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: 6.81s

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: 0.05s

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 48.0 0.082620 0.060121 0.196018 0.113921 0.072225 0.294356 0.912546 0.839195 0.568094 0.403453
1 0 49.0 0.049329 0.065133 0.364824 0.123405 0.109159 0.507428 0.882876 0.714090 0.589740 0.594417
2 0 50.0 0.055948 0.056322 0.159568 0.188488 0.051696 0.301199 0.759015 0.713410 0.730305 0.677861
3 0 51.0 0.085227 0.108017 0.263267 0.121330 0.084365 0.368686 0.838947 0.777509 0.586022 0.545453
4 0 52.0 0.073539 0.044140 0.383070 0.152411 0.011024 0.297112 0.784642 0.569088 0.828638 0.777341
5 0 53.0 0.053657 0.114640 0.265941 0.056333 0.176415 0.336634 0.846059 0.759150 0.707306 0.560700
6 0 54.0 0.164731 0.085557 0.154359 0.079580 0.183357 0.298657 0.747321 0.865993 0.706671 0.664610
7 0 55.0 0.049243 0.197857 0.300925 0.180697 0.124273 0.461153 0.754181 0.828697 0.739238 0.640222
8 0 56.0 0.061109 0.121964 0.238648 0.162513 0.131874 0.412425 0.883213 0.804650 0.588844 0.688872
9 0 57.0 0.152195 0.282577 0.229020 0.081195 0.126841 0.362385 0.927698 0.767671 0.716296 0.652593

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