pairwise.qmd

---
title: "Pairwise method comparison"
---

<details>

<summary>Difference metric explanation</summary>

<p>Rather than comparing absolute method performance (see [effect sizes](effect-sizes.qmd)), here we compare PGS effect sizes β relative to each other. For this, a baseline PGS against which we compare (baseline method) has to be chosen.</p>

<p>For each PGS with effect size βₓ, we calculate the difference to the baseline method with effect size βᵧ. Confidence intervals are calculated adjusting for the correlation between PGS x and y. These confidence intervals form the basis of significance tests reported in the manuscript.</p>

<p>The "raw" differences (βₓ - βᵧ) are on the same scale as the original effect sizes. Relative differences ((βₓ - βᵧ) / βᵧ) are often reported in methods comparisons, as different phenotypes and target data may have different baseline performance.</p>

</details>

This interactive plot corresponds to Figure 1C in the published article.

```{r setup, echo=FALSE}
library(pgsCompaR)
data(dst) # load data from R package
endpoints <- unique(metrics$phenotype)
# pass data to observable JS
ojs_define(dst)
ojs_define(endpoints)
```

```{ojs}
//| echo: false
//| panel: sidebar

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

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

```{ojs}
//| echo: false
//| panel: fill

Plot.plot({
  grid: true,
  marginLeft: 150,
  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: eur, 
    y: "bbid",
    marginRight: 75,
  },
  fy: {
    label: "Biobank"
  },
  x: {
    label: x_map[use_relative].get("x_label")
  },
  y: {
    label: "Score development method"
  },
  marks: [
    Plot.frame(),
    Plot.link(eur, {
      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.text([`EUR`], {
      fy: ["bbid"],
      frameAnchor: "bottom-right",
      lineWidth: 18,
      dx: -5,
      dy: -5
    }),
    Plot.ruleX([0], {stroke: "lightgray", strokeWidth: 2, strokeDasharray: "4 2"}),
    Plot.dot(eur, {
      x: x_map[use_relative].get("x"),
      y: "method_x",
      fill: "method_x",
      symbol: "method_type_x"
    })
  ]
})

Plot.plot({
  grid: true,
  marginLeft: 150,
  color: {
    domain: ["dbslmm", "sbayesr", "lassosum", "prscs", "ldpred2", "megaprs", "pt.clump", "UKBB.EnsPRS"],
    range: ["#5778a4", "#e49444", "#d1615d", "#85b6b2", "#6a9f58", "#e7ca60", "#a87c9f", "#f1a2a9"]
  },
  symbol: {
    legend: false
  },
  style: {
    fontSize: "12px"
  },
  facet: {
    data: sas, 
    y: "bbid",
    marginRight: 75,
    marginTop: 50
  },
  fy: {
    label: "Biobank"
  },
  x: {
    label: x_map[use_relative].get("x_label")
  },
  y: {
    label: "Score development method"
  },
  marks: [
    Plot.frame(),
    Plot.dot(sas, {
      x: x_map[use_relative].get("x"),
      y: "method_x",
      fill: "method_x",
      symbol: "method_type_x"
    }),
    Plot.link(sas, {
      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.text([`SAS`], {
      fy: ["bbid"],
      frameAnchor: "bottom-right",
      lineWidth: 18,
      dx: -5,
      dy: -5
    }),
    Plot.ruleX([0], {stroke: "lightgray", strokeWidth: 2, strokeDasharray: "4 2"})
  ]
}) 
```

```{ojs}
//| echo: false

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"]})
```

```{ojs}
//| echo: false

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

filtered = aq.fromJSON(dst)
  .select("method_x", "bbid", "ancestry", "method_x", "method_type_x", "beta_diff", "beta_y", "ci_low_diff", "ci_high_diff", "phenotype", "method_y", "method_type_y")
  .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: 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 ))
  
// need to filter before plotting to prevent empty facets appearing
eur = filtered.filter(d => d.ancestry == "EUR")
sas = filtered.filter(d => d.ancestry == "SAS")
```

## Conclusion

If you're using [pt.clump](glossary.html) (without cross validation) to develop new polygenic risk scores for type 2 diabetes, you could make a better score by using any of the other tested methods.