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help for ^staalen^                                           (STB-41: ssa10.1)
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Aalen's estimate of the cumulative rate from ^st^ data
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^staalen^ [^in^ range] [^if^ exp], ^or^igin^(^varname^)^ ^sc^ale^(^#^)^
        [^by(^varname^)^ ^fc^odes^(^rule^)^ ^fr^om^(^#^)^ ^to(^#^)^  ^rm^ult^(^varname^)^
        ^risk^  graph_options]


Description
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^staalen^ plots Aalen's estimate of the cumulative rate or intensity 
(sometimes also called the integrated hazard). Cumulative rates are 
plotted against a time scale defined in terms of its origin and scale.
In its simplest form, the estimate is the Nelson-Aalen estimate of the 
cumulative rate, and with "risk multipliers" it becomes the 
Breslow-Aalen estimate of the cumulative baseline rate in the 
proportional hazards model. Optionally, the cumulative risk may be plotted
instead of the cumulative rate, using the identity

      Cumulative risk   =    1   -   exp(- Cumulative rate).

Note that there are difficulties in interpreting the cumulative risk when 
there are competing causes of failure. 


Options
-------

^origin(^varname^)^ specifies the origin for the analysis time scale.

^scale(^#^)^ specifies the units for the analysis time scale.

^by(^varname^)^ causes a separate estimate to be calculated for each value
of varname. The estimates are plotted on the same graph for easier comparison.

^fcodes(^rule^)^ specifies, as a recode rule, codes to be treated as failure.

^from(^#^)^ provides left truncation of all observations at a fixed lower 
time limit.

^to(^#^)^ provides right censoring of all observations at a fixed upper 
time limit.

^risk^ causes the cumulative risk rather than the cumulative rate to be estimated

^rmult(^varname^)^ specifies the rate multipliers to be used when computing the
Breslow-Aalen estimate of the cumulative baseline rate.

^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 
and the y-axis may be relabelled using the ^l1^ option.


Example
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^staalen , by(job) origin(dob) scale(365.25) fr(45) to(65)^ 
 
^staalen , by(job) or(dob) sc(365.25)^ 
              ^l1(Cumulative rate by job) b2(Age) saving(mygraph)^


Authors
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      David Clayton
      MRC Biostatistical Research Unit
      Cambridge
      email: david.clayton@@mrc-bsu.cam.ac.uk

      Michael Hills
      London School of Hygiene and Tropical Medicine (retired)
      email: mhills@@regress.demon.co.uk


Also see
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    STB:  STB-41, ssa10.1, STB-40 ssa10