patch               package:bootstrap               R Documentation

_T_h_e _P_a_t_c_h _D_a_t_a

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

     Eight subjects wore medical patches designed to infuse a
     naturally-occuring hormone into the blood stream.

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

     data(patch)

_F_o_r_m_a_t:

     A data frame with 8 observations on the following 6 variables.

     _s_u_b_j_e_c_t a numeric vector

     _p_l_a_c_e_b_o a numeric vector

     _o_l_d_p_a_t_c_h a numeric vector

     _n_e_w_p_a_t_c_h a numeric vector

     _z a numeric vector, oldpatch - placebo

     _y a numeric vector, newpatch - oldpatch

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

     Eight subjects wore medical patches designed to infuse a certain
     naturally-occuring hormone into the blood stream. Each subject had
     his blood levels of the hormone measured after wearing three
     different patches: a placebo patch, an "old" patch manufactured at
     an older plant, and a "new" patch manufactured at a newly opened
     plant. 

     The purpose of the study was to show _bioequivalence_. Patchs from
     the old plant was already approved for sale by the FDA (food and
     drug  administration). Patches from the new facility would not
     need a full new approval, if they could be shown bioequivalent to
     the patches from  the old plant. 

     Bioequivalence was defined as 

             |E(new)-E(old)|/(E(old)-E(placebo)) <= 0.20


     The book uses this to investigate bias of ratio estimation.

_S_o_u_r_c_e:

     Efron, B. and Tibshirani, R. (1993) An Introduction to the
     Bootstrap.  Chapman and Hall, New York, London.

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

     str(patch) 
      theta <- function(ind){
           Y <- patch[ind,"y"]
           Z <- patch[ind,"z"]
           mean(Y)/mean(Z) }
     patch.boot <- bootstrap(1:8, 2000, theta)
     names(patch.boot)          
     hist(patch.boot$thetastar)
     abline(v=c(-0.2, 0.2), col="red2")
     theta(1:8) #sample plug-in estimator
     abline(v=theta(1:8) , col="blue")
     # The bootstrap bias estimate:
     mean(patch.boot$thetastar) - theta(1:8)
     sd(patch.boot$thetastar) # bootstrapped standard error

