working version of equivalency module

CHRIS.py

@@ -1,7 +1,7 @@
 from flask import Flask, render_template
 
 app = Flask(__name__)
-app.debug = True
+app.debug = False
 
 from color_module import blueprint
 app.register_blueprint(blueprint)

equivalency_module/equivalency.py

@@ -5,42 +5,44 @@ from scipy.special import erf
 from scipy import integrate
 from lmfit import minimize, Parameters, printfuncs, fit_report
 
-def max_CDF(x, mu, sigma, N):
+def MeanIntegrad(y, RSD, BN, CN, alpha, beta):
+    result = exp(-BN * (1. - y) ** 2. / 2. / RSD ** 2.) * (1. + erf(sqrt(CN) * (alpha * y - beta) / sqrt(2) / RSD / beta))
 
-    return (0.5 * (1. + erf((x - mu) / sigma / sqrt(2)))) ** N
+    return result
+def Means(RSD, BN, CN, alpha, beta):
+    tmp, err = integrate.quad(MeanIntegrad, -inf, inf, args=(RSD, BN, CN, alpha, beta))
+    prob = 1. - tmp * sqrt(BN) / sqrt(2. * pi) / RSD / 2.
 
-def max_PDF(x, mu, sigma, N):
+    return prob
 
-    return (1. + erf((x - mu) / sigma / sqrt(2))) ** (N - 1) * N * 2. ** (0.5 - N) * exp(
-        -(-mu + x) ** 2. / (2. * sigma ** 2.)) / sqrt(pi) / sigma
-
-def max_PDFCDF(y, lamb, mu_x, mu_y, sigma_x, sigma_y, N):
-
-    return max_PDF(y, mu_y, sigma_y, N) * max_CDF(y * lamb, mu_x, sigma_x, N)
-
-def alpha_residual(params, prob, sigma, N):
+def FPR_alpha_residual(params, prob, RSD, BN, CN, beta):
 
     alpha = params['alpha'].value
-    tmp, err = integrate.quad(max_PDFCDF, -inf, inf, args=(alpha, 1.0, 1., sigma, sigma, N))
+    tmp = Means(RSD, BN, CN, alpha, beta)
+    FPR = tmp
 
-    return prob - (1. - tmp)
+    return prob - FPR
 
-def beta_residual(params, prob, alpha, sigma, N):
+def FNR_beta_residual(params, prob, RSD, BN, CN, alpha):
 
     beta = params['beta'].value
-    tmp, err = integrate.quad(max_PDFCDF, -inf, inf, args=(alpha, beta, 1., beta * sigma, sigma, N))
+    tmp = Means(RSD, BN, CN, alpha, beta)
+    FNR = 1. - tmp
+
+    return prob - FNR
 
-    return prob - tmp
+def FitParams(FPR, FNR, Bmean, Bstd, BN, Cmean, Cstd, CN):
 
-def FitParams(FPR, FNR, RSD, N):
+    RSD = max(Bstd/Bmean,Cstd/Cmean)
 
+    beta = 1.
     alpha_params = Parameters()
     alpha_params.add('alpha', value=1.)
-    alpha_out = minimize(alpha_residual, alpha_params, args=(FPR/100., RSD, N))
+    alpha_out = minimize(FPR_alpha_residual, alpha_params, args=(FPR/100., RSD, BN, CN, beta))
 
     beta_params = Parameters()
-    beta_params.add('beta', value=4.)
-    beta_out = minimize(beta_residual, beta_params, args=(FNR/100., alpha_out.params['alpha'].value, RSD, N))
+    beta_params.add('beta', value=2.)
+    beta_out = minimize(FNR_beta_residual, beta_params, args=(FNR/100., RSD, BN, CN, alpha_out.params['alpha'].value))
 
     return alpha_out.params['alpha'].value, beta_out.params['beta'].value
 
@@ -52,18 +54,27 @@ def equivalency():
 
     alpha = 0.
     beta = 0.
-    RSD = 0.2
-    N = 3
-    FPR = 0.3
-    FNR = 0.3
+    Bmean = 100.
+    Cmean = 100.
+    Bstd = 20.
+    Cstd = 20.
+    BN = 3
+    CN = 3
+    FPR = 5.0
+    FNR = 5.0
 
     if request.method == 'POST':
-        RSD = float(request.form["RSD"])
-        N = int(request.form["N"])
+        Bmean = float(request.form["Bmean"])
+        Cmean = float(request.form["Cmean"])
+        Bstd = float(request.form["Bstd"])
+        Cstd = float(request.form["Cstd"])
+        BN = int(request.form["BN"])
+        CN = int(request.form["CN"])
         FPR = float(request.form["FPR"])
         FNR = float(request.form["FNR"])
 
-        alpha, beta = FitParams(FPR, FNR, RSD, N)
+        alpha, beta = FitParams(FPR, FNR, Bmean, Bstd, BN, Cmean, Cstd, CN)
 
 
-    return render_template('equivalency_index.html', RSD=RSD, N=N, FPR=FPR, FNR=FNR, alpha=alpha, beta=beta)
+    return render_template('equivalency_index.html', Bmean=Bmean, Cmean=Cmean, Bstd=Bstd, Cstd=Cstd, \
+                           BN=BN, CN=CN, FPR=FPR, FNR=FNR, alpha=alpha, beta=beta)

equivalency_module/templates/equivalency_index.html

@@ -8,13 +8,6 @@
   <script src="https://cdn.jsdelivr.net/npm/bootstrap@4.6.1/dist/js/bootstrap.min.js" integrity="sha384-VHvPCCyXqtD5DqJeNxl2dtTyhF78xXNXdkwX1CZeRusQfRKp+tA7hAShOK/B/fQ2" crossorigin="anonymous"></script>
   <link rel= "stylesheet" type= "text/css" href= "{{ url_for('static',filename='styles.css') }}">
 
-  <style>
-table, th, td {
-  border: 1px solid black;
-  border-collapse: collapse;
-}
-</style>
-
 </head>
 
 <img src="{{ url_for('static',filename='images/FDAlogo.png') }}" style="float: left;" height="100"/>
@@ -37,19 +30,30 @@ table, th, td {
 
 <form method="POST" id="theForm" align="left">
 
-  RSD: <input name="RSD" id="RSD" value="{{RSD}}" step="any" min="0.01" type="number" required> <br>
-  N: <input name="N" id="N" value="{{N}}" step="1" min="1" type="number" onchange="this.value = parseInt(this.value);" required> <br>
+  <h3> Baseline </h3>
+  Mean: <input name="Bmean" id="Bmean" value="{{Bmean}}" step="any" min="0.01" type="number" required> <br>
+  Stdev: <input name="Bstd" id="Bstd" value="{{Bstd}}" step="any" min="0.01" type="number" required> <br>
+  N: <input name="BN" id="BN" value="{{BN}}" step="1" min="1" type="number" onchange="this.value = parseInt(this.value);" required> <br>
+  <h3> Comparator </h3>
+  Mean: <input name="Cmean" id="Cmean" value="{{Cmean}}" step="any" min="0.01" type="number" required> <br>
+  Stdev: <input name="Cstd" id="Cstd" value="{{Cstd}}" step="any" min="0.01" type="number" required> <br>
+  N: <input name="CN" id="CN" value="{{CN}}" step="1" min="1" type="number" onchange="this.value = parseInt(this.value);" required> <br>
+  <h3> Statistical limits </h3>
   FPR (%): <input name="FPR" id="FPR" value="{{FPR}}" step="any" min="0.01" type="number"  required> <br>
-  FNR (%): <input name="FNR" id="FNR" value="{{FNR}}" step="any" min="0.01" type="number"  required> <br> <br>
+  FNR (%): <input name="FNR" id="FNR" value="{{FNR}}" step="any" min="0.01" type="number"  required> <br>
 
-  Acceptance criterion factor:
   {% if alpha != 0 %}
-    {{'%0.4f'%alpha|float}}
-  {% endif %} <br>
-  Minimum MOS:
-  {% if beta != 0 %}
-    {{'%0.4f'%beta|float}}
-  {% endif %} <br>
+     <h3> Result: </h3>
+    {% set accept = alpha*Bmean %}
+    The acceptance criterion factor is {{'%0.2f'%alpha|float}}.  Therefore, your mean comparator results must be less than
+    {{'%0.2f'%accept|float}}. <br>
+    {% if accept >= Cmean %}
+      The acceptance criteria has been met.  However, this only applies if the analyte of interest has a margin of safety (MOS)
+      greater than {{'%0.1f'%beta|float}}. <br>
+    {% else %}
+      The acceptance criteria has not been met.  Additional justification and/or analyses will be required. <br>
+    {% endif %}
+  {% endif %}
 
   <br> <button type="submit">Calculate</button>