Confidence bands for the survival function
In several medical reports, the survival function is graphed along with the confidence intervals. The endpoints of the confidence intervals are usually connected to draw an area where the entire survival curve is contained with a given confidence. Confidence intervals are pointwise, i.e., they refer to the survival probability at a single time, but they are not valid for all the estimates of the entire survival curve. To this aim, the appropriate measure is confidence bands, not yet available within Stata. Two methods are usually employed to construct these confidence bands. The first was proposed by Hall and Wellner (1980), and the second was proposed by Nair (1984). The latter produces the so-called equal precision (EP) confidence bands. For both methods, log-minus-log and arcsine square-root transformed versions have been proposed. stcband is a new Stata command that allows the user to graph the survival function, together with the confidence bands constructed according to the Hall–Wellner and EP methodologies. The available options allow the user to a) specify the lower and upper limits of the time where the bands are to be estimated; b) choose the linear, log, or arcsine transformation; c) set the confidence level at 90, 95, or 99%; d) save the estimates; and e) manage the aspect of the graph. A further option allows the user to estimate the confidence bands of the cumulative hazard function. Using an example, I illustrate * the results obtained by using stcband and the corresponding R function; * the use of the command and the differences of the estimates of its confidence bands versus the usual pointwise confidence intervals. Finally, I will compare the coverage probabilities of the confidence bands estimated according to the above mentioned approaches by using simulated data with various survival distributions. I will perform simulations using Stata’s bootstrap command. The new command also has an accompanying help file in which the user is able to run an example, taken from the second edition of Klein and Moeschberger’s Survival Analysis Techniques for Censored and Truncated Data (p. 109–117), by clicking on the Viewer window. stcband is available for download from the SSC Archives.
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