Polygenic risk score effect sizes

Metrics explanation

AUC

Area Under Receiver Operating Characteristic

This metric cares only about relative ordering of observations, and is available only for binary traits.

β

Standardized regression coefficients. For continuous traits, this is the change in the trait (in standard deviations) per standard deviation of the PGS. For binary traits, this is the change in the log-odds per standard deviation of the PGS.

This is the metric that was used for meta-analyses.

Odds Ratio (OR)

This is the change in the odds ratio per standard deviation of the PGS (exp(β))

R²

This is the variance explained by the PGS on the observed scale for continuous traits, or on the liability scale for binary traits

This interactive plot corresponds to Figure 1A and Supplementary Figures 1-5 in the published article.

viewof biobanks = Inputs.checkbox(
  new Map( 
    [["UK Biobank", "ukbb"], ["Estonia Biobank", "ebb"], ["Genes & Health", "gnh"], ["FinnGenn", "finngen"], ["HUNT", "hunt"]]),
  { value: ["ukbb", "ebb", "gnh", "finngen", "hunt"], 
    label: "Biobank:",
    format: ([name, value]) => `${name} (${value})`, 
    sort: true, 
    unique: true }
)

viewof methods = Inputs.checkbox(
  ["dbslmm", "sbayesr", "lassosum", "prscs", "ldpred2", "megaprs", "pt.clump", "UKBB.EnsPRS"],
  { value: ["dbslmm", "sbayesr", "lassosum", "prscs", "ldpred2", "megaprs", "pt.clump", "UKBB.EnsPRS"],
    label: "Method:",
    sort: true, 
    unique: true }
)

viewof ancestries = Inputs.checkbox(
  ["EUR", "SAS"],
  { label: "Ancestry",
    value: ["EUR", "SAS"],
    sort: true,
    unique: true
  })

viewof chosen_metric = Inputs.radio(new Map([["β", "BETA"], ["Area Under Curve (AUC)", "AUC"], ["Odds Ratio (OR)", "OR"], ["R²", "R2"]]), {label: "Metric", value: "BETA", disabled: disabled_metrics})

viewof endpoint = Inputs.select(endpoints, {value: "T2D", label: "Endpoint:"})

viewof best_method = Inputs.toggle({ label: "Filter best method?:", values: [["best"], ["best", "notbest"]]})

is_continuous = aq.fromJSON(metrics)
  .params({ endpoint: endpoint })
  .filter((d, $) => d.phenotype == $.endpoint)
  .sample(1, {shuffle: false})
  .get('is_continuous')

// continuous endpoints only support beta and r2 metrics
// binary endpoints support all endpoints, r2 is recalculated later
disabled_metrics = ({ true: ["AUC", "OR"], false: [] })[is_continuous]

beta_map = new Map([["x_label", "βₓ"], ["x", "BETA"], ["errorbar_high", "BETA_CI_HIGH"], ["errorbar_low", "BETA_CI_LOW"]])
auc_map = new Map([["x_label", "AUC"], ["x", "AUC_MEDIAN"], ["errorbar_high", "AUC_CI_HIGH"], ["errorbar_low", "AUC_CI_LOW"]])
r2_map = new Map([["x_label", "R²"], ["x", "r2"], ["errorbar_high", "r2_high"], ["errorbar_low", "r2_low"]])
or_map = new Map([["x_label", "Odds Ratio"], ["x", "OR"], ["errorbar_high", "OR_CI_HIGH"], ["errorbar_low", "OR_CI_LOW"]])

metrics_map = ({ "BETA": beta_map, "AUC": auc_map, "R2": r2_map, "OR": or_map })

Plot.plot({
  grid: true,
  // make plot accessible for screen readers
  ariaLabel: "Explanation of some stuff", // todo: fix
  marginTop: 50,
  marginLeft: 150,
  marginRight: 80,
  x: {
    label: metrics_map[chosen_metric].get("x_label") + " →",
    nice: true
  },
  y: {
    label: "Development method"
  },
  // tableau10 theme, manually assigning each method a colour to be consistent
  color: {
    domain: ["dbslmm", "sbayesr", "lassosum", "prscs", "ldpred2", "megaprs", "pt.clump", "UKBB.EnsPRS"],
    range: ["#5778a4", "#e49444", "#d1615d", "#85b6b2", "#6a9f58", "#e7ca60", "#a87c9f", "#f1a2a9"]
  },
  symbol: {
    legend: true
  },
  style: {
    fontSize: "12px"
  },
  facet: {
    data: filtered, 
    y: "bbid", 
    x: "ancestry",
    marginRight: 75,
    marginTop: 50
  },
  fx: {
    label: "Ancestry"
  },
  fy: {
    label: "Biobank"
  },
  marks: [
    Plot.frame(),
    // link == error bar
    Plot.link(filtered, {
      x1: metrics_map[chosen_metric].get("errorbar_low"),
      x2:  metrics_map[chosen_metric].get("errorbar_high"),
      y1: "method",
      y2: "method"
    }),
    Plot.dot(filtered, {
      x:  metrics_map[chosen_metric].get("x"), 
      y: "method",
      fill: "method",
      symbol: "method_type"
    })
  ]
})

import { aq, op } from '@uwdata/arquero'

// use arquero to dynamically filter and mutate data client-side
filtered = aq.fromJSON(metrics)
  .params({ biobanks: biobanks, methods: methods, ancestries: ancestries, endpoint: endpoint, best_method: best_method })
  .filter((d, $) => op.includes($.biobanks, d.bbid) &&
    op.includes($.ancestries, d.ancestry) &&
    op.includes($.methods, d.method) &&
    op.includes($.endpoint, d.phenotype))
  .groupby(['bbid', 'ancestry', 'phenotype'])
  .derive( { best_method: d => d.BETA == op.max(d.BETA) ? "best": "notbest" })
  .filter((d, $) => op.includes($.best_method, d.best_method ))
  // binary traits -> h2l (variance explained on the liability scale)
  // continuous traits -> R2_OBS (variance explained on the observed scale)
  // create a new r2 column which selects the correct scale
  .derive( { 
     r2: d => d.is_continuous ? d.R2_OBS : d.h2l,
     r2_high: d => d.is_continuous ? d.R2_OBS_CI_HIGH : d.h2l_ci_high,
     r2_low: d => d.is_continuous ? d.R2_OBS_CI_LOW : d.h2l_ci_low,
   })

Conclusion

Using an ensemble of scores, each created using a different PGS development method, can capture a larger effect size for a phenotype. This means that the strength of the relationship between genetic data and phenotype is greater.