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: 6.77s

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	53.0	0.155898	0.118853	0.351597	0.368132	0.053468	0.086003	0.714066	0.738918	0.670682	0.422618
1	0	54.0	0.103933	0.143772	0.261258	0.102074	0.034996	0.275067	0.863962	0.870770	0.363265	0.525199
2	0	55.0	0.217049	0.197348	0.219519	0.222060	0.071889	0.178917	0.699757	0.722475	0.532379	0.609583
3	0	56.0	0.085104	0.052183	0.195426	0.169035	0.055745	0.244480	0.837818	0.749473	0.546638	0.622183
4	0	57.0	0.295789	0.090025	0.367959	0.168639	0.191922	0.201405	0.866743	0.862373	0.642726	0.600590
5	0	58.0	0.345741	0.244821	0.172055	0.311372	0.116332	0.250161	0.592222	0.855079	0.659069	0.587703
6	0	59.0	0.268063	0.386708	0.215542	0.356714	0.313937	0.217469	0.785240	0.698636	0.501990	0.522023
7	0	60.0	0.171233	0.155168	0.270350	0.202249	0.195739	0.267264	0.695824	0.621570	0.763887	0.569596
8	0	61.0	0.130114	0.258922	0.213576	0.219509	0.146115	0.315394	0.892384	0.861153	0.761038	0.526635
9	0	62.0	0.113763	0.132007	0.175709	0.179988	0.175688	0.580131	0.880047	0.883341	0.761242	0.642723

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