is not None:
            packed = nn.utils.rnn.pack_padded_sequence(
                x, lengths.cpu(), batch_first=True, enforce_sorted=False)
            rnn_out, _ = self.rnn(packed)
            rnn_out, _ = nn.utils.rnn.pad_packed_sequence(rnn_out, batch_first=True)
        else:
            rnn_out, _ = self.rnn(x)
        attn_out, _ = self.attention(rnn_out, rnn_out, rnn_out)
        final = attn_out[:, -1, :]
        return self.progression_head(final)

model = RecurrentProgressionModel(input_dim=50, hidden_dim=64)
x = torch.randn(10, 20, 50)
lengths = torch.randint(10, 20, (10,))
output = model(x, lengths)
print(f'Progression output shape: {output.shape}')

Research Insight: Joint models that simultaneously model longitudinal markers and time-to-event outcomes outperform separate analyses because they leverage the correlation between repeated measurements and survival. Deep joint models using neural ODEs can capture non-linear trajectories and irregular sampling patterns common in real-world clinical data.