213 158 ###################################################### ## Effect of intervention on transition to CKD 3/4 ## #################################################### # Hypertension --> CKD 3/4 # 10 years incidence probability (Kanno et al 2012) # HR 1.83 [1.34 to 2.48] pt.10 <- 109 / 386 # exposure (hypertension) pc.10 <- 97 / 586 # control (no hypertension) # 1 year incidence probability pt.1 <- cumulative_p(pt.10, 1/10) pc.1 <- cumulative_p(pc.10, 1/10) rr_estimate <- rr_from_hr(.015, .30, 1.83) # 1.755239 max.bias(.015, .30, 1.83) |> pull(bias) |> max() # 1.055135 # lower bound lb_max_bias <- max.bias(.015, .30, 1.34) |> pull(bias) |> max() # 1.055135 (rr_bc_lb <- rr_from_hr(.015, .30, 1.34)) # 1.309881 biased approximation lb_rr_bc <- rr_bc_lb / lb_max_bias # 1.241434 correction for bias # upper bound ub_max_bias <- max.bias(.015, .30, 2.48) |> pull(bias) |> max() # 1.055135 (rr_bc_ub <- rr_from_hr(.015, .30, 2.48)) # 2.343614 biased approximation ub_rr_bc <- rr_bc_ub * ub_max_bias # 2.472829 correction for bias # Estimation of the main effect of the intervention rr_c.a <- rr_c_a(pb_a_treat, pb_a_ctrl, rr_estimate) # 0.8096753 # Estimation of confidence interval df <- map_dbl(1:10000, \(x) get_ca_ci(lb_rr_bc, ub_rr_bc)) quantile(df, probs = c(0.025, 0.50, 0.975)) # 0.7055800 0.7949278 0.9162919 C. Estimating the effect of the intervention on the transition from CKD 3/4 to ESRD We calculate the risk ratio of progression to ESRD just as above, using the hazard ratio reported by Kim et al.3 In this case, since the probability for the outcome (C) over the period in question is not more than 0.3%, the bias of the approximation in formula (2) is negligible, and we obtain an estimated risk ratio of 2.28 [1.71, 3.04]. Using the formula (1) to calculate the risk ratio of the intervention (A) on ESRD (C), we estimate the risk ratio to be 0.73 [0.65, 0.82] The calculations are demonstrated in the R script below: ################################################### ## Effect of intervention on transition to ESRD ## ################################################# # Hypertension --> ESRD # 4 years incidence probability (Kim et al 2021)
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