Graphical 'Check' of the proportional hazards assumption.
---------------------------------------------------------

^stcumh^ stratavar baseh [^in^ range] [^if^ exp],
	[^strc^ode^(^x,y^)^] [^save(^outsheet^)^] [^noc^urtail] [^k^eep^(^n^)^]
	[graph_options]


Description
-----------

Before ^stcumh^ can be effectuated, the dataset must be
1)	@^stset^@, and
2)	a stratified Cox regression analysis must have been performed;
	where
	2a) ^stratavar^
	was the (nominal or ordinal) stratifying variable
	(by specifying the ^st^rata(stratavar)-option of the @^stcox^@ command),
	and where
	2b)	^baseh^
	was the newvar specified to hold the thereby saved baseline hazards
	(by use of the ^baseh^azard^(^newvar^)^-option of the @^stcox^@
	command).

^stcumh^ plots estimates of the cumulative baseline hazards for two strata
in ^stratavar^ against each other. The slope of the plotted graph will (at
any time point) approximately be the relative risk between the two strata.
If the proportional hazards assumption between the two strata (in the
equivalent unstratified Cox regression analysis) is fulfilled, the plot
should be a straight line through (0,0).


The failure time range of the two strata plotted might not be the same, and
in default of specifying the ^noc^urtail-option (see options below), only
the common failure time range is plotted. Therefore, information of the
failure time range in each strata and the common range plotted is issued to
the 'Results'-window. Also, the plotted common failure time range is
indicated on the plot (as the t2title)!

Caution:
Whereas ^stcox^'s ^st^rata()-option allows for a list of variables, ^stcumh^
assumes that only one stratifying variable is specified at a time. This is a
limitation which can not be circumvented.


Options
-------
[^strc^ode^(^x,y^)^] is not optional if ^stratavar^ has more than two
strata!!
If there is more than two strata in the stratifying variable (^stratavar^),
the proportional hazards assumption between any two strata in ^stratavar^
can be 'checked' by specifying the code (integer) for the two strata x and y
to be plotted.

[^save(^outsheet^)^] Saves the failure time variable (time), the cumulative
hazards for stratum 'x' (cumh0) and the cumulative hazards for stratum 'y'
(cumh1) in the the outsheet file specified. (See help ^@outsheet@^).
This option is needed when the time corresponding to specific points of the
graph is of interest!! (typically when the proportional hazards assumption
can be seen to be violated, and the when the plotted graph can be described
as a piece by piece linear function. In this case, the time for the knots of
the lines can be used to specify a specific alternative model, which
includes the stratifying variable as a time dependent variable. This
alternative model should then be tested formally against the more restricted
model with the stratifying variable as a time independent variable (by use
of the @^lrtest^@, see also @^stlexis^@, @stegen@)).
To get the time for the corresponding to the knots, the outfile can be
entered into (for example) Excel, where the plot can be repeated. The
cumulative hazard for the knots must then be determined visually, and the
corresponding time be found in the spreedsheet.

Graph-options
-------------
[^noc^urtail] The cumulative hazards cumulates with time (the failure time
^(ftimevar)^ specified in the ^stset^ command). The time range for the two
strata to be plotted might not be the same, resulting in straight vertical
or horizontal (heading or tailing) lines! In default of specifying the
^noc^urtail-option, only the common failure time range is plotted!

[^k^eep^(^n^)^] In default of ^noc^urtail, possible a lot of non-censored
observations is dropped (due to non overlapping ranges of failure times). If
this is occurring only in the high end of the time range, a long tailing
line results. To improve readability of the plot, this tailing line can be
reduced in length by specifying the number of ^n^ observations to be kept.
If the number of observations in the tail is higher than ^n^, only ^n^
observations is plotted. The number of kept and dropped observations is
issued in the 'Results'-window.
To effectuate the ^k^eep^(^n^)^-option, the ^noc^urtile-option must be
specified.

^@graph@_options^ are allowed. Default labelling is supplied when
graph_options are absent, but the x-axis may be relabelled using the ^b2^
graphics option, the y-axis may be relabelled using the ^l1^ option, and the
top title may be relabelled using the ^t1^ option. The second top title
(t2titel) is used to specify the plotted failure time range, and can not be
changed!


Example
-------
1)	If only two strata in stratavar:

^stset^ ftimevar
^stcox^ varlist, st(stratavar) baseh(baseh)
^stcumh stratavar baseh, save(myout)^


2)	If six strata in stratavar, left and right censoring in Cox:

^stset^ ftimevar status, t0(entry_timevar)
^stcox^ varlist, st(stratavar) baseh(baseh)
^stcumh strata baseh, strc(1,6) l1(Stratum-'6'-name) b2(Stratum-'1'-name)
save(myout)^

(^strc(1,6)^ checks the proportional hazards assumption between stratum 1
and stratum 6).

In both examples above, the time, and the cumulative hazards for the two
strata is saved in the ascii outfile 'myout.raw'. This file can be read by
other programs, for example, Excel, where the hazards and the corresponding
time can be inspected (see save-options above).


3)	If display of non overlapping ranges of failure times is wonted:

^stcumh strata baseh, nocurtail keep(200)^

keeps up to 200 non-censored observation after the common failure time on
display.


Author
------

      Kim Lyngby Mikkelsen
      MD, Ph.D.-student
	  Institute of preventive Medicine
      Denmark
      kimmik@ipm.hosp.dk or kimmik@dadlnet.dk


Also see
--------

 Manual:  ^[R] st, stset, stcox

On-line:  help for @stset@; @stcox@, @graph@, @outsheet@, @^lrtest^@

STB:  STB-41, ssa10.1: 	@staalen@, @stlexis@, and others.
STB:  STB-41, ssa11:	@stegen@, and others.
