Discrete time to event interval censored data — interval.logitsurv.discrete • mets

$$ logit(P(T >t | x)) = log(G(t)) + x \beta $$ $$ P(T >t | x) = \frac{1}{1 + G(t) exp( x \beta) } $$

interval.logitsurv.discrete(
  formula,
  data,
  beta = NULL,
  no.opt = FALSE,
  method = "NR",
  stderr = TRUE,
  weights = NULL,
  offsets = NULL,
  exp.link = 1,
  increment = 1,
  ...
)

Arguments

formula: formula
data: data
beta: starting values
no.opt: optimization TRUE/FALSE
method: NR, nlm
stderr: to return only estimate
weights: weights following id for GLM
offsets: following id for GLM
exp.link: parametrize increments exp(alpha) > 0
increment: using increments dG(t)=exp(alpha) as parameters
...: Additional arguments to lower level funtions lava::NR optimizer or nlm

Details

This is thus also the cumulative odds model, since $$ P(T \leq t | x) = \frac{G(t) \exp(x \beta) }{1 + G(t) exp( x \beta) } $$

The baseline $G(t)$ is written as $cumsum(exp(\alpha))$ and this is not the standard parametrization that takes log of $G(t)$ as the parameters.

Input are intervals given by ]t_l,t_r] where t_r can be infinity for right-censored intervals When truly discrete ]0,1] will be an observation at 1, and ]j,j+1] will be an observation at j+1

Likelihood is maximized: $$ \prod P(T_i >t_{il} | x) - P(T_i> t_{ir}| x) $$

Author

Thomas Scheike

Examples

data(ttpd) 
dtable(ttpd,~entry+time2)
#> 
#>       time2   1   2   3   4   5   6 Inf
#> entry                                  
#> 0           316   0   0   0   0   0   0
#> 1             0 133   0   0   0   0   0
#> 2             0   0 150   0   0   0   0
#> 3             0   0   0  23   0   0   0
#> 4             0   0   0   0  90   0   0
#> 5             0   0   0   0   0  68   0
#> 6             0   0   0   0   0   0 220
out <- interval.logitsurv.discrete(Interval(entry,time2)~X1+X2+X3+X4,ttpd)
summary(out)
#>       Estimate Std.Err     2.5%   97.5%   P-value
#> time1  -2.0064  0.1523 -2.30496 -1.7079 1.273e-39
#> time2  -2.1749  0.1599 -2.48838 -1.8614 4.118e-42
#> time3  -1.4581  0.1544 -1.76071 -1.1554 3.636e-21
#> time4  -2.9260  0.2453 -3.40677 -2.4453 8.379e-33
#> time5  -1.2051  0.1706 -1.53946 -0.8706 1.633e-12
#> time6  -0.9102  0.1860 -1.27468 -0.5457 9.843e-07
#> X1      0.9913  0.1179  0.76024  1.2223 4.100e-17
#> X2      0.6962  0.1162  0.46847  0.9238 2.064e-09
#> X3      0.3466  0.1159  0.11941  0.5738 2.788e-03
#> X4      0.3223  0.1151  0.09668  0.5478 5.111e-03

pred <- predictlogitSurvd(out,se=FALSE)
plotSurvd(pred)