OptimalScanTimeCalculator/formula.html at main · ThomasYeoLab/OptimalScanTimeCalculator · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
<!DOCTYPE html>
<html lang="en">

<head>
    <meta charset="UTF-8">
    <meta http-equiv="X-UA-Compatible" content="IE=edge">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Ooi2025 Formula</title>
    <link rel="stylesheet" href="https://fonts.googleapis.com/css2?family=Barlow&display=swap">
    <link rel="stylesheet" href="style.css">
    <script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
</head>

<body>
    <!-- Menu -->
    <div class="menu-bar">
        <ul>
            <li><a onclick="jumpToSection('about')">About</a></li>
            <li><a onclick="jumpToSection('budgetcalc')">Budget and Scan Billing Calculator</a></li>
            <li><a onclick="jumpToSection('formula')">Formula</a></li>
            <!--
            <li><a onclick="jumpToSection('acccalc')">Accuracy Calculator</a></li>
            -->
        </ul>
    </div>

    <!-- Section 1: Introduction -->
    <section id="Formula">
        <div class="container" id="container1">
            <h1>Empirical Distributions of \(K_0\), \(K_1\) and \(K_2\)</h1>
            \[r = K_0 \sqrt{\frac{1}{1 + \frac{K_1}{N} + \frac{K_2}{NT}}}\]
            <p>
                where \(r\) is the prediction accuracy, \(N\) is the sample size and \(T\) is the scan duration.
                Intuitively, \(K_0\) is the maximum possible accuracy (given infinite sample size and scan time).
                \(K_1\) and \(K_2\) determine the relative significance of \(N\) and \(NT\). In the extreme case where
                \(K_1 >> K_2\), scan duration \(T\) has a much smaller contribution to \(r\) than sample size \(N\).
                On the other hand, if \(K_2 >> K_1\), \(r\) is essentially determined by the product of \(N\) and \(T\),
                meaning that \(N\) and \(T\) are largely interchangeble.
            </p>
            <p>
                The following are the empirical distributions of \(K_0\), \(K_1\) and \(K_2\), generated based on
                phenotypes across 6 large datasets.
            </p>
            <img src="K0_distribution.png" width="500" height="400" alt="K0 distribution">
            <img src="K1_distribution.png" width="500" height="400" alt="K1 distribution">
            <img src="K2_distribution.png" width="500" height="400" alt="K2 distribution">
            <hr class="section-divider">
        </div>
    </section>

    <!-- Include Sheetjs to read xlsx -->
    <script src="https://cdn.jsdelivr.net/npm/xlsx@0.17.0/dist/xlsx.full.min.js"></script>
    <!-- Include Plotly.js for graph plotting -->
    <script src="https://cdn.plot.ly/plotly-latest.min.js"></script>
    <!-- Script for navigating pages -->
    <script>
        function jumpToSection(containerId) {
            // Check the containerId and redirect to the appropriate page
            if (containerId === 'acccalc') {
                window.location.href = 'acccalc.html';
            } else if (containerId === 'budgetcalc') {
                window.location.href = 'budgetcalc.html';
            } else if (containerId === 'about') {
                window.location.href = 'index.html';
            }
        }
    </script>
    <!-- Google Analytics -->
    <script async src="https://www.googletagmanager.com/gtag/js?id=G-R33XW8PFE9"></script>
    <script>
        window.dataLayer = window.dataLayer || [];
        function gtag() { dataLayer.push(arguments); }
        gtag('js', new Date());
        gtag('config', 'G-R33XW8PFE9');
    </script>

</body>

</html>