Brier Score and Integrated Brier Score
Brier Score
The Brier score is used to evaluate the accuracy of a predicted survival function at a given time ; it represents the average squared distances between the observed survival status and the predicted survival probability and is always a number between 0 and 1, with 0 being the best possible value.
Given a dataset of samples, is the format of a datapoint, and the predicted survival function is :
In the absence of right censoring, the Brier score can be calculated such that:
However, if the dataset contains samples that are right censored, then it is necessary to adjust the score by weighting the squared distances using the inverse probability of censoring weights method. Let be the estimator of the conditional survival function of the censoring times calculated using the KaplanMeier method, where is the censoring time.
In terms of benchmarks, a useful model will have a Brier score below . Indeed, it is easy to see that if , then .
Location
The function can be found at pysurvival.utils.metrics.brier_score
.
API
brier_score
 Brier score computations
brier_score(model, X, T, E, t_max=None)
Parameters:

model
: Pysurvival object  Pysurvival model 
X
: arraylike  input samples; where the rows correspond to an individual sample and the columns represent the features (shape=[n_samples, n_features]). 
T
: arraylike  target values describing the time when the event of interest or censoring occurred. 
E
: arraylike  values that indicate if the event of interest occurred i.e.: E[i]=1 corresponds to an event, and E[i] = 0 means censoring, for all i. 
t_max
: float ( default=None ) Maximal time for estimating the prediction error curves. If missing the largest value of the response variable is used.
Returns:

times
: arraylike. A vector of timepoints. At each timepoint the brier score is estimated 
brier_scores
: arraylike. A vector of brier scores
Integrated Brier Score
The Integrated Brier Score (IBS) provides an overall calculation of the model performance at all available times.
Location
The function can be found at pysurvival.utils.metrics.integrated_brier_score
to output the values and pysurvival.utils.display.integrated_brier_score
to display the predictive error curve.
API
integrated_brier_score
 Integrated Brier score computations
integrated_brier_score(model, X, T, E, t_max=None, figure_size=(20, 10))
Parameters:

model
: Pysurvival object  Pysurvival model 
X
: arraylike  input samples; where the rows correspond to an individual sample and the columns represent the features (shape=[n_samples, n_features]). 
T
: arraylike  target values describing the time when the event of interest or censoring occurred. 
E
: arraylike  values that indicate if the event of interest occurred i.e.: E[i]=1 corresponds to an event, and E[i] = 0 means censoring, for all i. 
t_max
: float ( default=None ) Maximal time for estimating the prediction error curves. If missing the largest value of the response time variable is used. 
figure_size
: tuple of double ( default=(20, 10) ) width, height in inches representing the size of the chart of the survival function. Option available if the function is being called frompysurvival.utils.display
Returns:
ibs
: double The integrated brier score