# Test of Maller-Zhou This function carries out the nonparametric test of Maller and Zhou (1992). ```r testmz(t, d, dataset) ``` ## Arguments - `t`: If `dataset` is missing, a numeric object giving the the observed times. If `dataset` is a data frame, it is interpreted as the name of the variable corresponding to the observed times in the data frame. - `d`: If `dataset` is missing, an integer object giving the values of the uncensoring indicator. Censored observations must be coded as 0, uncensored ones as 1. If `dataset` is a data frame, it is interpreted as the name of the variable corresponding to the uncensoring indicator. - `dataset`: An optional data frame in which the variables named in `x`, `t` and `d` are interpreted. If it is missing, `x`, `t` and `d` must be objects of the workspace. ## Details The function implements Maller and Zhou's (1992) method to test the null hypothesis c("$H_0 :\n$", "$ tau_F_0 > tau_G$") vs. c("$H_1 :\n$", "$ tau_F_0 <= tau_G$"), where $tau_F_0$ and $tau_G$ are the supports of, respectively, the distribution function of the survival time of the uncured and the distribution function of the censoring time. ## Returns An object of S3 class 'npcure'. Formally, a list of components: - **type**: The constant character string c("test", "Maller-Zhou"). - **pvalue**: The p-value of the test. - **aux**: A list of components: `statistic`, the test statistic, `n` the sample size, `delta`, the difference between the largest observed time $t_n$ and the largest uncensored time $t_n^*$, and `interval`, a vector giving the range between $max(0, t_n^* - delta)$ and $t_n^*$. ## References Maller R. A., Zhou S. (1992). Estimating the proportion of immunes in a censored sample. Biometrika, 79: 731-739. [https://doi.org/10.1093/biomet/79.4.731](https://doi.org/10.1093/biomet/79.4.731). ## Author(s) Ignacio López-de-Ullibarri [aut, cre], Ana López-Cheda [aut], Maria Amalia Jácome [aut] ## See Also `latency`, `probcure` ## Examples ```r ## Some artificial data set.seed(123) n <- 50 y <- qweibull(runif(n)*pweibull(2, shape = 2), shape = 2) ## True lifetimes c <- qexp(runif(n)*pexp(2.5)) ## Censoring values u <- runif(n) ## Probability of being susceptible is constantly equal to .5 t <- ifelse(u < .5, pmin(y, c), c) ## Observed times d <- ifelse(u < .5, ifelse(y < c, 1, 0), 0) ## Uncensoring indicator data <- data.frame(t = t, d = d) ## Maller-Zhou test testmz(t, d, data) ```

testmz function