ProMOTe

Overview

This project involves the application of Variational Bayes (VB) methods to fit a probabilistic model to the presence and onset times of various LTCs within a study population. The data is structured in an .rds file containing a named list with multiple components, each representing different aspects of the dataset.

Dependencies

To run the code in this project, the following R libraries are required:

• extraDistr: For working with additional distributions not available in base R.

Data Structure

The .rds file contains a named list with the following components:

• d: An N x M matrix containing data about the presence of conditions for each individual. Each element represents whether a specific condition is present (1 for presence, 0 for absence).
• t: An N x M matrix containing data about the onset ages of conditions for each individual. Each element represents the age at which the condition was observed or diagnosed.
• rho: A vector of length N containing the study start age for each individual. Each element represents the age at the start of the study for a corresponding individual.
• tau: A vector of length N containing the study end age for each individual. Each element represents the age at the of the study for a corresponding individual.
• iota: A vector of length N indicating the status of each individual at the time of tau. Each element is a binary indicator, where 1 represents that the individual is alive and 0 represents that the individual is deceased.
• N: An integer representing the number of individuals in the dataset.
• K: An integer representing the number of clusters in the dataset.
• M: An integer representing the number of conditions in the dataset.
• sex: A vector representing the sex of the individuals in the dataset. This is set to NULL if the information is not available.
• birth_conds: A vector containing the column indices in d that correspond to conditions which only occur at birth. This is set to NULL if there are no such conditions or the information is not available.
• male_conds: A vector containing the column indices in d that correspond to conditions which only occur in males. This is set to NULL if there are no such conditions or the information is not available.
• female_conds: A vector containing the column indices in d that correspond to conditions which only occur in females. This is set to NULL if there are no such conditions or the information is not available.
• cond_list: A string vector containing the names of the conditions included in the dataset. Each element in the vector corresponds to a condition listed in the matrix d.

Functions

1. VB_gaussian_update

Purpose: Perform Variational Bayes (VB) updates for the Gaussian latent class model with fixed K and censored data.

Inputs:

• d: A N x M matrix containing data about the presence of conditions.
• t: A N x M matrix containing data about the onset ages of conditions.
• rho: A vector of length N containing study start ages.
• tau: A vector of length N containing study end ages.
• iota: A vector of length N indicating if individuals are alive/deceased at age tau.
• hyperparameters: A list of hyperparameters of the prior.
• initial_Cstar: A N x K matrix containing an initial value to initialize the latent variable z.
• initial_Dstar: A N x M matrix containing an initial value to initialize the latent variable d.
• initial_pstar: A N x M matrix containing an initial value to initialize the latent variable d.
• initial_qstar: A N x M matrix containing an initial value to initialize the latent variable t.
• initial_rstar: A N x M matrix containing an initial value to initialize the latent variable t.
• N: The number of individuals in the data.
• K: The number of clusters.
• M: The number of conditions in the data.
• epsilon: A number used to determine the stopping condition.
• sex: The sex of individuals in the data.
• birth_conds: Column indices for d indicating conditions that only occur at birth.
• male_conds: Column indices for d indicating conditions which only occur in males.
• female_conds: Column indices for d indicating conditions which only occur in females.
• cond_list: A string vector containing the names of the conditions.

Outputs:

• theta_star: A vector of parameters for the VB posterior of gamma.
• a_star: A M x K matrix of parameters for the VB posterior of pi.
• b_star: A M x K matrix of parameters for the VB posterior of pi.
• u_star, v_star, alpha_star, beta_star: M x K matrices of parameters for the VB posterior of mu and sigma^2.
• C_star: A N x K matrix of parameters for the VB posterior of z.
• p_star, q_star, r_star, D_star: N x M matrices of parameters for the VB posterior of d and t.
• n_steps: The number of iterations required to achieve the stopping condition.

2. expected_lst_lefttrunc

Purpose: Calculate the expected value of a left-truncated location-scale t-distribution.

Inputs:

• df: Degrees of freedom of the t-distribution.
• mu: Location parameter of the t-distribution.
• sigma: Scale parameter of the t-distribution.
• tau: The left truncation point.

Outputs:

• u: The expected value.

3. VB_gaussian_predictive_density

Purpose: Estimate the parameters of the posterior predictive distribution for a new individual.

Inputs:

• hyperparameters: A list of hyperparameters of the posterior.
• M_obs: Indices of the individual's fully observed conditions.
• M_part: Indices of the individual's partially observed conditions.
• M_unobs: Indices of the individual's unobserved conditions.
• d_obs: A vector containing the absence/presence of the fully observed conditions as 0s and 1s.
• t_obs: A vector containing the onset ages of the fully observed conditions.
• d_part: A vector containing the absence/presence of the partially observed conditions as 0s and 1s.
• rho: A vector of length N containing observation start ages.
• tau: A vector of length N containing observation end ages.
• M: The number of conditions in the data.

Outputs:

• phi: A vector of cluster probabilities.
• eta: A matrix of condition probabilities given cluster.
• varpi: A vector of useful intermediate condition probabilities conditional on clusters.

4. expected_LTHC_t_after_tau

Purpose: Estimate the expected time of occurrence of conditions in an individual after tau.

Inputs:

• parameters: A list of posterior predictive parameters (the output of VB_gaussian_predictive_density).
• hyperparameters: A list of hyperparameters of the posterior.
• tau: The individual's age at end of observation.
• M: The number of conditions.

Outputs:

• Et: Expected onset times.

5. probability_LTHC_by_T

Purpose: Estimate the probability of conditions occurring in an individual by time T.

Inputs:

• parameters: A list of posterior predictive parameters (the output of VB_gaussian_predictive_density).
• hyperparameters: A list of hyperparameters of the posterior.
• T: The age by which the conditions should occur.
• tau: The individual's age at end of observation.
• M: The number of conditions.

Outputs:

• prob: A vector of probabilities.