SPSloess                package:USPS                R Documentation

_L_O_E_S_S _S_m_o_o_t_h_i_n_g _o_f _O_u_t_c_o_m_e _b_y _T_r_e_a_t_m_e_n_t _i_n _S_u_p_e_r_v_i_s_e_d _P_r_o_p_e_n_s_i_y _S_c_o_r_i_n_g

_D_e_s_c_r_i_p_t_i_o_n:

     Express Expected Outcome by Treatment as LOESS Smooths of Fitted
     Propensity Scores.

_U_s_a_g_e:

       losobj <- SPSloess(dframe, trtm, pscr, yvar, faclev=3, deg=2, span=0.75, fam="symmetric")

_A_r_g_u_m_e_n_t_s:

  dframe: data.frame of the form returned by SPSlogit().

    trtm: the two-level factor on the left-hand-side in the formula
          argument to SPSlogit().

    pscr: fitted propensity scores of the form returned by SPSlogit().

    yvar: continuous outcome measure or result unknown at the time
          patient was assigned (possibly non-randomly) to treatment;
          "NA"s are allowed in yvar.

  faclev: optional; maximum number of distinct numerical values a
          variable can assume and yet still be converted into a factor
          variable; faclev=1 causes a binary indicator to be treated as
          a continuous variable determining a proportion.

     deg: optional; degree (1=linear or 2=quadratic) of the local fit.

    span: optional; span (0 to 2) argument for the loess() function.

     fam: optional; "gaussian" or "symmetric".

_D_e_t_a_i_l_s:

     Once one has fitted a somewhat smooth curve through scatters of
     observed outcomes, Y, versus the fitted propensity scores, X, for
     the patients in each of the two treatment groups, one can consider
     the question: "Over the range where both smooth curves are defined
     (i.e. their common support), what is the (weighted) average signed
     difference between these two curves?"

     If the distribution of patients (either treated or untreated) were
     UNIFORM over this range, the (unweighted) average signed
     difference (treated minus untreated) would be an appropriate
     estimate of the overall difference in outcome due to choice of
     treatment.

     Histogram patient counts within 100 cells of width 0.01 provide a
     naive "non-parametric density estimate" for the distribution of
     total patients (treated or untreated) along the propensity score
     axis.  The weighted average difference (and standard error)
     displayed by SPSsmoot() are based on an R density() smooth of
     these counts.

     In situations where the propensity scoring distribution for all
     patients in a therapeutic class is known to differ from that of
     the patients within the current study, that population weighted
     average would also be of interest.  Thus the SPSloess() output
     object contains two data frames, logrid and lofit, useful in
     further computations.

_V_a_l_u_e:

     An output list object of class SPSloess: 

  logrid: loess grid data.frame containing 11 variables and 100
          observations. The PS variable contains propensity score "cell
          means" of 0.005 to 0.995 in steps of 0.010. Variables F0, S0
          and C0 for treatment 0 and variables F1, S1 and C1 for
          treatment 1 contain fitted smooth spline values, standard
          error estimates and patient counts, respectively.  The DIF
          variable is simply (F1\-F0), the SED variable is
          sqrt(S1\^2+S0\^2), the HST variable is proportional to
          (C0+C1), and the DEN variable is the estimated probability
          density of patients along the PS axis.  Observations with
          "NA" for variables F0, S0, F1 or S1 represent "extremes"
          where the lowess fits could not be extrapolated because no
          observed outcomes were available.

losub0, losub1: loess fit data.frame contains 4 variables for each
          distinct PS value in lofit. These 4 variables are named PS,
          YAVG, TRT==0 and 1, respectively, and FIT = spline prediction
          for the specified degrees-of-freedom (default df=1.)

    span: loess span setting.

  lotdif: outcome treatment difference mean.

  lotsde: outcome treatment difference standard deviation.

_A_u_t_h_o_r(_s):

     Bob Obenchain <sunsetstats@earthlink.net>

_R_e_f_e_r_e_n_c_e_s:

     Cleveland WS, Devlin SJ. (1988) Locally-weighted regression: an
     approach to regression analysis by local fitting. _J Amer Stat
     Assoc_ *83*: 596-610.

     Cleveland WS, Grosse E, Shyu WM. (1992) Local regression models.
     Chapter 8 of *Statistical Models in S* eds Chambers JM and Hastie
     TJ. _Wadsworth & Brooks/Cole_.

     Obenchain RL. (2005) *USPSinR.pdf*  ../R_HOME/library/USPS  40
     pages.

     Ripley BD, loess() based on the 'cloess' package of Cleveland,
     Grosse and Shyu.

_S_e_e _A_l_s_o:

     'SPSlogit', 'SPSsmoot' and 'SPSoutco'.

_E_x_a_m_p_l_e_s:

       data(lindner)
       PStreat <- abcix~stent+height+female+diabetic+acutemi+ejecfrac+ves1proc
       logtSPS <- SPSlogit(lindner, PStreat, PSfit, PSrnk, PSbin, appn="lindSPS")

       SPScbls5 <- SPSloess(lindSPS, abcix, PSfit, cardbill, span=.5)
       SPScbls5 
       plot(SPScbls5)   

