# GORH: The Main Function to Fit the GORH Model with Interval... In ICGOR: Fit Generalized Odds Rate Hazards Model with Interval Censored Data

## Description

The Generalized Odds Rate Hazards model is fitted for interval censored survival data. The EM algorithm facilitated by a gamma-poisson data augmentation is applied for estimating the coefficients in the model. The covariance matrix has closed forms based on the Louis method.

## Usage

 ```1 2``` ```GORH(formula = formula(data), data = parent.frame(), r = 1, n.int = 5, order = 3, max.iter = 1000, cov.rate = 0.001) ```

## Arguments

 `formula` The formula for the GORH model, defined using the Surv() function. `data` The interval censored sorvival data, including the left and right end points of the time intervals and the covariates. If a subject is left(right) censored, the left(right) end point of the subject should be defined as “NA", see example. `r` The transformation parameter in the GORH model, should be greater than 0. The default is r=1 (the PO model). `n.int` Number of equally spaced interior knots of the splines. Default is 5. `order` Order of the spline basis functions. Default is 3, i.e. the cubic splines. `max.iter` The maximum number of interations for the EM algorithm. Default is 100. `cov.rate` The bound for convergence of the algorithm, which defined as the difference between the log-likelihood values of two consecutive iterations smaller than this value. Default is 0.001.

## Details

The formula defined for “formula" is based on the Surv() function, where the left and right end points of the time interval are included and the type is equal to “interval2". The left(right) end points of left(right) censored individuals should be defined as “NA" in the data frame before running the function.\ The transformation parameter r is a positive number corresponding to a specific model in the GORH family of models. The special case POMC model(r=1) is set as the default. Other positive numbers can also be specified. The result for a PH model can be approximated by specifying an extremely small number for r, e.g. r=1e-6.\ The grid search method is suggested to find the best model in practice. That is, try a sequence of r values and choose the one with the greatest log-likelihood value.

## Value

 `ParEst` A list includes the estimated coefficients (Beta,gl), the whole hessian matrix (Hessian), AIC, and the log-likelihood value(loglik). `ParVcov` The estimated covariance matrix of the coefficient Beta.

## Note

The estimated hessian matrix can be very large and sometimes not invertable. In which case, we try the QR decomposition, g-inverse or even numerical methods to get the covariance matrix. Different values of hess in the ParVcov indicating the different cases. hess=0:the hessian matrix is invertable; hess=1:the QR decomposition is applied to solve the hessian matrix; hess=2:the g-inverce is applied to the hessian matrix; hess=3:the hessian matrix is obtained from numerical methods. The variance estimates may be unreliable for the cases when hess>0.

## References

Zhou, J., Zhang, J. and Lu, W. (2017+). An EM Algorithm for fitting the Generalized Odds-Rate Model to Interval Censored Data. Accepted by Statistics in Medicine.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```data(Hemophilia) # Set Left/Right Interval End Points as NA Hemophilia\$L[Hemophilia\$d1==1]<-Hemophilia\$R[Hemophilia\$d3==1]<-NA # Fit PO Model (r=1) fit<-GORH(Surv(L,R)~Low+Medium+High,data=Hemophilia,r=1) summary(fit) # Predict Survival Curve for a New Individual # Specify coveriate vectors for new.x pred1<-predict(fit,new.x=c(0,0,0)) pred2<-predict(fit,new.x=c(1,0,0)) pred3<-predict(fit,new.x=c(0,1,0)) pred4<-predict(fit,new.x=c(0,0,1)) # Plot the Survival Curves plot(pred1,xlab="Time",ylab="Survival Probability",ylim=c(0,1)) lines(pred2\$SurvTime,pred2\$SurvProb,col=2) lines(pred3\$SurvTime,pred3\$SurvProb,col=3) lines(pred4\$SurvTime,pred4\$SurvProb,col=4) legend(0,0.2,c("None","Low","Medium","High"),lty=1,col=1:4) ```

ICGOR documentation built on May 1, 2019, 10:31 p.m.