# individual_RR_RD: Estimating Three Individual Risk Difference and Risk Ratio... In semicmprskcoxmsm: Use Inverse Probability Weighting to Estimate Treatment Effect for Semi Competing Risks Data

 individual_RR_RD R Documentation

## Estimating Three Individual Risk Difference and Risk Ratio Using the General Markov Model Conditional on Predicted Random Effect

### Description

individual_RR_RD estimates the individual risk difference and risk ratio based on the MSM illness-death general Markov model conditional on predicted random effect for each data point at a fixed time point.

### Usage

individual_RR_RD(dat1,res1,t1_star ,t)


### Arguments

 dat1 The dataset, includes non-terminal events, terminal events as well as event indicator. res1 The output from em_illness_death_phmm_weight, the general Markov model result, the result data includes the predicted random effect. t1_star Fixed non-terminal event time for estimating risk difference/ratio for terminal event following the non-terminal event. t Fixed time point of interest to compare the individual risk difference / ratio.

### 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 the predicted 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) },

The frailty term, or equivalently, the random effect b represents the unobserved heterogeneity among the individuals. As such, the above conditional risk represents individual risk, and the risk contrasts the individual risk contrasts. We therefore have the individual risk difference (IRD) and the individual risk ratio (IRR).

Under the random effects model, for i = 1,2,...,n, the predicted random effect is \hat{b}_i = E(b_i \mid O_i, \hat{θ}). We then obtain the predicted IRD and the predicted IRR.

### Value

Returns a data frame that includes the individual risk difference / ratio for three type of events.

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