This is used to set various numeric parameters controlling a Cox model fit.
Typically it would only be used in a call to coxph.
coxph.control(eps = 1e-09, toler.chol = .Machine$double.eps^0.75,
iter.max = 20, toler.inf = sqrt(eps), outer.max = 10, timefix=TRUE)a list containing the values of each of the above constants
Iteration continues until the relative change in the log partial likelihood is less than eps, or the absolute change is less than sqrt(eps). Must be positive.
Tolerance for detection of singularity during a Cholesky decomposition of the variance matrix, i.e., for detecting a redundant predictor variable.
Maximum number of iterations to attempt for convergence.
Tolerance criteria for the warning message about a possible infinite coefficient value.
For a penalized coxph model, e.g. with pspline terms, there is an outer loop of iteration to determine the penalty parameters; maximum number of iterations for this outer loop.
Resolve any near ties in the time variables.
The convergence tolerances are a balance. Users think they want THE maximum point of the likelihood surface, and for well behaved data sets where this is quadratic near the max a high accuracy is fairly inexpensive: the number of correct digits approximately doubles with each iteration. Conversely, a drop of .0001 from the maximum in any given direction will be correspond to only about 1/20 of a standard error change in the coefficient. Statistically, more precision than this is straining at a gnat. Based on this the author originally had set the tolerance to 1e-5, but relented in the face of multiple "why is the answer different than package X" queries.
Asking for results that are too close to machine precision
(double.eps) is a fool's errand; a reasonable critera is often the
square root of that precision. The Cholesky decompostion needs to be
held to a higher standard than the overall convergence criterion, however.
The tolerance.inf value controls a warning message; if it is
too small incorrect warnings can appear, if too large some actual cases of
an infinite coefficient will not be detected.
The most difficult cases are data sets where the MLE coefficient is
infinite; an example is a data set where at each death time,
it was the subject with the largest
covariate value who perished. In that situation the coefficient
increases at each iteration while the log-likelihood asymptotes to a
maximum. As iteration proceeds there is a race condition
condition for three endpoint: exp(coef) overflows,
the Hessian matrix become singular, or the change in loglik is small
enough to satisfy the convergence criterion. The first two are
difficult to anticipate and lead to numeric diffculties, which is
another argument for moderation in the choice of eps.
See the vignette "Roundoff error and tied times" for a more
detailed explanation of the timefix option. In short, when
time intervals are created via subtraction then two time intervals that are
actually identical can appear to be different due to floating point
round off error, which in turn can make coxph and
survfit results dependent
on things such as the order in which operations were done or the
particular computer that they were run on.
Such cases are unfortunatedly not rare in practice.
The timefix=TRUE option adds
logic similar to all.equal to ensure reliable results.
In analysis of simulated data sets, however, where often by defintion there
can be no duplicates, the option will often need to be set to
FALSE to avoid spurious merging of close numeric values.
coxph