Meta analysis across biobanks

Meta analysis explanation

We meta-analysed PGS effect sizes β using meta-analytic mixed models. The absolute performance of PGS varied considerably between biobanks for some phenotypes. For this reason, confidence intervals may appear larger than they do for individual biobanks.

By looking at differences between PGS effect sizes (βₓ - βₓ), we can partially adjust for the variability between biobanks. As for the the results in the relative effect size comparisons, the confidence intervals of these differences are adjusted for the correlation between PGS. We provide the option to divide by the effect size of the chosen baseline method ((βₓ - βₓ) / βᵧ) to display “relative” performance.

While we sometimes cannot confidently estimate the absolute performance (β) of methods across biobanks in the meta-analytical mixed model, we generally can make more accurate claims about “raw” differences in performance (βₓ - βₓ).

Instead of comparing biobanks separately, we can pool information across all of the biobanks and perform a meta-analysis, which improves the fidelity of our absolute effect size and relative effect size benchmarks.

Explore the data

Absolute effect sizes

This figure corresponds to Figure 4 in the published article.

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

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

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: "β →",
    nice: true
  },
  y: {
    label: "Development method"
  },
  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, 
    x: "ancestry",
    marginRight: 75,
    marginTop: 50
  },
  fx: {
    label: "Ancestry"
  },
  marks: [
    Plot.frame(),
    // link == error bar
    Plot.link(filtered, {
      x1: "ci_high",
      x2:  "ci_low",
      y1: "method",
      y2: "method"
    }),
    Plot.dot(filtered, {
      x: "beta",
      y: "method",
      fill: "method",
      symbol: "tuning_type"
    })
  ]
})

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

filtered = aq.fromJSON(meta_res) 
  .params({methods: methods, ancestries: ancestries, endpoint: endpoint, best_method: best_method })
  .filter((d, $) => op.includes($.ancestries, d.ancestry) && 
    op.includes($.methods, d.method) &&
    op.includes($.endpoint, d.phenotype))
  .groupby(['ancestry', 'phenotype'])
  .derive( { best_method: d => d.beta == op.max(d.beta) ? "best": "notbest" })
  .filter((d, $) => op.includes($.best_method, d.best_method ))

Relative effect size

This figure corresponds to Figure 3A and Table 3 in the accompanying paper.

viewof method_y = Inputs.radio(
  ["dbslmm", "sbayesr", "lassosum", "prscs", "ldpred2", "megaprs", "pt.clump", "UKBB.EnsPRS"],
  { value: ["dbslmm", "sbayesr", "lassosum", "prscs", "ldpred2", "megaprs", "pt.clump", "UKBB.EnsPRS"],
  value: "pt.clump",
  label: "Baseline method:",
  sort: true, 
  unique: true,
  disabled: disable_method_type[method_type]}
)

viewof method_type = Inputs.radio(["CV", "auto"],
{ label: "Tuning method:",
  value: "CV"})
  
viewof pairwise_endpoint = Inputs.select(pairwise_endpoints, {value: "T2D", label: "Endpoint:"})

viewof use_relative = Inputs.radio(["relative", "raw"],
{ label: "Difference metric",
  value: "relative"})

beta_map = new Map([["x_label", "βₓ - βᵧ →"], ["x", "beta_diff"], ["error_bar_low", "ci_low_diff"], ["error_bar_high", "ci_high_diff"]])
relative_map = new Map([["x_label", "(βₓ - βᵧ) / βᵧ →"], ["x", "relative_beta_diff"], ["error_bar_low", "relative_ci_low_diff"], ["error_bar_high", "relative_ci_high_diff"]])
x_map = ({ "relative": relative_map, "raw": beta_map })
// some methods only have one method type, so disable the radio button
disable_method_type = ({ "CV": ["prscs", "sbayesr", "dbslmm"], "auto": ["UKBB.EnsPRS"]})

Plot.plot({
  grid: true,
  marginLeft: 150,
  marginRight: 80,
  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_pairwise, 
    x: "ancestry",
    marginRight: 75,
  },
  x: {
    label: x_map[use_relative].get("x_label")
  },
  y: {
    label: "Score development method"
  },
  fx: {
    label: "Ancestry"
  },
  marks: [
    Plot.frame(),
    Plot.link(filtered_pairwise, {
      x1: x_map[use_relative].get("error_bar_low"),
      x2: x_map[use_relative].get("error_bar_high"),
      y1: "method_x",
      y2: "method_x"
    }),
    Plot.ruleX([0], {stroke: "lightgray", strokeWidth: 2, strokeDasharray: "4 2"}),
    Plot.dot(filtered_pairwise, {
      x: x_map[use_relative].get("x"),
      y: "method_x",
      fill: "method_x",
      symbol: "method_type_x"
    })
  ]
})

filtered_pairwise = aq.fromJSON(pv_mrg)
  .derive({ relative_beta_diff: d => d.beta_diff / d.beta_y,
    relative_ci_high_diff: d => d.ci_high_diff / d.beta_y,
    relative_ci_low_diff: d => d.ci_low_diff / d.beta_y })
  .params({endpoint: pairwise_endpoint, method_y: method_y, method_type: method_type})
  .filter((d, $) => op.includes($.method_type, d.method_type_y ) &&
    op.includes($.method_y, d.method_y) &&
    op.includes($.endpoint, d.phenotype ))