statsmodels.duration.survfunc.CumIncidenceRight

class statsmodels.duration.survfunc.CumIncidenceRight(time, status, title=None, freq_weights=None, exog=None, bw_factor=1.0, dimred=True)

Estimation and inference for a cumulative incidence function

If J = 1, 2, … indicates the event type, the cumulative incidence function for cause j is:

I(t, j) = P(T <= t and J=j)

Only right censoring is supported. If frequency weights are provided, the point estimate is returned without a standard error.

Parameters:

timearray_like

An array of times (censoring times or event times)

statusarray_like

If status >= 1 indicates which event occurred at time t. If status = 0, the subject was censored at time t.

titlestr

Optional title used for plots and summary output.

freq_weightsarray_like

Optional frequency weights

exogarray_like

Optional, if present used to account for violation of independent censoring.

bw_factorfloat

Band-width multiplier for kernel-based estimation. Only used if exog is provided.

dimredbool

If True, proportional hazards regression models are used to reduce exog to two columns by predicting overall events and censoring in two separate models. If False, exog is used directly for calculating kernel weights without dimension reduction.

Attributes:

timesarray_like

The distinct times at which the incidence rates are estimated

cinclist of arrays

cinc[k-1] contains the estimated cumulative incidence rates for outcome k=1,2,…

cinc_selist of arrays

The standard errors for the values in cinc. Not available when exog and/or frequency weights are provided.

Notes

When exog is provided, a local estimate of the cumulative incidence rate around each point is provided, and these are averaged to produce an estimate of the marginal cumulative incidence functions. The procedure is analogous to that described in Zeng (2004) for estimation of the marginal survival function. The approach removes bias resulting from dependent censoring when the censoring becomes independent conditioned on the columns of exog.

References

The Stata stcompet procedure:

http://www.stata-journal.com/sjpdf.html?articlenum=st0059

Dinse, G. E. and M. G. Larson. 1986. A note on semi-Markov models for partially censored data. Biometrika 73: 379-386.

Marubini, E. and M. G. Valsecchi. 1995. Analysing Survival Data from Clinical Trials and Observational Studies. Chichester, UK: John Wiley & Sons.

D. Zeng (2004). Estimating marginal survival function by adjusting for dependent censoring using many covariates. Annals of Statistics 32:4. https://arxiv.org/pdf/math/0409180.pdf

Methods