conditional_cif_b: Estimating Three Conditional Cumulative Incidence Functions...

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

Estimating Three Conditional Cumulative Incidence Functions Using the General Markov Model Conditional on Random Effect

Description

conditional_cif_b estimates the cumulative incidence function based on the MSM illness-death general Markov model conditional on the fixed random effect b.

Usage

conditional_cif_b(res1,
                  t1_star,
                  b)

Arguments

res1	The output from em_illness_death_phmm_weight, the general Markov model result.
t1_star	Fixed non-terminal event time for estimating CIF function for terminal event following the non-terminal event.
b	Fixed random effect value.

Details

Similar as cif_est_usual, after estimating the parameters in the illness-death model λ_{j}^a using IPW, we could estimate the corresponding conditional CIF under fixed b:

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

\hat{P}(T_2^a<t,δ_1^a=0,δ_2^a=1 \mid b) = \int_{0}^{t} \hat{S}^a(u \mid b) d\hat{Λ}_{2}^a(u \mid b),

and

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

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.

where S(t \mid b;a) = \exp[- \int_0^{t} \{ λ_{01} (u)e^{β_1a + b} + λ_{02} (u )e^{β_2a + b} \} d u ] = \exp \{- e^{β_1a + b} Λ_{01}(t) - e^{β_2a + b} Λ_{02} (t ) \}

Value

a1	The step function for estimated CIF conditional on b for time to non-terminal event for control group.
b1	The step function for estimated CIF conditional on b for time to non-terminal event for treated group.
a2	The step function for estimated CIF conditional on b for time to terminal event without non-terminal event for control group.
b2	The step function for estimated CIF conditional on b for time to terminal event without non-terminal event for treated group.
a3	The step function for estimated CIF conditional on b for time to terminal event following non-terminal event by t1_start for control group.
b3	The step function for estimated CIF conditional on b for time to terminal event without non-terminal event by t1_start for treated group.
cif.1	A data frame with time and estimated CIF conditional on b if is treated or controlled for time to non-terminal event.
cif.2	A data frame with time and estimated CIF conditional on b if is treated or controlled for time to terminal event without non-terminal event.
cif.3	A data frame with time and estimated CIF conditional on b if is treated or controlled for time to terminal event without non-terminal event by t1_start.

See Also

cif_est_usual

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