| Full factorial randomization | Two-group randomization | |||||||
---|---|---|---|---|---|---|---|---|---|
 | Men (N = 1606) | Women (N = 301) | Women (N = 666) | ||||||
 | Randomized | Voluntary run-in failure | p | Randomized | Voluntary run-in failure | p | Randomized | Voluntary run-in failure | p |
 | N (%) | N (%) |  | N (%) | N (%) |  | N (%) | N (%) |  |
 | 1423 (89) | 183 (11) |  | 252 (84) | 49 (16) |  | 584 (88) | 82 (12) |  |
BASELINE FACTORS | |||||||||
 Preference: If you could choose, which kind of pill would you like to receive during the study? | |||||||||
  Calcium + vitamin D | 854 (90) | 96 (10) | 0.08 | 174 (87) | 27 (13) | 0.10a | 450 (88) | 62 (12) | 0.37 |
  Calcium only | 67 (83) | 14 (17) |  | 13 (65) | 7 (35) |  | 34 (81) | 8 (19) |  |
  Vitamin D only | 63 (83) | 13 (17) |  | 8 (80) | 2 (20) |  | N/A | N/A |  |
  Placebo | 32 (94) | 2 (5.9) |  | 4 (100) | 0 |  | N/A | N/A |  |
  Don’t know/refused | 407 (88) | 57 (12) |  | 53 (80) | 13 (20) |  | 99 (89) | 12 (11) |  |
  Missing | 0 | 1 (100) |  | 0 | 0 |  | 1 (100) | 0 |  |
 Efficacy belief: How likely do you think it is that vitamin D supplements … | |||||||||
 Are helpful in preventing polyps |  |  | 0.74 |  |  | 0.72 |  |  | 0.44 |
  Very/somewhat likely | 852 (89) | 108 (11) |  | 173 (83) | 36 (17) |  | 381 (87) | 58 (13) |  |
  Don’t know | 530 (89) | 67 (11) |  | 70 (86) | 11 (14) |  | 182 (89) | 23 (11) |  |
  Very/somewhat unlikely | 40 (85) | 7 (15) |  | 8 (80) | 2 (20) |  | 20 (95) | 1 (4.8) |  |
  Refused/missing | 1 (50) | 1 (50) |  | 1 (100) | 0 |  | 1 (100) | 0 |  |
 Improve health |  |  | 0.20 |  |  | 0.42a |  |  | 0.30 |
  Very/somewhat likely | 1189 (89) | 143 (11) |  | 239 (84) | 45 (16) |  | 514 (87) | 76 (13) |  |
  Don’t know | 177 (85) | 31 (15) |  | 10 (77) | 3 (23) |  | 56 (90) | 6 (9.7) |  |
  Very/somewhat unlikely | 56 (88) | 8 (13) |  | 3 (75) | 1 (25) |  | 13 (100) | 0 |  |
  Refused/missing | 1 (50) | 1 (50) |  | 0 | 0 |  | 1 (100) | 0 |  |
 Improve pain in bones and joints |  |  | 0.59 |  |  | 0.63 |  |  | 0.18 |
  Very/somewhat likely | 902 (89) | 109 (11) |  | 176 (83) | 37 (17) |  | 347 (86) | 57 (14) |  |
  Don’t know | 374 (88) | 51 (12) |  | 44 (85) | 8 (15) |  | 184 (91) | 18 (8.9) |  |
  Very/somewhat unlikely | 145 (87) | 22 (13) |  | 32 (89) | 4 (11) |  | 52 (88) | 7 (12) |  |
  Refused/missing | 2 (67) | 1 (33) |  | 0 | 0 |  | 1 (100) | 0 |  |
 Improve mood |  |  | 0.31 |  |  | 0.47 |  |  | 0.06 |
  Very/somewhat likely | 375 (87) | 56 (13) |  | 86 (83) | 18 (17) |  | 240 (84) | 45 (16) |  |
  Don’t know | 632 (90) | 71 (10) |  | 89 (87) | 13 (13) |  | 245 (91) | 25 (9.3) |  |
  Very/somewhat unlikely | 414 (88) | 55 (12) |  | 77 (81) | 18 (19) |  | 98 (89) | 12 (11) |  |
  Refused/missing | 2 (67) | 1 (33) |  | 0 | 0 |  | 1 (100) | 0 |  |
 Cause constipation |  |  | 0.36 |  |  | 0.46 |  |  | 0.09 |
  Very/somewhat likely | 240 (86) | 38 (14) |  | 82 (87) | 12 (13) |  | 117 (82) | 25 (18) |  |
  Don’t know | 669 (89) | 85 (11) |  | 91 (83) | 18 (17) |  | 282 (90) | 33 (10) |  |
  Very/somewhat unlikely | 511 (90) | 59 (10) |  | 79 (81) | 19 (19) |  | 184 (88) | 24 (12) |  |
  Refused/missing | 3 (75) | 1 (25) |  | 0 | 0 |  | 1 (100) | 0 |  |
 Efficacy scoreb mean (SD) compared with [randomized participants] | 2.8 (2.6) | 2.5 (2.9) | 0.20 | 3.1 (2.5) | 3.4 (2.7) | 0.39 | 3.3 (2.6) | 3.6 (2.9) | 0.26 |
 Efficacy scoreb |  |  | 0.16 |  |  | 0.94a |  |  | 0.81 |
  −9 to −1 (benefit unlikely) | 97 (85) | 17 (15) |  | 21 (88) | 3 (13) |  | 29 (88) | 4 (12) |  |
  0 (no benefit) | 149 (85) | 26 (15) |  | 16 (80) | 4 (20) |  | 49 (89) | 6 (11) |  |
  1–5 (little benefit) | 957 (90) | 109 (10) |  | 168 (84) | 33 (16) |  | 390 (88) | 52 (12) |  |
  6–10 (some benefit) | 220 (88) | 31 (12) |  | 47 (84) | 9 (16) |  | 116 (85) | 20 (15) |  |
 Allocation belief: If you were to place a bet, which pill would you bet you’ll be given during the trial? | |||||||||
  Calcium + vitamin D | 236 (90) | 25 (9.6) | 0.96 | 38 (83) | 8 (17) | 0.89a | 116 (85) | 21 (15) | 0.73 |
  Calcium only | 102 (89) | 13 (11) |  | 18 (82) | 4 (18) |  | 95 (88) | 13 (12) |  |
  Vitamin D only | 91 (90) | 10 (9.9) |  | 11 (79) | 3 (21) |  | N/A | N/A |  |
  Placebo | 206 (89) | 25 (11) |  | 31 (79) | 8 (21) |  | N/A | N/A |  |
  Don’t know/refused | 150 (91) | 15 (9.1) |  | 18 (90) | 2 (10) |  | 29 (88) | 4 (12) |  |
  Missing/not askedc | 638 (87) | 95 (13) |  | 136 (85) | 24 (15) |  | 344 (89) | 44 (11) |  |
POST-ENROLLMENT FACTOR | |||||||||
 Perceived toxicity during the run-in periodd | |||||||||
  No | 1412 (89) | 169 (11) | <0.0001a | 249 (85) | 43 (15) | 0.001a | 581 (89) | 73 (11) | <0.0001a |
  Yes | 11 (44) | 14 (56) |  | 3 (33) | 6 (67) |  | 3 (25) | 9 (75) |  |