Aalen's additive regression model for censored data
Returns an object of class "aareg" that
represents an Aalen model.
aareg(formula, data, weights, subset, na.action,
qrtol=1e-07, nmin, dfbeta=FALSE, taper=1,
test = c('aalen', 'variance', 'nrisk'),
model=FALSE, x=FALSE, y=FALSE)formula |
a formula object, with the response on the left of a ‘~’ operator and
the terms,
separated by |
data |
data frame in which to interpret the variables named in the
|
weights |
vector of observation weights. If supplied, the fitting algorithm
minimizes the sum of the weights multiplied by the squared residuals
(see below for additional technical details). The length of
|
subset |
expression specifying which subset of observations should be used in the fit. Th is can be a logical vector (which is replicated to have length equal to the numb er of observations), a numeric vector indicating the observation numbers to be included, or a character vector of the observation names that should be included. All observations are included by default. |
na.action |
a function to filter missing data. This is applied to the
|
qrtol |
tolerance for detection of singularity in the QR decomposition |
nmin |
minimum number of observations for an estimate; defaults to 3 times the number of covariates. This essentially truncates the computations near the tail of the data set, when n is small and the calculations can become numerically unstable. |
dfbeta |
should the array of dfbeta residuals be computed. This implies computation
of the sandwich variance estimate.
The residuals will always be computed if there is a
|
taper |
allows for a smoothed variance estimate.
Var(x), where x is the set of covariates, is an important component of the
calculations for the Aalen regression model.
At any given time point t, it is computed over all subjects who are still
at risk at time t.
The tape argument allows smoothing these estimates,
for example |
test |
selects the weighting to be used, for computing an overall “average” coefficient vector over time and the subsequent test for equality to zero. |
model, x, y |
should copies of the model frame, the x matrix of predictors, or the response vector y be included in the saved result. |
The Aalen model assumes that the cumulative hazard H(t) for a subject can be expressed as a(t) + X B(t), where a(t) is a time-dependent intercept term, X is the vector of covariates for the subject (possibly time-dependent), and B(t) is a time-dependent matrix of coefficients. The estimates are inherently non-parametric; a fit of the model will normally be followed by one or more plots of the estimates.
The estimates may become unstable near the tail of a data set, since the
increment to B at time t is based on the subjects still at risk at time
t. The tolerance and/or nmin parameters may act to truncate the estimate
before the last death.
The taper argument can also be used to smooth
out the tail of the curve.
In practice, the addition of a taper such as 1:10 appears to have little
effect on death times when n is still reasonably large, but can considerably
dampen wild occilations in the tail of the plot.
an object of class "aareg"
representing the fit, with the following components:
n |
vector containing the number of observations in the data set, the number of event times, and the number of event times used in the computation |
times |
vector of sorted event times, which may contain duplicates |
nrisk |
vector containing the number of subjects at risk, of the
same length as |
coefficient |
matrix of coefficients, with one row per event and one column per covariate |
test.statistic |
the value of the test statistic, a vector with one element per covariate |
test.var |
variance-covariance matrix for the test |
test |
the type of test; a copy of the |
tweight |
matrix of weights used in the computation, one row per event |
call |
a copy of the call that produced this result |
Aalen, O.O. (1989). A linear regression model for the analysis of life times. Statistics in Medicine, 8:907-925.
Aalen, O.O (1993). Further results on the non-parametric linear model in survival analysis. Statistics in Medicine. 12:1569-1588.
print.aareg, summary.aareg, plot.aareg
# Fit a model to the lung cancer data set
lfit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, data=lung,
nmin=1)
## Not run:
lfit
Call:
aareg(formula = Surv(time, status) ~ age + sex + ph.ecog, data = lung, nmin = 1
)
n=227 (1 observations deleted due to missing values)
138 out of 138 unique event times used
slope coef se(coef) z p
Intercept 5.26e-03 5.99e-03 4.74e-03 1.26 0.207000
age 4.26e-05 7.02e-05 7.23e-05 0.97 0.332000
sex -3.29e-03 -4.02e-03 1.22e-03 -3.30 0.000976
ph.ecog 3.14e-03 3.80e-03 1.03e-03 3.70 0.000214
Chisq=26.73 on 3 df, p=6.7e-06; test weights=aalen
plot(lfit[4], ylim=c(-4,4)) # Draw a plot of the function for ph.ecog
## End(Not run)
lfit2 <- aareg(Surv(time, status) ~ age + sex + ph.ecog, data=lung,
nmin=1, taper=1:10)
## Not run: lines(lfit2[4], col=2) # Nearly the same, until the last point
# A fit to the mulitple-infection data set of children with
# Chronic Granuomatous Disease. See section 8.5 of Therneau and Grambsch.
fita2 <- aareg(Surv(tstart, tstop, status) ~ treat + age + inherit +
steroids + cluster(id), data=cgd)
## Not run:
n= 203
69 out of 70 unique event times used
slope coef se(coef) robust se z p
Intercept 0.004670 0.017800 0.002780 0.003910 4.55 5.30e-06
treatrIFN-g -0.002520 -0.010100 0.002290 0.003020 -3.36 7.87e-04
age -0.000101 -0.000317 0.000115 0.000117 -2.70 6.84e-03
inheritautosomal 0.001330 0.003830 0.002800 0.002420 1.58 1.14e-01
steroids 0.004620 0.013200 0.010600 0.009700 1.36 1.73e-01
Chisq=16.74 on 4 df, p=0.0022; test weights=aalen
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.