R/eefun_NEH.R
In bblette1/psbinary: Assess effect modification by binary post-randomization variable
Defines functions
eefun_NEH
# Estimating equation vector for ignorance interval under NEH
# Used for M estimation variance calculation
eefun_NEH <- function(data, beta0range, beta1range, beta2range, beta3range,
contrast, design, whichmin_00, whichmax_00,
whichmin_10, whichmax_10,
whichmin_diff, whichmax_diff) {
function(theta) {
with(data,
c( # Identifiable terms
# risk_0 = theta[1]
(1-Y_tau)*(1-Z)*(Y-theta[1]),
# v = theta[2]
theta[2]*(1-Y_tau)*Z - (1-Y_tau)*(1-Z),
# p_1 = theta[3]
(1-Y_tau)*Z*((!is.na(S_star) & S_star==1)-theta[3])*W*
(design != "cc") +
(1-Y_tau)*Z*((!is.na(S_star) & S_star==1)-theta[3])*W*
(1/theta[47]*(1-Y)*R+Y)*(design == "cc"),
# Partially identifiable terms and helpers
# p_10_first = theta[4]
theta[4]*theta[2] + theta[5]*(1-theta[2]) - theta[3],
# p_10_mix_first = theta[5]
exp(min(beta3range))*theta[5]/(1-theta[5]) -
theta[4]/(1-theta[4]),
# p_10_second = theta[6]
theta[6]*theta[2] + theta[7]*(1-theta[2]) - theta[3],
# p_10_mix_second = theta[7]
exp(max(beta3range))*theta[7]/(1-theta[7]) -
theta[6]/(1-theta[6]),
# risk_0_00_first = theta[8]
theta[1] - theta[8]*(1-theta[4]) - theta[9]*theta[4],
# risk_0_10_first = theta[9]
exp(min(beta0range))*theta[9]/(1-theta[9]) -
theta[8]/(1-theta[8]),
# risk_0_00_second = theta[10]
theta[1] - theta[10]*(1-theta[4]) - theta[11]*theta[4],
# risk_0_10_second = theta[11]
exp(max(beta0range))*theta[11]/(1-theta[11]) -
theta[10]/(1-theta[10]),
# risk_0_00_third = theta[12]
theta[1] - theta[12]*(1-theta[6]) - theta[13]*theta[6],
# risk_0_10_third = theta[13]
exp(min(beta0range))*theta[13]/(1-theta[13]) -
theta[12]/(1-theta[12]),
# risk_0_00_fourth = theta[14]
theta[1] - theta[14]*(1-theta[6]) - theta[15]*theta[6],
# risk_0_10_fourth = theta[15]
exp(max(beta0range))*theta[15]/(1-theta[15]) -
theta[14]/(1-theta[14]),
# row1 = theta[16]
Z*(1-Y_tau)*(!is.na(S_star) & S_star==0)*W*(Y-theta[16])*
(design != "cc") +
Z*(1-Y_tau)*(!is.na(S_star) & S_star==0)*W*(Y-theta[16])*
(1/theta[47]*(1-Y)*R+Y)*(design == "cc"),
# Ytau_prob = theta[17]
(1-Z)*(1-Y_tau-theta[17]),
# r1_00_helper = theta[18]
(1-Y_tau)*(!is.na(S_star) & S_star==0)*Z*W - Z*theta[18]*
(design != "cc") +
(1-Y_tau)*(!is.na(S_star) & S_star==0)*Z*W - Z*theta[18]*
(1/theta[47]*(1-Y)*R+Y)*(design == "cc"),
# r1_00_mix_first = theta[19]
(1-theta[4])*theta[17] - theta[19]*theta[18], # r1_00_mix_second = theta[20]
(1-theta[6])*theta[17] - theta[20]*theta[18],
# risk_1_00_first = theta[21]
theta[16] - theta[21]*theta[19] - theta[22]*(1-theta[19]),
# risk_1_0star_first = theta[22]
exp(min(beta1range))*theta[22]/(1-theta[22]) -
theta[21]/(1-theta[21]),
# risk_1_00_second = theta[23]
theta[16] - theta[23]*theta[19] - theta[24]*(1-theta[19]),
# risk_1_0star_second = theta[24]
exp(max(beta1range))*theta[24]/(1-theta[24]) -
theta[23]/(1-theta[23]),
# risk_1_00_third = theta[25]
theta[16] - theta[25]*theta[20] - theta[26]*(1-theta[20]),
# risk_1_0star_third = theta[26]
exp(min(beta1range))*theta[26]/(1-theta[26]) -
theta[25]/(1-theta[25]),
# risk_1_00_fourth = theta[27]
theta[16] - theta[27]*theta[20] - theta[28]*(1-theta[20]),
# risk_1_0star_fourth = theta[28]
exp(max(beta1range))*theta[28]/(1-theta[28]) -
theta[27]/(1-theta[27]),
# row2 = theta[29]
Z*(1-Y_tau)*(!is.na(S_star) & S_star==1)*W*(Y-theta[29])*
(design != "cc") +
Z*(1-Y_tau)*(!is.na(S_star) & S_star==1)*W*(Y-theta[29])*
(1/theta[47]*(1-Y)*R+Y)*(design == "cc"),
# Ytau_prob1 = theta[30]
Z*(1-Y_tau-theta[30]),
# r_10_mix_first = theta[31]
theta[4]*theta[19] - theta[31]*theta[30]*theta[3],
# r_10_mix_second = theta[32]
theta[6]*theta[20] - theta[32]*theta[30]*theta[3],
# risk_1_10_first = theta[33]
theta[29] - theta[33]*theta[31] - theta[34]*(1-theta[31]),
# risk_1_1star_first = theta[34]
exp(min(beta2range))*theta[34]/(1-theta[34]) -
theta[33]/(1-theta[33]),
# risk_1_10_second = theta[35]
theta[29] - theta[35]*theta[31] - theta[36]*(1-theta[31]),
# risk_1_1star_second = theta[36]
exp(max(beta2range))*theta[36]/(1-theta[36]) -
theta[35]/(1-theta[35]),
# risk_1_10_third = theta[37]
theta[29] - theta[37]*theta[32] - theta[38]*(1-theta[32]),
# risk_1_1star_third = theta[38]
exp(min(beta2range))*theta[38]/(1-theta[38]) -
theta[37]/(1-theta[37]),
# risk_1_10_fourth = theta[39]
theta[29] - theta[39]*theta[32] - theta[40]*(1-theta[32]),
# risk_1_1star_fourth = theta[40]
exp(max(beta2range))*theta[40]/(1-theta[40]) -
theta[39]/(1-theta[39]),
# CEP terms
# Lower bound of CEP(0, 0) = theta[41]
( theta[41] - (1- theta[21]/theta[8]) )*
(contrast == "VE" & whichmin_00 == 1) +
( theta[41] - (1- theta[21]/theta[10]) )*
(contrast == "VE" & whichmin_00 == 2) +
( theta[41] - (1- theta[23]/theta[8]) )*
(contrast == "VE" & whichmin_00 == 3) +
( theta[41] - (1- theta[23]/theta[10]) )*
(contrast == "VE" & whichmin_00 == 4) +
( theta[41] - (1- theta[25]/theta[12]) )*
(contrast == "VE" & whichmin_00 == 5) +
( theta[41] - (1- theta[25]/theta[14]) )*
(contrast == "VE" & whichmin_00 == 6) +
( theta[41] - (1- theta[27]/theta[12]) )*
(contrast == "VE" & whichmin_00 == 7) +
( theta[41] - (1- theta[27]/theta[14]) )*
(contrast == "VE" & whichmin_00 == 8) +
( theta[41] - (theta[21] - theta[8]) )*
(contrast == "Difference" & whichmin_00 == 1) +
( theta[41] - (theta[21] - theta[10]) )*
(contrast == "Difference" & whichmin_00 == 2) +
( theta[41] - (theta[23] - theta[8]) )*
(contrast == "Difference" & whichmin_00 == 3) +
( theta[41] - (theta[23] - theta[10]) )*
(contrast == "Difference" & whichmin_00 == 4) +
( theta[41] - (theta[25] - theta[12]) )*
(contrast == "Difference" & whichmin_00 == 5) +
( theta[41] - (theta[25] - theta[14]) )*
(contrast == "Difference" & whichmin_00 == 6) +
( theta[41] - (theta[27] - theta[12]) )*
(contrast == "Difference" & whichmin_00 == 7) +
( theta[41] - (theta[27] - theta[14]) )*
(contrast == "Difference" & whichmin_00 == 8) +
( theta[41] - (log(theta[21]) - log(theta[8])) )*
(contrast == "logRR" & whichmin_00 == 1) +
( theta[41] - (log(theta[21]) - log(theta[10])) )*
(contrast == "logRR" & whichmin_00 == 2) +
( theta[41] - (log(theta[23]) - log(theta[8])) )*
(contrast == "logRR" & whichmin_00 == 3) +
( theta[41] - (log(theta[23]) - log(theta[10])) )*
(contrast == "logRR" & whichmin_00 == 4) +
( theta[41] - (log(theta[25]) - log(theta[12])) )*
(contrast == "logRR" & whichmin_00 == 5) +
( theta[41] - (log(theta[25]) - log(theta[14])) )*
(contrast == "logRR" & whichmin_00 == 6) +
( theta[41] - (log(theta[27]) - log(theta[12])) )*
(contrast == "logRR" & whichmin_00 == 7) +
( theta[41] - (log(theta[27]) - log(theta[14])) )*
(contrast == "logRR" & whichmin_00 == 8),
# Upper bound of CEP(0, 0) = theta[42]
( theta[42] - (1- theta[21]/theta[8]) )*
(contrast == "VE" & whichmax_00 == 1) +
( theta[42] - (1- theta[21]/theta[10]) )*
(contrast == "VE" & whichmax_00 == 2) +
( theta[42] - (1- theta[23]/theta[8]) )*
(contrast == "VE" & whichmax_00 == 3) +
( theta[42] - (1- theta[23]/theta[10]) )*
(contrast == "VE" & whichmax_00 == 4) +
( theta[42] - (1- theta[25]/theta[12]) )*
(contrast == "VE" & whichmax_00 == 5) +
( theta[42] - (1- theta[25]/theta[14]) )*
(contrast == "VE" & whichmax_00 == 6) +
( theta[42] - (1- theta[27]/theta[12]) )*
(contrast == "VE" & whichmax_00 == 7) +
( theta[42] - (1- theta[27]/theta[14]) )*
(contrast == "VE" & whichmax_00 == 8) +
( theta[42] - (theta[21] - theta[8]) )*
(contrast == "Difference" & whichmax_00 == 1) +
( theta[42] - (theta[21] - theta[10]) )*
(contrast == "Difference" & whichmax_00 == 2) +
( theta[42] - (theta[23] - theta[8]) )*
(contrast == "Difference" & whichmax_00 == 3) +
( theta[42] - (theta[23] - theta[10]) )*
(contrast == "Difference" & whichmax_00 == 4) +
( theta[42] - (theta[25] - theta[12]) )*
(contrast == "Difference" & whichmax_00 == 5) +
( theta[42] - (theta[25] - theta[14]) )*
(contrast == "Difference" & whichmax_00 == 6) +
( theta[42] - (theta[27] - theta[12]) )*
(contrast == "Difference" & whichmax_00 == 7) +
( theta[42] - (theta[27] - theta[14]) )*
(contrast == "Difference" & whichmax_00 == 8) +
( theta[42] - (log(theta[21]) - log(theta[8])) )*
(contrast == "logRR" & whichmax_00 == 1) +
( theta[42] - (log(theta[21]) - log(theta[10])) )*
(contrast == "logRR" & whichmax_00 == 2) +
( theta[42] - (log(theta[23]) - log(theta[8])) )*
(contrast == "logRR" & whichmax_00 == 3) +
( theta[42] - (log(theta[23]) - log(theta[10])) )*
(contrast == "logRR" & whichmax_00 == 4) +
( theta[42] - (log(theta[25]) - log(theta[12])) )*
(contrast == "logRR" & whichmax_00 == 5) +
( theta[42] - (log(theta[25]) - log(theta[14])) )*
(contrast == "logRR" & whichmax_00 == 6) +
( theta[42] - (log(theta[27]) - log(theta[12])) )*
(contrast == "logRR" & whichmax_00 == 7) +
( theta[42] - (log(theta[27]) - log(theta[14])) )*
(contrast == "logRR" & whichmax_00 == 8),
# Lower bound of CEP(1, 0) = theta[43]
( theta[43] - (1- theta[33]/theta[9]) )*
(contrast == "VE" & whichmin_10 == 1) +
( theta[43] - (1- theta[33]/theta[11]) )*
(contrast == "VE" & whichmin_10 == 2) +
( theta[43] - (1- theta[35]/theta[9]) )*
(contrast == "VE" & whichmin_10 == 3) +
( theta[43] - (1- theta[35]/theta[11]) )*
(contrast == "VE" & whichmin_10 == 4) +
( theta[43] - (1- theta[37]/theta[13]) )*
(contrast == "VE" & whichmin_10 == 5) +
( theta[43] - (1- theta[37]/theta[15]) )*
(contrast == "VE" & whichmin_10 == 6) +
( theta[43] - (1- theta[39]/theta[13]) )*
(contrast == "VE" & whichmin_10 == 7) +
( theta[43] - (1- theta[39]/theta[15]) )*
(contrast == "VE" & whichmin_10 == 8) +
( theta[43] - (theta[33] - theta[9]) )*
(contrast == "Difference" & whichmin_10 == 1) +
( theta[43] - (theta[33] - theta[11]) )*
(contrast == "Difference" & whichmin_10 == 2) +
( theta[43] - (theta[35] - theta[9]) )*
(contrast == "Difference" & whichmin_10 == 3) +
( theta[43] - (theta[35] - theta[11]) )*
(contrast == "Difference" & whichmin_10 == 4) +
( theta[43] - (theta[37] - theta[13]) )*
(contrast == "Difference" & whichmin_10 == 5) +
( theta[43] - (theta[37] - theta[15]) )*
(contrast == "Difference" & whichmin_10 == 6) +
( theta[43] - (theta[39] - theta[13]) )*
(contrast == "Difference" & whichmin_10 == 7) +
( theta[43] - (theta[39] - theta[15]) )*
(contrast == "Difference" & whichmin_10 == 8) +
( theta[43] - (log(theta[33]) - log(theta[9])) )*
(contrast == "logRR" & whichmin_10 == 1) +
( theta[43] - (log(theta[33]) - log(theta[11])) )*
(contrast == "logRR" & whichmin_10 == 2) +
( theta[43] - (log(theta[35]) - log(theta[9])) )*
(contrast == "logRR" & whichmin_10 == 3) +
( theta[43] - (log(theta[35]) - log(theta[11])) )*
(contrast == "logRR" & whichmin_10 == 4) +
( theta[43] - (log(theta[37]) - log(theta[13])) )*
(contrast == "logRR" & whichmin_10 == 5) +
( theta[43] - (log(theta[37]) - log(theta[15])) )*
(contrast == "logRR" & whichmin_10 == 6) +
( theta[43] - (log(theta[39]) - log(theta[13])) )*
(contrast == "logRR" & whichmin_10 == 7) +
( theta[43] - (log(theta[39]) - log(theta[15])) )*
(contrast == "logRR" & whichmin_10 == 8),
# Upper bound of CEP(1, 0) = theta[44]
( theta[44] - (1- theta[33]/theta[9]) )*
(contrast == "VE" & whichmax_10 == 1) +
( theta[44] - (1- theta[33]/theta[11]) )*
(contrast == "VE" & whichmax_10 == 2) +
( theta[44] - (1- theta[35]/theta[9]) )*
(contrast == "VE" & whichmax_10 == 3) +
( theta[44] - (1- theta[35]/theta[11]) )*
(contrast == "VE" & whichmax_10 == 4) +
( theta[44] - (1- theta[37]/theta[13]) )*
(contrast == "VE" & whichmax_10 == 5) +
( theta[44] - (1- theta[37]/theta[15]) )*
(contrast == "VE" & whichmax_10 == 6) +
( theta[44] - (1- theta[39]/theta[13]) )*
(contrast == "VE" & whichmax_10 == 7) +
( theta[44] - (1- theta[39]/theta[15]) )*
(contrast == "VE" & whichmax_10 == 8) +
( theta[44] - (theta[33] - theta[9]) )*
(contrast == "Difference" & whichmax_10 == 1) +
( theta[44] - (theta[33] - theta[11]) )*
(contrast == "Difference" & whichmax_10 == 2) +
( theta[44] - (theta[35] - theta[9]) )*
(contrast == "Difference" & whichmax_10 == 3) +
( theta[44] - (theta[35] - theta[11]) )*
(contrast == "Difference" & whichmax_10 == 4) +
( theta[44] - (theta[37] - theta[13]) )*
(contrast == "Difference" & whichmax_10 == 5) +
( theta[44] - (theta[37] - theta[15]) )*
(contrast == "Difference" & whichmax_10 == 6) +
( theta[44] - (theta[39] - theta[13]) )*
(contrast == "Difference" & whichmax_10 == 7) +
( theta[44] - (theta[39] - theta[15]) )*
(contrast == "Difference" & whichmax_10 == 8) +
( theta[44] - (log(theta[33]) - log(theta[9])) )*
(contrast == "logRR" & whichmax_10 == 1) +
( theta[44] - (log(theta[33]) - log(theta[11])) )*
(contrast == "logRR" & whichmax_10 == 2) +
( theta[44] - (log(theta[35]) - log(theta[9])) )*
(contrast == "logRR" & whichmax_10 == 3) +
( theta[44] - (log(theta[35]) - log(theta[11])) )*
(contrast == "logRR" & whichmax_10 == 4) +
( theta[44] - (log(theta[37]) - log(theta[13])) )*
(contrast == "logRR" & whichmax_10 == 5) +
( theta[44] - (log(theta[37]) - log(theta[15])) )*
(contrast == "logRR" & whichmax_10 == 6) +
( theta[44] - (log(theta[39]) - log(theta[13])) )*
(contrast == "logRR" & whichmax_10 == 7) +
( theta[44] - (log(theta[39]) - log(theta[15])) )*
(contrast == "logRR" & whichmax_10 == 8),
# Lower bound of CEP(1, 0) - CEP(0, 0) = theta[45]
( theta[45] - (1 - theta[33]/theta[9]) +
(1 - theta[21]/theta[8]) )*
(contrast == "VE" & whichmin_diff == 1) +
( theta[45] - (1 - theta[33]/theta[9]) +
(1 - theta[23]/theta[8]) )*
(contrast == "VE" & whichmin_diff == 2) +
( theta[45] - (1 - theta[33]/theta[11]) +
(1 - theta[21]/theta[10]) )*
(contrast == "VE" & whichmin_diff == 3) +
( theta[45] - (1 - theta[33]/theta[11]) +
(1 - theta[23]/theta[10]) )*
(contrast == "VE" & whichmin_diff == 4) +
( theta[45] - (1 - theta[35]/theta[9]) +
(1 - theta[21]/theta[8]) )*
(contrast == "VE" & whichmin_diff == 5) +
( theta[45] - (1 - theta[35]/theta[9]) +
(1 - theta[23]/theta[8]) )*
(contrast == "VE" & whichmin_diff == 6) +
( theta[45] - (1 - theta[35]/theta[11]) +
(1 - theta[21]/theta[10]) )*
(contrast == "VE" & whichmin_diff == 7) +
( theta[45] - (1 - theta[35]/theta[11]) +
(1 - theta[23]/theta[10]) )*
(contrast == "VE" & whichmin_diff == 8) +
( theta[45] - (1 - theta[37]/theta[13]) +
(1 - theta[25]/theta[12]) )*
(contrast == "VE" & whichmin_diff == 9) +
( theta[45] - (1 - theta[37]/theta[13]) +
(1 - theta[27]/theta[12]) )*
(contrast == "VE" & whichmin_diff == 10) +
( theta[45] - (1 - theta[37]/theta[15]) +
(1 - theta[25]/theta[14]) )*
(contrast == "VE" & whichmin_diff == 11) +
( theta[45] - (1 - theta[37]/theta[15]) +
(1 - theta[27]/theta[14]) )*
(contrast == "VE" & whichmin_diff == 12) +
( theta[45] - (1 - theta[39]/theta[13]) +
(1 - theta[25]/theta[12]) )*
(contrast == "VE" & whichmin_diff == 13) +
( theta[45] - (1 - theta[39]/theta[13]) +
(1 - theta[27]/theta[12]) )*
(contrast == "VE" & whichmin_diff == 14) +
( theta[45] - (1 - theta[39]/theta[15]) +
(1 - theta[25]/theta[14]) )*
(contrast == "VE" & whichmin_diff == 15) +
( theta[45] - (1 - theta[39]/theta[15]) +
(1 - theta[27]/theta[14]) )*
(contrast == "VE" & whichmin_diff == 16) +
( theta[45] - (theta[33] - theta[9]) +
(theta[21] - theta[8]) )*
(contrast == "Difference" & whichmin_diff == 1) +
( theta[45] - (theta[33] - theta[9]) +
(theta[23] - theta[8]) )*
(contrast == "Difference" & whichmin_diff == 2) +
( theta[45] - (theta[33] - theta[11]) +
(theta[21] - theta[10]) )*
(contrast == "Difference" & whichmin_diff == 3) +
( theta[45] - (theta[33] - theta[11]) +
(theta[23] - theta[10]) )*
(contrast == "Difference" & whichmin_diff == 4) +
( theta[45] - (theta[35] - theta[9]) +
(theta[21] - theta[8]) )*
(contrast == "Difference" & whichmin_diff == 5) +
( theta[45] - (theta[35] - theta[9]) +
(theta[23] - theta[8]) )*
(contrast == "Difference" & whichmin_diff == 6) +
( theta[45] - (theta[35] - theta[11]) +
(theta[21] - theta[10]) )*
(contrast == "Difference" & whichmin_diff == 7) +
( theta[45] - (theta[35] - theta[11]) +
(theta[23] - theta[10]) )*
(contrast == "Difference" & whichmin_diff == 8) +
( theta[45] - (theta[37] - theta[13]) +
(theta[25] - theta[12]) )*
(contrast == "Difference" & whichmin_diff == 9) +
( theta[45] - (theta[37] - theta[13]) +
(theta[27] - theta[12]) )*
(contrast == "Difference" & whichmin_diff == 10) +
( theta[45] - (theta[37] - theta[15]) +
(theta[25] - theta[14]) )*
(contrast == "Difference" & whichmin_diff == 11) +
( theta[45] - (theta[37] - theta[15]) +
(theta[27] - theta[14]) )*
(contrast == "Difference" & whichmin_diff == 12) +
( theta[45] - (theta[39] - theta[13]) +
(theta[25] - theta[12]) )*
(contrast == "Difference" & whichmin_diff == 13) +
( theta[45] - (theta[39] - theta[13]) +
(theta[27] - theta[12]) )*
(contrast == "Difference" & whichmin_diff == 14) +
( theta[45] - (theta[39] - theta[15]) +
(theta[25] - theta[14]) )*
(contrast == "Difference" & whichmin_diff == 15) +
( theta[45] - (theta[39] - theta[15]) +
(theta[27] - theta[14]) )*
(contrast == "Difference" & whichmin_diff == 16) +
( theta[45] - (log(theta[33]) - log(theta[9])) +
(log(theta[21]) - log(theta[8])) )*
(contrast == "logRR" & whichmin_diff == 1) +
( theta[45] - (log(theta[33]) - log(theta[9])) +
(log(theta[23]) - log(theta[8])) )*
(contrast == "logRR" & whichmin_diff == 2) +
( theta[45] - (log(theta[33]) - log(theta[11])) +
(log(theta[21]) - log(theta[10])) )*
(contrast == "logRR" & whichmin_diff == 3) +
( theta[45] - (log(theta[33]) - log(theta[11])) +
(log(theta[23]) - log(theta[10])) )*
(contrast == "logRR" & whichmin_diff == 4) +
( theta[45] - (log(theta[35]) - log(theta[9])) +
(log(theta[21]) - log(theta[8])) )*
(contrast == "logRR" & whichmin_diff == 5) +
( theta[45] - (log(theta[35]) - log(theta[9])) +
(log(theta[23]) - log(theta[8])) )*
(contrast == "logRR" & whichmin_diff == 6) +
( theta[45] - (log(theta[35]) - log(theta[11])) +
(log(theta[21]) - log(theta[10])) )*
(contrast == "logRR" & whichmin_diff == 7) +
( theta[45] - (log(theta[35]) - log(theta[11])) +
(log(theta[23]) - log(theta[10])) )*
(contrast == "logRR" & whichmin_diff == 8) +
( theta[45] - (log(theta[37]) - log(theta[13])) +
(log(theta[25]) - log(theta[12])) )*
(contrast == "logRR" & whichmin_diff == 9) +
( theta[45] - (log(theta[37]) - log(theta[13])) +
(log(theta[27]) - log(theta[12])) )*
(contrast == "logRR" & whichmin_diff == 10) +
( theta[45] - (log(theta[37]) - log(theta[15])) +
(log(theta[25]) - log(theta[14])) )*
(contrast == "logRR" & whichmin_diff == 11) +
( theta[45] - (log(theta[37]) - log(theta[15])) +
(log(theta[27]) - log(theta[14])) )*
(contrast == "logRR" & whichmin_diff == 12) +
( theta[45] - (log(theta[39]) - log(theta[13])) +
(log(theta[25]) - log(theta[12])) )*
(contrast == "logRR" & whichmin_diff == 13) +
( theta[45] - (log(theta[39]) - log(theta[13])) +
(log(theta[27]) - log(theta[12])) )*
(contrast == "logRR" & whichmin_diff == 14) +
( theta[45] - (log(theta[39]) - log(theta[15])) +
(log(theta[25]) - log(theta[14])) )*
(contrast == "logRR" & whichmin_diff == 15) +
( theta[45] - (log(theta[39]) - log(theta[15])) +
(log(theta[27]) - log(theta[14])) )*
(contrast == "logRR" & whichmin_diff == 16),
# Upper bound of CEP(1, 0) - CEP(0, 0) = theta[45]
( theta[46] - (1 - theta[33]/theta[9]) +
(1 - theta[21]/theta[8]) )*
(contrast == "VE" & whichmax_diff == 1) +
( theta[46] - (1 - theta[33]/theta[9]) +
(1 - theta[23]/theta[8]) )*
(contrast == "VE" & whichmax_diff == 2) +
( theta[46] - (1 - theta[33]/theta[11]) +
(1 - theta[21]/theta[10]) )*
(contrast == "VE" & whichmax_diff == 3) +
( theta[46] - (1 - theta[33]/theta[11]) +
(1 - theta[23]/theta[10]) )*
(contrast == "VE" & whichmax_diff == 4) +
( theta[46] - (1 - theta[35]/theta[9]) +
(1 - theta[21]/theta[8]) )*
(contrast == "VE" & whichmax_diff == 5) +
( theta[46] - (1 - theta[35]/theta[9]) +
(1 - theta[23]/theta[8]) )*
(contrast == "VE" & whichmax_diff == 6) +
( theta[46] - (1 - theta[35]/theta[11]) +
(1 - theta[21]/theta[10]) )*
(contrast == "VE" & whichmax_diff == 7) +
( theta[46] - (1 - theta[35]/theta[11]) +
(1 - theta[23]/theta[10]) )*
(contrast == "VE" & whichmax_diff == 8) +
( theta[46] - (1 - theta[37]/theta[13]) +
(1 - theta[25]/theta[12]) )*
(contrast == "VE" & whichmax_diff == 9) +
( theta[46] - (1 - theta[37]/theta[13]) +
(1 - theta[27]/theta[12]) )*
(contrast == "VE" & whichmax_diff == 10) +
( theta[46] - (1 - theta[37]/theta[15]) +
(1 - theta[25]/theta[14]) )*
(contrast == "VE" & whichmax_diff == 11) +
( theta[46] - (1 - theta[37]/theta[15]) +
(1 - theta[27]/theta[14]) )*
(contrast == "VE" & whichmax_diff == 12) +
( theta[46] - (1 - theta[39]/theta[13]) +
(1 - theta[25]/theta[12]) )*
(contrast == "VE" & whichmax_diff == 13) +
( theta[46] - (1 - theta[39]/theta[13]) +
(1 - theta[27]/theta[12]) )*
(contrast == "VE" & whichmax_diff == 14) +
( theta[46] - (1 - theta[39]/theta[15]) +
(1 - theta[25]/theta[14]) )*
(contrast == "VE" & whichmax_diff == 15) +
( theta[46] - (1 - theta[39]/theta[15]) +
(1 - theta[27]/theta[14]) )*
(contrast == "VE" & whichmax_diff == 16) +
( theta[46] - (theta[33] - theta[9]) +
(theta[21] - theta[8]) )*
(contrast == "Difference" & whichmax_diff == 1) +
( theta[46] - (theta[33] - theta[9]) +
(theta[23] - theta[8]) )*
(contrast == "Difference" & whichmax_diff == 2) +
( theta[46] - (theta[33] - theta[11]) +
(theta[21] - theta[10]) )*
(contrast == "Difference" & whichmax_diff == 3) +
( theta[46] - (theta[33] - theta[11]) +
(theta[23] - theta[10]) )*
(contrast == "Difference" & whichmax_diff == 4) +
( theta[46] - (theta[35] - theta[9]) +
(theta[21] - theta[8]) )*
(contrast == "Difference" & whichmax_diff == 5) +
( theta[46] - (theta[35] - theta[9]) +
(theta[23] - theta[8]) )*
(contrast == "Difference" & whichmax_diff == 6) +
( theta[46] - (theta[35] - theta[11]) +
(theta[21] - theta[10]) )*
(contrast == "Difference" & whichmax_diff == 7) +
( theta[46] - (theta[35] - theta[11]) +
(theta[23] - theta[10]) )*
(contrast == "Difference" & whichmax_diff == 8) +
( theta[46] - (theta[37] - theta[13]) +
(theta[25] - theta[12]) )*
(contrast == "Difference" & whichmax_diff == 9) +
( theta[46] - (theta[37] - theta[13]) +
(theta[27] - theta[12]) )*
(contrast == "Difference" & whichmax_diff == 10) +
( theta[46] - (theta[37] - theta[15]) +
(theta[25] - theta[14]) )*
(contrast == "Difference" & whichmax_diff == 11) +
( theta[46] - (theta[37] - theta[15]) +
(theta[27] - theta[14]) )*
(contrast == "Difference" & whichmax_diff == 12) +
( theta[46] - (theta[39] - theta[13]) +
(theta[25] - theta[12]) )*
(contrast == "Difference" & whichmax_diff == 13) +
( theta[46] - (theta[39] - theta[13]) +
(theta[27] - theta[12]) )*
(contrast == "Difference" & whichmax_diff == 14) +
( theta[46] - (theta[39] - theta[15]) +
(theta[25] - theta[14]) )*
(contrast == "Difference" & whichmax_diff == 15) +
( theta[46] - (theta[39] - theta[15]) +
(theta[27] - theta[14]) )*
(contrast == "Difference" & whichmax_diff == 16) +
( theta[46] - (log(theta[33]) - log(theta[9])) +
(log(theta[21]) - log(theta[8])) )*
(contrast == "logRR" & whichmax_diff == 1) +
( theta[46] - (log(theta[33]) - log(theta[9])) +
(log(theta[23]) - log(theta[8])) )*
(contrast == "logRR" & whichmax_diff == 2) +
( theta[46] - (log(theta[33]) - log(theta[11])) +
(log(theta[21]) - log(theta[10])) )*
(contrast == "logRR" & whichmax_diff == 3) +
( theta[46] - (log(theta[33]) - log(theta[11])) +
(log(theta[23]) - log(theta[10])) )*
(contrast == "logRR" & whichmax_diff == 4) +
( theta[46] - (log(theta[35]) - log(theta[9])) +
(log(theta[21]) - log(theta[8])) )*
(contrast == "logRR" & whichmax_diff == 5) +
( theta[46] - (log(theta[35]) - log(theta[9])) +
(log(theta[23]) - log(theta[8])) )*
(contrast == "logRR" & whichmax_diff == 6) +
( theta[46] - (log(theta[35]) - log(theta[11])) +
(log(theta[21]) - log(theta[10])) )*
(contrast == "logRR" & whichmax_diff == 7) +
( theta[46] - (log(theta[35]) - log(theta[11])) +
(log(theta[23]) - log(theta[10])) )*
(contrast == "logRR" & whichmax_diff == 8) +
( theta[46] - (log(theta[37]) - log(theta[13])) +
(log(theta[25]) - log(theta[12])) )*
(contrast == "logRR" & whichmax_diff == 9) +
( theta[46] - (log(theta[37]) - log(theta[13])) +
(log(theta[27]) - log(theta[12])) )*
(contrast == "logRR" & whichmax_diff == 10) +
( theta[46] - (log(theta[37]) - log(theta[15])) +
(log(theta[25]) - log(theta[14])) )*
(contrast == "logRR" & whichmax_diff == 11) +
( theta[46] - (log(theta[37]) - log(theta[15])) +
(log(theta[27]) - log(theta[14])) )*
(contrast == "logRR" & whichmax_diff == 12) +
( theta[46] - (log(theta[39]) - log(theta[13])) +
(log(theta[25]) - log(theta[12])) )*
(contrast == "logRR" & whichmax_diff == 13) +
( theta[46] - (log(theta[39]) - log(theta[13])) +
(log(theta[27]) - log(theta[12])) )*
(contrast == "logRR" & whichmax_diff == 14) +
( theta[46] - (log(theta[39]) - log(theta[15])) +
(log(theta[25]) - log(theta[14])) )*
(contrast == "logRR" & whichmax_diff == 15) +
( theta[46] - (log(theta[39]) - log(theta[15])) +
(log(theta[27]) - log(theta[14])) )*
(contrast == "logRR" & whichmax_diff == 16),
# pi = theta[47]
(1-Y)*(R-theta[47])
))
}
}
bblette1/psbinary documentation built on June 18, 2021, 10:11 p.m.
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Defines functions eefun_NEH
# Estimating equation vector for ignorance interval under NEH
# Used for M estimation variance calculation
eefun_NEH <- function(data, beta0range, beta1range, beta2range, beta3range,
contrast, design, whichmin_00, whichmax_00,
whichmin_10, whichmax_10,
whichmin_diff, whichmax_diff) {
function(theta) {
with(data,
c( # Identifiable terms
# risk_0 = theta[1]
(1-Y_tau)*(1-Z)*(Y-theta[1]),
# v = theta[2]
theta[2]*(1-Y_tau)*Z - (1-Y_tau)*(1-Z),
# p_1 = theta[3]
(1-Y_tau)*Z*((!is.na(S_star) & S_star==1)-theta[3])*W*
(design != "cc") +
(1-Y_tau)*Z*((!is.na(S_star) & S_star==1)-theta[3])*W*
(1/theta[47]*(1-Y)*R+Y)*(design == "cc"),
# Partially identifiable terms and helpers
# p_10_first = theta[4]
theta[4]*theta[2] + theta[5]*(1-theta[2]) - theta[3],
# p_10_mix_first = theta[5]
exp(min(beta3range))*theta[5]/(1-theta[5]) -
theta[4]/(1-theta[4]),
# p_10_second = theta[6]
theta[6]*theta[2] + theta[7]*(1-theta[2]) - theta[3],
# p_10_mix_second = theta[7]
exp(max(beta3range))*theta[7]/(1-theta[7]) -
theta[6]/(1-theta[6]),
# risk_0_00_first = theta[8]
theta[1] - theta[8]*(1-theta[4]) - theta[9]*theta[4],
# risk_0_10_first = theta[9]
exp(min(beta0range))*theta[9]/(1-theta[9]) -
theta[8]/(1-theta[8]),
# risk_0_00_second = theta[10]
theta[1] - theta[10]*(1-theta[4]) - theta[11]*theta[4],
# risk_0_10_second = theta[11]
exp(max(beta0range))*theta[11]/(1-theta[11]) -
theta[10]/(1-theta[10]),
# risk_0_00_third = theta[12]
theta[1] - theta[12]*(1-theta[6]) - theta[13]*theta[6],
# risk_0_10_third = theta[13]
exp(min(beta0range))*theta[13]/(1-theta[13]) -
theta[12]/(1-theta[12]),
# risk_0_00_fourth = theta[14]
theta[1] - theta[14]*(1-theta[6]) - theta[15]*theta[6],
# risk_0_10_fourth = theta[15]
exp(max(beta0range))*theta[15]/(1-theta[15]) -
theta[14]/(1-theta[14]),
# row1 = theta[16]
Z*(1-Y_tau)*(!is.na(S_star) & S_star==0)*W*(Y-theta[16])*
(design != "cc") +
Z*(1-Y_tau)*(!is.na(S_star) & S_star==0)*W*(Y-theta[16])*
(1/theta[47]*(1-Y)*R+Y)*(design == "cc"),
# Ytau_prob = theta[17]
(1-Z)*(1-Y_tau-theta[17]),
# r1_00_helper = theta[18]
(1-Y_tau)*(!is.na(S_star) & S_star==0)*Z*W - Z*theta[18]*
(design != "cc") +
(1-Y_tau)*(!is.na(S_star) & S_star==0)*Z*W - Z*theta[18]*
(1/theta[47]*(1-Y)*R+Y)*(design == "cc"),
# r1_00_mix_first = theta[19]
(1-theta[4])*theta[17] - theta[19]*theta[18], # r1_00_mix_second = theta[20]
(1-theta[6])*theta[17] - theta[20]*theta[18],
# risk_1_00_first = theta[21]
theta[16] - theta[21]*theta[19] - theta[22]*(1-theta[19]),
# risk_1_0star_first = theta[22]
exp(min(beta1range))*theta[22]/(1-theta[22]) -
theta[21]/(1-theta[21]),
# risk_1_00_second = theta[23]
theta[16] - theta[23]*theta[19] - theta[24]*(1-theta[19]),
# risk_1_0star_second = theta[24]
exp(max(beta1range))*theta[24]/(1-theta[24]) -
theta[23]/(1-theta[23]),
# risk_1_00_third = theta[25]
theta[16] - theta[25]*theta[20] - theta[26]*(1-theta[20]),
# risk_1_0star_third = theta[26]
exp(min(beta1range))*theta[26]/(1-theta[26]) -
theta[25]/(1-theta[25]),
# risk_1_00_fourth = theta[27]
theta[16] - theta[27]*theta[20] - theta[28]*(1-theta[20]),
# risk_1_0star_fourth = theta[28]
exp(max(beta1range))*theta[28]/(1-theta[28]) -
theta[27]/(1-theta[27]),
# row2 = theta[29]
Z*(1-Y_tau)*(!is.na(S_star) & S_star==1)*W*(Y-theta[29])*
(design != "cc") +
Z*(1-Y_tau)*(!is.na(S_star) & S_star==1)*W*(Y-theta[29])*
(1/theta[47]*(1-Y)*R+Y)*(design == "cc"),
# Ytau_prob1 = theta[30]
Z*(1-Y_tau-theta[30]),
# r_10_mix_first = theta[31]
theta[4]*theta[19] - theta[31]*theta[30]*theta[3],
# r_10_mix_second = theta[32]
theta[6]*theta[20] - theta[32]*theta[30]*theta[3],
# risk_1_10_first = theta[33]
theta[29] - theta[33]*theta[31] - theta[34]*(1-theta[31]),
# risk_1_1star_first = theta[34]
exp(min(beta2range))*theta[34]/(1-theta[34]) -
theta[33]/(1-theta[33]),
# risk_1_10_second = theta[35]
theta[29] - theta[35]*theta[31] - theta[36]*(1-theta[31]),
# risk_1_1star_second = theta[36]
exp(max(beta2range))*theta[36]/(1-theta[36]) -
theta[35]/(1-theta[35]),
# risk_1_10_third = theta[37]
theta[29] - theta[37]*theta[32] - theta[38]*(1-theta[32]),
# risk_1_1star_third = theta[38]
exp(min(beta2range))*theta[38]/(1-theta[38]) -
theta[37]/(1-theta[37]),
# risk_1_10_fourth = theta[39]
theta[29] - theta[39]*theta[32] - theta[40]*(1-theta[32]),
# risk_1_1star_fourth = theta[40]
exp(max(beta2range))*theta[40]/(1-theta[40]) -
theta[39]/(1-theta[39]),
# CEP terms
# Lower bound of CEP(0, 0) = theta[41]
( theta[41] - (1- theta[21]/theta[8]) )*
(contrast == "VE" & whichmin_00 == 1) +
( theta[41] - (1- theta[21]/theta[10]) )*
(contrast == "VE" & whichmin_00 == 2) +
( theta[41] - (1- theta[23]/theta[8]) )*
(contrast == "VE" & whichmin_00 == 3) +
( theta[41] - (1- theta[23]/theta[10]) )*
(contrast == "VE" & whichmin_00 == 4) +
( theta[41] - (1- theta[25]/theta[12]) )*
(contrast == "VE" & whichmin_00 == 5) +
( theta[41] - (1- theta[25]/theta[14]) )*
(contrast == "VE" & whichmin_00 == 6) +
( theta[41] - (1- theta[27]/theta[12]) )*
(contrast == "VE" & whichmin_00 == 7) +
( theta[41] - (1- theta[27]/theta[14]) )*
(contrast == "VE" & whichmin_00 == 8) +
( theta[41] - (theta[21] - theta[8]) )*
(contrast == "Difference" & whichmin_00 == 1) +
( theta[41] - (theta[21] - theta[10]) )*
(contrast == "Difference" & whichmin_00 == 2) +
( theta[41] - (theta[23] - theta[8]) )*
(contrast == "Difference" & whichmin_00 == 3) +
( theta[41] - (theta[23] - theta[10]) )*
(contrast == "Difference" & whichmin_00 == 4) +
( theta[41] - (theta[25] - theta[12]) )*
(contrast == "Difference" & whichmin_00 == 5) +
( theta[41] - (theta[25] - theta[14]) )*
(contrast == "Difference" & whichmin_00 == 6) +
( theta[41] - (theta[27] - theta[12]) )*
(contrast == "Difference" & whichmin_00 == 7) +
( theta[41] - (theta[27] - theta[14]) )*
(contrast == "Difference" & whichmin_00 == 8) +
( theta[41] - (log(theta[21]) - log(theta[8])) )*
(contrast == "logRR" & whichmin_00 == 1) +
( theta[41] - (log(theta[21]) - log(theta[10])) )*
(contrast == "logRR" & whichmin_00 == 2) +
( theta[41] - (log(theta[23]) - log(theta[8])) )*
(contrast == "logRR" & whichmin_00 == 3) +
( theta[41] - (log(theta[23]) - log(theta[10])) )*
(contrast == "logRR" & whichmin_00 == 4) +
( theta[41] - (log(theta[25]) - log(theta[12])) )*
(contrast == "logRR" & whichmin_00 == 5) +
( theta[41] - (log(theta[25]) - log(theta[14])) )*
(contrast == "logRR" & whichmin_00 == 6) +
( theta[41] - (log(theta[27]) - log(theta[12])) )*
(contrast == "logRR" & whichmin_00 == 7) +
( theta[41] - (log(theta[27]) - log(theta[14])) )*
(contrast == "logRR" & whichmin_00 == 8),
# Upper bound of CEP(0, 0) = theta[42]
( theta[42] - (1- theta[21]/theta[8]) )*
(contrast == "VE" & whichmax_00 == 1) +
( theta[42] - (1- theta[21]/theta[10]) )*
(contrast == "VE" & whichmax_00 == 2) +
( theta[42] - (1- theta[23]/theta[8]) )*
(contrast == "VE" & whichmax_00 == 3) +
( theta[42] - (1- theta[23]/theta[10]) )*
(contrast == "VE" & whichmax_00 == 4) +
( theta[42] - (1- theta[25]/theta[12]) )*
(contrast == "VE" & whichmax_00 == 5) +
( theta[42] - (1- theta[25]/theta[14]) )*
(contrast == "VE" & whichmax_00 == 6) +
( theta[42] - (1- theta[27]/theta[12]) )*
(contrast == "VE" & whichmax_00 == 7) +
( theta[42] - (1- theta[27]/theta[14]) )*
(contrast == "VE" & whichmax_00 == 8) +
( theta[42] - (theta[21] - theta[8]) )*
(contrast == "Difference" & whichmax_00 == 1) +
( theta[42] - (theta[21] - theta[10]) )*
(contrast == "Difference" & whichmax_00 == 2) +
( theta[42] - (theta[23] - theta[8]) )*
(contrast == "Difference" & whichmax_00 == 3) +
( theta[42] - (theta[23] - theta[10]) )*
(contrast == "Difference" & whichmax_00 == 4) +
( theta[42] - (theta[25] - theta[12]) )*
(contrast == "Difference" & whichmax_00 == 5) +
( theta[42] - (theta[25] - theta[14]) )*
(contrast == "Difference" & whichmax_00 == 6) +
( theta[42] - (theta[27] - theta[12]) )*
(contrast == "Difference" & whichmax_00 == 7) +
( theta[42] - (theta[27] - theta[14]) )*
(contrast == "Difference" & whichmax_00 == 8) +
( theta[42] - (log(theta[21]) - log(theta[8])) )*
(contrast == "logRR" & whichmax_00 == 1) +
( theta[42] - (log(theta[21]) - log(theta[10])) )*
(contrast == "logRR" & whichmax_00 == 2) +
( theta[42] - (log(theta[23]) - log(theta[8])) )*
(contrast == "logRR" & whichmax_00 == 3) +
( theta[42] - (log(theta[23]) - log(theta[10])) )*
(contrast == "logRR" & whichmax_00 == 4) +
( theta[42] - (log(theta[25]) - log(theta[12])) )*
(contrast == "logRR" & whichmax_00 == 5) +
( theta[42] - (log(theta[25]) - log(theta[14])) )*
(contrast == "logRR" & whichmax_00 == 6) +
( theta[42] - (log(theta[27]) - log(theta[12])) )*
(contrast == "logRR" & whichmax_00 == 7) +
( theta[42] - (log(theta[27]) - log(theta[14])) )*
(contrast == "logRR" & whichmax_00 == 8),
# Lower bound of CEP(1, 0) = theta[43]
( theta[43] - (1- theta[33]/theta[9]) )*
(contrast == "VE" & whichmin_10 == 1) +
( theta[43] - (1- theta[33]/theta[11]) )*
(contrast == "VE" & whichmin_10 == 2) +
( theta[43] - (1- theta[35]/theta[9]) )*
(contrast == "VE" & whichmin_10 == 3) +
( theta[43] - (1- theta[35]/theta[11]) )*
(contrast == "VE" & whichmin_10 == 4) +
( theta[43] - (1- theta[37]/theta[13]) )*
(contrast == "VE" & whichmin_10 == 5) +
( theta[43] - (1- theta[37]/theta[15]) )*
(contrast == "VE" & whichmin_10 == 6) +
( theta[43] - (1- theta[39]/theta[13]) )*
(contrast == "VE" & whichmin_10 == 7) +
( theta[43] - (1- theta[39]/theta[15]) )*
(contrast == "VE" & whichmin_10 == 8) +
( theta[43] - (theta[33] - theta[9]) )*
(contrast == "Difference" & whichmin_10 == 1) +
( theta[43] - (theta[33] - theta[11]) )*
(contrast == "Difference" & whichmin_10 == 2) +
( theta[43] - (theta[35] - theta[9]) )*
(contrast == "Difference" & whichmin_10 == 3) +
( theta[43] - (theta[35] - theta[11]) )*
(contrast == "Difference" & whichmin_10 == 4) +
( theta[43] - (theta[37] - theta[13]) )*
(contrast == "Difference" & whichmin_10 == 5) +
( theta[43] - (theta[37] - theta[15]) )*
(contrast == "Difference" & whichmin_10 == 6) +
( theta[43] - (theta[39] - theta[13]) )*
(contrast == "Difference" & whichmin_10 == 7) +
( theta[43] - (theta[39] - theta[15]) )*
(contrast == "Difference" & whichmin_10 == 8) +
( theta[43] - (log(theta[33]) - log(theta[9])) )*
(contrast == "logRR" & whichmin_10 == 1) +
( theta[43] - (log(theta[33]) - log(theta[11])) )*
(contrast == "logRR" & whichmin_10 == 2) +
( theta[43] - (log(theta[35]) - log(theta[9])) )*
(contrast == "logRR" & whichmin_10 == 3) +
( theta[43] - (log(theta[35]) - log(theta[11])) )*
(contrast == "logRR" & whichmin_10 == 4) +
( theta[43] - (log(theta[37]) - log(theta[13])) )*
(contrast == "logRR" & whichmin_10 == 5) +
( theta[43] - (log(theta[37]) - log(theta[15])) )*
(contrast == "logRR" & whichmin_10 == 6) +
( theta[43] - (log(theta[39]) - log(theta[13])) )*
(contrast == "logRR" & whichmin_10 == 7) +
( theta[43] - (log(theta[39]) - log(theta[15])) )*
(contrast == "logRR" & whichmin_10 == 8),
# Upper bound of CEP(1, 0) = theta[44]
( theta[44] - (1- theta[33]/theta[9]) )*
(contrast == "VE" & whichmax_10 == 1) +
( theta[44] - (1- theta[33]/theta[11]) )*
(contrast == "VE" & whichmax_10 == 2) +
( theta[44] - (1- theta[35]/theta[9]) )*
(contrast == "VE" & whichmax_10 == 3) +
( theta[44] - (1- theta[35]/theta[11]) )*
(contrast == "VE" & whichmax_10 == 4) +
( theta[44] - (1- theta[37]/theta[13]) )*
(contrast == "VE" & whichmax_10 == 5) +
( theta[44] - (1- theta[37]/theta[15]) )*
(contrast == "VE" & whichmax_10 == 6) +
( theta[44] - (1- theta[39]/theta[13]) )*
(contrast == "VE" & whichmax_10 == 7) +
( theta[44] - (1- theta[39]/theta[15]) )*
(contrast == "VE" & whichmax_10 == 8) +
( theta[44] - (theta[33] - theta[9]) )*
(contrast == "Difference" & whichmax_10 == 1) +
( theta[44] - (theta[33] - theta[11]) )*
(contrast == "Difference" & whichmax_10 == 2) +
( theta[44] - (theta[35] - theta[9]) )*
(contrast == "Difference" & whichmax_10 == 3) +
( theta[44] - (theta[35] - theta[11]) )*
(contrast == "Difference" & whichmax_10 == 4) +
( theta[44] - (theta[37] - theta[13]) )*
(contrast == "Difference" & whichmax_10 == 5) +
( theta[44] - (theta[37] - theta[15]) )*
(contrast == "Difference" & whichmax_10 == 6) +
( theta[44] - (theta[39] - theta[13]) )*
(contrast == "Difference" & whichmax_10 == 7) +
( theta[44] - (theta[39] - theta[15]) )*
(contrast == "Difference" & whichmax_10 == 8) +
( theta[44] - (log(theta[33]) - log(theta[9])) )*
(contrast == "logRR" & whichmax_10 == 1) +
( theta[44] - (log(theta[33]) - log(theta[11])) )*
(contrast == "logRR" & whichmax_10 == 2) +
( theta[44] - (log(theta[35]) - log(theta[9])) )*
(contrast == "logRR" & whichmax_10 == 3) +
( theta[44] - (log(theta[35]) - log(theta[11])) )*
(contrast == "logRR" & whichmax_10 == 4) +
( theta[44] - (log(theta[37]) - log(theta[13])) )*
(contrast == "logRR" & whichmax_10 == 5) +
( theta[44] - (log(theta[37]) - log(theta[15])) )*
(contrast == "logRR" & whichmax_10 == 6) +
( theta[44] - (log(theta[39]) - log(theta[13])) )*
(contrast == "logRR" & whichmax_10 == 7) +
( theta[44] - (log(theta[39]) - log(theta[15])) )*
(contrast == "logRR" & whichmax_10 == 8),
# Lower bound of CEP(1, 0) - CEP(0, 0) = theta[45]
( theta[45] - (1 - theta[33]/theta[9]) +
(1 - theta[21]/theta[8]) )*
(contrast == "VE" & whichmin_diff == 1) +
( theta[45] - (1 - theta[33]/theta[9]) +
(1 - theta[23]/theta[8]) )*
(contrast == "VE" & whichmin_diff == 2) +
( theta[45] - (1 - theta[33]/theta[11]) +
(1 - theta[21]/theta[10]) )*
(contrast == "VE" & whichmin_diff == 3) +
( theta[45] - (1 - theta[33]/theta[11]) +
(1 - theta[23]/theta[10]) )*
(contrast == "VE" & whichmin_diff == 4) +
( theta[45] - (1 - theta[35]/theta[9]) +
(1 - theta[21]/theta[8]) )*
(contrast == "VE" & whichmin_diff == 5) +
( theta[45] - (1 - theta[35]/theta[9]) +
(1 - theta[23]/theta[8]) )*
(contrast == "VE" & whichmin_diff == 6) +
( theta[45] - (1 - theta[35]/theta[11]) +
(1 - theta[21]/theta[10]) )*
(contrast == "VE" & whichmin_diff == 7) +
( theta[45] - (1 - theta[35]/theta[11]) +
(1 - theta[23]/theta[10]) )*
(contrast == "VE" & whichmin_diff == 8) +
( theta[45] - (1 - theta[37]/theta[13]) +
(1 - theta[25]/theta[12]) )*
(contrast == "VE" & whichmin_diff == 9) +
( theta[45] - (1 - theta[37]/theta[13]) +
(1 - theta[27]/theta[12]) )*
(contrast == "VE" & whichmin_diff == 10) +
( theta[45] - (1 - theta[37]/theta[15]) +
(1 - theta[25]/theta[14]) )*
(contrast == "VE" & whichmin_diff == 11) +
( theta[45] - (1 - theta[37]/theta[15]) +
(1 - theta[27]/theta[14]) )*
(contrast == "VE" & whichmin_diff == 12) +
( theta[45] - (1 - theta[39]/theta[13]) +
(1 - theta[25]/theta[12]) )*
(contrast == "VE" & whichmin_diff == 13) +
( theta[45] - (1 - theta[39]/theta[13]) +
(1 - theta[27]/theta[12]) )*
(contrast == "VE" & whichmin_diff == 14) +
( theta[45] - (1 - theta[39]/theta[15]) +
(1 - theta[25]/theta[14]) )*
(contrast == "VE" & whichmin_diff == 15) +
( theta[45] - (1 - theta[39]/theta[15]) +
(1 - theta[27]/theta[14]) )*
(contrast == "VE" & whichmin_diff == 16) +
( theta[45] - (theta[33] - theta[9]) +
(theta[21] - theta[8]) )*
(contrast == "Difference" & whichmin_diff == 1) +
( theta[45] - (theta[33] - theta[9]) +
(theta[23] - theta[8]) )*
(contrast == "Difference" & whichmin_diff == 2) +
( theta[45] - (theta[33] - theta[11]) +
(theta[21] - theta[10]) )*
(contrast == "Difference" & whichmin_diff == 3) +
( theta[45] - (theta[33] - theta[11]) +
(theta[23] - theta[10]) )*
(contrast == "Difference" & whichmin_diff == 4) +
( theta[45] - (theta[35] - theta[9]) +
(theta[21] - theta[8]) )*
(contrast == "Difference" & whichmin_diff == 5) +
( theta[45] - (theta[35] - theta[9]) +
(theta[23] - theta[8]) )*
(contrast == "Difference" & whichmin_diff == 6) +
( theta[45] - (theta[35] - theta[11]) +
(theta[21] - theta[10]) )*
(contrast == "Difference" & whichmin_diff == 7) +
( theta[45] - (theta[35] - theta[11]) +
(theta[23] - theta[10]) )*
(contrast == "Difference" & whichmin_diff == 8) +
( theta[45] - (theta[37] - theta[13]) +
(theta[25] - theta[12]) )*
(contrast == "Difference" & whichmin_diff == 9) +
( theta[45] - (theta[37] - theta[13]) +
(theta[27] - theta[12]) )*
(contrast == "Difference" & whichmin_diff == 10) +
( theta[45] - (theta[37] - theta[15]) +
(theta[25] - theta[14]) )*
(contrast == "Difference" & whichmin_diff == 11) +
( theta[45] - (theta[37] - theta[15]) +
(theta[27] - theta[14]) )*
(contrast == "Difference" & whichmin_diff == 12) +
( theta[45] - (theta[39] - theta[13]) +
(theta[25] - theta[12]) )*
(contrast == "Difference" & whichmin_diff == 13) +
( theta[45] - (theta[39] - theta[13]) +
(theta[27] - theta[12]) )*
(contrast == "Difference" & whichmin_diff == 14) +
( theta[45] - (theta[39] - theta[15]) +
(theta[25] - theta[14]) )*
(contrast == "Difference" & whichmin_diff == 15) +
( theta[45] - (theta[39] - theta[15]) +
(theta[27] - theta[14]) )*
(contrast == "Difference" & whichmin_diff == 16) +
( theta[45] - (log(theta[33]) - log(theta[9])) +
(log(theta[21]) - log(theta[8])) )*
(contrast == "logRR" & whichmin_diff == 1) +
( theta[45] - (log(theta[33]) - log(theta[9])) +
(log(theta[23]) - log(theta[8])) )*
(contrast == "logRR" & whichmin_diff == 2) +
( theta[45] - (log(theta[33]) - log(theta[11])) +
(log(theta[21]) - log(theta[10])) )*
(contrast == "logRR" & whichmin_diff == 3) +
( theta[45] - (log(theta[33]) - log(theta[11])) +
(log(theta[23]) - log(theta[10])) )*
(contrast == "logRR" & whichmin_diff == 4) +
( theta[45] - (log(theta[35]) - log(theta[9])) +
(log(theta[21]) - log(theta[8])) )*
(contrast == "logRR" & whichmin_diff == 5) +
( theta[45] - (log(theta[35]) - log(theta[9])) +
(log(theta[23]) - log(theta[8])) )*
(contrast == "logRR" & whichmin_diff == 6) +
( theta[45] - (log(theta[35]) - log(theta[11])) +
(log(theta[21]) - log(theta[10])) )*
(contrast == "logRR" & whichmin_diff == 7) +
( theta[45] - (log(theta[35]) - log(theta[11])) +
(log(theta[23]) - log(theta[10])) )*
(contrast == "logRR" & whichmin_diff == 8) +
( theta[45] - (log(theta[37]) - log(theta[13])) +
(log(theta[25]) - log(theta[12])) )*
(contrast == "logRR" & whichmin_diff == 9) +
( theta[45] - (log(theta[37]) - log(theta[13])) +
(log(theta[27]) - log(theta[12])) )*
(contrast == "logRR" & whichmin_diff == 10) +
( theta[45] - (log(theta[37]) - log(theta[15])) +
(log(theta[25]) - log(theta[14])) )*
(contrast == "logRR" & whichmin_diff == 11) +
( theta[45] - (log(theta[37]) - log(theta[15])) +
(log(theta[27]) - log(theta[14])) )*
(contrast == "logRR" & whichmin_diff == 12) +
( theta[45] - (log(theta[39]) - log(theta[13])) +
(log(theta[25]) - log(theta[12])) )*
(contrast == "logRR" & whichmin_diff == 13) +
( theta[45] - (log(theta[39]) - log(theta[13])) +
(log(theta[27]) - log(theta[12])) )*
(contrast == "logRR" & whichmin_diff == 14) +
( theta[45] - (log(theta[39]) - log(theta[15])) +
(log(theta[25]) - log(theta[14])) )*
(contrast == "logRR" & whichmin_diff == 15) +
( theta[45] - (log(theta[39]) - log(theta[15])) +
(log(theta[27]) - log(theta[14])) )*
(contrast == "logRR" & whichmin_diff == 16),
# Upper bound of CEP(1, 0) - CEP(0, 0) = theta[45]
( theta[46] - (1 - theta[33]/theta[9]) +
(1 - theta[21]/theta[8]) )*
(contrast == "VE" & whichmax_diff == 1) +
( theta[46] - (1 - theta[33]/theta[9]) +
(1 - theta[23]/theta[8]) )*
(contrast == "VE" & whichmax_diff == 2) +
( theta[46] - (1 - theta[33]/theta[11]) +
(1 - theta[21]/theta[10]) )*
(contrast == "VE" & whichmax_diff == 3) +
( theta[46] - (1 - theta[33]/theta[11]) +
(1 - theta[23]/theta[10]) )*
(contrast == "VE" & whichmax_diff == 4) +
( theta[46] - (1 - theta[35]/theta[9]) +
(1 - theta[21]/theta[8]) )*
(contrast == "VE" & whichmax_diff == 5) +
( theta[46] - (1 - theta[35]/theta[9]) +
(1 - theta[23]/theta[8]) )*
(contrast == "VE" & whichmax_diff == 6) +
( theta[46] - (1 - theta[35]/theta[11]) +
(1 - theta[21]/theta[10]) )*
(contrast == "VE" & whichmax_diff == 7) +
( theta[46] - (1 - theta[35]/theta[11]) +
(1 - theta[23]/theta[10]) )*
(contrast == "VE" & whichmax_diff == 8) +
( theta[46] - (1 - theta[37]/theta[13]) +
(1 - theta[25]/theta[12]) )*
(contrast == "VE" & whichmax_diff == 9) +
( theta[46] - (1 - theta[37]/theta[13]) +
(1 - theta[27]/theta[12]) )*
(contrast == "VE" & whichmax_diff == 10) +
( theta[46] - (1 - theta[37]/theta[15]) +
(1 - theta[25]/theta[14]) )*
(contrast == "VE" & whichmax_diff == 11) +
( theta[46] - (1 - theta[37]/theta[15]) +
(1 - theta[27]/theta[14]) )*
(contrast == "VE" & whichmax_diff == 12) +
( theta[46] - (1 - theta[39]/theta[13]) +
(1 - theta[25]/theta[12]) )*
(contrast == "VE" & whichmax_diff == 13) +
( theta[46] - (1 - theta[39]/theta[13]) +
(1 - theta[27]/theta[12]) )*
(contrast == "VE" & whichmax_diff == 14) +
( theta[46] - (1 - theta[39]/theta[15]) +
(1 - theta[25]/theta[14]) )*
(contrast == "VE" & whichmax_diff == 15) +
( theta[46] - (1 - theta[39]/theta[15]) +
(1 - theta[27]/theta[14]) )*
(contrast == "VE" & whichmax_diff == 16) +
( theta[46] - (theta[33] - theta[9]) +
(theta[21] - theta[8]) )*
(contrast == "Difference" & whichmax_diff == 1) +
( theta[46] - (theta[33] - theta[9]) +
(theta[23] - theta[8]) )*
(contrast == "Difference" & whichmax_diff == 2) +
( theta[46] - (theta[33] - theta[11]) +
(theta[21] - theta[10]) )*
(contrast == "Difference" & whichmax_diff == 3) +
( theta[46] - (theta[33] - theta[11]) +
(theta[23] - theta[10]) )*
(contrast == "Difference" & whichmax_diff == 4) +
( theta[46] - (theta[35] - theta[9]) +
(theta[21] - theta[8]) )*
(contrast == "Difference" & whichmax_diff == 5) +
( theta[46] - (theta[35] - theta[9]) +
(theta[23] - theta[8]) )*
(contrast == "Difference" & whichmax_diff == 6) +
( theta[46] - (theta[35] - theta[11]) +
(theta[21] - theta[10]) )*
(contrast == "Difference" & whichmax_diff == 7) +
( theta[46] - (theta[35] - theta[11]) +
(theta[23] - theta[10]) )*
(contrast == "Difference" & whichmax_diff == 8) +
( theta[46] - (theta[37] - theta[13]) +
(theta[25] - theta[12]) )*
(contrast == "Difference" & whichmax_diff == 9) +
( theta[46] - (theta[37] - theta[13]) +
(theta[27] - theta[12]) )*
(contrast == "Difference" & whichmax_diff == 10) +
( theta[46] - (theta[37] - theta[15]) +
(theta[25] - theta[14]) )*
(contrast == "Difference" & whichmax_diff == 11) +
( theta[46] - (theta[37] - theta[15]) +
(theta[27] - theta[14]) )*
(contrast == "Difference" & whichmax_diff == 12) +
( theta[46] - (theta[39] - theta[13]) +
(theta[25] - theta[12]) )*
(contrast == "Difference" & whichmax_diff == 13) +
( theta[46] - (theta[39] - theta[13]) +
(theta[27] - theta[12]) )*
(contrast == "Difference" & whichmax_diff == 14) +
( theta[46] - (theta[39] - theta[15]) +
(theta[25] - theta[14]) )*
(contrast == "Difference" & whichmax_diff == 15) +
( theta[46] - (theta[39] - theta[15]) +
(theta[27] - theta[14]) )*
(contrast == "Difference" & whichmax_diff == 16) +
( theta[46] - (log(theta[33]) - log(theta[9])) +
(log(theta[21]) - log(theta[8])) )*
(contrast == "logRR" & whichmax_diff == 1) +
( theta[46] - (log(theta[33]) - log(theta[9])) +
(log(theta[23]) - log(theta[8])) )*
(contrast == "logRR" & whichmax_diff == 2) +
( theta[46] - (log(theta[33]) - log(theta[11])) +
(log(theta[21]) - log(theta[10])) )*
(contrast == "logRR" & whichmax_diff == 3) +
( theta[46] - (log(theta[33]) - log(theta[11])) +
(log(theta[23]) - log(theta[10])) )*
(contrast == "logRR" & whichmax_diff == 4) +
( theta[46] - (log(theta[35]) - log(theta[9])) +
(log(theta[21]) - log(theta[8])) )*
(contrast == "logRR" & whichmax_diff == 5) +
( theta[46] - (log(theta[35]) - log(theta[9])) +
(log(theta[23]) - log(theta[8])) )*
(contrast == "logRR" & whichmax_diff == 6) +
( theta[46] - (log(theta[35]) - log(theta[11])) +
(log(theta[21]) - log(theta[10])) )*
(contrast == "logRR" & whichmax_diff == 7) +
( theta[46] - (log(theta[35]) - log(theta[11])) +
(log(theta[23]) - log(theta[10])) )*
(contrast == "logRR" & whichmax_diff == 8) +
( theta[46] - (log(theta[37]) - log(theta[13])) +
(log(theta[25]) - log(theta[12])) )*
(contrast == "logRR" & whichmax_diff == 9) +
( theta[46] - (log(theta[37]) - log(theta[13])) +
(log(theta[27]) - log(theta[12])) )*
(contrast == "logRR" & whichmax_diff == 10) +
( theta[46] - (log(theta[37]) - log(theta[15])) +
(log(theta[25]) - log(theta[14])) )*
(contrast == "logRR" & whichmax_diff == 11) +
( theta[46] - (log(theta[37]) - log(theta[15])) +
(log(theta[27]) - log(theta[14])) )*
(contrast == "logRR" & whichmax_diff == 12) +
( theta[46] - (log(theta[39]) - log(theta[13])) +
(log(theta[25]) - log(theta[12])) )*
(contrast == "logRR" & whichmax_diff == 13) +
( theta[46] - (log(theta[39]) - log(theta[13])) +
(log(theta[27]) - log(theta[12])) )*
(contrast == "logRR" & whichmax_diff == 14) +
( theta[46] - (log(theta[39]) - log(theta[15])) +
(log(theta[25]) - log(theta[14])) )*
(contrast == "logRR" & whichmax_diff == 15) +
( theta[46] - (log(theta[39]) - log(theta[15])) +
(log(theta[27]) - log(theta[14])) )*
(contrast == "logRR" & whichmax_diff == 16),
# pi = theta[47]
(1-Y)*(R-theta[47])
))
}
}
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