# Fit a lucid model for integrated analysis on exposure, outcome and multi-omics data, allowing for tuning ```r 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` ## Returns 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 ```r # 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) ```

lucid function