Fit Generalized Semiparametric Proportional 0dds Model

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Description

Fits a semiparametric proportional odds model:

logit(1-S_{X,Z}(t)) = log(X^T A(t)) + β^T Z

where A(t) is increasing but otherwise unspecified. Model is fitted by maximising the modified partial likelihood. A goodness-of-fit test by considering the score functions is also computed by resampling methods.

An alternative way of writing the model :

S_{X,Z}(t)) = \frac{ \exp( - β^T Z )}{ (X^T A(t)) + \exp( - β^T Z) }

such that β is the log-odds-ratio of dying before time t, and A(t) is the odds-ratio.

The modelling formula uses the standard survival modelling given in the survival package.

Usage

 1 2 3 Gprop.odds(formula = formula(data),data=sys.parent(),beta=0,Nit=50, detail=0,start.time=0,max.time=NULL,id=NULL,n.sim=500,weighted.test=0, sym=0,mle.start=0) 

Arguments

 formula a formula object, with the response on the left of a '~' operator, and the terms on the right. The response must be a survival object as returned by the ‘Surv’ function. data a data.frame with the variables. start.time start of observation period where estimates are computed. max.time end of observation period where estimates are computed. Estimates thus computed from [start.time, max.time]. This is very useful to obtain stable estimates, especially for the baseline. Default is max of data. id For timevarying covariates the variable must associate each record with the id of a subject. n.sim number of simulations in resampling. weighted.test to compute a variance weighted version of the test-processes used for testing time-varying effects. beta starting value for relative risk estimates Nit number of iterations for Newton-Raphson algorithm. detail if 0 no details is printed during iterations, if 1 details are given. sym to use symmetrized second derivative in the case of the estimating equation approach (profile=0). This may improve the numerical performance. mle.start starting values for relative risk parameters.

Details

The data for a subject is presented as multiple rows or "observations", each of which applies to an interval of observation (start, stop]. The program essentially assumes no ties, and if such are present a little random noise is added to break the ties.

Value

returns an object of type 'cox.aalen'. With the following arguments:

 cum cumulative timevarying regression coefficient estimates are computed within the estimation interval. var.cum the martingale based pointwise variance estimates. robvar.cum robust pointwise variances estimates. gamma estimate of proportional odds parameters of model. var.gamma variance for gamma. robvar.gamma robust variance for gamma. residuals list with residuals. Estimated martingale increments (dM) and corresponding time vector (time). obs.testBeq0 observed absolute value of supremum of cumulative components scaled with the variance. pval.testBeq0 p-value for covariate effects based on supremum test. sim.testBeq0 resampled supremum values. obs.testBeqC observed absolute value of supremum of difference between observed cumulative process and estimate under null of constant effect. pval.testBeqC p-value based on resampling. sim.testBeqC resampled supremum values. obs.testBeqC.is observed integrated squared differences between observed cumulative and estimate under null of constant effect. pval.testBeqC.is p-value based on resampling. sim.testBeqC.is resampled supremum values. conf.band resampling based constant to construct robust 95% uniform confidence bands. test.procBeqC observed test-process of difference between observed cumulative process and estimate under null of constant effect over time. loglike modified partial likelihood, pseudo profile likelihood for regression parameters. D2linv inverse of the derivative of the score function. score value of score for final estimates. test.procProp observed score process for proportional odds regression effects. pval.Prop p-value based on resampling. sim.supProp re-sampled supremum values. sim.test.procProp list of 50 random realizations of test-processes for constant proportional odds under the model based on resampling.

Thomas Scheike

References

Scheike, A flexible semiparametric transformation model for survival data, Lifetime Data Anal. (to appear).

Martinussen and Scheike, Dynamic Regression Models for Survival Data, Springer (2006).

Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 data(sTRACE) ### runs slowly and is therefore donttest data(sTRACE) # Fits Proportional odds model with stratified baseline age.c<-scale(sTRACE\$age,scale=FALSE); out<-Gprop.odds(Surv(time,status==9)~-1+factor(diabetes)+prop(age.c)+prop(chf)+ prop(sex)+prop(vf),data=sTRACE,max.time=7,n.sim=50) summary(out) par(mfrow=c(2,3)) plot(out,sim.ci=2); plot(out,score=1) # Fits Proportional odds model with baseline on additive form # thus giving odds-ratio of dyings for vf and diabetes out<-Gprop.odds(Surv(time,status==9)~vf+diabetes+prop(age.c)+prop(chf)+ prop(sex),data=sTRACE,max.time=7,n.sim=50) summary(out) par(mfrow=c(2,3)) plot(out,sim.ci=2); plot(out,score=1) 

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