Joint Model

This notebook contains the code for a simple implementation of the Leaspy Joint model on synthetic data.

The following imports are required libraries for numerical computation and data manipulation.

import os
import pandas as pd
import leaspy
from leaspy.io.data import Data

leaspy_root = os.path.dirname(leaspy.__file__)
data_path = os.path.join(leaspy_root, "datasets/data/simulated_data_for_joint.csv")

df = pd.read_csv(data_path, dtype={"ID": str}, sep=";")
print(df.head())

    ID    TIME  EVENT_TIME  EVENT_BOOL       Y0    Y1   Y2   Y3
0  116  78.461        85.5           1  0.44444  0.04  0.0  0.0
1  116  78.936        85.5           1  0.60000  0.00  0.0  0.2
2  116  79.482        85.5           1  0.39267  0.04  0.0  0.2
3  116  79.939        85.5           1  0.58511  0.00  0.0  0.0
4  116  80.491        85.5           1  0.57044  0.00  0.0  0.0

To use the Joint Model in Leaspy, your dataset must include the following columns:

1. ID : Patient identifier

2. TIME : Time of measurement

3. EVENT_TIME : Time of the event

4. EVENT_BOOL : Event indicator:

   • 1 if the event occurred

   • 0 if censored

   • 2 if a competing event occurred

For one patient, the event time and event bool are the same for each row.

We load the Joint Model from the leaspy.models and transform the dataset in a leaspy-compatible form with the built-in functions.

from leaspy.models import JointModel

data = Data.from_dataframe(df, "joint")
model = JointModel(name="test_model", nb_events=1, source_dimension=2)

The parameter nb_events should match the number of distinct event types present in the EVENT_BOOL column:

• If EVENT_BOOL contains values {0, 1}, then nb_events=1.

• If it contains values {0, 1, 2}, then nb_events=2.

Once the model is initialized, we can fit it to the data.

model.fit(data, "mcmc_saem", seed=1312, n_iter=100, progress_bar=False)
model.summary()

Fit with `AlgorithmName.FIT_MCMC_SAEM` took: 1.82s

================================================================================
                                 Model Summary                                  
================================================================================
Model Name: test_model
Model Type: JointModel
Features (4): Y0, Y1, Y2, Y3
Sources (2): Source 0 (s0), Source 1 (s1)
Observation Models: gaussian-scalar, weibull-right-censored-with-sources
Neg. Log-Likelihood: -415.8537

Training Metadata
--------------------------------------------------------------------------------
Algorithm: AlgorithmName.FIT_MCMC_SAEM
Seed: 1312
Iterations: 100

Data Context
--------------------------------------------------------------------------------
Subjects: 17
Visits: 157
Total Observations: 628

Leaspy Version: 2.0.1
================================================================================

Population Parameters
--------------------------------------------------------------------------------
  log_rho_mean       [1.8040]
  n_log_nu_mean      [-1.9862]
  betas_mean:
                          s0        s1
            b0       -0.0163   -0.0908
            b1       -0.0079   -0.0469
            b2       -0.1058   -0.0088
                          Y0        Y1        Y2        Y3
  log_g_mean          0.1157    2.8874    2.5624    1.3001
                          Y0        Y1        Y2        Y3
  log_v0_mean        -3.0789   -3.8272   -3.8023   -2.7624

Individual Parameters
--------------------------------------------------------------------------------
  tau_mean           [78.4523]
  tau_std            [5.7890]
  xi_std             [0.4379]
  zeta_mean:
            s0        0.0421
            s1        0.0660

Noise Model
--------------------------------------------------------------------------------
  noise_std          0.0947
================================================================================

The Joint Model includes specific parameters such as log_rho_mean and zeta_mean.

print(model.parameters)

{'betas_mean': tensor([[-0.0163, -0.0908],
        [-0.0079, -0.0469],
        [-0.1058, -0.0088]]), 'log_g_mean': tensor([0.1157, 2.8874, 2.5624, 1.3001]), 'log_rho_mean': tensor([1.8040]), 'log_v0_mean': tensor([-3.0789, -3.8272, -3.8023, -2.7624]), 'n_log_nu_mean': tensor([-1.9862]), 'noise_std': tensor(0.0947, dtype=torch.float64), 'tau_mean': tensor([78.4523], dtype=torch.float64), 'tau_std': tensor([5.7890], dtype=torch.float64), 'xi_std': tensor([0.4379], dtype=torch.float64), 'zeta_mean': tensor([[0.0421],
        [0.0660]])}

We have seend how to fit a Joint Model using Leaspy. It also provides other models as the Mixture Model that can be explored in the next examples.