# Summarizing Nonparametric Kernel-Smoothed Stratified Mark-Specific Proportional Hazards Model Fits `summary` method for an object of class `kernel_sievePH`. ```r ## S3 method for class 'kernel_sievePH' summary( object, contrast = c("te", "hr", "loghr"), sieveAlternative = c("twoSided", "oneSided"), confLevel = 0.95, ... ) ## S3 method for class 'summary.kernel_sievePH' print(x, digits = 4, ...) ``` ## Arguments - `object`: an object of class `kernel_sievePH`, a result of a call to `kernel_sievePH` and `kernel_sievePHaipw`. - `contrast`: a character string specifying the treatment effect parameter of interest. The default value is `"te"` (treatment efficacy); other options are `"hr"` (hazard ratio) and `"loghr"` (log hazard ratio). - `sieveAlternative`: a character string specifying the alternative hypothesis for the sieve tests, which can be either `"twoSided"` (default) or `"oneSided"`. - `confLevel`: the confidence level (0.95 by default) of reported confidence intervals - `...`: further arguments passed to or from other methods - `x`: an object of class `summary.kernel_sievePH`, usually a result of a call to `summary.kernel_sievePH` - `digits`: the number of significant digits to use when printing (4 by default) ## Returns An object of class `summary.kernel_sievePH`, which is a list with the following components: * `estBeta`: a data frame summarizing point estimates and standard errors of the mark-specific coefficients for treatment. * `HRunity.2sided`: a data frame with test statistics (first row) and corresponding p-values (second row) for testing $H_{10}: HR(v) = 1$ vs. $H_{1a}: HR(v) \neq 1$ for any v $\in [a, b]$ (general alternative). `TSUP1` is based on an extension of the classic Kolmogorov-Smirnov supremum-based test. `Tint1` is a generalization of the integration-based Cramer-von Mises test. * `HRunity.1sided`: a data frame with test statistics (first row) and corresponding p-values (second row) for testing $H_{10}: HR(v) = 1$ vs. $H_{1m}: HR(v) \leq 1$ with strict inequality for some v $\in [a, b]$ (monotone alternative). `TSUP1m` is based on an extension of the classic Kolmogorov-Smirnov supremum-based test. `Tint1m` is a generalization of the integration-based Cramer-von Mises test. * `HRconstant.2sided`: a data frame with test statistics (first row) and corresponding p-values (second row) for testing $H_{20}$: HR(v) does not depend on v $\in [a, b]$ vs. $H_{2a}$: HR depends on v $\in [a, b]$ (general alternative). `TSUP2` is based on an extension of the classic Kolmogorov-Smirnov supremum-based test. `Tint2` is a generalization of the integration-based Cramer-von Mises test. This component is available if `sieveAlternative="twoSided"`. * `HRconstant.1sided`: a data frame with test statistics (first row) and corresponding p-values (second row) for testing $H_{20}$: HR(v) does not depend on v $\in [a, b]$ vs. $H_{2m}$: HR increases as v increases $\in [a, b]$ (monotone alternative). `TSUP2m` is based on an extension of the classic Kolmogorov-Smirnov supremum-based test. `Tint2m` is a generalization of the integration-based Cramer-von Mises test. This component is available if `sieveAlternative="oneSided"`. * `te`: a data frame summarizing point and interval estimates of the mark-specific treatment efficacy on the grid of mark values defined by `nvgrid` spanning from the minimum and maximum of the mark (available if `contrast="te"`). The confidence level is specified by `confLevel`. * `hr`: a data frame summarizing point and interval estimates of the mark-specific hazard ratio on the grid of mark values defined by `nvgrid` spanning from the minimum and maximum of the mark (available if `contrast="hr"`). The confidence level is specified by `confLevel`. * `loghr`: a data frame summarizing point and interval estimates of the mark-specific log hazard ratio on the grid of mark values defined by `nvgrid` spanning from the minimum and maximum of the mark (available if `contrast="loghr"`). The confidence level is specified by `confLevel`. ## Details `print.summary.kernel_sievePH` prints a formatted summary of results. Inference about coefficients in the kernel-smoothed mark-specific proportional hazards model is tabulated. Additionally, a summary is generated from the tests of two relevant null hypotheses: (1) {$H_0: HR(v)=1$ for all $v$}, and (2) {$H_0: HR(v)=HR$ for all $v$}. For the tests of (2), `sieveAlternative` controls the choice of the alternative hypothesis. ## Examples ```r set.seed(20240410) beta <- 2.1 gamma <- -1.3 n <- 200 tx <- rep(0:1, each = n / 2) tm <- c(rexp(n / 2, 0.2), rexp(n / 2, 0.2 * exp(gamma))) cens <- runif(n, 0, 15) eventTime <- pmin(tm, cens, 3) eventInd <- as.numeric(tm <= pmin(cens, 3)) alpha <- function(b){ log((1 - exp(-2)) * (b - 2) / (2 * (exp(b - 2) - 1))) } mark0 <- log(1 - (1 - exp(-2)) * runif(n / 2)) / (-2) mark1 <- log(1 + (beta - 2) * (1 - exp(-2)) * runif(n / 2) / (2 * exp(alpha(beta)))) / (beta - 2) mark <- ifelse(eventInd == 1, c(mark0, mark1), NA) # the true TE(v) curve underlying the data-generating mechanism is: # TE(v) = 1 - exp{alpha(beta) + beta * v + gamma} # a binary auxiliary covariate A <- sapply(exp(-0.5 - 0.2 * mark) / (1 + exp(-0.5 - 0.2 * mark)), function(p){ ifelse(is.na(p), NA, rbinom(1, 1, p)) }) linPred <- 1 + 0.4 * tx - 0.2 * A probs <- exp(linPred) / (1 + exp(linPred)) R <- rep(NA, n) while (sum(R, na.rm = TRUE) < 10){ R[eventInd == 1] <- sapply(probs[eventInd == 1], function(p){ rbinom(1, 1, p) }) } # a missing-at-random mark mark[eventInd == 1] <- ifelse(R[eventInd == 1] == 1, mark[eventInd == 1], NA) # AIPW estimation; auxiliary covariate is used (not required) fit <- kernel_sievePHaipw(eventTime, eventInd, mark, tx, aux = A, auxType = "binary", formulaMiss = ~ eventTime, formulaAux = ~ eventTime + tx + mark, tau = 3, tband = 0.5, hband = 0.3, nvgrid = 20, nboot = 20) sfit <- summary(fit) # print the formatted summary sfit # treatment efficacy estimates on the grid sfit$te ``` ## References Gilbert, P. B. and Sun, Y. (2015). Inferences on relative failure rates in stratified mark-specific proportional hazards models with missing marks, with application to human immunodeficiency virus vaccine efficacy trials. **Journal of the Royal Statistical Society Series C: Applied Statistics**, 64(1), 49-73. Sun, Y. and Gilbert, P. B. (2012). Estimation of stratified mark‐specific proportional hazards models with missing marks. **Scandinavian Journal of Statistics**, 39(1), 34-52. ## See Also `kernel_sievePH`

summary.kernel_sievePH function