# Compute Cox-regression for ordered predictors This function computes estimates in Cox-regression where coefficients corresponding to dummy variables of ordered factors are estimated to be in non-decreasing order and at least 0. An active set algorithm as described in Duembgen et al. (2007) is used. ```r ordFacRegCox(ttf, tf, Z, fact, ordfact, ordering = NA, intercept = TRUE, display = 0, eps = 0) ``` ## Arguments - `ttf`: Survival times. - `tf`: Censoring indicator (1 = event, 0 = censored). - `Z`: Matrix of predictors. Factors are coded with levels from 1 to $j$. - `fact`: Specify columns in $Z$ that correspond to unordered factors. - `ordfact`: Specify columns in $Z$ that correspond to ordered factors. - `ordering`: Vector of the same length as `ordfact`. Specifies ordering of ordered factors: `"i"` means that the coefficients of the corresponding ordered factor are estimated in non-decreasing order and `"d"` means non-increasing order. See the examples in `ordFacReg` for details. - `intercept`: If `TRUE`, an intercept (= column of all 1's) is added to the design matrix. - `display`: If `display == 1` progress of the algorithm is output. - `eps`: Quantity to which the criterion in the Basic Procedure 2 in Duembgen et al. (2007) is compared. ## Details For a detailed description of the problem and the algorithm we refer to Rufibach (2010). ## Returns - **L**: Value of the criterion function at the maximum. - **beta**: Computed regression coefficients. - **A**: Set $A$ of active constraints. - **design.matrix**: Design matrix that was generated. ## References Duembgen, L., Huesler, A. and Rufibach, K. (2010). Active set and EM algorithms for log-concave densities based on complete and censored data. Technical report 61, IMSV, Univ. of Bern, available at [http://arxiv.org/abs/0707.4643](http://arxiv.org/abs/0707.4643). Rufibach, K. (2010). An Active Set Algorithm to Estimate Parameters in Generalized Linear Models with Ordered Predictors. **Comput. Statist. Data Anal.**, 54 , 1442-1456. ## Author(s) Kaspar Rufibach (maintainer) kaspar.rufibach@gmail.com [http://www.kasparrufibach.ch](http://www.kasparrufibach.ch) ## See Also `ordFacReg` computes estimates for least squares and logistic regression. ## Examples ```r ## ======================================================== ## Artificial data is used to illustrate Cox-regression. ## ======================================================== ## -------------------------------------------------------- ## initialization ## -------------------------------------------------------- set.seed(1977) n <- 500 Z <- NULL intercept <- FALSE ## -------------------------------------------------------- ## quantitative variables ## -------------------------------------------------------- n.q <- 2 if (n.q > 0){for (i in 1:n.q){Z <- cbind(Z, rnorm(n, rgamma(2, 2, 1)))}} ## -------------------------------------------------------- ## unordered factors ## -------------------------------------------------------- un.levels <- c(8, 2)[2] for (i in 1:length(un.levels)){Z <- cbind(Z, sample(round(runif(n, 0, un.levels[i] - 1)) + 1))} fact <- n.q + 1:length(un.levels) ## -------------------------------------------------------- ## ordered factors ## -------------------------------------------------------- levels <- c(4, 5, 10) for (i in 1:length(levels)){Z <- cbind(Z, sample(round(runif(n, 0, levels[i] - 1)) + 1))} ordfact <- n.q + length(un.levels) + 1:length(levels) ## -------------------------------------------------------- ## generate response ## -------------------------------------------------------- ttf <- rexp(n) tf <- round(runif(n)) ## -------------------------------------------------------- ## generate design matrix ## -------------------------------------------------------- Y <- prepareData(Z, fact, ordfact, ordering = NA, intercept)$Y ## -------------------------------------------------------- ## compute estimates ## -------------------------------------------------------- res1 <- eha::coxreg.fit(Y, Surv(ttf, tf), max.survs = length(tf), strats = rep(1, length(tf)))$coefficients res2 <- ordFacRegCox(ttf, tf, Z, fact, ordfact, ordering = NA, intercept = intercept, display = 1, eps = 0) b1 <- matrix(res1, ncol = 1) g1 <- coxDeriv(b1, ttf, tf, Y)$dL b2 <- res2$beta g2 <- coxDeriv(b2, ttf, tf, Y)$dL Ls <- c(coxLoglik(b1, ttf, tf, Y)$L, res2$L) names(Ls) <- c("MLE", "ordFact") disp <- cbind(1:length(b1), round(cbind(b1, g1, cumsum(g1)), 4), round(cbind(b2, g2, cumsum(g2)), 4)) ## -------------------------------------------------------- ## display results ## -------------------------------------------------------- disp Ls ```

ordFacRegCox function