Table 3.

MEAN (SD) of expected benefit of a derived treatment-selection rule in the population and MEAN(SD) of naive and cross-validated estimate of corresponding expected benefit

	TYPE	PAR	NPAR1	NPAR2	WLOGIS1	WLOGIS2	WCLASS1	WCLASS2
Cost ratio
200	True	0.0406 (0.0035)	0.0337 (0.011)	0.0363 (0.0084)	0.0329 (0.0105)	0.0362 (0.0085)	0.0335 (0.0122)	0.0377 (0.0072)
	Naive	0.0454 (0.0208)	0.0586 (0.0299)	0.0552 (0.0298)	0.0404 (0.0368)	0.0432 (0.0339)	0.0602 (0.0331)	0.0559 (0.033)
	CV	0.0391 (0.0325)	0.0303 (0.0329)	0.0328 (0.031)	0.0316 (0.036)	0.0336 (0.0336)	0.0307 (0.0381)	0.0358 (0.0351)
500	True	0.042 (0.0012)	0.0385 (0.006)	0.0398 (0.004)	0.0345 (0.0069)	0.0401 (0.004)	0.038 (0.0071)	0.04 (0.0038)
	Naive	0.0439 (0.0133)	0.0513 (0.0198)	0.0499 (0.019)	0.0374 (0.0244)	0.0426 (0.0218)	0.0524 (0.0218)	0.0499 (0.0211)
	CV	0.041 (0.0209)	0.0364 (0.022)	0.0381 (0.0198)	0.0336 (0.0239)	0.0382 (0.0217)	0.0357 (0.0251)	0.0383 (0.0222)
2000	True	0.0427 (3e04)	0.0415 (0.002)	0.0418 (0.0015)	0.0359 (0.0034)	0.0422 (0.001)	0.0412 (0.0025)	0.0417 (0.0016)
	Naive	0.0433 (0.0065)	0.0468 (0.0102)	0.0463 (0.0095)	0.0368 (0.0125)	0.0432 (0.0109)	0.0472 (0.0114)	0.0462 (0.0106)
	CV	0.0428 (0.0105)	0.0413 (0.0108)	0.0417 (0.0099)	0.0359 (0.0124)	0.0421 (0.0109)	0.0409 (0.0123)	0.0416 (0.0111)
Cost ratio
200	True	0.0542 (0.0067)	0.0474 (0.0136)	0.049 (0.0119)	0.0366 (0.0221)	0.0403 (0.0173)	0.0472 (0.0181)	0.0515 (0.0119)
	Naive	0.0518 (0.0194)	0.0653 (0.0273)	0.0629 (0.0262)	0.0398 (0.0322)	0.0374 (0.0298)	0.064 (0.0294)	0.0598 (0.0287)
	CV	0.0379 (0.0306)	0.0299 (0.031)	0.0318 (0.0287)	0.0178 (0.0344)	0.0217 (0.0314)	0.0287 (0.0383)	0.0343 (0.0333)
500	True	0.0572 (0.002)	0.0536 (0.0066)	0.0543 (0.0055)	0.0477 (0.0127)	0.0471 (0.0092)	0.0538 (0.007)	0.0553 (0.0045)
	Naive	0.0559 (0.0127)	0.0633 (0.0185)	0.0623 (0.0175)	0.0474 (0.0224)	0.0442 (0.0188)	0.0627 (0.0202)	0.0606 (0.019)
	CV	0.0501 (0.0197)	0.0454 (0.0206)	0.0464 (0.0186)	0.0373 (0.0241)	0.0387 (0.0193)	0.0455 (0.0238)	0.0478 (0.0205)
2000	True	0.0585 (5e04)	0.0571 (0.0022)	0.0573 (0.002)	0.0543 (0.0044)	0.0487 (0.0049)	0.0569 (0.0024)	0.0573 (0.0017)
	Naive	0.0588 (0.0069)	0.0622 (0.0103)	0.0619 (0.0096)	0.0547 (0.0106)	0.0488 (0.0097)	0.0618 (0.0114)	0.061 (0.0104)
	CV	0.0575 (0.0106)	0.0557 (0.0109)	0.056 (0.0099)	0.0524 (0.0111)	0.0478 (0.0096)	0.0555 (0.0122)	0.0561 (0.0109)
Cost ratio
200	True	0.0577 (0.0072)	0.0514 (0.0136)	0.0529 (0.0119)	0.0356 (0.0233)	0.0397 (0.0185)	0.0489 (0.0203)	0.0535 (0.0143)
	Naive	0.0485 (0.0197)	0.0625 (0.0265)	0.0605 (0.0255)	0.0318 (0.0309)	0.0293 (0.0294)	0.0595 (0.0284)	0.0552 (0.0278)
	CV	0.0327 (0.0298)	0.0257 (0.0302)	0.0275 (0.0282)	0.009 (0.0328)	0.0131 (0.0306)	0.0214 (0.0379)	0.0275 (0.0334)
500	True	0.0611 (0.0022)	0.0577 (0.0067)	0.0583 (0.0056)	0.0465 (0.0148)	0.0457 (0.011)	0.0569 (0.0079)	0.0584 (0.0051)
	Naive	0.0531 (0.013)	0.0608 (0.0177)	0.06 (0.0169)	0.0389 (0.0224)	0.0355 (0.02)	0.0587 (0.0194)	0.0567 (0.0183)
	CV	0.0463 (0.0191)	0.0419 (0.0199)	0.0428 (0.0186)	0.0285 (0.0238)	0.03 (0.0201)	0.0406 (0.0235)	0.0432 (0.0204)
2000	True	0.0626 (6e04)	0.0611 (0.0024)	0.0613 (0.0021)	0.052 (0.0069)	0.047 (0.0057)	0.0602 (0.0024)	0.0606 (0.0018)
	Naive	0.0575 (0.0068)	0.0607 (0.0094)	0.0604 (0.0089)	0.0464 (0.0114)	0.0411 (0.0105)	0.0592 (0.0102)	0.0585 (0.0095)
	CV	0.0555 (0.0096)	0.0537 (0.01)	0.0539 (0.0094)	0.0445 (0.0114)	0.0401 (0.0104)	0.0528 (0.011)	0.0534 (0.01)
Cost ratio
200	True	0.042 (0.008)	0.0368 (0.0127)	0.038 (0.0111)	0.0164 (0.0221)	0.0205 (0.0171)	0.0309 (0.021)	0.0356 (0.0152)
	Naive	0.0429 (0.0205)	0.058 (0.0261)	0.0562 (0.0254)	0.0227 (0.0293)	0.0199 (0.0287)	0.0529 (0.0277)	0.0484 (0.0272)
	CV	0.0255 (0.0293)	0.0199 (0.0294)	0.0217 (0.028)	(0.0301)	0.0038 (0.0286)	0.0121 (0.0372)	0.018 (0.0337)
500	True	0.0459 (0.0025)	0.0426 (0.0071)	0.0432 (0.0061)	0.0246 (0.0151)	0.0245 (0.0113)	0.0399 (0.0092)	0.0415 (0.0063)
	Naive	0.0462 (0.0148)	0.0549 (0.018)	0.0542 (0.0176)	0.0253 (0.0236)	0.0227 (0.0218)	0.0504 (0.0199)	0.0485 (0.019)
	CV	0.0389 (0.0195)	0.0348 (0.0202)	0.0357 (0.0194)	0.0155 (0.0235)	0.0174 (0.0211)	0.0307 (0.0248)	0.0336 (0.0221)
2000	True	0.0476	0.0463 (0.0024)	0.0464 (0.0022)	0.0275 (0.0081)	0.0251 (0.0059)	0.0437 (0.0024)	0.0441 (0.0019)
	Naive	0.048 (0.009)	0.0519 (0.0104)	0.0516 (0.0104)	0.0277 (0.0147)	0.025 (0.0128)	0.0485 (0.0112)	0.0477 (0.0109)
	CV	0.0462 (0.0107)	0.0444 (0.011)	0.0446 (0.011)	0.0262 (0.0144)	0.024 (0.0127)	0.042 (0.0119)	0.0425 (0.0114)
Cost ratio
200	True	0.0214 (0.0075)	0.0179 (0.0106)	0.0191 (0.009)	0.0044 (0.0183)	(0.012)	0.0054 (0.0194)	0.01 (0.0139)
	Naive	0.0318 (0.0209)	0.0489 (0.0257)	0.0474 (0.0254)	0.0094 (0.0247)	0.007 (0.0242)	0.0404 (0.0261)	0.0354 (0.0259)
	CV	0.013 (0.0274)	0.0097 (0.0275)	0.0113 (0.0272)	0.0117 (0.0242)	0.0079 (0.0231)	0.004 (0.0341)	0.0014 (0.0318)
500	True	0.0257 (0.0035)	0.0227 (0.007)	0.023 (0.0067)	0.0011 (0.0094)	(0.0065)	0.0135 (0.0107)	0.0154 (0.0077)
	Naive	0.0313 (0.0158)	0.0417 (0.0184)	0.0412 (0.0184)	0.0052 (0.0191)	0.0032 (0.0183)	0.0326 (0.0201)	0.0305 (0.0197)
	CV	0.0234 (0.0198)	0.0204 (0.0202)	0.0211 (0.0201)	0.0029 (0.0177)	0.0015 (0.0172)	0.0093 (0.0254)	0.0124 (0.0237)
2000	True	0.028	0.0266 (0.0032)	0.0266 (0.0031)	0.003 (0.0041)	0.0024 (0.0035)	0.0189 (0.0038)	0.0193 (0.0034)
	Naive	0.0293 (0.0085)	0.0339 (0.0103)	0.0337 (0.0104)	0.0014 (0.0107)	0.0012 (0.0103)	0.0254 (0.0116)	0.0246 (0.0114)
	CV	0.0274 (0.0106)	0.0257 (0.0111)	0.0258 (0.0112)	0.0025 (0.0101)	0.0022 (0.01)	0.0177 (0.0133)	0.0183 (0.0129)

PAR: corresponds to the rule where is the estimated risk difference based on the GLM risk model NPAR1, NPAR2: correspond to with chosen to maximize the empirical or augmented estimate of EB; WLOGIS1, WLOGIS2: correspond to rule where and are estimated based on converting the problem to a weighted classification problem, which is solved using weighted logistic regression with empirical weight or augmented weight, respectively; WCLASS1, WCLASS2: correspond to rule where and are estimated based on converting the problem to a weighted classification problem, which is solved using a grid search with empirical weight or augmented weight, respectively;True: indicates population performance of a treatment-selection rule derived from a training data.