Draws the scaled total time on test transform, a distribution-free way of judging hazard shape before any model is fitted.
Usage
bd_ttt_plot(
time,
status = NULL,
add = FALSE,
col = "steelblue",
lwd = 2,
main = "Scaled total time on test",
xlab = "i / n",
ylab = expression(phi(i/n)),
...
)Arguments
- time
Numeric vector of observed times, or a fitted `"betadanish"` object, from which the times are taken.
- status
Optional event indicator. Censored observations are dropped, since the transform is defined for complete samples.
- add
Logical; add to an existing plot rather than starting a new one.
- col, lwd
Colour and line width for the curve.
- main, xlab, ylab
Labels.
- ...
Further graphical parameters.
Value
Invisibly, a data frame with the plotting coordinates `i_n` and `phi`, and an attribute `"shape"` giving the suggested hazard shape.
Details
For an ordered sample \(x_{(1)} \le \cdots \le x_{(n)}\), the scaled transform at \(i/n\) is $$\phi(i/n) = \frac{\sum_{j=1}^{i} x_{(j)} + (n-i)x_{(i)}} {\sum_{j=1}^{n} x_{(j)}}.$$
Read it against the diagonal. A curve entirely above the diagonal indicates an increasing hazard, entirely below a decreasing one; a curve that starts below and crosses above suggests a bathtub shape, and the reverse suggests a unimodal one. A curve close to the diagonal indicates a constant hazard, that is an exponential sample.
This is a shape diagnostic, not a test. It is worth drawing before choosing between the four-parameter model and its submodel, because it says which hazard shapes the data can support without assuming any of them.
