# Joint modeling of longitudinal continuous data and competing risks ```r jmcs( ydata, cdata, long.formula, random = NULL, surv.formula, REML = TRUE, quadpoint = NULL, maxiter = 10000, print.para = FALSE, initial.para = NULL, survinitial = TRUE, tol = 1e-04, method = "pseudo-adaptive", opt = "nlminb" ) ``` ## Arguments - `ydata`: a longitudinal data frame in long format. - `cdata`: a survival data frame with competing risks or single failure. Each subject has one data entry. - `long.formula`: a formula object with the response variable and fixed effects covariates to be included in the longitudinal sub-model. - `random`: a one-sided formula object describing the random effects part of the longitudinal sub-model. For example, fitting a random intercept model takes the form `~ 1|ID`. Alternatively. Fitting a random intercept and slope model takes the form `~ x1 + ... + xn|ID`. - `surv.formula`: a formula object with the survival time, event indicator, and the covariates to be included in the survival sub-model. - `REML`: a logic object that indicates the use of REML estimator. Default is TRUE. - `quadpoint`: the number of pseudo-adaptive Gauss-Hermite quadrature points. to be chosen for numerical integration. Default is 6 which produces stable estimates in most dataframes. - `maxiter`: the maximum number of iterations of the EM algorithm that the function will perform. Default is 10000. - `print.para`: Print detailed information of each iteration. Default is FALSE, i.e., not to print the iteration details. - `initial.para`: a list of initialized parameters for EM iteration. Default is NULL. - `survinitial`: Fit a Cox model to obtain initial values of the parameter estimates. Default is TRUE. - `tol`: Tolerance parameter. Default is 0.0001. - `method`: Method for proceeding numerical integration in the E-step. Default is pseudo-adaptive. - `opt`: Optimization method to fit a linear mixed effects model, either `nlminb` (default) or `optim`. ## Returns Object of class `jmcs` with elements - **beta**: the vector of fixed effects for the linear mixed effects model. - **gamma1**: the vector of fixed effects for type 1 failure for the survival model. - **gamma2**: the vector of fixed effects for type 2 failure for the survival model. Valid only if `CompetingRisk = TRUE`. - **nu1**: the vector of association parameter(s) for type 1 failure. - **nu2**: the vector of association parameter(s) for type 2 failure. Valid only if `CompetingRisk = TRUE`. - **H01**: the matrix that collects baseline hazards evaluated at each uncensored event time for type 1 failure. The first column denotes uncensored event times, the second column the number of events, and the third columns the hazards obtained by Breslow estimator. - **H02**: the matrix that collects baseline hazards evaluated at each uncensored event time for type 2 failure. The data structure is the same as `H01`. Valid only if `CompetingRisk = TRUE`. - **Sig**: the variance-covariance matrix of the random effects. - **sigma**: the variance of the measurement error for the linear mixed effects model. - **iter**: the total number of iterations until convergence. - **convergence**: convergence identifier: 1 corresponds to successful convergence, whereas 0 to a problem (i.e., when 0, usually more iterations are required). - **vcov**: the variance-covariance matrix of all the fixed effects for both models. - **sebeta**: the standard error of `beta`. - **segamma1**: the standard error of `gamma1`. - **segamma2**: the standard error of `gamma2`. Valid only if `CompetingRisk = TRUE`. - **senu1**: the standard error of `nu1`. - **senu2**: the standard error of `nu2`. Valid only if `CompetingRisk = TRUE`. - **seSig**: the vector of standard errors of covariance of random effects. - **sesigma**: the standard error of variance of measurement error for the linear mixed effects model. - **loglike**: the log-likelihood value. - **fitted**: a list with the fitted values: - **resid**: the vector of estimated residuals for the linear mixed effects model. - **fitted**: the vector of fitted values for the linear mixed effects model. - **fittedmar**: the vector of marginal fitted values for the linear mixed effects model. - **residmar**: the vector of estimated marginal residuals for the linear mixed effects model. - **fittedSurv**: the estimated survival rate evaluated at each uncensored event time. - **FUNB**: the estimated random effects for each subject. - **CompetingRisk**: logical value; TRUE if a competing event are accounted for. - **quadpoint**: the number of Gauss Hermite quadrature points used for numerical integration. - **ydata**: the input longitudinal dataset for fitting a joint model. It has been re-ordered in accordance with descending observation times in `cdata`. - **cdata**: the input survival dataset for fitting a joint model. It has been re-ordered in accordance with descending observation times. - **PropEventType**: a frequency table of number of events. - **LongitudinalSubmodel**: the component of the `long.formula`. - **SurvivalSubmodel**: the component of the `surv.formula`. - **random**: the component of the `random`. - **call**: the matched call. - **Quad.method**: the quadrature rule used for integration. If pseudo-adaptive quadrature rule is used, then return `pseudo-adaptive`. Otherwise return `standard`. - **id**: the grouping vector for the longitudinal outcome. ## Examples ```r require(FastJM) require(survival) # Load a simulated longitudinal dataset data(ydata) # Load a simulated survival dataset with two competing events data(cdata) # Fit a joint model fit <- jmcs(ydata = ydata, cdata = cdata, long.formula = response ~ time + gender + x1 + race, surv.formula = Surv(surv, failure_type) ~ x1 + gender + x2 + race, random = ~ time| ID) fit # Extract the parameter estimates of longitudinal sub-model fixed effects fixef(fit, process = "Longitudinal") # Extract the parameter estimates of survival sub-model fixed effects fixef(fit, process = "Event") # Obtain the random effects estimates for first 6 subjects head(ranef(fit)) # Obtain the variance-covariance matrix of all parameter estimates vcov(fit) # Obtain the result summaries of the joint model fit summary(fit, process = "Longitudinal") summary(fit, process = "Event") # Prediction of cumulative incidence for competing risks data # Predict the conditional probabilities for two patients who are alive (censored) ND <- ydata[ydata$ID %in% c(419, 218), ] ID <- unique(ND$ID) NDc <- cdata[cdata$ID %in% ID, ] survfit <- survfitjmcs(fit, ynewdata = ND, cnewdata = NDc, u = seq(3, 4.8, by = 0.2), method = "GH", obs.time = "time") survfit PE <- PEjmcs(fit, seed = 100, landmark.time = 3, horizon.time = c(3.6, 4, 4.4), obs.time = "time", method = "GH", quadpoint = NULL, maxiter = 1000, n.cv = 3, survinitial = TRUE) Brier <- summary(PE, error = "Brier") Brier MAEQ <- MAEQjmcs(fit, seed = 100, landmark.time = 3, horizon.time = c(3.6, 4, 4.4), obs.time = "time", method = "GH", quadpoint = NULL, maxiter = 1000, n.cv = 3, survinitial = TRUE) APE <- summary(MAEQ, digits = 3) APE ## evaluate prediction accuracy of fitted joint model using cross-validated mean AUC AUC <- AUCjmcs(fit, seed = 100, landmark.time = 3, horizon.time = c(3.6, 4, 4.4), obs.time = "time", method = "GH", quadpoint = NULL, maxiter = 1000, n.cv = 3, metric = "AUC") summary(AUC, digits = 3) ## or using cross-validated mean C-index Cindex <- AUCjmcs(fit, seed = 100, landmark.time = 3, horizon.time = c(3.6, 4, 4.4), obs.time = "time", method = "GH", quadpoint = NULL, maxiter = 1000, n.cv = 3, metric = "Cindex") summary(Cindex, digits = 3) ``` ## See Also `ranef, fixef, fitted.jmcs, residuals.jmcs, survfitjmcs, plot.jmcs,vcov.jmcs` ## Author(s) Shanpeng Li lishanpeng0913@ucla.edu

jmcs function