aareg                package:survival                R Documentation

_A_a_l_e_n'_s _a_d_d_i_t_i_v_e _r_e_g_r_e_s_s_i_o_n _m_o_d_e_l _f_o_r _c_e_n_s_o_r_e_d _d_a_t_a

_D_e_s_c_r_i_p_t_i_o_n:

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

_U_s_a_g_e:

     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) 

_A_r_g_u_m_e_n_t_s:

 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. 

    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 speci al cases - see below
          for details. If 'data' is missi ng, 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 i s 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. 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 i ncluded, 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.fr ame' after any 'subset' argument has be en applied.
          The default is 'na.fail', which returns a n error if any
          missing values are found. An alternative is 'na.excl ude',
          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. This essentially truncates
          the computations near the tail of the data set, when n is
          small and the calcualtions 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 'cluster'
          term in the model formula. 

   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 'taper=(1:4)/4' would cause the
          variance estimate used at any event time to be a weighted
          average of the estimated variance matrices at the last 4
          death times, with a weight of 1 for the current death time
          and decreasing to 1/4 for prior event times. The default
          value gives the standard Aalen model. 

    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. 

_D_e_t_a_i_l_s:

     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 inheritly
     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.

_V_a_l_u_e:

     an object of class '"aareg"'  representing the fit.

_R_e_f_e_r_e_n_c_e_s:

     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.

_S_e_e _A_l_s_o:

     print.aareg, summary.aareg, plot.aareg

_E_x_a_m_p_l_e_s:

     # 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)

