cif_est_usual {semicmprskcoxmsm}

Estimating Three Cumulative Incidence Functions Using the Usual Markov Model

Description

cif_est_usual estimates the cumulative incidence function (CIF, i.e.risk) based on the MSM illness-death usual Markov model.

Usage

cif_est_usual(data,X1,X2,event1,event2,w,Trt,
              t1_star = t1_star)

Arguments

data

The dataset, includes non-terminal events, terminal events as well as event indicator.

X1

Time to non-terminal event, could be censored by terminal event or lost to follow up.

X2

Time to terminal event, could be censored by lost to follow up.

event1

Event indicator for non-terminal event.

event2

Event indicator for terminal event.

w

IP weights.

Trt

Treatment variable.

t1_star

Fixed non-terminal event time for estimating CIF function for terminal event following the non-terminal event.

Details

After estimating the parameters in the illness-death model \lambda_{j}^a using IPW, we could estimate the corresponding CIF:

\hat{P}(T_1^a<t,\delta_1^a=1) = \int_{0}^{t} \hat{S}^a(u) d\hat{\Lambda}_{1}^a(u),

\hat{P}(T_2^a<t,\delta_1^a=0,\delta_2^a=1) = \int_{0}^{t} \hat{S}^a(u) d\hat{\Lambda}_{2}^a(u),

and

\hat{P}(T_2^a<t_2 \mid T_1^a<t_1, T_2^a>t_1) = 1- e^{- \int_{t_1}^{t_2} d \hat{\Lambda}_{12}^a(u) },

where \hat{S}^a is the estimated overall survial function for joint T_1^a, T_2^a, \hat{S}^a(u) = e^{-\hat{\Lambda}_{1}^a(u)} - \hat{\Lambda}_{2}^a(u) . We obtain three hazards by fitting the MSM illness-death model \hat\Lambda_{j}^a(u) = \hat\Lambda_{0j}(u)e^{\hat\beta_j*a} , \hat\Lambda_{12}^a(u) = \hat\Lambda_{03}(u)e^{\hat\beta_3*a} , and \hat\Lambda_{0j}(u) is a Breslow-type estimator of the baseline cumulative hazard.

Value

Returns a table containing the estimated CIF for the event of interest for control and treated group.

References

Meira-Machado, Luis and Sestelo, Marta (2019). “Estimation in the progressive illness-death model: A nonexhaustive review,” Biometrical Journal 61(2), 245–263.