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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.