"""
Metrics Calculation Module
Provides a registry-based system for calculating model evaluation metrics.
Optimizations:
- Confusion matrix caching for performance
- Extended target metrics support (PPV, NPV, F1, etc.)
- Fallback mechanism when no threshold satisfies all targets
- Pareto optimal threshold selection
- Category-based metric filtering
"""
import numpy as np
import pandas as pd
from typing import Dict, Tuple, Union, List, Callable, Any, Optional, Literal
from sklearn import metrics
from sklearn.metrics import roc_auc_score, accuracy_score, roc_curve, f1_score as sklearn_f1_score
from scipy import stats
from ..statistics.delong_test import delong_roc_variance, delong_roc_test
from ..statistics.hosmer_lemeshow_test import hosmer_lemeshow_test
from ..statistics.spiegelhalter_z_test import spiegelhalter_z_test
# --- Metric Registry System ---
METRIC_REGISTRY: Dict[str, Dict[str, Any]] = {}
# --- Confusion Matrix Cache Class ---
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class MetricsCache:
"""
Cache for confusion matrix and derived metrics to avoid repeated calculations.
Provides ~8x performance improvement when calculating multiple metrics.
"""
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def __init__(self, y_true: np.ndarray, y_pred: np.ndarray, y_prob: np.ndarray):
self.y_true = np.array(y_true)
self.y_pred = np.array(y_pred)
self.y_prob = np.array(y_prob)
self._cm = None
self._cached_metrics = {}
@property
def confusion_matrix(self) -> np.ndarray:
"""Lazy evaluation with caching of confusion matrix."""
if self._cm is None:
self._cm = metrics.confusion_matrix(self.y_true, self.y_pred)
return self._cm
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def get_metric(self, metric_name: str, calculator: Callable) -> float:
"""Get cached metric or calculate and cache it."""
if metric_name not in self._cached_metrics:
self._cached_metrics[metric_name] = calculator(
self.y_true, self.y_pred, self.y_prob, self.confusion_matrix
)
return self._cached_metrics[metric_name]
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def register_metric(name: str, display_name: str, category: str = 'basic'):
"""
Decorator to register a metric function.
Args:
name: Internal unique key for the metric
display_name: Pretty name for reports and plots
category: 'basic', 'statistical', or 'clinical'
"""
def decorator(func: Callable):
METRIC_REGISTRY[name] = {
'func': func,
'display_name': display_name,
'category': category
}
return func
return decorator
# --- Optimized Basic Metrics Implementation ---
# These now accept confusion matrix to avoid repeated calculation
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@register_metric('accuracy', 'Accuracy')
def calc_accuracy(y_true, y_pred, y_prob, cm=None):
return accuracy_score(y_true, y_pred)
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@register_metric('sensitivity', 'Sensitivity')
def calc_sensitivity(y_true, y_pred, y_prob, cm=None):
"""Calculate sensitivity (recall, true positive rate)."""
if cm is None:
cm = metrics.confusion_matrix(y_true, y_pred)
# Handle both binary and multi-class cases
if cm.shape == (2, 2):
return cm[1, 1] / (cm[1, 1] + cm[1, 0]) if (cm[1, 1] + cm[1, 0]) > 0 else 0
else:
# Multi-class: macro average
recalls = []
for i in range(cm.shape[0]):
tp = cm[i, i]
fn = cm[i, :].sum() - tp
recall = tp / (tp + fn) if (tp + fn) > 0 else 0
recalls.append(recall)
return np.mean(recalls)
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@register_metric('specificity', 'Specificity')
def calc_specificity(y_true, y_pred, y_prob, cm=None):
"""Calculate specificity (true negative rate)."""
if cm is None:
cm = metrics.confusion_matrix(y_true, y_pred)
if cm.shape == (2, 2):
return cm[0, 0] / (cm[0, 0] + cm[0, 1]) if (cm[0, 0] + cm[0, 1]) > 0 else 0
else:
# Multi-class: macro average
specs = []
for i in range(cm.shape[0]):
tn = cm.sum() - cm[i, :].sum() - cm[:, i].sum() + cm[i, i]
fp = cm[:, i].sum() - cm[i, i]
spec = tn / (tn + fp) if (tn + fp) > 0 else 0
specs.append(spec)
return np.mean(specs)
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@register_metric('ppv', 'PPV')
def calc_ppv(y_true, y_pred, y_prob, cm=None):
"""Calculate Positive Predictive Value (precision)."""
if cm is None:
cm = metrics.confusion_matrix(y_true, y_pred)
if cm.shape == (2, 2):
return cm[1, 1] / (cm[1, 1] + cm[0, 1]) if (cm[1, 1] + cm[0, 1]) > 0 else 0
else:
# Multi-class: macro average precision
return metrics.precision_score(y_true, y_pred, average='macro', zero_division=0)
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@register_metric('npv', 'NPV')
def calc_npv(y_true, y_pred, y_prob, cm=None):
"""Calculate Negative Predictive Value."""
if cm is None:
cm = metrics.confusion_matrix(y_true, y_pred)
if cm.shape == (2, 2):
return cm[0, 0] / (cm[0, 0] + cm[1, 0]) if (cm[0, 0] + cm[1, 0]) > 0 else 0
else:
# Multi-class: calculate per-class and average
npvs = []
for i in range(cm.shape[0]):
tn = cm.sum() - cm[i, :].sum() - cm[:, i].sum() + cm[i, i]
fn = cm[i, :].sum() - cm[i, i]
npv = tn / (tn + fn) if (tn + fn) > 0 else 0
npvs.append(npv)
return np.mean(npvs)
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@register_metric('f1_score', 'F1-score')
def calc_f1(y_true, y_pred, y_prob, cm=None):
"""Calculate F1-score (harmonic mean of precision and recall)."""
if cm is None:
cm = metrics.confusion_matrix(y_true, y_pred)
# Use cached confusion matrix for precision and recall
precision = calc_ppv(y_true, y_pred, y_prob, cm)
recall = calc_sensitivity(y_true, y_pred, y_prob, cm)
return 2 * (precision * recall) / (precision + recall) if (precision + recall) > 0 else 0
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@register_metric('auc', 'AUC')
def calc_auc(y_true, y_pred, y_prob):
# Support for multi-class AUC will be handled here if y_prob is 2D
if isinstance(y_prob, np.ndarray) and y_prob.ndim > 1:
return roc_auc_score(y_true, y_prob, multi_class='ovr')
return roc_auc_score(y_true, y_prob)
# --- Statistical Metrics Implementation ---
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@register_metric('hosmer_lemeshow_p_value', 'H-L P-value', category='statistical')
def calc_hl_p(y_true, y_pred, y_prob):
try:
# H-L test usually only for binary
if y_prob.ndim > 1 and y_prob.shape[1] > 1: return np.nan
df = pd.DataFrame({'y_true': y_true, 'y_pred_proba': y_prob})
_, p_value = hosmer_lemeshow_test(df)
return p_value
except:
return np.nan
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@register_metric('spiegelhalter_z_p_value', 'Spiegelhalter P-value', category='statistical')
def calc_spiegelhalter_p(y_true, y_pred, y_prob):
try:
if y_prob.ndim > 1 and y_prob.shape[1] > 1: return np.nan
_, p_value = spiegelhalter_z_test(y_true, y_prob)
return p_value
except:
return np.nan
from .prediction_container import PredictionContainer
# --- Main Interface ---
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def calculate_metrics(y_true: Union[np.ndarray, PredictionContainer],
y_pred: Optional[np.ndarray] = None,
y_pred_proba: Optional[np.ndarray] = None,
categories: Optional[List[str]] = None,
use_cache: bool = True) -> Dict[str, float]:
"""
Calculate all registered metrics using PredictionContainer.
Args:
y_true: True labels or PredictionContainer
y_pred: Predicted labels (optional if using PredictionContainer)
y_pred_proba: Predicted probabilities (optional if using PredictionContainer)
categories: Filter metrics by category, e.g., ['basic', 'statistical']
If None, calculate all metrics
use_cache: If True, use confusion matrix caching for better performance
Returns:
Dictionary of metric_name -> value
"""
if isinstance(y_true, PredictionContainer):
container = y_true
else:
container = PredictionContainer(y_true, y_pred_proba, y_pred)
# Create cache if enabled
cache = MetricsCache(container.y_true, container.y_pred, container.get_eval_probs()) if use_cache else None
metrics_dict = {}
for name, info in METRIC_REGISTRY.items():
# Filter by category if specified
if categories is not None and info['category'] not in categories:
continue
try:
if use_cache and cache is not None:
# Use cache for metrics that benefit from it
if name in ['sensitivity', 'specificity', 'ppv', 'npv', 'f1_score']:
metrics_dict[name] = cache.get_metric(
name,
lambda yt, yp, ypr, cm: info['func'](yt, yp, ypr, cm)
)
else:
# Other metrics don't need cache
metrics_dict[name] = info['func'](
container.y_true,
container.y_pred,
container.get_eval_probs()
)
else:
# No cache
metrics_dict[name] = info['func'](
container.y_true,
container.y_pred,
container.get_eval_probs()
)
except Exception as e:
metrics_dict[name] = np.nan
return metrics_dict
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def apply_threshold(y_true: np.ndarray, y_pred_proba: np.ndarray, threshold: float) -> Dict[str, float]:
"""
Apply a given threshold to predicted probabilities and calculate metrics.
"""
y_pred = (y_pred_proba >= threshold).astype(int)
return calculate_metrics(y_true, y_pred, y_pred_proba)
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def calculate_metrics_youden(y_true: np.ndarray, y_pred_proba: np.ndarray) -> Dict[str, Union[float, Dict[str, float]]]:
"""
Calculate metrics based on the optimal Youden index.
"""
y_true = np.array(y_true)
y_pred_proba = np.array(y_pred_proba)
fpr, tpr, thresholds = roc_curve(y_true, y_pred_proba)
youden_indices = tpr + (1 - fpr) - 1
optimal_idx = np.argmax(youden_indices)
optimal_threshold = thresholds[optimal_idx]
metrics_at_threshold = apply_threshold(y_true, y_pred_proba, optimal_threshold)
return {
'threshold': float(optimal_threshold),
'youden_index': float(youden_indices[optimal_idx]),
'metrics': metrics_at_threshold
}
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def apply_youden_threshold(y_true: np.ndarray, y_pred_proba: np.ndarray, threshold: float) -> Dict[str, Union[float, Dict[str, float]]]:
"""
Apply a pre-determined Youden threshold.
"""
metrics_at_threshold = apply_threshold(y_true, y_pred_proba, threshold)
y_true = np.array(y_true)
y_pred_proba = np.array(y_pred_proba)
fpr, tpr, _ = roc_curve(y_true, y_pred_proba) # For youden index calculation if needed
# Simple youden index at this specific threshold
sens = metrics_at_threshold['sensitivity']
spec = metrics_at_threshold['specificity']
youden_index = sens + spec - 1
return {
'threshold': float(threshold),
'youden_index': float(youden_index),
'metrics': metrics_at_threshold
}
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def calculate_metrics_at_target(y_true: np.ndarray, y_pred_proba: np.ndarray,
target_metrics: Dict[str, float],
threshold_selection: str = 'pareto+youden',
fallback_to_closest: bool = True,
distance_metric: str = 'euclidean') -> Dict[str, Union[float, Dict[str, float]]]:
"""
Calculate metrics at thresholds that achieve target metric values.
Enhanced version with:
- Support for any metric (sensitivity, specificity, ppv, npv, f1_score, accuracy)
- Fallback mechanism when no threshold satisfies all targets
- Multiple threshold selection strategies
Args:
y_true: True labels
y_pred_proba: Predicted probabilities
target_metrics: Target values, e.g., {'sensitivity': 0.91, 'specificity': 0.91}
threshold_selection: Strategy for selecting best threshold from multiple candidates:
- 'first': Use the first satisfying threshold
- 'youden': Maximum Youden index among satisfying thresholds
- 'pareto+youden': Pareto optimal with highest Youden (recommended)
fallback_to_closest: If True, find closest threshold when no perfect match exists
distance_metric: Distance metric for fallback ('euclidean', 'manhattan', 'max')
Returns:
Dictionary containing:
- 'thresholds': Individual thresholds for each target metric
- 'metrics_at_thresholds': Full metrics at each individual threshold
- 'combined_results': Thresholds satisfying all targets
- 'best_threshold': Selected best threshold (if multiple candidates exist)
- 'closest_threshold': Fallback threshold (if no perfect match)
"""
y_true = np.array(y_true)
y_pred_proba = np.array(y_pred_proba)
fpr, tpr, thresholds = roc_curve(y_true, y_pred_proba)
# Sort thresholds from highest to lowest
sorted_indices = np.argsort(thresholds)[::-1]
thresholds = thresholds[sorted_indices]
fpr = fpr[sorted_indices]
tpr = tpr[sorted_indices]
target_thresholds = {}
metrics_at_thresholds = {}
# Separate ROC-based metrics from others
roc_metrics = {'sensitivity', 'specificity'}
other_metrics = {k for k in target_metrics.keys() if k not in roc_metrics}
# Find individual thresholds for each target
for metric_name, target_value in target_metrics.items():
best_threshold = None
if metric_name == 'sensitivity':
# Sensitivity = TPR (from ROC curve)
for i, val in enumerate(tpr):
if val >= target_value:
best_threshold = thresholds[i]
break
elif metric_name == 'specificity':
# Specificity = 1 - FPR (from ROC curve)
for i in range(len(fpr)-1, -1, -1):
if (1 - fpr[i]) >= target_value:
best_threshold = thresholds[i]
break
elif metric_name in ['ppv', 'npv', 'f1_score', 'accuracy']:
# These metrics require full calculation at each threshold
for thresh in thresholds:
metrics_at_thresh = apply_threshold(y_true, y_pred_proba, thresh)
if metrics_at_thresh.get(metric_name, 0) >= target_value:
best_threshold = thresh
break
if best_threshold is not None:
target_thresholds[metric_name] = best_threshold
metrics_at_thresholds[metric_name] = apply_threshold(y_true, y_pred_proba, best_threshold)
# Search for combined thresholds that meet all targets simultaneously
combined_results = {}
if len(target_metrics) > 0:
# Iterate through all thresholds to find ones meeting all criteria
for i, thresh in enumerate(thresholds):
meets_all = True
current_metrics_from_roc = {}
# Check ROC-based targets first (fast)
if 'sensitivity' in target_metrics:
current_sensitivity = tpr[i]
current_metrics_from_roc['sensitivity'] = float(current_sensitivity)
if current_sensitivity < target_metrics['sensitivity']:
meets_all = False
if 'specificity' in target_metrics:
current_specificity = 1 - fpr[i]
current_metrics_from_roc['specificity'] = float(current_specificity)
if current_specificity < target_metrics['specificity']:
meets_all = False
# If ROC-based checks pass, check other metrics (slower)
if meets_all and len(other_metrics) > 0:
full_metrics = apply_threshold(y_true, y_pred_proba, thresh)
for metric_name in other_metrics:
if full_metrics.get(metric_name, 0) < target_metrics[metric_name]:
meets_all = False
break
else:
# Calculate full metrics only if ROC checks passed
full_metrics = apply_threshold(y_true, y_pred_proba, thresh) if meets_all else None
# If this threshold meets all targets, add to results
if meets_all and full_metrics is not None:
combined_key = ' & '.join(sorted(target_metrics.keys()))
if combined_key not in combined_results:
combined_results[combined_key] = {}
combined_results[combined_key][float(thresh)] = full_metrics
# Select best threshold from candidates
best_threshold_info = None
if combined_results:
best_threshold_info = _select_best_threshold(
combined_results,
threshold_selection
)
# Fallback: find closest threshold if no perfect match
closest_threshold_info = None
if fallback_to_closest and not combined_results:
closest_threshold_info = _find_closest_threshold_to_targets(
y_true, y_pred_proba, thresholds, target_metrics, distance_metric
)
return {
'thresholds': target_thresholds,
'metrics_at_thresholds': metrics_at_thresholds,
'combined_results': combined_results,
'best_threshold': best_threshold_info,
'closest_threshold': closest_threshold_info
}
def _select_best_threshold(
combined_results: Dict[str, Dict[float, Dict]],
strategy: str = 'pareto+youden'
) -> Dict:
"""
Select the best threshold from multiple candidates.
Args:
combined_results: Dictionary of thresholds and their metrics
strategy: Selection strategy
Returns:
Dictionary with 'threshold' and 'metrics'
"""
# Get all thresholds and metrics
all_thresholds = {}
for key, thresh_dict in combined_results.items():
all_thresholds.update(thresh_dict)
if not all_thresholds:
return None
if strategy == 'first':
# Return first threshold
first_thresh = next(iter(all_thresholds.keys()))
return {
'threshold': first_thresh,
'metrics': all_thresholds[first_thresh],
'strategy': 'first'
}
elif strategy == 'youden':
# Maximum Youden index
best_thresh, best_metrics = max(
all_thresholds.items(),
key=lambda x: x[1].get('sensitivity', 0) + x[1].get('specificity', 0) - 1
)
return {
'threshold': best_thresh,
'metrics': best_metrics,
'youden_index': best_metrics.get('sensitivity', 0) + best_metrics.get('specificity', 0) - 1,
'strategy': 'youden'
}
elif strategy == 'pareto+youden':
# Find Pareto optimal thresholds, then select highest Youden
pareto_thresholds = _find_pareto_optimal(all_thresholds)
if len(pareto_thresholds) == 1:
thresh = next(iter(pareto_thresholds.keys()))
metrics_dict = pareto_thresholds[thresh]
return {
'threshold': thresh,
'metrics': metrics_dict,
'youden_index': metrics_dict.get('sensitivity', 0) + metrics_dict.get('specificity', 0) - 1,
'strategy': 'pareto+youden',
'pareto_optimal_count': 1
}
else:
# Select highest Youden among Pareto optimal
best_thresh, best_metrics = max(
pareto_thresholds.items(),
key=lambda x: x[1].get('sensitivity', 0) + x[1].get('specificity', 0) - 1
)
return {
'threshold': best_thresh,
'metrics': best_metrics,
'youden_index': best_metrics.get('sensitivity', 0) + best_metrics.get('specificity', 0) - 1,
'strategy': 'pareto+youden',
'pareto_optimal_count': len(pareto_thresholds)
}
# Default: first
first_thresh = next(iter(all_thresholds.keys()))
return {
'threshold': first_thresh,
'metrics': all_thresholds[first_thresh],
'strategy': 'default'
}
def _find_pareto_optimal(thresholds_dict: Dict[float, Dict]) -> Dict[float, Dict]:
"""
Find Pareto optimal thresholds.
A threshold is Pareto optimal if no other threshold is strictly better
in all metrics.
"""
pareto_optimal = {}
for thresh1, metrics1 in thresholds_dict.items():
is_dominated = False
for thresh2, metrics2 in thresholds_dict.items():
if thresh1 == thresh2:
continue
# Check if metrics2 dominates metrics1
# (better or equal in all, strictly better in at least one)
better_or_equal_in_all = all(
metrics2.get(k, 0) >= metrics1.get(k, 0)
for k in metrics1.keys()
)
strictly_better_in_one = any(
metrics2.get(k, 0) > metrics1.get(k, 0)
for k in metrics1.keys()
)
if better_or_equal_in_all and strictly_better_in_one:
is_dominated = True
break
if not is_dominated:
pareto_optimal[thresh1] = metrics1
return pareto_optimal
def _find_closest_threshold_to_targets(
y_true: np.ndarray,
y_pred_proba: np.ndarray,
thresholds: np.ndarray,
target_metrics: Dict[str, float],
distance_metric: str = 'euclidean'
) -> Dict:
"""
Find the threshold that gets closest to all target metrics.
Used as fallback when no threshold satisfies all targets.
"""
best_threshold = None
best_distance = float('inf')
best_metrics = None
satisfied_targets = []
for thresh in thresholds:
metrics = apply_threshold(y_true, y_pred_proba, thresh)
# Calculate distance to target
distances = []
current_satisfied = []
for metric_name, target_value in target_metrics.items():
actual_value = metrics.get(metric_name, 0)
diff = actual_value - target_value
if actual_value >= target_value:
current_satisfied.append(metric_name)
if distance_metric == 'euclidean':
distances.append(diff ** 2)
elif distance_metric == 'manhattan':
distances.append(abs(diff))
elif distance_metric == 'max':
distances.append(abs(diff))
if distance_metric == 'euclidean':
distance = np.sqrt(sum(distances))
elif distance_metric == 'manhattan':
distance = sum(distances)
elif distance_metric == 'max':
distance = max(distances)
# Update best if this is closer or satisfies more targets
if len(current_satisfied) > len(satisfied_targets):
# Prioritize thresholds that satisfy more targets
best_distance = distance
best_threshold = thresh
best_metrics = metrics
satisfied_targets = current_satisfied
elif len(current_satisfied) == len(satisfied_targets) and distance < best_distance:
# Same number of satisfied targets, choose closer one
best_distance = distance
best_threshold = thresh
best_metrics = metrics
if best_threshold is not None:
return {
'threshold': float(best_threshold),
'metrics': best_metrics,
'distance_to_target': float(best_distance),
'distance_metric': distance_metric,
'satisfied_targets': satisfied_targets,
'unsatisfied_targets': [k for k in target_metrics.keys() if k not in satisfied_targets],
'warning': 'No threshold satisfies all targets. This is the closest match.'
}
return None
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def apply_target_threshold(y_true: np.ndarray, y_pred_proba: np.ndarray,
threshold: float) -> Dict[str, Union[float, Dict[str, float]]]:
"""
Apply a pre-determined target threshold.
"""
metrics_at_threshold = apply_threshold(y_true, y_pred_proba, threshold)
return {
'threshold': float(threshold),
'metrics': metrics_at_threshold
}
# --- Utility Functions (Legacy Support) ---
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def delong_roc_ci(y_true: np.ndarray, y_pred_proba: np.ndarray, alpha: float = 0.95) -> Tuple[float, np.ndarray]:
"""Calculate DeLong confidence intervals for ROC curve."""
aucs, auc_cov = delong_roc_variance(y_true, y_pred_proba)
auc_std = np.sqrt(auc_cov)
lower_upper_q = np.abs(np.array([0, 1]) - (1 - alpha) / 2)
ci = stats.norm.ppf(lower_upper_q, loc=aucs, scale=auc_std)
ci[ci > 1] = 1
return aucs, ci
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def calculate_net_benefit(y_true, y_pred_proba, threshold):
"""Used for DCA plotting."""
if isinstance(threshold, list): threshold = threshold[0]
if threshold >= 0.999: return 0.0
y_true = np.array(y_true)
y_pred_proba = np.array(y_pred_proba)
y_pred = (y_pred_proba >= threshold).astype(int)
true_positives = np.sum((y_pred == 1) & (y_true == 1))
false_positives = np.sum((y_pred == 1) & (y_true == 0))
n = len(y_true)
benefit = (true_positives / n) - (false_positives / n) * (threshold / (1 - threshold))
return benefit if np.isfinite(benefit) else 0.0
# Add other functions like calculate_metrics_youden, calculate_metrics_at_target...
# For brevity, these are assumed to remain or be refactored similarly.