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CRC Data Analysis

We applied Zinck to meta-analyze five metagenomic studies of CRC. The five studies correspond to five different countries for the CRC data, which are named “AT” (Australia), “US” (USA), “CN” (China), “DE” (Germany), and “FR” (France). The sample sizes are 109, 127, 120, 114, and 104, respectively, and the number of cases and controls is roughly balanced in each study. We focus on the most abundant \(300\) species.

##################### CRC data species level ##########################
#######################################################################
library(randomForest)
randomForest 4.7-1.1
Type rfNews() to see new features/changes/bug fixes.
library(zinck)
library(reshape2)
library(knockoff)
library(ggplot2)

Attaching package: 'ggplot2'
The following object is masked from 'package:randomForest':

    margin
library(rstan)
Loading required package: StanHeaders
rstan (Version 2.21.8, GitRev: 2e1f913d3ca3)
For execution on a local, multicore CPU with excess RAM we recommend calling
options(mc.cores = parallel::detectCores()).
To avoid recompilation of unchanged Stan programs, we recommend calling
rstan_options(auto_write = TRUE)
load("/Users/Patron/Documents/zinLDA research/count.Rdata")
load("/Users/Patron/Documents/zinLDA research/meta.RData")
dcount <- count[,order(decreasing=T,colSums(count,na.rm=T),
                       apply(count,2L,paste,collapse=''))][,1:300]
## ordering the columns w/ decreasing abundance
X <- dcount
Y <- as.factor(meta$Group)
lookup <- c("CTR" = 0, "CRC" = 1)
Y <- lookup[Y]    ## Converting into 0/1 data

We train the zinck model on \(X\) using ADVI with an optimal number of clusters (19). We generate the knockoff matrix \(\tilde{X}\) by plugging in the learnt parameters into the generative model.

dlt <- rep(0,ncol(X)) ## Initializing deltas with the individual column sparsities

for(t in (1:ncol(X)))
{
  dlt[t] <- 1-mean(X[,t]>0)
  if(dlt[t]==0)
  {
    dlt[t] = dlt[t]+0.01
  }
  if (dlt[t]==1)
  {
    dlt[t] = dlt[t]-0.01
  }
  
}

zinLDA_stan_data <- list(
  K = 19,
  V = ncol(X),
  D = nrow(X),
  n = X,
  delta = dlt
)

zinck_code <- "data {
  int<lower=1> K; // num topics
  int<lower=1> V; // num words
  int<lower=0> D; // num docs
  int<lower=0> n[D, V]; // word counts for each doc

  // hyperparameters
  vector<lower=0, upper=1>[V] delta;
}

parameters {
  simplex[K] theta[D]; // topic mixtures
  vector<lower=0, upper=1>[V] zeta[K]; // zero-inflated betas
  vector<lower=0>[V] gamma1[K];
  vector<lower=0>[V] gamma2[K];
  vector<lower=0>[K] alpha;
}

transformed parameters {
  vector[V] beta[K];

  // Efficiently compute beta using vectorized operations
  for (k in 1:K) {
    vector[V] cum_log1m;
    cum_log1m[1:(V - 1)] = cumulative_sum(log1m(zeta[k, 1:(V - 1)]));
    cum_log1m[V] = 0;
    beta[k] = zeta[k] .* exp(cum_log1m);
    beta[k] = beta[k] / sum(beta[k]);
  }
}


model {
  for (k in 1:K) {
    alpha[k] ~ gamma(100,100);  // Change these hyperparameters as needed
  }
  for (d in 1:D) {
    theta[d] ~ dirichlet(alpha);
  }
  for (k in 1:K) {
    for (m in 1:V) {
        gamma1[k,m] ~ gamma(1,1);
        gamma2[k,m] ~ gamma(1,1);
    }
  }

  // Zero-inflated beta likelihood and data likelihood
  for (k in 1:K) {
    for (m in 1:V) {
      real lp_non_zero = bernoulli_lpmf(0 | delta[m]) + beta_lpdf(zeta[k, m] | gamma1[k, m], gamma2[k, m]);
      real lp_zero = bernoulli_lpmf(1 | delta[m]);
      target += log_sum_exp(lp_non_zero, lp_zero);
    }
  }

  // Compute the eta values and data likelihood more efficiently
  for (d in 1:D) {
    vector[V] eta = theta[d, 1] * beta[1];
    for (k in 2:K) {
      eta += theta[d, k] * beta[k];
    }
    eta = eta / sum(eta);
    n[d] ~ multinomial(eta);
  }
}
"

stan.model = stan_model(model_code = zinck_code)

set.seed(1)
fitCRC <- vb(stan.model, data=zinLDA_stan_data, algorithm="meanfield", iter=10000) ## Fitting the zinck model

theta <- fitCRC@sim[["est"]][["theta"]]
beta <- fitCRC@sim[["est"]][["beta"]]
X_tilde_CRC <- zinck::generateKnockoff(X,theta,beta,seed=1) ## Generating the knockoff copy

We move on to fit a tuned Random Forest model relating the augmented set of covariates with the outcome of interest \(Y\).

X_aug <- cbind(X,X_tilde_CRC) ## Creating the augmented matrix

######### Tuning the Random Forest model ####################
bestmtry <- tuneRF(X_aug,as.factor(Y),stepFactor = 1.5,improve=1e-5,ntree=1000, plot=FALSE) ## Getting the best mtry hyperparameter
mtry = 24  OOB error = 26.31% 
Searching left ...
mtry = 16   OOB error = 28.92% 
-0.09933775 1e-05 
Searching right ...
mtry = 36   OOB error = 24.56% 
0.06622517 1e-05 
mtry = 54   OOB error = 24.56% 
0 1e-05 
m <- bestmtry[as.numeric(which.min(bestmtry[,"OOBError"])),1]
df_X <- as.data.frame(X_aug)
colnames(df_X) <- NULL
rownames(df_X) <- NULL
df_X$Y <- Y
model_rf <- randomForest(formula=as.factor(Y)~.,ntree=1000,mtry=m,
                         importance=TRUE,data=as.matrix(df_X)) ## Fitting the tuned Random Forest model
cf <- as.data.frame(importance(model_rf))[,3] ## Extracting the Mean Decrease in Impurities for each variable
W <- abs(cf[1:300])-abs(cf[301:600])
T <- knockoff.threshold(W,fdr = 0.1, offset = 0) ## This is the knockoff threshold
print(which(W>=T))
 [1]   8  33  47  54  81 124 130 136 146 193 215 245 255 263 264 268 283
names_zinck <- colnames(X[,which(W>=T)])

Finally, we can visualize the importance of these selected species using the Feature Statistics obtained by contrasting the Random Forest importance scores of the original and the knockoff features.

data.species <- data.frame(impscores=sort(W[which(W>=T)],decreasing = FALSE), 
                         name=factor(names_zinck, levels=names_zinck), y=seq(length(names_zinck))*0.9)

plot.species <- ggplot(data.species)+geom_col(aes(impscores,name),
                                          fill="black",width=0.6)+theme_bw()+
  ylab("Species")+xlab("Feature Statistic")

plot.species

Version Author Date
ab6400d Patron 2024-06-18 

sessionInfo()
R version 4.1.3 (2022-03-10)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur/Monterey 10.16

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] rstan_2.21.8         StanHeaders_2.21.0-7 ggplot2_3.4.2       
[4] knockoff_0.3.6       reshape2_1.4.4       zinck_0.0.0.9000    
[7] randomForest_4.7-1.1 workflowr_1.7.1     

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.10        lattice_0.21-8     prettyunits_1.1.1  getPass_0.2-2     
 [5] ps_1.7.5           glmnet_4.1-7       rprojroot_2.0.3    digest_0.6.31     
 [9] foreach_1.5.2      utf8_1.2.3         R6_2.5.1           plyr_1.8.8        
[13] stats4_4.1.3       evaluate_0.21      highr_0.10         httr_1.4.6        
[17] pillar_1.9.0       rlang_1.1.1        rstudioapi_0.14    whisker_0.4.1     
[21] callr_3.7.3        jquerylib_0.1.4    Matrix_1.5-1       rmarkdown_2.22    
[25] labeling_0.4.2     splines_4.1.3      stringr_1.5.0      loo_2.6.0         
[29] munsell_0.5.0      compiler_4.1.3     httpuv_1.6.11      xfun_0.39         
[33] pkgconfig_2.0.3    pkgbuild_1.4.2     shape_1.4.6        htmltools_0.5.5   
[37] tidyselect_1.2.0   gridExtra_2.3      tibble_3.2.1       matrixStats_0.63.0
[41] codetools_0.2-19   fansi_1.0.4        withr_2.5.0        crayon_1.5.2      
[45] dplyr_1.1.2        later_1.3.1        grid_4.1.3         DBI_1.1.3         
[49] jsonlite_1.8.5     gtable_0.3.3       lifecycle_1.0.3    git2r_0.32.0      
[53] magrittr_2.0.3     scales_1.2.1       RcppParallel_5.1.7 cli_3.6.1         
[57] stringi_1.7.12     cachem_1.0.8       farver_2.1.1       fs_1.6.2          
[61] promises_1.2.0.1   bslib_0.5.0        generics_0.1.3     vctrs_0.6.5       
[65] iterators_1.0.14   tools_4.1.3        glue_1.6.2         parallel_4.1.3    
[69] processx_3.8.1     fastmap_1.1.1      survival_3.5-5     yaml_2.3.7        
[73] inline_0.3.19      colorspace_2.1-0   knitr_1.43         sass_0.4.6