Simulating Data with Leaspy

This example demonstrates how to use Leaspy to simulate longitudinal data based on a fitted model.

The following imports bring in the required modules and load the synthetic Parkinson dataset from Leaspy. A logistic model will be fitted on this dataset and then used to simulate new longitudinal data.

from leaspy.datasets import load_dataset
from leaspy.io.data import Data

df = load_dataset("parkinson")

The clinical and imaging features of interest are selected and the DataFrame is converted into a Leaspy Data object that can be used for model fitting.

data = Data.from_dataframe(
    df[
        [
            "MDS1_total",
            "MDS2_total",
            "MDS3_off_total",
            "SCOPA_total",
            "MOCA_total",
            "REM_total",
            "PUTAMEN_R",
            "PUTAMEN_L",
            "CAUDATE_R",
            "CAUDATE_L",
        ]
    ]
)

A logistic model with a two-dimensional latent space is initialized.

from leaspy.models import LogisticModel

model = LogisticModel(name="test-model", source_dimension=2)

The model is fitted to the data using the MCMC-SAEM algorithm. A fixed seed is used for reproducibility and 100 iterations are performed.

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

Fit with `AlgorithmName.FIT_MCMC_SAEM` took: 4.17s

The parameters for simulating patient visits are defined. These parameters specify the number of patients, the visit spacing, and the timing variability.

visit_params = {
    "patient_number": 5,
    "visit_type": "random",  # The visit type could also be 'dataframe' with df_visits.
    # "df_visits": df_test           # Example for custom visit schedule.
    "first_visit_mean": 0.0,  # The mean of the first visit age/time.
    "first_visit_std": 0.4,  # The standard deviation of the first visit age/time.
    "time_follow_up_mean": 11,  # The mean follow-up time.
    "time_follow_up_std": 0.5,  # The standard deviation of the follow-up time.
    "distance_visit_mean": 2 / 12,  # The mean spacing between visits in years.
    "distance_visit_std": 0.75
    / 12,  # The standard deviation of the spacing between visits in years.
    "min_spacing_between_visits": 1,  # The minimum allowed spacing between visits.
}

A new longitudinal dataset is simulated from the fitted model using the specified parameters.

df_sim = model.simulate(
    algorithm="simulate",
    features=[
        "MDS1_total",
        "MDS2_total",
        "MDS3_off_total",
        "SCOPA_total",
        "MOCA_total",
        "REM_total",
        "PUTAMEN_R",
        "PUTAMEN_L",
        "CAUDATE_R",
        "CAUDATE_L",
    ],
    visit_parameters=visit_params,
)

Simulate with `simulate` took: 0.03s

The simulated data is converted back to a pandas DataFrame for inspection.

df_sim = df_sim.data.to_dataframe()

The simulated longitudinal dataset is displayed below.

df_sim.head(10)
ID TIME MDS1_total MDS2_total MDS3_off_total SCOPA_total MOCA_total REM_total PUTAMEN_R PUTAMEN_L CAUDATE_R CAUDATE_L
0 0 67.0 0.056451 0.058039 0.230159 0.062639 0.059808 0.114918 0.821016 0.714938 0.588145 0.526200
1 0 68.0 0.002603 0.027123 0.202961 0.081504 0.188143 0.253846 0.664004 0.864308 0.507004 0.616428
2 0 69.0 0.105405 0.046672 0.181350 0.098864 0.089694 0.242480 0.726539 0.663749 0.544198 0.588475
3 0 70.0 0.141412 0.215193 0.141201 0.338784 0.062953 0.304016 0.720180 0.801322 0.684520 0.622316
4 0 71.0 0.090930 0.115712 0.241580 0.188332 0.112838 0.313152 0.753145 0.799685 0.742272 0.700213
5 0 72.0 0.154567 0.161833 0.292684 0.425679 0.064513 0.214714 0.785086 0.703949 0.532459 0.654753
6 0 73.0 0.135401 0.200666 0.212516 0.164426 0.147430 0.243140 0.721107 0.951013 0.882440 0.801490
7 0 74.0 0.282612 0.249392 0.336619 0.197981 0.236832 0.218571 0.855503 0.755934 0.831121 0.675773
8 0 75.0 0.136870 0.180738 0.255311 0.161814 0.075605 0.194809 0.751832 0.853540 0.822887 0.730259
9 0 76.0 0.172981 0.251232 0.425894 0.443622 0.101551 0.231374 0.949818 0.850079 0.836381 0.516746

This concludes the simulation example using Leaspy. Stay tuned for more examples on model fitting and analysis!