In USCbiostats/LUCid: Latent Unknown Clustering with Integrated Data

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(LUCIDus)

About LUCIDus

The LUCIDus package is aiming to provide researchers in the genetic epidemiology community with an integrative tool in R to obtain a joint estimation of latent or unknown clusters/subgroups with multi-omics data and phenotypic traits.

This package is an implementation for the novel statistical method proposed in the research paper "A Latent Unknown Clustering Integrating Multi-Omics Data (LUCID) with Phenotypic Traits^[https://doi.org/10.1093/bioinformatics/btz667]" published by the Bioinformatics. LUCID improves the subtype classification which leads to better diagnostics as well as prognostics and could be the potential solution for efficient targeted treatments and successful personalized medicine.

LUCIDus Functions and Model Fitting

Four main functions, including est_lucid, boot_lucid, sem_lucid, and tune_lucid, are currently available for model fitting and feature selection. The model outputs can be summarized and visualized using summary_lucid and plot_lucid respectively. Predictions could be made with pred_lucid.

Here are the descriptions of LUCIDus functions:

| Function | Description | |:-----:|:---------------------| | est_lucid() | Estimates latent clusters using multi-omics data with/without the outcome of interest, and producing an IntClust object; missing values in biomarker data (Z) are allowed | | boot_lucid() | Latent cluster estimation through bootstrapping for statistical inference | | sem_lucid() | Latent cluster estimation with supplemented E-M algorithm for statistical inference | | tune_lucid() | Grid search for tuning parameters using parallel computing to determine an optimal choice of three tuning parameters with minimum model BIC | | summary_lucid() | Summarizes the results of integrative clustering based on an IntClust object | | plot_lucid() | Produces a Sankey diagram for the results of integrative clustering based on an IntClust object | | pred_lucid() | Predicts latent clusters and outcomes with an IntClust object and new data | | def_initial() | Defines initial values of model parameters in est_lucid(), sem_lucid() , and tune_lucid() fitting | | def_tune() | Defines selection options and tuning parameters in est_lucid(), sem_lucid() , and tune_lucid() fitting | | def_tol() | Defines tolerance settings in est_lucid(), sem_lucid() , and tune_lucid() fitting |

Examples

For a simulated data with 10 genetic features (5 causal) and 4 biomarkers (2 causal)

• Integrative clustering without feature selection applying est_lucid()^[Parameter initials and stopping criteria can be specified using def_initial() and def_tol()]

set.seed(10)
IntClusFit <- est_lucid(G=G1,Z=Z1,Y=Y1,K=2,family="binary",Pred=TRUE)

• Check important model outputs with summary_lucid()

summary_lucid(IntClusFit)

• Visualize the results with a Sankey diagram via plot_lucid()

plot_lucid(IntClusFit)

• Run LUCID to select informative features
• Parallel grid-search with 27 combinations of tuning parameters using tune_lucid()

GridSearch <- tune_lucid(G=G1, Z=Z1, Y=Y1, K=2, Family="binary", USEY = TRUE, NoCores = 2,
                         LRho_g = 0.008, URho_g = 0.012, NoRho_g = 3,
                         LRho_z_invcov = 0.04, URho_z_invcov = 0.06, NoRho_z_invcov = 3,
                         LRho_z_covmu = 90, URho_z_covmu = 100, NoRho_z_covmu = 3)

• Check the grid-search results

GridSearch$Results

• Determine the best tuning parameters

GridSearch$Optimal

• Run LUCID to select informative features^[Note tuning parameters in est_lucid() are defined by def_tune()]

set.seed(0.01*0.05*95)
IntClusFit <- est_lucid(G=G1,Z=Z1,Y=Y1,K=2,family="binary",Pred=TRUE,
                        tunepar = def_tune(Select_G=TRUE,Select_Z=TRUE,
                                           Rho_G=0.01,Rho_Z_InvCov=0.05,Rho_Z_CovMu=95))

• Identify selected features

summary_lucid(IntClusFit)$No0G; summary_lucid(IntClusFit)$No0Z
colnames(G1)[summary_lucid(IntClusFit)$select_G]; colnames(Z1)[summary_lucid(IntClusFit)$select_Z]

• Select the informative features

if(!all(summary_lucid(IntClusFit)$select_G==FALSE)){
    G_select <- G1[,summary_lucid(IntClusFit)$select_G]
}
if(!all(summary_lucid(IntClusFit)$select_Z==FALSE)){
    Z_select <- Z1[,summary_lucid(IntClusFit)$select_Z]
}

• Re-fit with selected features

set.seed(10)
IntClusFitFinal <- est_lucid(G=G_select,Z=Z_select,Y=Y1,K=2,family="binary",Pred=TRUE)

• Visualize the results

plot_lucid(IntClusFitFinal)

• Covariates can be easily adjusted in LUCID

# Re-run the model with covariates in the G->X path
set.seed(10)
IntClusCoFit <- est_lucid(G=G1,CoG=CoG,Z=Z1,Y=Y1,K=2,family="binary",Pred=TRUE)

• Check clustering summary and visualize the results

# Check important model outputs
summary_lucid(IntClusCoFit)

# Visualize the results
plot_lucid(IntClusCoFit)

• Feature selection can be done with covariates which are forced to stay in the model

# Re-run feature selection with covariates in both paths
set.seed(10)
IntClusCoFit <- est_lucid(G=G1,CoG=CoG,Z=Z1,Y=Y1,CoY=CoY,K=2,family="binary",Pred=TRUE,
                          initial=def_initial(), itr_tol=def_tol(),
                          tunepar = def_tune(Select_G=TRUE,Select_Z=TRUE,
                          Rho_G=0.02,Rho_Z_InvCov=0.1,Rho_Z_CovMu=93))

# Re-fit with selected features with covariates
set.seed(10)
IntClusCoFitFinal <- est_lucid(G=G_select,CoG=CoG,Z=Z_select,Y=Y1,CoY=CoY,K=2,
                               family="binary",Pred=TRUE)

# Visualize the results
plot_lucid(IntClusCoFitFinal)

• Bootstrap method for variance estimation

set.seed(10)
BootCIs <- boot_lucid(G = G1, CoG = CoG, Z = Z1, Y = Y1, CoY = CoY, 
                      useY = TRUE, family = "binary", K = 2, R=50)
BootCIs$Results

• Supplemented EM-algorithm for variance estimation

set.seed(10)
sem_lucid(G=G2,Z=Z2,Y=Y2,useY=TRUE,K=2,Pred=TRUE,family="normal",Get_SE=TRUE,
            itr_tol = def_tol(tol_b = 1e-02, tol_m = 1e-02, tol_s = 1e-02, tol_g = 1e-02))

Final Remarks

• We recommend applying LUCIDus as a framework instead of separate functions;
• The bootstrap method to obtain SE of parameter estimates works best for K=2.

Acknowledgments

• David V. Conti, Ph.D.
• Zhao Yang, Ph.D.
• USC IMAGE Group^[Supported by the National Cancer Institute at the National Institutes of Health Grant P01 CA196569]

USCbiostats/LUCid documentation built on Feb. 22, 2020, 8:57 p.m.