cif_est_usual: Estimating Three Cumulative Incidence Functions Using the...

In semicmprskcoxmsm: Use Inverse Probability Weighting to Estimate Treatment Effect for Semi Competing Risks Data

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 λ_{j}^a using IPW, we could estimate the corresponding CIF:

\hat{P}(T_1^a<t,δ_1^a=1) = \int_{0}^{t} \hat{S}^a(u) d\hat{Λ}_{1}^a(u),

\hat{P}(T_2^a<t,δ_1^a=0,δ_2^a=1) = \int_{0}^{t} \hat{S}^a(u) d\hat{Λ}_{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{Λ}_{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{Λ}_{1}^a(u)} - \hat{Λ}_{2}^a(u) . We obtain three hazards by fitting the MSM illness-death model \hatΛ_{j}^a(u) = \hatΛ_{0j}(u)e^{\hatβ_j*a} , \hatΛ_{12}^a(u) = \hatΛ_{03}(u)e^{\hatβ_3*a} , and \hatΛ_{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.

semicmprskcoxmsm documentation built on April 30, 2022, 1:08 a.m.