{"id":3470,"date":"2025-09-02T11:12:59","date_gmt":"2025-09-02T09:12:59","guid":{"rendered":"https:\/\/neuraldesigner.com\/learning\/breast-cancer-mortality\/"},"modified":"2026-09-18T16:07:37","modified_gmt":"2026-09-18T14:07:37","slug":"breast-cancer-mortality","status":"publish","type":"learning","link":"https:\/\/www.neuraldesigner.com\/learning\/examples\/breast-cancer-mortality\/","title":{"rendered":"Breast cancer mortality prediction with machine learning"},"content":{"rendered":"<style data-nd-chart-migration=\"1\">\n.nd-chart-bundle{width:100%;max-width:760px;min-width:0;margin:24px auto;box-sizing:border-box;position:relative;overflow-x:auto;text-align:center;background:#fff;color:#30343b}\n.nd-chart-bundle .nd-chart-host{width:100%;height:440px;min-width:0;box-sizing:border-box}\n.nd-chart-bundle:not(.is-ready) .nd-chart-host{position:absolute;visibility:hidden}\n.nd-chart-bundle.is-ready .nd-chart-fallback{display:none!important}\n.nd-chart-bundle 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#dce8ef;border-radius:15px;background:#f8fbfd}.nds-centered-figure img{display:block;width:100%;max-width:100%;margin:0 auto 12px}\n.nds-roc-figure{max-width:600px;margin:24px auto!important;padding:16px;border:1px solid #dce8ef;border-radius:15px;background:#f8fbfd}.nds-roc-figure img{display:block;width:min(520px,100%);max-width:100%;margin:0 auto 12px}\n.nds-validation-grid{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:22px;align-items:start}.nds-validation-grid table{margin-top:0}.nds-confusion td,.nds-metrics td:nth-child(2){text-align:right;font-variant-numeric:tabular-nums}\n.nds-stage{display:grid;grid-template-columns:repeat(3,minmax(0,1fr));gap:14px;margin:22px 0}.nds-stage div{display:flex;min-height:112px;flex-direction:column;align-items:center;justify-content:center;padding:18px;border-radius:14px;background:#12354b;color:#fff;text-align:center}.nds-stage strong{font-size:20px}.nds-stage span{margin-top:7px;font-size:14px}\n.nds-flow{display:grid;grid-template-columns:repeat(6,minmax(0,1fr));gap:10px;margin:24px 0}.nds-flow div{position:relative;display:flex;min-height:105px;align-items:center;justify-content:center;padding:13px 9px;border-radius:13px;background:#12354b;color:#fff;text-align:center;font-weight:700}.nds-flow div:not(:last-child):after{content:\"\u2192\";position:absolute;right:-15px;top:50%;z-index:2;transform:translateY(-50%);color:#56a1c8;font-size:21px}\n@media(max-width:960px){.nds-validation-grid{grid-template-columns:1fr}.nds-flow{grid-template-columns:repeat(3,1fr)}.nds-flow div:after{display:none}}\n@media(max-width:760px){.nds-stage,.nds-flow{grid-template-columns:1fr}.nds-flow div:after{display:none}}\n<\/style>\n<div class=\"nds\" data-science-profile=\"life-health\">\n<div class=\"nds-wrap\">\n<section class=\"nds-executive\">\n<h2>Analyse five-year breast cancer survival from clinical and molecular data<\/h2>\n<p>This fixed-horizon survival analysis asks whether the recorded outcome occurs within five years. It combines clinical, treatment, gene-expression and mutation variables and implements the survival endpoint as binary classification. After growing-input selection, the final 95-feature sigmoid classifier reaches ROC AUC 0.746 on 351 held-out rows.<\/p>\n<div class=\"nds-kpis\">\n<div class=\"nds-kpi\"><strong>0.746<\/strong><span>testing ROC AUC (95% CI 0.685\u20130.806)<\/span><\/div>\n<div class=\"nds-kpi\"><strong>65.7%<\/strong><span>sensitivity at threshold 0.50<\/span><\/div>\n<div class=\"nds-kpi\"><strong>70.1%<\/strong><span>specificity at threshold 0.50<\/span><\/div>\n<div class=\"nds-kpi\"><strong>351<\/strong><span>held-out testing rows<\/span><\/div>\n<\/div>\n<div class=\"nds-actions\"><a href=\"#6-validation\">Review the testing evidence<\/a><a href=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2025\/09\/5_years_mortality.csv\">Download the data<\/a><\/div>\n<\/section>\n<ul class=\"nds-toc\">\n<li><a href=\"#1-scientific-objective\">Scientific objective<\/a><\/li>\n<li><a href=\"#2-data-provenance\">Data and provenance<\/a><\/li>\n<li><a href=\"#3-model\">Model<\/a><\/li>\n<li><a href=\"#4-training\">Training<\/a><\/li>\n<li><a href=\"#5-selection\">Selection<\/a><\/li>\n<li><a href=\"#6-validation\">Validation<\/a><\/li>\n<li><a href=\"#7-inference\">Inference<\/a><\/li>\n<li><a href=\"#8-validity\">Validity<\/a><\/li>\n<\/ul>\n<section id=\"1-scientific-objective\" class=\"nds-card\">\n<h2>1. Scientific objective<\/h2>\n<p>The scientific objective is five-year overall-survival analysis. For each eligible row, the prepared target <code>overall_mortality<\/code> indicates whether death was recorded within the five-year horizon: label 1 is the event class and label 0 is five-year survival. Neural Designer therefore solves a <strong>fixed-horizon survival classification<\/strong> problem. Unlike a time-to-event model, it estimates one endpoint at five years and does not produce a complete survival or hazard curve.<\/p>\n<div class=\"nds-value-grid\">\n<div class=\"nds-value\">\n<h3>Method development<\/h3>\n<p>Explore mixed clinical, categorical, transcriptomic and mutation inputs in one reproducible classification pipeline.<\/p>\n<\/div>\n<div class=\"nds-value\">\n<h3>Five-year stratification<\/h3>\n<p>Quantify how well the model separates the recorded five-year mortality and survival classes in a held-out subset.<\/p>\n<\/div>\n<div class=\"nds-value\">\n<h3>Reproducible review<\/h3>\n<p>Export the trained calculation and its exact 76-to-95 feature encoding for retrospective batch analysis.<\/p>\n<\/div>\n<\/div>\n<div class=\"nds-audience\"><span>Clinical data scientists<\/span><span>Biostatisticians<\/span><span>Translational researchers<\/span><span>Bioinformaticians<\/span><span>Oncology research teams<\/span><\/div>\n<div class=\"nds-note\"><strong>Scope.<\/strong> This is an educational retrospective survival analysis at a fixed five-year horizon. It demonstrates model construction and evaluation; it is not a validated individual survival calculator and must not guide diagnosis, treatment or patient counselling.<\/div>\n<\/section>\n<section id=\"2-data-provenance\" class=\"nds-card\">\n<h2>2. Data and provenance<\/h2>\n<p>The prepared table contains 1,880 rows and 689 columns: one local identifier, 687 candidate predictors and the target. The predictors comprise 25 clinical\/treatment descriptors, 489 gene-expression measurements and 173 mutation indicators. The target is observed for 1,755 rows; 125 rows labelled <code>NA<\/code> are unused.<\/p>\n<div class=\"nds-table-scroll\">\n<table>\n<thead>\n<tr>\n<th>Subset<\/th>\n<th>Rows<\/th>\n<th>Positive labels<\/th>\n<th>Purpose<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>Training<\/th>\n<td>1,053<\/td>\n<td>Stored in project<\/td>\n<td>Estimate model parameters<\/td>\n<\/tr>\n<tr>\n<th>Selection<\/th>\n<td>351<\/td>\n<td>Stored in project<\/td>\n<td>Select the input subset and monitor training<\/td>\n<\/tr>\n<tr>\n<th>Testing<\/th>\n<td>351<\/td>\n<td>67<\/td>\n<td>Final internal evaluation<\/td>\n<\/tr>\n<tr>\n<th>Unused<\/th>\n<td>125<\/td>\n<td>Target unavailable<\/td>\n<td>Excluded from modelling<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>Among the 1,755 eligible rows, 325 (18.5%) carry the five-year mortality label and 1,430 (81.5%) carry the five-year survival label. This imbalance makes raw accuracy a poor headline metric.<\/p>\n<div class=\"nds-figure-grid\">\n<figure>\n<div class=\"nd-chart-bundle\" tabindex=\"0\" role=\"group\" aria-label=\"Interactive chart; scroll horizontally on narrow screens\" data-native-chart=\"nd-3470-00\">\n<div class=\"nd-chart-host\" id=\"nd-3470-00\" role=\"img\" aria-label=\"Interactive chart: Distribution of the five-year survival outcome\"><\/div>\n<p><img decoding=\"async\" class=\"nd-chart-fallback\" src=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/breast-cancer-mortality-target-distribution-2026.png\" alt=\"Distribution of the five-year survival outcome\"><script type=\"application\/json\" id=\"nd-3470-00-data\">{\"config\":{\"displayModeBar\":true,\"displaylogo\":false,\"editable\":false,\"responsive\":true,\"scrollZoom\":true,\"toImageButtonOptions\":{\"filename\":\"neural-designer-chart\",\"format\":\"svg\"}},\"data\":[{\"direction\":\"clockwise\",\"hovertemplate\":\"%{label}\\u003cbr\\u003e%{value}\\u003cbr\\u003e%{percent}\\u003cextra\\u003e\\u003c\/extra\\u003e\",\"labels\":[\"0\",\"1\"],\"marker\":{\"colors\":[\"#209fdf\",\"#092d40\"]},\"showlegend\":true,\"sort\":false,\"textinfo\":\"label+percent\",\"type\":\"pie\",\"values\":[81.5,18.5]}],\"layout\":{\"autosize\":true,\"font\":{\"color\":\"#30343b\",\"family\":\"Arial, sans-serif\",\"size\":14},\"hovermode\":\"closest\",\"legend\":{},\"margin\":{\"b\":68,\"l\":72,\"pad\":4,\"r\":36,\"t\":112},\"paper_bgcolor\":\"#ffffff\",\"plot_bgcolor\":\"#ffffff\",\"title\":{\"automargin\":true,\"pad\":{\"t\":48},\"text\":\"overall_mortality pie chart\",\"x\":0.5,\"xanchor\":\"center\",\"y\":1,\"yanchor\":\"top\",\"yref\":\"container\"}}}<\/script><\/div><figcaption>Mortality within five years represents 18.5% of eligible rows; 125 rows without an available endpoint are excluded.<\/figcaption><\/figure>\n<figure>\n<div class=\"nd-chart-bundle\" tabindex=\"0\" role=\"group\" aria-label=\"Interactive chart; scroll horizontally on narrow screens\" data-native-chart=\"nd-3470-01\">\n<div class=\"nd-chart-host\" id=\"nd-3470-01\" role=\"img\" aria-label=\"Interactive chart: Largest univariate correlations with the mortality target\"><\/div>\n<p><img decoding=\"async\" class=\"nd-chart-fallback\" src=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/breast-cancer-mortality-correlations-2026.png\" alt=\"Largest univariate correlations with the mortality target\"><script type=\"application\/json\" id=\"nd-3470-01-data\">{\"config\":{\"displayModeBar\":true,\"displaylogo\":false,\"editable\":false,\"responsive\":true,\"scrollZoom\":true,\"toImageButtonOptions\":{\"filename\":\"neural-designer-chart\",\"format\":\"svg\"}},\"data\":[{\"marker\":{\"color\":\"#209fdf\"},\"name\":\"\",\"opacity\":1,\"orientation\":\"h\",\"showlegend\":false,\"type\":\"bar\",\"x\":[-0.2540000081062317,-0.23600000143051147,0.2370000034570694,0.23800000548362732,0.23999999463558197,0.23999999463558197,0.24300000071525574,0.25999999046325684,0.2849999964237213,0.28999999165534973],\"y\":[\"er_status\",\"er_status_measured_by_ihc\",\"pam50_+_claudin-1_subtype\",\"BCL2\",\"MAPT\",\"TP53_MUT\",\"chemotherapy\",\"3-gene_classifier_subtype\",\"lymph_nodes_examined_positive\",\"tumor_stage\"]}],\"layout\":{\"autosize\":true,\"font\":{\"color\":\"#30343b\",\"family\":\"Arial, sans-serif\",\"size\":14},\"hovermode\":\"closest\",\"margin\":{\"b\":68,\"l\":72,\"pad\":4,\"r\":36,\"t\":112},\"paper_bgcolor\":\"#ffffff\",\"plot_bgcolor\":\"#ffffff\",\"title\":{\"automargin\":true,\"pad\":{\"t\":48},\"text\":\"overall_mortality Pearson correlations chart\",\"x\":0.5,\"xanchor\":\"center\",\"y\":1,\"yanchor\":\"top\",\"yref\":\"container\"},\"xaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[-1,1],\"title\":{\"text\":\"Correlation\"},\"zerolinecolor\":\"#aeb6c2\"},\"yaxis\":{\"automargin\":true,\"autorange\":\"reversed\",\"categoryarray\":[\"er_status\",\"er_status_measured_by_ihc\",\"pam50_+_claudin-1_subtype\",\"BCL2\",\"MAPT\",\"TP53_MUT\",\"chemotherapy\",\"3-gene_classifier_subtype\",\"lymph_nodes_examined_positive\",\"tumor_stage\"],\"categoryorder\":\"array\",\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"type\":\"category\",\"zerolinecolor\":\"#aeb6c2\"}}}<\/script><\/div><figcaption>Tumour stage and positive lymph-node count have the largest displayed absolute correlations. These are univariate associations, not causal effects or multivariable feature importance.<\/figcaption><\/figure>\n<\/div>\n<h3>Predictor groups<\/h3>\n<div class=\"nds-table-scroll\">\n<table>\n<thead>\n<tr>\n<th>Group<\/th>\n<th>Examples<\/th>\n<th>Important timing question<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>Clinical and tumour<\/th>\n<td><code>age_at_diagnosis<\/code>, stage, size, receptor status, positive nodes<\/td>\n<td>Available at or shortly after diagnosis?<\/td>\n<\/tr>\n<tr>\n<th>Treatment<\/th>\n<td>Surgery type, chemotherapy, hormone therapy, radiotherapy<\/td>\n<td>Assigned before the intended prediction time?<\/td>\n<\/tr>\n<tr>\n<th>Molecular<\/th>\n<td>489 expression measurements and 173 mutation indicators<\/td>\n<td>Assay platform and preprocessing compatible?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"nds-note nds-note--provenance\"><strong>Survival-endpoint provenance.<\/strong> The table is derived from the METABRIC collection distributed through cBioPortal. It preserves the five-year binary outcome used by this example, but not the underlying follow-up time, event time or censoring rule. Those fields are required to audit the endpoint or extend the study to full time-to-event modelling.<\/div>\n<\/section>\n<section id=\"3-model\" class=\"nds-card\">\n<h2>3. Model<\/h2>\n<p>The initial model uses all 687 raw candidate predictors. Categorical expansion produces 722 numeric inputs, followed by scaling and one sigmoid output. With no hidden layer, this is a linear, logistic-like classifier with 723 trainable parameters\u2014not a deep network.<\/p>\n<div class=\"nds-note\"><strong>Output contract.<\/strong> A larger sigmoid value means stronger evidence for the five-year mortality class under this fitted cohort; a smaller value favours the five-year survival class. The score orders cases, but no calibration analysis shows that it equals an individual mortality or survival probability.<\/div>\n<figure class=\"nds-architecture-figure\" data-model-stage=\"initial\"><img decoding=\"async\" class=\"nds-architecture\" src=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/breast-cancer-mortality-initial-network-2026.png\" alt=\"Initial network with 687 raw candidate predictors and one mortality output\"><figcaption>Initial all-input architecture. The graph summarizes 687 raw predictors; categorical encoding expands them to 722 numeric model inputs.<\/figcaption><\/figure>\n<\/section>\n<section id=\"4-training\" class=\"nds-card\">\n<h2>4. Training strategy<\/h2>\n<p>The first direct classifier is optimized with the quasi-Newton method using weighted squared error. Training error falls from 0.8825 to 0.0818 across 72 epochs, while selection error reaches its minimum early and ends at 0.7460. 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sans-serif\",\"size\":14},\"hovermode\":\"closest\",\"legend\":{\"orientation\":\"h\",\"x\":0.5,\"xanchor\":\"center\",\"y\":-0.24,\"yanchor\":\"top\"},\"margin\":{\"b\":120,\"l\":72,\"pad\":4,\"r\":36,\"t\":112},\"paper_bgcolor\":\"#ffffff\",\"plot_bgcolor\":\"#ffffff\",\"title\":{\"automargin\":true,\"pad\":{\"t\":48},\"text\":\"Quasi-Newton method error history\",\"x\":0.5,\"xanchor\":\"center\",\"y\":1,\"yanchor\":\"top\",\"yref\":\"container\"},\"xaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[0,72],\"title\":{\"text\":\"Epoch\"},\"zerolinecolor\":\"#aeb6c2\"},\"yaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[0,1.0002],\"title\":{\"text\":\"WeightedSquaredError\"},\"zerolinecolor\":\"#aeb6c2\"}}}<\/script><\/div><figcaption>The all-input model continues fitting the training rows after selection performance has stopped improving.<\/figcaption><\/figure>\n<div class=\"nds-note nds-note--warning\"><strong>Why selection is needed.<\/strong> With 722 encoded inputs but only 1,053 training rows, the unrestricted direct model has enough flexibility to memorize cohort-specific structure.<\/div>\n<\/section>\n<section id=\"5-selection\" class=\"nds-card\">\n<h2>5. Model selection and baseline<\/h2>\n<p>This project performs <strong>input selection<\/strong>, not neuron selection. A growing-input search adds variables according to selection performance and reaches its lowest stored selection error with 76 raw variables.<\/p>\n<figure class=\"nds-centered-figure\">\n<div class=\"nd-chart-bundle\" tabindex=\"0\" role=\"group\" aria-label=\"Interactive chart; scroll horizontally on narrow screens\" data-native-chart=\"nd-3470-04\">\n<div class=\"nd-chart-host\" id=\"nd-3470-04\" role=\"img\" aria-label=\"Interactive chart: Growing-input training and selection errors\"><\/div>\n<p><img decoding=\"async\" class=\"nd-chart-fallback\" src=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/breast-cancer-mortality-input-selection-2026.png\" alt=\"Growing-input training and selection errors\"><script type=\"application\/json\" 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Because the minimum is boundary-adjacent, the result should be treated as one fitted subset rather than a stable biological signature.<\/figcaption><\/figure>\n<h3>Final model<\/h3>\n<p>The 76 selected raw variables expand to 95 numeric inputs: 19 clinical\/categorical indicators, 63 gene-expression measurements and three mutation indicators. The final 95-to-1 sigmoid classifier contains 96 trainable parameters.<\/p>\n<div class=\"nds-stage\">\n<div><strong>76 raw variables<\/strong><span>Selected clinical and molecular fields<\/span><\/div>\n<div><strong>95 numeric inputs<\/strong><span>Scaling and one-hot encoding<\/span><\/div>\n<div><strong>1 sigmoid score<\/strong><span>Direct linear classification layer<\/span><\/div>\n<\/div>\n<p>Retraining the reduced model for 33 epochs lowers training weighted squared error from 0.7571 to 0.4609 and selection error from 0.4354 to 0.3151.<\/p>\n<figure class=\"nds-centered-figure\">\n<div class=\"nd-chart-bundle\" tabindex=\"0\" role=\"group\" aria-label=\"Interactive chart; scroll horizontally on narrow screens\" data-native-chart=\"nd-3470-05\">\n<div class=\"nd-chart-host\" id=\"nd-3470-05\" role=\"img\" aria-label=\"Interactive chart: Final training history after growing-input selection\"><\/div>\n<p><img decoding=\"async\" class=\"nd-chart-fallback\" src=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/breast-cancer-mortality-final-training-2026.png\" alt=\"Final training history after growing-input selection\"><script type=\"application\/json\" id=\"nd-3470-05-data\">{\"config\":{\"displayModeBar\":true,\"displaylogo\":false,\"editable\":false,\"responsive\":true,\"scrollZoom\":true,\"toImageButtonOptions\":{\"filename\":\"neural-designer-chart\",\"format\":\"svg\"}},\"data\":[{\"connectgaps\":false,\"line\":{\"color\":\"#529cc2\",\"dash\":\"solid\",\"width\":2},\"mode\":\"lines\",\"name\":\"Training error\",\"opacity\":1,\"showlegend\":true,\"type\":\"scatter\",\"x\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],\"y\":[0.7570000290870667,0.6169999837875366,0.5889999866485596,0.5260000228881836,0.5170000195503235,0.49799999594688416,0.4869999885559082,0.4790000021457672,0.4740000069141388,0.47099998593330383,0.4690000116825104,0.46700000762939453,0.4659999907016754,0.4650000035762787,0.46399998664855957,0.46299999952316284,0.4620000123977661,0.4620000123977661,0.4620000123977661,0.460999995470047,0.460999995470047,0.460999995470047,0.460999995470047,0.460999995470047,0.460999995470047,0.460999995470047,0.460999995470047,0.460999995470047,0.460999995470047,0.460999995470047,0.460999995470047,0.460999995470047,0.460999995470047,0.460999995470047]},{\"connectgaps\":false,\"line\":{\"color\":\"#ed982a\",\"dash\":\"solid\",\"width\":2},\"mode\":\"lines\",\"name\":\"Selection error\",\"opacity\":1,\"showlegend\":true,\"type\":\"scatter\",\"x\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],\"y\":[0.4350000023841858,0.41200000047683716,0.3630000054836273,0.36500000953674316,0.3490000069141388,0.3370000123977661,0.3319999873638153,0.33000001311302185,0.32899999618530273,0.3269999921321869,0.32499998807907104,0.3230000138282776,0.3199999928474426,0.3179999887943268,0.31700000166893005,0.3160000145435333,0.3160000145435333,0.3160000145435333,0.3160000145435333,0.3160000145435333,0.3149999976158142,0.3149999976158142,0.3149999976158142,0.3149999976158142,0.3149999976158142,0.3149999976158142,0.3149999976158142,0.3149999976158142,0.3149999976158142,0.3149999976158142,0.3149999976158142,0.3149999976158142,0.3149999976158142,0.3149999976158142]}],\"layout\":{\"autosize\":true,\"font\":{\"color\":\"#30343b\",\"family\":\"Arial, sans-serif\",\"size\":14},\"hovermode\":\"closest\",\"legend\":{\"orientation\":\"h\",\"x\":0.5,\"xanchor\":\"center\",\"y\":-0.24,\"yanchor\":\"top\"},\"margin\":{\"b\":120,\"l\":72,\"pad\":4,\"r\":36,\"t\":112},\"paper_bgcolor\":\"#ffffff\",\"plot_bgcolor\":\"#ffffff\",\"title\":{\"automargin\":true,\"pad\":{\"t\":48},\"text\":\"Quasi-Newton method error history\",\"x\":0.5,\"xanchor\":\"center\",\"y\":1,\"yanchor\":\"top\",\"yref\":\"container\"},\"xaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[0,33],\"title\":{\"text\":\"Epoch\"},\"zerolinecolor\":\"#aeb6c2\"},\"yaxis\":{\"automargin\":true,\"gridcolor\":\"#d9dde3\",\"linecolor\":\"#9aa3ad\",\"range\":[0,0.8002],\"title\":{\"text\":\"WeightedSquaredError\"},\"zerolinecolor\":\"#aeb6c2\"}}}<\/script><\/div><figcaption>The reduced model trains without the severe divergence seen in the all-input baseline.<\/figcaption><\/figure>\n<\/section>\n<section id=\"6-validation\" class=\"nds-card\">\n<h2>6. Scientific validation<\/h2>\n<p>The final model is evaluated on the 351 testing rows only after training and input selection. Neural Designer reports ROC AUC 0.746 with a 95% confidence interval of 0.685\u20130.806. This indicates moderate internal discrimination with substantial uncertainty.<\/p>\n<figure class=\"nds-roc-figure\">\n<div class=\"nd-chart-bundle\" tabindex=\"0\" role=\"group\" aria-label=\"Interactive chart; scroll horizontally on narrow screens\" data-native-chart=\"nd-3470-06\">\n<div class=\"nd-chart-host\" id=\"nd-3470-06\" role=\"img\" aria-label=\"Interactive chart: Testing ROC curve for the breast-cancer mortality classifier\"><\/div>\n<p><img decoding=\"async\" class=\"nd-chart-fallback\" src=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/breast-cancer-mortality-roc-2026.png\" alt=\"Testing ROC curve for the breast-cancer mortality classifier\"><script type=\"application\/json\" 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The marked threshold is selected from this same curve and is descriptive, not a prespecified clinical cutoff.<\/figcaption><\/figure>\n<div class=\"nds-validation-grid\">\n<div class=\"nds-table-scroll\">\n<table class=\"nds-confusion\">\n<thead>\n<tr>\n<th>Actual \/ predicted at 0.50<\/th>\n<th>Label 1<\/th>\n<th>Label 0<\/th>\n<th>Total<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>Actual label 1<\/th>\n<td>44<\/td>\n<td>23<\/td>\n<td>67<\/td>\n<\/tr>\n<tr>\n<th>Actual label 0<\/th>\n<td>85<\/td>\n<td>199<\/td>\n<td>284<\/td>\n<\/tr>\n<tr>\n<th>Total<\/th>\n<td>129<\/td>\n<td>222<\/td>\n<td>351<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"nds-table-scroll\">\n<table class=\"nds-metrics\">\n<thead>\n<tr>\n<th>Testing metric<\/th>\n<th>Value<\/th>\n<th>Professional reading<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>Sensitivity<\/th>\n<td>65.7%<\/td>\n<td>44 of 67 positive labels detected<\/td>\n<\/tr>\n<tr>\n<th>Specificity<\/th>\n<td>70.1%<\/td>\n<td>199 of 284 negative labels rejected<\/td>\n<\/tr>\n<tr>\n<th>Precision<\/th>\n<td>34.1%<\/td>\n<td>44 of 129 positive calls match label 1<\/td>\n<\/tr>\n<tr>\n<th>F1 score<\/th>\n<td>0.449<\/td>\n<td>Limited balance of precision and sensitivity<\/td>\n<\/tr>\n<tr>\n<th>Balanced accuracy<\/th>\n<td>67.9%<\/td>\n<td>More informative here than raw accuracy<\/td>\n<\/tr>\n<tr>\n<th>Raw accuracy<\/th>\n<td>69.2%<\/td>\n<td>Below the 80.9% majority-label baseline<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div class=\"nds-figure-grid\"><\/div>\n<div class=\"nds-note\"><strong>Interpretation.<\/strong> The ROC AUC shows useful ranking information, but the 0.50 operating point misses 23 positive testing rows and generates 85 false-positive calls. The high negative-label prevalence explains why a trivial all-negative classifier has higher raw accuracy; that baseline has zero sensitivity and cannot distinguish different survival profiles.<\/div>\n<\/section>\n<section id=\"7-inference\" class=\"nds-card\">\n<h2>7. Inference and reproducibility<\/h2>\n<p>The defensible deployment is a versioned retrospective <strong>five-year survival-stratification<\/strong> workflow. It can assign model scores to a research cohort, compare operating thresholds and identify groups for aggregate survival research. A patient-facing calculator would hide the 76-field data contract, assay dependencies and missing-value policy.<\/p>\n<div class=\"nds-flow\">\n<div>Versioned METABRIC-format cohort<\/div>\n<div>Five-year endpoint and schema checks<\/div>\n<div>76-to-95 feature encoding<\/div>\n<div>Exported survival classifier<\/div>\n<div>Declared research threshold<\/div>\n<div>Aggregate survival-strata review<\/div>\n<\/div>\n<h3>Illustrative threshold scenarios<\/h3>\n<p>The following values are recalculated with the exported model on the same 351 testing rows. They show how the chosen score threshold changes detection of the five-year mortality class; they are not treatment thresholds.<\/p>\n<div class=\"nds-table-scroll\">\n<table>\n<thead>\n<tr>\n<th>Retrospective policy<\/th>\n<th>Threshold<\/th>\n<th>Sensitivity<\/th>\n<th>Specificity<\/th>\n<th>False negatives<\/th>\n<th>False positives<\/th>\n<th>Possible research purpose<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>Sensitivity-first review<\/th>\n<td>0.30<\/td>\n<td>88.1%<\/td>\n<td>48.2%<\/td>\n<td>8<\/td>\n<td>147<\/td>\n<td>Reduce missed labelled cases at the cost of extensive review<\/td>\n<\/tr>\n<tr>\n<th>Nearest ROC corner<\/th>\n<td>0.43<\/td>\n<td>79.1%<\/td>\n<td>62.0%<\/td>\n<td>14<\/td>\n<td>108<\/td>\n<td>Best internal sensitivity\/specificity balance on this curve<\/td>\n<\/tr>\n<tr>\n<th>Specificity-first review<\/th>\n<td>0.70<\/td>\n<td>43.3%<\/td>\n<td>84.5%<\/td>\n<td>38<\/td>\n<td>44<\/td>\n<td>Fewer false flags, with many more missed positives<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"nds-note nds-note--warning\"><strong>Not clinical thresholds.<\/strong> The operating points were examined on the internal testing set, the score is uncalibrated and no decision-curve or outcome-impact analysis is available.<\/div>\n<h3>Run the final model in Python<\/h3>\n<p>The package includes the executable 95-input model, ordered schema, raw-row encoder and batch scorer. It does not include patient-level data.<\/p>\n<pre><code>python score_csv.py 5_years_mortality.csv scored_rows.csv --threshold 0.50<\/code><\/pre>\n<h3>Reproduce the calculation<\/h3>\n<p>The encoder applies the selected categorical expansion and stored mean replacement for missing numeric or binary values. The downloadable dataset retains all candidate predictors, while the package selects the final 76 raw fields in the required order.<\/p>\n<div class=\"nds-downloads\"><a href=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2026\/08\/breast-cancer-mortality-python-model-2026.zip\">Download Python model (ZIP)<\/a><a href=\"https:\/\/www.neuraldesigner.com\/wp-content\/uploads\/2025\/09\/5_years_mortality.csv\" download>Download 5_years_mortality.csv<\/a><\/div>\n<\/section>\n<section id=\"8-validity\" class=\"nds-card\">\n<h2>8. Validity, uncertainty and limitations<\/h2>\n<ul>\n<li><strong>Fixed-horizon endpoint documentation.<\/strong> The example is a valid binary survival formulation only if every label 0 row was known to survive beyond five years. Survival time, vital-status timing and censoring are not retained in the derivative table, so that rule cannot be rechecked here.<\/li>\n<li><strong>Prediction time is undefined.<\/strong> Surgery type and systemic treatment variables are retained in the final model. Their availability and meaning depend on whether the intended prediction occurs at diagnosis, after surgery or after treatment assignment.<\/li>\n<li><strong>Random internal split only.<\/strong> The 1,053\/351\/351 partition samples one derived cohort; there is no temporal, geographic or external-centre evaluation.<\/li>\n<li><strong>Input selection is optimistic unless nested.<\/strong> The same selection subset guides the 76-variable search. Stability across repeated grouped resampling is not reported.<\/li>\n<li><strong>No calibration evidence.<\/strong> AUC measures ranking, not agreement between scores and five-year event frequencies. Calibration-in-the-large, slope, plots and recalibration are missing.<\/li>\n<li><strong>High-dimensional assay dependence.<\/strong> Gene-expression normalization, platform effects, batch correction, mutation calling and missingness must match the development pipeline.<\/li>\n<li><strong>Fixed-horizon simplification.<\/strong> The binary endpoint answers one five-year question but discards when the event occurred, survival beyond that horizon, cause of death and competing risks. Historical treatments may also differ from current practice.<\/li>\n<li><strong>Subgroup performance is untested.<\/strong> Aggregate discrimination does not establish comparable performance across age, receptor status, stage, molecular subtype, cohort or demographic groups.<\/li>\n<li><strong>No clinical-utility evaluation.<\/strong> There is no comparison with established prognostic models, decision-curve analysis, prospective workflow study or evidence of improved patient outcomes.<\/li>\n<\/ul>\n<div class=\"nds-note nds-note--warning\"><strong>Decision boundary.<\/strong> Use this example for software education and retrospective methods research only. Do not use its score for diagnosis, treatment decisions, follow-up scheduling or individual prognosis.<\/div>\n<h3>From fixed-horizon to full survival modelling<\/h3>\n<p>The present classifier is appropriate for demonstrating a single five-year endpoint. A more complete study would define the index date, retain event and censoring times, compare the classifier with a time-to-event survival model, freeze predictors to those available at the index date, assess calibration and clinical net benefit, and perform temporal plus external-centre validation under TRIPOD+AI and PROBAST+AI.<\/p>\n<\/section>\n<section id=\"references\" class=\"nds-card\">\n<h2>References<\/h2>\n<ul>\n<li>Curtis C, Shah SP, Chin SF, et al. <a href=\"https:\/\/doi.org\/10.1038\/nature10983\">The genomic and transcriptomic architecture of 2,000 breast tumours reveals novel subgroups<\/a>. <em>Nature<\/em>. 2012;486:346\u2013352.<\/li>\n<li>Pereira B, Chin SF, Rueda OM, et al. <a href=\"https:\/\/doi.org\/10.1038\/ncomms11479\">The somatic mutation profiles of 2,433 breast cancers refine their genomic and transcriptomic landscapes<\/a>. <em>Nature Communications<\/em>. 2016;7:11479.<\/li>\n<li><a href=\"https:\/\/www.cbioportal.org\/study\/summary?id=brca_metabric\">Breast Cancer METABRIC study<\/a>. cBioPortal for Cancer Genomics.<\/li>\n<li>Collins GS, Moons KGM, Dhiman P, et al. <a href=\"https:\/\/doi.org\/10.1136\/bmj-2023-078378\">TRIPOD+AI statement<\/a>. <em>BMJ<\/em>. 2024;385:e078378.<\/li>\n<li>Moons KGM, Damen JAAG, Kaul T, et al. <a href=\"https:\/\/doi.org\/10.1136\/bmj-2024-082505\">PROBAST+AI<\/a>. <em>BMJ<\/em>. 2025;388:e082505.<\/li>\n<li><a href=\"https:\/\/nemhesys.usal.es\/\">NEMHESYS \u2014 NGS Establishment in Multidisciplinary Healthcare Education System<\/a> supported the original educational application.<\/li>\n<\/ul>\n<\/section>\n<\/div>\n<\/div>\n<p><script data-nd-chart-migration=\"1\" data-noptimize=\"1\" data-cfasync=\"false\" src=\"https:\/\/cdn.plot.ly\/plotly-basic-4.0.0.min.js\"><\/script><script data-nd-chart-migration=\"1\" data-noptimize=\"1\">(()=>{const 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