# PiecewiseExponentialRegressionFitter¶

class lifelines.fitters.piecewise_exponential_regression_fitter.PiecewiseExponentialRegressionFitter(breakpoints, alpha=0.05, penalizer=0.0)

This implements a piecewise constant-hazard model at pre-specified break points.

$\begin{split}h(t) = \begin{cases} 1/\lambda_0(x) & \text{if t \le \tau_0} \\ 1/\lambda_1(x) & \text{if \tau_0 < t \le \tau_1} \\ 1/\lambda_2(x) & \text{if \tau_1 < t \le \tau_2} \\ ... \end{cases}\end{split}$

where $$\lambda_i(x) = \exp{\beta_i x}$$.

Parameters:
• breakpoints (list) – a list of times when a new exponential model is constructed.

• penalizer (float) – penalize the variance of the $$\lambda_i$$. See blog post below.

• alpha (float, optional (default=0.05)) – the level in the confidence intervals.

Examples

See blog post here and paper replication here

fit_intercept = True
predict_cumulative_hazard(df, times=None, conditional_after=None) DataFrame

Return the cumulative hazard rate of subjects in X at time points.

Parameters:
• X (numpy array or DataFrame) – a (n,d) covariate numpy array or DataFrame. If a DataFrame, columns can be in any order. If a numpy array, columns must be in the same order as the training data.

• times (iterable, optional) – an iterable of increasing times to predict the cumulative hazard at. Default is the set of all durations (observed and unobserved). Uses a linear interpolation if points in time are not in the index.

Returns:

cumulative_hazard_ – the cumulative hazard of individuals over the timeline

Return type:

DataFrame