Aalen's Additive Regression Model for Censored Data

DESCRIPTION:

Returns an object of class "aareg" that represents an Aalen model.

USAGE:

aareg(formula, data=<<see below>>,
weights=<<see below>>,  
    subset=<<see below>>, na.action, 
   qrtol=1e-07, nmin, dfbeta=F,
   test = c('aalen', 'nrisk'),
    model=F, x=F, y=F)

REQUIRED ARGUMENTS:

formula
a formula object, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. The response must be a Surv object. Due to a particular computational approach that is used, the model MUST include an intercept term. If "-1" is used in the model formula the program will ignore it.

OPTIONAL ARGUMENTS:

data
data frame in which to interpret the variables named in the formula, subset, and weights arguments. This may also be a single number to handle some special cases -- see below for details. If data is missing, the variables in the model formula should be in the search path.
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 weights must be the same as the number of observations. The weights must be nonnegative and it is recommended that they be strictly positive, since zero weights are ambiguous. To exclude particular observations from the model, use the subset argument instead of zero weights.
subset
expression specifying which subset of observations should be used in the fit. This can be a logical vector (which is replicated to have length equal to the number 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 model.frame after any subset argument has been applied. The default is na.fail, which returns an error if any missing values are found. An alternative is na.exclude, which deletes observations that contain one or more missing values.
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.
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 cluster term in the model formula.
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.

VALUE:

an object of class "aareg" representing the fit.

DETAILS:

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.

REFERENCES:

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.

Therneau, T. and Grambsch, P. (2000). Modeling Survival Data: Extending the Cox Model. New York: Springer.

SEE ALSO:

, , .

EXAMPLES:

# Fit a model to the lung cancer data set
lfit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, data=lung,
    action=na.omit)
lfit
# Prints:
#   n=227 (1 observations deleted due to missing values)
#     136 out of 138 unique event times used
# 
#               slope      coef se(coef)      z        p 
# Intercept  5.05e-03  5.87e-03 4.74e-03  1.240 0.216000
#       age  4.01e-05  7.15e-05 7.23e-05  0.989 0.323000
#       sex -3.16e-03 -4.03e-03 1.22e-03 -3.310 0.000935
#   ph.ecog  3.01e-03  3.67e-03 1.02e-03  3.610 0.000303
# 
# Chisq=26.18 on 3 df, p=8.7e-06; test weights=aalen

plot(lfit[4])  # Draw a plot of the function for ph.ecog
# A fit to the multiple-infection data set of children with
# Chronic Granuomatous Disease.  See section 8.5 of
# Therneau and Grambsch (2000).
fita2 <- aareg(Surv(tstart, tstop, status) ~ rx + age + inherit +
    steroids + cluster(id), data=cgd1)
fit2a
# Prints:
#   n= 203 
#     69 out of 70 unique event times used
# 
#               slope      coef se(coef) robust se     z        p 
# Intercept  0.012800  0.040600 0.021300  0.019600  2.08 0.037800
#        rx -0.002520 -0.010100 0.002290  0.003020 -3.36 0.000787
#       age -0.000101 -0.000317 0.000115  0.000117 -2.70 0.006840
#   inherit  0.001330  0.003830 0.002800  0.002420  1.58 0.114000
#  steroids -0.004620 -0.013200 0.010600  0.009700 -1.36 0.173000
# 
# Chisq=16.74 on 4 df, p=0.0022; test weights=aalen