# T1D Application

In this vignette, we walk through an example to illustrate how the `fcfdr` R package can be used to leverage various relevant genetic and genomic data with GWAS \(p\)-values for type 1 diabetes (T1D) to find new genetic associations. This vignette will take approximately 30 minutes to complete.

The data required for this example is available to download within the `fcfdr` R package and includes:

1. GWAS \(p\)-values for T1D (Onengut-Gumuscu et al. 2015) downloaded from the NHGRI-EBI GWAS Catalog (study GCST005536 accessed on 08/10/21).

2. GWAS \(p\)-values for rheumatoid arthritis (RA) (Eyre et al. 2012) downloaded from the NHGRI-EBI GWAS Catalog (study GCST90013445 accessed on 08/10/21).

3. Binary measure of SNP overlap with regulatory factor binding sites, derived from merging all DNaseI digital genomic footprinting (DGF) regions from the narrow-peak classifications across 57 cell types (see https://www.nature.com/articles/nature11247). SNP annotations were downloaded for all 1000 Genomes phase 3 SNPs from the LDSC data repository and the binary `DGF_ENCODE` annotation was extracted for all SNPs in our analysis.

4. Average fold-enrichment ratios of H3K27ac ChIP-seq counts relative to expected background counts in T1D-relevant cell types. Fold-enrichment ratios were downloaded from NIH Roadmap for CD3, CD4+ CD25int CD127+ Tmem, CD4+ CD25+ CD127- Treg, CD4+ CD25- Th, CD4+ CD25- CD45RA+, CD4 memory, CD4 naive, CD8 memory and CD8 naive primary cells (from https://egg2.wustl.edu/roadmap/data/byFileType/signal/consolidated/macs2signal/foldChange/ see epigenome ID to cell type conversion table here). The fold-enrichment ratios were averaged over cell types to derive the values in column `H3K27ac`.

Firstly, we download the data:

    set.seed(1)
    library(fcfdr)
    library(cowplot)
    library(ggplot2)
    library(dplyr)

    data(T1D_application_data, package = "fcfdr")
    head(T1D_application_data)

In this application we leverage GWAS \(p\)-values for RA, binary SNP overlap with regulatory factor binding sites and H3K27ac counts in T1D-relevant cell types with GWAS \(p\)-values for T1D to generate adjusted \(p\)-values (called \(v\)-values).

    orig_p <- T1D_application_data$T1D_pval
    chr <- T1D_application_data$CHR19
    MAF <- T1D_application_data$MAF
    q1 <- T1D_application_data$RA_pval
    q2 <- T1D_application_data$DGF
    q3 <- log(T1D_application_data$H3K27ac+1) # deal with long tail

The data frame also contains a column of LDAK weights for each SNP (https://dougspeed.com/calculate-weightings/). An LDAK weight of zero means that the signal is (almost) perfectly captured by neighbouring SNPs, and so we use the subset of SNPs with non-zero LDAK weights as our independent subset of SNPs.

    ind_snps <- which(T1D_application_data$LDAK_weight != 0)

We are now ready to use the `fcfdr` R package to generate \(v\)-values. Firstly, we generate \(v\)-values by leveraging GWAS \(p\)-values for RA. We supply MAF values to prevent a bias of the KDE fit towards the behaviour of rarer SNPs (the function intrinsically down-samples the independent subset of SNPs to match the MAF distribution in this subset to that in the whole set of SNPs).

    iter1_res <- flexible_cfdr(p = orig_p,
                               q = q1,
                               indep_index = ind_snps,
                               maf = MAF)

    v1 <- iter1_res[[1]]$v

Since the outputted \(v\)-values are analogous to \(p\)-values, they can be used directly in any error-rate controlling procedure. Here, we use the Benjamini-Hochberg (BH) procedure to derive FDR-adjusted \(v\)-values and plot the resultant FDR values.

    res1 <- data.frame(p = orig_p, q1, v1)
    mid1 <- median(res1$q1)

    ggplot(res1, aes(x = p.adjust(p, method = "BH"), y = p.adjust(v1, method = "BH"), col = q1)) + geom_point(cex = 0.5) + theme_cowplot(12) + background_grid(major = "xy", minor = "none") + geom_abline(intercept = 0, slope = 1,  linetype="dashed") + xlab("Original FDR") + ylab("V1 (FDR)") + ggtitle(paste0("Iteration 1")) + scale_color_gradient2(midpoint = mid1, low = "blue", mid = "white", high = "red", space = "Lab")

The resultant \(v\)-values for this first iteration (`v1`) are then used in the next iteration to leverage binary data on SNP overlap with regulatory factor binding sites. Note that the binary cFDR function implements a leave-one-out procedure and therefore requires a group index for each SNP. This will generally be the chromosome on which that SNP resides but can also be indices relating to LD blocks, for example.

    iter2_res <- binary_cfdr(p = v1,
                             q = q2,
                             group = chr)

    v2 <- iter2_res$v

    res2 <- data.frame(p = v1, v2, q2)
    res2$q2 <- as.factor(res2$q2)

    ggplot(res2, aes(x = p.adjust(p, method = "BH"), y = p.adjust(v2, method = "BH"), col = q2)) + geom_point(cex = 0.5) + theme_cowplot(12) + background_grid(major = "xy", minor = "none") + geom_abline(intercept = 0, slope = 1,  linetype="dashed") + xlab("V1 (FDR)") + ylab("V2 (FDR)") + ggtitle(paste0("Iteration 2")) + scale_colour_manual(values = c("grey", "black"))

The resultant \(v\)-values for this second iteration (`v2`) are then used in the next iteration to leverage H3K27ac counts.

    iter3_res <- flexible_cfdr(p = v2,
                               q = q3,
                               indep_index = ind_snps,
                               maf = MAF)
    v3 <- iter3_res[[1]]$v

    res3 <- data.frame(p = v2, q3, v3)

    ggplot(res3, aes(x = p.adjust(p, method = "BH"), y = p.adjust(v3, method = "BH"), col = q3)) + geom_point(cex = 0.5) + theme_cowplot(12) + background_grid(major = "xy", minor = "none") + geom_abline(intercept = 0, slope = 1,  linetype="dashed") + xlab("V2 (FDR)") + ylab("V3 (FDR)") + ggtitle(paste0("Iteration 3")) + scale_color_gradient2(midpoint = 1, low = "blue", mid = "white", high = "red", space = "Lab")

We then create a final data frame containing the results from our analysis. Note that the sign is flipped for \(q2\) and \(q3\). This is because these are negatively correlated with `p` and the flexible cFDR software automatically flips the sign of `q` to ensure that low `p` are enriched for low `q`.

    res <- data.frame(orig_p, q1 = iter1_res[[1]]$q, q2 = as.factor(iter2_res$q), q3 = iter3_res[[1]]$q, v1, v2, v3)

    head(res)

We can plot the original \(p\)-values for T1D against the final adjusted \(v\)-values.

    mid1 <- median(res$q1)

    ggplot(res, aes(x = p.adjust(orig_p, method = "BH"), y = p.adjust(v3, method = "BH"))) + geom_point(cex = 0.5, alpha = 0.5) + theme_cowplot(12) + background_grid(major = "xy", minor = "none") + geom_abline(intercept = 0, slope = 1,  linetype="dashed", col = "red") + xlab("Original P (FDR)") + ylab("V3 (FDR)") + ggtitle(paste0("FDR adjusted v-values\nagainst original FDR values"))

    ggplot(res, aes(x = -log10(orig_p), y = -log10(v3))) + geom_point(cex = 0.5, alpha = 0.5) + theme_cowplot(12) + background_grid(major = "xy", minor = "none") + geom_abline(intercept = 0, slope = 1,  linetype="dashed", col = "red") + xlab("Original P (FDR) (-log10)") + ylab("V3 (FDR) (-log10)") + ggtitle(paste0("FDR adjusted v-values against\noriginal FDR values (FDR)")) + coord_cartesian(ylim = c(0,10), xlim = c(0,10))

We find that our implementation of cFDR identifies newly FDR significant SNPs that have relatively small GWAS \(p\)-values for rheumatoid arthritis, are more likely to be found in genomic regions where regulatory factors bind and have relatively high H3K27ac counts in T1D relevant cell types.

    p_fdr <- p.adjust(orig_p, method = "BH")
    v3_fdr <- p.adjust(v3, method = "BH")

    # choose fdr threshold corresponding to genome-wide significance threshold
    fdr_thr <- max(p_fdr[which(orig_p <= 5*10^{-8})])

    median(T1D_application_data$RA_p[which(v3_fdr < fdr_thr & p_fdr > fdr_thr)])
    median(T1D_application_data$RA_p)

    mean(T1D_application_data$DGF[which(v3_fdr < fdr_thr & p_fdr > fdr_thr)])
    mean(T1D_application_data$DGF)

    median(T1D_application_data$H3K27ac[which(v3_fdr < fdr_thr & p_fdr > fdr_thr)])
    median(T1D_application_data$H3K27ac)

Side comment: code to create the Manhattan plot in the manuscript:

    T1D_application_data$v3_fdr <- v3_fdr

    nCHR <- length(unique(T1D_application_data$CHR19))
    T1D_application_data$BPcum <- NA
    s <- 0
    nbp <- c()
    T1D_application_data <- data.frame(T1D_application_data)
    for (i in unique(T1D_application_data$CHR19)){
      nbp[i] <- max(T1D_application_data[T1D_application_data$CHR19 == i,]$BP19)
      T1D_application_data[T1D_application_data$CHR19 == i,"BPcum"] <- T1D_application_data[T1D_application_data$CHR19 == i,"BP19"] + s
      s <- s + nbp[i]
    }

    axis.set <- T1D_application_data %>%
      group_by(CHR19) %>%
      summarize(center = (max(BPcum) + min(BPcum)) / 2)

    ggplot(T1D_application_data, aes(x = BPcum, y = -log10(v3_fdr), col = as.factor(CHR19))) + geom_point(cex = 0.75) + theme_cowplot(12) + background_grid(major = "xy", minor = "none") + geom_hline(yintercept = -log10(fdr_thr), linetype = "dashed") + xlab("Position") +  scale_color_manual(values = rep(c("#276FBF", "#183059"), nCHR)) +
      scale_x_continuous(label = axis.set$CHR19, breaks = axis.set$center) + theme(legend.position = "none")+ theme(axis.text.x = element_text(size = 6, angle = 0)) + coord_cartesian(ylim=c(0,10)) + ylab(expression(paste("-log"[10],"(FDR)")))