# trialML: Preparing a machine learning model for a statistical trial

This post summarizes a newly released `python`

package: `trialML`

. This package is designed to help researchers and practitioners prepare their machine learning models for a statistical trial to establish a lower-bound on model performance. Specifically, this package helps to calibrating the operating threshold of a binary classifier and carry out a power analysis. A more formal description of these techniques can be found in the corresponding arXiv paper.

## Features

The main modules from `trialML`

can be called in with one line of code: `from trialML import trial, power`

. Their key methods are outlined below, and are described with more detail by the docstrings (e.g. `help('trialML.trial.classification')`

).

`trial.classification(gamma, m, alpha)`

: determine optimal threshold and calculate power of future trial`statistic(y, s, threshold, pval=..)`

: return the performance measure for a given threshold (and possibly p-value from null hypothesis)`learn_threshold(y, s, method='..')`

: calibrate the opearting threshold to obtain at least`gamma`

1-`alpha`

% of the time.`calculate_power(spread, n_trial, threshold)`

: estimate power for a given trial sample size and null hypothesis margin (spread). Threshold can be provided to estimate percent of samples that are class-specific.

`power.twosided_classification(m1, m2, alpha)`

: estimate performance measure and power range (confidence interval) for two performance measures:`m1`

and`m2`

.`set_threshold(y, s, gamma1)`

: Set the threshold to get a performance level of`gamma1`

for the first performance measure`m1`

.`statistic_CI(y, s, threshold)`

: Get the (1-`alpha`

) confidence interval for the empirical values of`m1`

and`m2`

.`statistic_pval(y, s, gamma0)`

: Get the p-value on trial data for a given null hypothesis.

## How to use

The code blocks below provide two examples on different calibration exercises. The first shows shows how to pick a conservative operating threshold so that the classier will have a 95% likelihood of generalizing to at least 50% sensitivity. After this calibration, a trial is run and a test statistic value is returned. The second example shows how to estimate the range of performance measures and power for two test statistics for a given threshold estimated by a point estimate. See the tutorials folder for more information.

### (i) Calibrating for sensitivity

```
# Load modules
import numpy as np
from sklearn.linear_model import LogisticRegression
from trialML.trial import classification
## (1) Train a model and obtain scores on a test set
np.random.seed(1)
n, p = 150, 10
k1, k2 = 50, 100
X, y = np.random.randn(n, p), np.random.binomial(1, 0.5, n)
X_train, y_train, X_test, y_test = X[:k1], y[:k1], X[k1:k2], y[k1:k2]
mdl = LogisticRegression(penalty='none', solver='lbfgs')
mdl.fit(X=X_train, y=y_train)
# test set scores
s_test = mdl.predict_proba(X_test)[:,1]
s_test = np.log(s_test / (1-s_test)) # logit transform
## (2) Calibrate operating threshold to achieve 50% sensitivity, 95% of the time
gamma = 0.5 # performance measure target
alpha = 0.05 # type-I error rate for threshold selection
m = 'sensitivity' # currently supports sensitivity/specificity/precision
# Set up statistical tool
calibration = classification(gamma=gamma, alpha=alpha, m=m)
# Learn threshold
calibration.learn_threshold(y=y_test, s=s_test, method='percentile', n_bs=1000, seed=1)
# Observe test-set performance
gamma_hat_test = calibration.statistic(y=y_test, s=s_test, threshold=calibration.threshold_hat)
print('Empirical sensitivity on test-set: %0.1f%%' % (100*gamma_hat_test))
## (3) Estimate power for trial data
X_trial, y_trial = X[k1:], y[k1:]
n_trial = len(X_trial)
gamma0 = 0.45
spread = gamma - gamma0
calibration.calculate_power(spread, n_trial, threshold=calibration.threshold_hat)
print('Expected trial power for a %0.1f%% margin is at least %0.1f%%' % (100*spread, 100*calibration.power_hat))
## (4) Run trial
s_trial = mdl.predict_proba(X_trial)[:,1]
s_trial = np.log(s_trial / (1-s_trial)) # logit transform
gamma_trial, pval_trial = calibration.statistic(y=y_trial, s=s_trial, gamma0=gamma0, threshold=calibration.threshold_hat)
print('Trial sensitivity: %0.1f%%, trial null-hypothesis: %0.1f%%, trial p-value: %0.5f' % (100*gamma_trial, 100*gamma0, pval_trial))
```

### (ii) Joint estimation for sensitivity and specificity

```
# Load modules
import numpy as np
from sklearn.linear_model import LogisticRegression
from trialML.power import twosided_classification
## (1) Train a model and obtain scores on a test set
np.random.seed(1)
n, p = 150, 10
k1, k2 = 50, 100
X, y = np.random.randn(n, p), np.random.binomial(1, 0.5, n)
X_train, y_train, X_test, y_test = X[:k1], y[:k1], X[k1:k2], y[k1:k2]
X_trial, y_trial = X[k1:], y[k1:]
mdl = LogisticRegression(penalty='none', solver='lbfgs')
mdl.fit(X=X_train, y=y_train)
# test set scores
s_test = mdl.predict_proba(X_test)[:,1]
s_test = np.log(s_test / (1-s_test)) # logit transform
## (2) Select a point on the ROC curve when sensitivity equals 50%
m1 = 'sensitivity'
m2 = 'specificity'
alpha = 0.05 # type-I error rate for test
gamma1 = 0.5 # for sensitivity
power_2s = twosided_classification(m1, m2, alpha)
power_2s.set_threshold(y=y_test, s=s_test, gamma1=gamma1)
## (3) Get performance range
df_gamma = power_2s.statistic_CI(y=y_test, s=s_test, threshold=power_2s.threshold)
df_gamma.round(3)
## (4) Estimate power range
n_trial = len(X_trial)
margin = 0.05
df_power = power_2s.get_power(n_trial=n_trial, margin=margin, adjust=True)
df_power.round(3)
## (5) Run trial
gamma0 = df_gamma['gamma_hat'] - margin
s_trial = mdl.predict_proba(X_trial)[:,1]
s_trial = np.log(s_trial / (1-s_trial)) # logit transform
df_trial = power_2s.statistic_pval(y=y_trial, s=s_trial, gamma0=gamma0)
df_trial.round(3)
```

## How to install

`trialML`

is available on PyPI can be installed in one line: `pip install trialML`

.