Dag
2010-04-15 16:28:45 UTC
Hello all,
(Please have patience with the long intro to my question.)
On
http://faculty.chass.ncsu.edu/garson/PA765/cox.htm#assume
it says:
"In addition to statistical output, the Plots button in Cox regression
in PASW/SPSS supports cumulative hazard, cumulative survival, log-
minus-log, and partial residual plots. Use of these plots is discussed
above in the "Baseline hazard, survival, and cumulative hazard rates"
section and below in the "Assumptions" section. The Plots button
dialog for PASW/SPSS is shown below."
[Figure at website]
Further:
"Assumption of proportional hazards. Cox regression with time-
invariant covariates assumes that the ratio of hazards for any two
observations is the same across time periods. For instance, in a time-
invariant Cox model the ratio of hazards for persons a and b should be
the same this year as in the period 10 years from now. This can be a
false assumption, as when 10 years from now person B is in their 70's,
when mortality spikes, considering age as the covariate. This is a
critical assumption of Cox regression and must be checked for each
covariate. Gray (1996; quoted in Box-Steffensmeier & Zorn, 2001: 974)
has reported as much as a 90% reduction in the power of significance
tests (power = chance of false negatives, rejecting the existence of
true covariate effects) when rates cross rather than are
proportionate.
If a covariate fails this assumption, then for hazard ratios that
increase over time for that covariate, relative risk is overestimated
(that is, for diverging hazards, coefficient estimates are inflated).
For ratios that decrease over time, relative risk is often
underestimated (that is, for converging hazards, coefficient estimates
are deflated and biased toward zero). ["Converging" means that the
hazard rates for two groups formed by a covariate factor are tending
toward the same rate over time]. Correspondingly, standard errors are
incorrect and significance tests are decreased in power (Box-
Steffensmeier & Zorn, 2001: 972). It is common for a covariate to fail
the assumption of proportional hazards, and the implication for
estimation should be reported. There are alternative ways to check:
Partial residual plots (Schoenfeld residuals PH test), Graphical
methods may be used to examine covariates. In SPSS one may create a
plot of scaled Schoenfeld residuals on the y axis against time on the
x axis, with one such plot per covariate. A lowess smoothing line
summarizing the residuals should be close to the horizontal 0
reference line for the y axis, since the average value of residuals at
an tiime should be zero if the effects of the covariate being plotted
are proportional (see Box-Steffensmeier & Zorn, 2001: 978-981).
Partial residual methods are the most common and preferred methods for
testing for non-proportionality in Cox models.
In PASW/SPSS select "Partial residual plots" under the Plots button
after first having saved partial residuals by checking "Partial
residuals" in the "Save New Variables" dialog box under the Save
button in the Cox regression dialog. The X axis is survival time. The
Y axis is the partial residual for a given covariate. In a well-
fitting model, distribution of residuals over time is random. This can
be checked further in the Chart Editor by adding a loess smoothing
line or linear regression line to show non-random trends. If random,
fit lines should not diverge much from the Y-axis 0 reference line."
I'm sure all this is true - but I can find no alternative for Partial
residual plots in the Plots button dialog. There is no such
alternative in the dialog showed on the website either. How should I
do?
Very grateful for all help,
Dag Tidemalm, Stockholm, Sweden
(Please have patience with the long intro to my question.)
On
http://faculty.chass.ncsu.edu/garson/PA765/cox.htm#assume
it says:
"In addition to statistical output, the Plots button in Cox regression
in PASW/SPSS supports cumulative hazard, cumulative survival, log-
minus-log, and partial residual plots. Use of these plots is discussed
above in the "Baseline hazard, survival, and cumulative hazard rates"
section and below in the "Assumptions" section. The Plots button
dialog for PASW/SPSS is shown below."
[Figure at website]
Further:
"Assumption of proportional hazards. Cox regression with time-
invariant covariates assumes that the ratio of hazards for any two
observations is the same across time periods. For instance, in a time-
invariant Cox model the ratio of hazards for persons a and b should be
the same this year as in the period 10 years from now. This can be a
false assumption, as when 10 years from now person B is in their 70's,
when mortality spikes, considering age as the covariate. This is a
critical assumption of Cox regression and must be checked for each
covariate. Gray (1996; quoted in Box-Steffensmeier & Zorn, 2001: 974)
has reported as much as a 90% reduction in the power of significance
tests (power = chance of false negatives, rejecting the existence of
true covariate effects) when rates cross rather than are
proportionate.
If a covariate fails this assumption, then for hazard ratios that
increase over time for that covariate, relative risk is overestimated
(that is, for diverging hazards, coefficient estimates are inflated).
For ratios that decrease over time, relative risk is often
underestimated (that is, for converging hazards, coefficient estimates
are deflated and biased toward zero). ["Converging" means that the
hazard rates for two groups formed by a covariate factor are tending
toward the same rate over time]. Correspondingly, standard errors are
incorrect and significance tests are decreased in power (Box-
Steffensmeier & Zorn, 2001: 972). It is common for a covariate to fail
the assumption of proportional hazards, and the implication for
estimation should be reported. There are alternative ways to check:
Partial residual plots (Schoenfeld residuals PH test), Graphical
methods may be used to examine covariates. In SPSS one may create a
plot of scaled Schoenfeld residuals on the y axis against time on the
x axis, with one such plot per covariate. A lowess smoothing line
summarizing the residuals should be close to the horizontal 0
reference line for the y axis, since the average value of residuals at
an tiime should be zero if the effects of the covariate being plotted
are proportional (see Box-Steffensmeier & Zorn, 2001: 978-981).
Partial residual methods are the most common and preferred methods for
testing for non-proportionality in Cox models.
In PASW/SPSS select "Partial residual plots" under the Plots button
after first having saved partial residuals by checking "Partial
residuals" in the "Save New Variables" dialog box under the Save
button in the Cox regression dialog. The X axis is survival time. The
Y axis is the partial residual for a given covariate. In a well-
fitting model, distribution of residuals over time is random. This can
be checked further in the Chart Editor by adding a loess smoothing
line or linear regression line to show non-random trends. If random,
fit lines should not diverge much from the Y-axis 0 reference line."
I'm sure all this is true - but I can find no alternative for Partial
residual plots in the Plots button dialog. There is no such
alternative in the dialog showed on the website either. How should I
do?
Very grateful for all help,
Dag Tidemalm, Stockholm, Sweden