1 Introduction
2 Functional approximation of the critical value parameter
3 OptBand for the cumulative hazard function
3.1 One-sample problem
3.2 Two-sample problem
4 OptBand for the survival function
4.1 One-sample problem
5 Simulation
(Empirical coverage, average area between bands) | |||||||
---|---|---|---|---|---|---|---|
p | r | n | OptBand | FD-I | EL | EP | HW |
0 | (.05, .95) | 100 | (.940, .854) | (.953, .886) | (.970, .882) | (.948, .895) | (.974, 1) |
500 | (.942, .850) | (.949, .969) | (.967, .884) | (.955, .885) | (.959, 1) | ||
1000 | (.942, .849) | (.940, .979) | (.964, .882) | (.952, .884) | (.952, 1) | ||
(.05, .8) | 100 | (.952, .961) | (.946, .927) | (.963, .989) | (.960, 1.01) | (.961, 1) | |
500 | (.952, .964) | (.949, .971) | (.947, 1.01) | (.958, 1.01) | (.958, 1) | ||
1000 | (.949, .964) | (.949, .981) | (.948, 1.01) | (.949, 1.01) | (.958, 1) | ||
(.2, .95) | 100 | (.943, .853) | (.953, .889) | (.971, .863) | (.934, .876) | (.970, 1) | |
500 | (.950, .847) | (.952, .969) | (.965, .865) | (.963, .866) | (.961, 1) | ||
1000 | (.952, .844) | (.957, .979) | (.967, .866) | (.961, .864) | (.966, 1) | ||
(.2, .8) | 100 | (.961, .973) | (.942, .935) | (.955, .976) | (.963, .996) | (.962, 1) | |
500 | (.940, .973) | (.945, .973) | (.955, .990) | (.949, .995) | (.953, 1) | ||
1000 | (.948, .972) | (.946, .981) | (.958, .991) | (.951, .994) | (.952, 1) | ||
.2 | (.05, .95) | 100 | (.942, .856) | (.959, .824) | (.973, .864) | (.950, .888) | (.972, 1) |
500 | (.945, .839) | (.947, .869) | (.959, .866) | (.944, .869) | (.955, 1) | ||
1000 | (.950, .838) | (.954, .877) | (.956, .864) | (.964, .867) | (.962, 1) | ||
(.05, .8) | 100 | (.953, .964) | (.938, .914) | (.961, .986) | (.954, 1.01) | (.965, 1) | |
500 | (.962, .965) | (.958, .967) | (.964, 1.00) | (.962, 1.01) | (.966, 1) | ||
1000 | (.952, .966) | (.952, .973) | (.965, 1.01) | (.960, 1.01) | (.960, 1) | ||
(.2, .95) | 100 | (.942, .855) | (.936, .819) | (.963, .850) | (.949, .868) | (.955, 1) | |
500 | (.944, .834) | (.955, .859) | (.947, .845) | (.957, .848) | (.965, 1) | ||
1000 | (.950, .832) | (.941, .866) | (.951, .849) | (.950, .846) | (.950, 1) | ||
(.2, .8) | 100 | (.962, .978) | (.944, .918) | (,961, .973) | (.967, .996) | (.972, 1) | |
500 | (.944, .975) | (.938, .957) | (.959, .988) | (.942, .994) | (.945, 1) | ||
1000 | (.951, .975) | (.954, .964) | (.954, .989) | (.957, .993) | (.956, 1) | ||
.5 | (.05, .95) | 100 | (.953, .896) | (.959, .800) | (.974, .858) | (.950, .902) | (.961, 1) |
500 | (.949, .830) | (.950, .835) | (.954, .842) | (.950, .850) | (.958, 1) | ||
1000 | (.956, .819) | (.951, .822) | (.959, .837) | (.951, .840) | (.947, 1) | ||
(.05, .8) | 100 | (.958, .976) | (.961, .932) | (.967, .979) | (.948, 1.01) | (.962, 1) | |
500 | (.951, .970) | (.944, .995) | (.956, .998) | (.958, 1.00) | (.956, 1) | ||
1000 | (.960, .970) | (.953, 1.01) | (.958, 1.00) | (.949, 1.00) | (.959, 1) | ||
(.2, .95) | 100 | (.957, .896) | (.963, .784) | (.963, .847) | (.954, .881) | (.957, 1) | |
500 | (.954, .823) | (.949, .787) | (.956, .820) | (.964, .826) | (.968, 1) | ||
1000 | (.954, .814) | (.946, .794) | (.953, .815) | (.952, .819) | (.952, 1) | ||
(.2, .8) | 100 | (.959, .995) | (.950, .927) | (.959, .972) | (.964, 1.00) | (.966, 1) | |
500 | (.957, .982) | (.949, .969) | (.947, .986) | (.954, .992) | (.952, 1) | ||
1000 | (.957, .981) | (.954, .981) | (.951, .988) | (.958, .991) | (.961, 1) | ||
.9 | (.05, .95) | 100 | (.908, .911) | (.983, 1.15) | (.955, .928) | (.860, .928) | (.940, 1) |
500 | (.938, 1.03) | (.974, 1.49) | (.955, .967) | (.902, .955) | (.889, 1) | ||
1000 | (.936, .988) | (.984, 1.57) | (.941, .939) | (.903, .923) | (.888, 1) | ||
(.05, .8) | 100 | (.908, .908) | (.988, 1.17) | (.952, .949) | (.859, .924) | (.948, 1) | |
500 | (.935, 1.04) | (.983, 1.39) | (.942, 1.01) | (.887, .995) | (.891, 1) | ||
1000 | (.934, 1.01) | (.980, 1.36) | (.959, 1.01) | (.906, .994) | (.908, 1) | ||
(.2, .95) | 100 | (.954, .998) | (.982, 1.17) | (.957, .946) | (.925, .972) | (.960, 1) | |
500 | (.946, 1.04) | (.979, 1.42) | (.954, .967) | (.912, .945) | (.900, 1) | ||
1000 | (.944, .991) | (.988, 1.46) | (.945, .928) | (.906, .909) | (.894, 1) | ||
(.2, .8) | 100 | (.944, 1.01) | (.993, 1.21) | (.955, .981) | (.919, .978) | (.950, 1) | |
500 | (.953, 1.08) | (.995, 1.34) | (.946, 1.04) | (.926, 1.02) | (.926, 1) | ||
1000 | (.943, 1.04) | (.983, 1.25) | (.951, 1.02) | (.915, 1.01) | (.906, 1) |
6 Primary biliary cirrhosis data analysis
7 Discussion
Average area between bands | |||||||
---|---|---|---|---|---|---|---|
Group | p | n | OptBand | FD-I | EL | EP | HW |
Placebo | .535 | 158 | .980 | 1.035 | .964 | .981 | 1 |
D-penicillamine | .563 | 154 | .987 | 1.044 | .971 | .989 | 1 |
Overall | .558 | 312 | .957 | 1.030 | .960 | .970 | 1 |