interval_logitsurv_discrete: Discrete Time-to-Event Analysis with Interval Censoring

Description

Fits a cumulative odds model for discrete time-to-event data, handling interval censoring where the event time is known only to lie within an interval $(t_l, t_r]$. The model assumes: $$ \text{logit}(P(T \leq t | x)) = \log(G(t)) + x \beta $$ where $G(t)$ is the baseline cumulative odds function and $\beta$ are the regression coefficients. This is equivalent to: $$ P(T \leq t | x) = \frac{G(t) \exp(x \beta)}{1 + G(t) \exp(x \beta)} $$

Usage

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

Value

An object of class "cumoddsreg" containing:

coef: Estimated coefficients (baseline time effects and covariate effects).
se.coef: Standard errors of the coefficients.
var: Variance-covariance matrix.
iid: Influence function (IID) decomposition for robust variance estimation.
ntimes: Number of distinct time intervals.
utimes: Unique time points.
ploglik: Log-likelihood at convergence.
gradient, hessian: Optimization results.
call: Original function call.

Arguments

formula: Formula with an Interval object (e.g., Interval(entry, time)) on the left-hand side and covariates on the right. Can include cluster() for correlated data.
data: Data frame containing the variables in the formula.
beta: Starting values for the optimization (vector of length $p + k$, where $p$ is the number of covariates and $k$ is the number of time intervals).
no.opt: Logical; if TRUE, skips optimization and returns estimates based on the provided beta (useful for initialization).
method: Optimization method: "NR" (Newton-Raphson, default) or "nlm".
stderr: Logical; if FALSE, returns only the coefficient estimates.
weights: Observation weights (follows ID).
offsets: Offsets (follows ID).
exp.link: Logical; if TRUE, parameterizes increments as $\exp(\alpha) > 0$.
increment: Logical; if TRUE, uses increments $dG(t) = \exp(\alpha)$ as parameters.
...: Additional arguments passed to the optimizer (lava::NR or nlm).

Author

Thomas Scheike

Details

The baseline $G(t)$ is parameterized as the cumulative sum of exponentials ($G(t) = \sum \exp(\alpha)$), ensuring positivity. The regression coefficients describe the log-odds of the event occurring by time $t$.

The likelihood is maximized over the observed intervals: $$ L = \prod_i [ P(T_i > t_{il} | x_i) - P(T_i > t_{ir} | x_i) ] $$ where $t_{il}$ and $t_{ir}$ are the left and right endpoints of the interval for subject $i$. Right-censored intervals have $t_{ir} = \infty$.

References

Scheike, T. H. (2024). Discrete time survival analysis with interval censoring. mets package documentation.

Examples

Run this code

data(ttpd) 
dtable(ttpd,~entry+time2)

out <- interval_logitsurv_discrete(Interval(entry,time2)~X1+X2+X3+X4,ttpd)
summary(out)
head(iid(out)) 

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

ttpd <- dfactor(ttpd,fentry~entry)
out <- cumoddsreg(fentry~X1+X2+X3+X4,ttpd)
summary(out)

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