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: 3.71s

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	59.0	0.189837	0.108346	0.333539	0.129448	0.047005	0.420709	0.613526	0.773531	0.529728	0.343298
1	0	60.0	0.193939	0.062798	0.254718	0.114945	0.046977	0.431756	0.504392	0.703654	0.450950	0.333464
2	0	61.0	0.030214	0.171499	0.307285	0.253302	0.226160	0.430963	0.719570	0.732159	0.357568	0.451332
3	0	62.0	0.118672	0.152737	0.300467	0.437961	0.029535	0.508501	0.741038	0.903827	0.491854	0.541575
4	0	63.0	0.085761	0.217857	0.320099	0.153371	0.217154	0.630533	0.788019	0.862324	0.623736	0.523061
5	0	64.0	0.253548	0.155311	0.256859	0.272580	0.046067	0.563549	0.647653	0.839016	0.700722	0.570511
6	0	65.0	0.270736	0.280015	0.285188	0.169387	0.034665	0.700266	0.896325	0.802742	0.658602	0.734675
7	0	66.0	0.242705	0.252954	0.205068	0.376477	0.155729	0.633043	0.808777	0.911349	0.629066	0.555425
8	0	67.0	0.275077	0.150783	0.245891	0.233559	0.184104	0.795353	0.810372	0.752424	0.723899	0.673273
9	0	68.0	0.305548	0.321285	0.393659	0.368660	0.156345	0.780888	0.805010	0.954272	0.424553	0.750659

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