lucid {LUCIDus}

Fit a lucid model for integrated analysis on exposure, outcome and multi-omics data, allowing for tuning

Description

Fit a lucid model for integrated analysis on exposure, outcome and multi-omics data, allowing for tuning

Usage

lucid(
  G,
  Z,
  Y,
  CoG = NULL,
  CoY = NULL,
  family = c("normal", "binary"),
  K = 2,
  lucid_model = c("early", "parallel", "serial"),
  Rho_G = 0,
  Rho_Z_Mu = 0,
  Rho_Z_Cov = 0,
  verbose_tune = FALSE,
  ...
)

Arguments

G

Exposures, a numeric vector, matrix, or data frame. Categorical variable should be transformed into dummy variables. If a matrix or data frame, rows represent observations and columns correspond to variables.

Z

Omics data. If "early", an N by M matrix; If "parallel", a list, each element i is a matrix with N rows and P_i features; If "serial", a list, each element i is a matrix with N rows and p_i features or a list with two or more matrices with N rows and a certain number of features If "serial", a list, each element is a matrix with N rows or a list with two or more matrices with N rows

Y

Outcome, a numeric vector. Categorical variable is not allowed. Binary outcome should be coded as 0 and 1.

CoG

Optional, covariates to be adjusted for estimating the latent cluster. A numeric vector, matrix or data frame. Categorical variable should be transformed into dummy variables.

CoY

Optional, covariates to be adjusted for estimating the association between latent cluster and the outcome. A numeric vector, matrix or data frame. Categorical variable should be transformed into dummy variables.

family

Distribution of outcome. For continuous outcome, use "normal"; for binary outcome, use "binary". Default is "normal".

K

Number of latent clusters to be tuned. For lucid_model = "early", number of latent clusters (should be greater or equal than 2). Either an integer or a vector of integer. If K is a vector, model selection on K is performed. For lucid_model = "parallel",a list with vectors of integers or just integers, same length as Z, if the element itself is a vector, model selection on K is performed; For lucid_model = "serial", a list, each element is either an integer or an list of integers, same length as Z, if the smallest element (integer) itself is a vector, model selection on K is performed

lucid_model

Specifying LUCID model, "early" for early integration, "parallel" for lucid in parallel, "serial" for lucid in serial

Rho_G

A scalar or a vector. This parameter is the LASSO penalty to regularize exposures. If it is a vector, lucid will call tune_lucid to conduct model selection and variable selection. User can try penalties from 0 to 1. Work for LUCID early only.

Rho_Z_Mu

A scalar or a vector. This parameter is the LASSO penalty to regularize cluster-specific means for omics data (Z). If it is a vector, lucid will call tune_lucid to conduct model selection and variable selection. User can try penalties from 1 to 100. Work for LUCID early only.

Rho_Z_Cov

A scalar or a vector. This parameter is the graphical LASSO penalty to estimate sparse cluster-specific variance-covariance matrices for omics data (Z). If it is a vector, lucid will call tune_lucid to conduct model selection and variable selection. User can try penalties from 0 to 1. Work for LUCID early only.

verbose_tune

A flag to print details of tuning process.

...

Other parameters passed to estimate_lucid

Value

An optimal LUCID model

1. res_Beta: estimation for G->X associations

2. res_Mu: estimation for the mu of the X->Z associations

3. res_Sigma: estimation for the sigma of the X->Z associations

4. res_Gamma: estimation for X->Y associations

5. inclusion.p: inclusion probability of cluster assignment for each observation

6. K: umber of latent clusters for "early"/list of numbers of latent clusters for "parallel" and "serial"

7. var.names: names for the G, Z, Y variables

8. init_omic.data.model: pre-specified geometric model of multi-omics data

9. likelihood: converged LUCID model log likelihood

10. family: the distribution of the outcome

11. select: for LUCID early integration only, indicators of whether each exposure and omics feature is selected

12. useY: whether this LUCID model is supervised

13. Z: multi-omics data

14. init_impute: pre-specified imputation method

15. init_par: pre-specified parameter initialization method

16. Rho: for LUCID early integration only, pre-specified regularity tuning parameter

17. N: number of observations

18. submodel: for LUCID in serial only, storing all the submodels

Examples

# LUCID early integration
G <- sim_data$G
Z <- sim_data$Z
Y_normal <- sim_data$Y_normal
Y_binary <- sim_data$Y_binary
cov <- sim_data$Covariate

# fit lucid model
fit1 <- lucid(G = G, Z = Z, Y = Y_normal, lucid_model = "early", family = "normal")
fit2 <- lucid(G = G, Z = Z, Y = Y_binary, lucid_model = "early", family = "binary", useY = FALSE)

# including covariates
fit3 <- lucid(G = G, Z = Z, Y = Y_binary, lucid_model = "early", family = "binary", CoG = cov)
fit4 <- lucid(G = G, Z = Z, Y = Y_binary, lucid_model = "early", family = "binary", CoY = cov)

# tune K
fit5 <- lucid(G = G, Z = Z, Y = Y_binary, lucid_model = "early", family = "binary", K = 2:3)

# variable selection
fit6 <- lucid(G = G, Z = Z, Y = Y_binary, lucid_model = "early", 
family = "binary", Rho_G = seq(0.01, 0.02, by = 0.01))

# LUCID in parallel
i <- 1008
set.seed(i)
G <- matrix(rnorm(500), nrow = 100)
Z1 <- matrix(rnorm(1000),nrow = 100)
Z2 <- matrix(rnorm(1000), nrow = 100)
Z <- list(Z1 = Z1, Z2 = Z2)
CoY <- matrix(rnorm(200), nrow = 100)
CoG <- matrix(rnorm(200), nrow = 100)
Y <- rnorm(100)
best_parallel <- lucid(G = G, Z = Z, Y = Y, K = list(2:3,2),
CoG = CoG, CoY = CoY, lucid_model = "parallel",
family = "normal", init_omic.data.model = "VVV",
seed = i, init_impute = "mix", init_par = "mclust",
useY = TRUE)

# LUCID in serial
best_serial <- lucid(G = G, Z = Z, Y = Y, K = list(2:3,2),
CoG = CoG, CoY = CoY, lucid_model = "serial",
family = "normal", init_omic.data.model = "VVV",
seed = i, init_impute = "mix", init_par = "mclust",
useY = TRUE)