survexp               package:survival               R Documentation

_C_o_m_p_u_t_e _E_x_p_e_c_t_e_d _S_u_r_v_i_v_a_l

_D_e_s_c_r_i_p_t_i_o_n:

     Returns either the expected survival of a cohort of subjects, or
     the  individual expected survival for each subject.

_U_s_a_g_e:

     survexp(formula, data, weights, subset, na.action, times, cohort=TRUE, 
             conditional=FALSE, ratetable=survexp.us, scale=1, npoints, 
             se.fit, model=FALSE, x=FALSE, y=FALSE)

_A_r_g_u_m_e_n_t_s:

 formula: formula object.  The response variable is a vector of
          follow-up times  and is optional.  The predictors consist of
          optional grouping variables  separated by the '+' operator
          (as in 'survfit'), along with a 'ratetable'   term.  The
          'ratetable' term matches each subject to his/her expected
          cohort.  

    data: data frame in which to interpret the variables named in  the
          'formula', 'subset' and 'weights' arguments.  

 weights: case weights.  

  subset: expression indicating a subset of the rows of 'data' to be
          used in the fit.  

na.action: function to filter missing data. This is applied to the
          model frame after   'subset' has been applied.  Default is
          'options()$na.action'. A possible  value for 'na.action' is
          'na.omit', which deletes observations that contain  one or
          more missing values.  

   times: vector of follow-up times at which the resulting survival
          curve is   evaluated.  If absent, the result will be reported
          for each unique   value of the vector of follow-up times
          supplied in 'formula'.  

  cohort: logical value: if 'FALSE', each subject is treated as a
          subgroup of size 1.  The default is 'TRUE'.  

conditional: logical value: if 'TRUE', the follow-up times supplied in
          'formula'  are death times and conditional expected survival
          is computed.  If 'FALSE', the follow-up times are potential
          censoring times.   If follow-up times are missing in
          'formula', this argument is ignored.    

ratetable: a table of event rates, such as 'survexp.uswhite', or a
          fitted Cox model.  

   scale: numeric value to scale the results.  If 'ratetable' is in
          units/day,  'scale = 365.25' causes the output to be reported
          in years.  

 npoints: number of points at which to calculate intermediate results,
          evenly spaced   over the range of the follow-up times.  The
          usual (exact) calculation is done   at each unique follow-up
          time. For very large data sets specifying 'npoints'   can
          reduce the amount of memory and computation required.  For a
          prediction from a Cox model 'npoints' is ignored.  

  se.fit: compute the standard error of the predicted survival.   The
          default is to compute standard errors whenever   possible,
          which at this time is only for the Ederer method and a Cox  
          model as the rate table.  

model,x,y: flags to control what is returned.  If any of these is true,
          then the model frame, the model matrix, and/or the vector of
          response times will be returned as components of the final
          result, with the same names as the flag arguments. 

_D_e_t_a_i_l_s:

     Individual expected survival is usually used in models or testing,
     to  `correct' for the age and sex composition of a group of
     subjects.  For instance, assume that birth date, entry date into
     the study,  sex and actual survival time are all known for a group
     of subjects.  The 'survexp.uswhite' population tables contain
     expected death rates  based on calendar year, sex and age.  Then 


     haz <- -log(survexp(death.time ~ ratetable(sex=sex, year=entry.dt, 
                 age=(birth.dt-entry.dt)), cohort=FALSE))

     gives for each subject the total hazard experienced up to their
     observed  death time or censoring time.  This probability can be
     used as a rescaled time value in models: 


     glm(status ~ 1 + offset(log(haz)), family=poisson) 
     glm(status ~ x + offset(log(haz)), family=poisson)

     In the first model, a test for intercept=0 is the one sample
     log-rank  test of whether the observed group of subjects has
     equivalent survival to  the baseline population.  The second model
     tests for an effect of variable  'x' after adjustment for age and
     sex. 

     Cohort survival is used to produce an overall survival curve. 
     This is then  added to the Kaplan-Meier plot of the study group
     for visual comparison  between these subjects and the population
     at large.  There are three common  methods of computing cohort
     survival.  In the "exact method" of Ederer the cohort is not
     censored; this corresponds  to having no response variable in the
     formula.  Hakulinen recommends censoring  the cohort at the
     anticipated censoring time of each patient, and Verheul 
     recommends censoring the cohort at the actual observation time of
     each  patient.  The last of these is the conditional method. 
     These are obtained by using the respective time values as the 
     follow-up time or response in the formula.

_V_a_l_u_e:

     if 'cohort=TRUE' an object of class 'survexp',  otherwise a vector
     of per-subject expected survival values.  The former contains the
     number of subjects at risk  and the expected survival for the
     cohort at each requested time.

_R_e_f_e_r_e_n_c_e_s:

     Berry, G. (1983). The analysis of mortality by the subject-years
     method.  _Biometrics_, 39:173-84.

     Ederer, F., Axtell, L. and Cutler, S. (1961).  The relative
     survival rate: a statistical methodology.  _Natl Cancer Inst
     Monogr_, 6:101-21.

     Hakulinen, T. (1982).  Cancer survival corrected for heterogeneity
     in patient withdrawal.  _Biometrics_, 38:933-942.

     Verheul, H., Dekker, E., Bossuyt, P., Moulijn, A. and Dunning, A.
     (1993).  Background mortality in clinical survival studies. 
     _Lancet_, 341: 872-875.

_S_e_e _A_l_s_o:

     'survfit', 'pyears',  'survexp.us',  'survexp.fit'.

_E_x_a_m_p_l_e_s:

     # 
     # Stanford heart transplant data
     # Estimate of conditional survival  
     survexp(futime ~ ratetable(sex="male", year=accept.dt,   
               age=(accept.dt-birth.dt)), conditional=TRUE, data=jasa) 
     # Estimate of conditional survival stratified by prior surgery 
     survexp(futime ~ surgery + ratetable(sex="male", year=accept.dt,  
             age=(accept.dt-birth.dt)), conditional=TRUE, data=jasa) 

     ## Compare the survival curves for the Mayo PBC data to Cox model fit
     ## 
     pfit <-coxph(Surv(time,status>0) ~ trt + log(bili) + log(protime) + age +
                     platelet, data=pbc)
     plot(survfit(Surv(time, status>0) ~ trt, data=pbc))
     lines(survexp( ~ trt, ratetable=pfit, data=pbc), col='purple')