‘MCID’ is an R package used to provide the point and interval estimation on the minimal clinically important difference (MCID) at the population and individual level. For population level, it produces a constant value for the estimation of MCID. For individual level, the MCID is defined as a linear function of patient’s clinical characteristics, and the estimated linear coefficients can be obtained.
You can install the released version of MCID from GitHub with:
# install.packages("devtools") devtools::install_github("zzhou0721/MCID")
rm(list = ls()) library(MCID) #> Welcome to MCID package n <- 500 lambdaseq <- 10 ^ seq(-3, 3, 0.1) deltaseq <- seq(0.1, 0.3, 0.1) a <- 0.1 b <- 0.55 c <- -0.1 d <- 0.45 set.seed(115) p <- 0.5 y <- 2 * rbinom(n, 1, p) - 1 z <- rnorm(n, 1, 0.1) y_1 <- which(y == 1) y_0 <- which(y == -1) x <- c() x[y_1] <- a + z[y_1] * b + rnorm(length(y_1), 0, 0.1) x[y_0] <- c + z[y_0] * d + rnorm(length(y_0), 0, 0.1)
To determine MCID at the populaton level, we first need to select an optimal value for the tuning parameter δ, which is used to control the difference between 0-1 loss and surrogate loss.
sel <- cv.pmcid(x = x, y = y, delseq = deltaseq, k = 5, maxit = 100, tol = 1e-02) delsel <- sel$'Selected delta' delsel #>  0.1
Then with selected optimal value of δ, we can determine the point and interval estimation of MCID at the population level. The confidence interval is constructed based on the asymptotic normality. In our simulated data, the true population MCID is 0.5.
result <- pmcid(x = x, y = y, n = n, delta = delsel, maxit = 100, tol = 1e-02, alpha = 0.05) result$'Point estimate' #>  0.4961217 result$'Standard error' #>  0.0101217 result$'Confidence interval' #>  0.4762836 0.5159599
To determine MCID at the individual level, we first need to select a combination of the optimal values for the tuning parameters δ and λ. δ is used to control the difference between 0-1 loss and surrogate loss. λ is the coefficient of the penalty term used to avoid the overfitting issue.
sel <- cv.imcid(x = x, y = y, z = z, lamseq = lambdaseq, delseq = deltaseq, k = 5, maxit = 100, tol = 1e-02) lamsel <- sel$'Selected lambda' delsel <- sel$'Selected delta' lamsel #>  0.004496472 delsel #>  0.2
Then with selected δ and λ, we can determine the point and interval estimation for the linear coefficients of the individualized MCID function. The confidence intervals are constructed based on the asymptotic normalities. In our simulated data, the true linear coefficients of the individualized MCID are β0 = 0 and β1 = 0.5
result <- imcid(x = x, y = y, z = z, n = n, lambda = lamsel, delta = delsel, maxit = 100, tol = 1e-02, alpha = 0.05) result$'Point estimates' #> [,1] #> beta0 -0.01551779 #> beta1 0.51193914 result$'Standard errors' #> [,1] #> beta0 0.1292652 #> beta1 0.1227669 result$'Confidence intervals' #> Lower bound Upper bound #> beta0 -0.2688728 0.2378373 #> beta1 0.2713205 0.7525577
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