Chapter 1 1. y NA s NA 6.84 9.29 3.83 5.95 5.77 31.68 6.336 5 5 (6.84 6.336) 2 (9.29 6.336) 2 (3.83 6.336) 2 (5.95 6.336) 2 (5.77 6.336) 2 5 1 1.98 cv NA 100% 31.25% 6.336 15.73 1.98 4 y A 6.24 s A 2.12 cv A 33.95% Very similar levels 2. ^ 1 ^ 171 153 0.9607 2 0.8596 178 178 3. 1273 0.1153 11036 1293 b) P(C | B ) 0.1172 11035 c) No, very similar risks a ) P(C | B) 4. a) P(C ) .009418 407 3702 .002375 P(C | L) .013974 171363 264913 c) 94.18, 23.75, 139.74 b) P(C | L) 5. Sensitivity: 45/50 = 0.90 (90%) Specificity: 24/63 = 0.38 (38%) PV+ : 45/84 = 0.54 (54%) PV- : 24/29 = 0.83 (83%) Accuracy: (45+24)/113 = 0.61 (61%) 6. Sensitivity: 116/140 = 0.83 (83%) Specificity: 211/215 = 0.98 (98%) + PV : 116/120 = 0.97 (97%) PV : 211/235 = 0.90 (90%) Accuracy: (116+211)/355 = 0.92 (92%) 7. a) b) c) d) Cross-sectional Cohort study Randomized clinical trial Historical controls 8. a) Dependents: Ability to obtain erection (ordinal), EDITS (Numeric) Independent: Dose (Numeric) b) Approx. 41 c) Validity: It is accurately measuring patient satisfaction. Reliability: Reproducability of responses within subjects d) Yes Chapter 2 9. 72 67.9 a ) P (Y 72) P Z 1.46 .0721 2.8 60 63.3 b) P (Y 60) P Z 1.27 .1020 2.6 d ) P ( Z 1.28) .10 P(Y 143 1.28(15.5) 162.8) .10 e) P( Z 1.645) .05 P(Y 123 1.645(14.3) 99.5) .05 f ) P ( 1.96 Y 1.96 ) .95 219 1.96(39.2) 219 77 (142,296) g ) P ( Z 2.33) .01 P(Y 74 2.33(12.2) 45.6) .99 for men 45.6 40 for women : P (Y 45.6) P Z 0.77 .2206 7 .3 10. a ) N Y b) N Y c) N Y d ) N Y 0.56 25 1.3 33.9 , Y 0.22 35 3.0 69.9 , Y 1.00 9 14.3 123 , Y 2.02 50 67.9 , Y 2.8 11. 70 67.9 a) P(Y 70) P Z 3.75 P( Z 3.09) .0010 0.56 32 33.9 b) P(Y 32) P Z 8.64 0 0.22 71 69.9 69 69.9 c) P(69 Y 71) P Z P(0.9 Z 1.1) 1 .1357 .1841 .6802 1 1 125 123 d ) P(Y 125) P Z 0.99 .1611 2.02 Chapter 3 12. H 0 : 1 2 0 H A : 1 2 0 TS : z obs RR : | z obs 30.6 38.6 (7.54) 2 (12.43) 2 37 36 | z.05 / 2 z.025 1.96 8.0 3.33 2.4 P : 2 P( Z | 3.33 | 3.33) 2(.0010) .002 Conclusion :Reject the null hypothesis , difference s exist 13. H 0 : 1 2 0 H A : 1 2 0 TS : t obs RR : | t obs 40.31 44.89 2 2 4.58 1.43 3.21 (5.07) (8.67) 13 9 | t.05,139 2 t.05, 20 1.725 P : P(t 1.43) .10 and .05 Conclusion :Fail to Reject the null hypothesis , don' t conclude fluoxetine reduces POMS 14. H Rank PT Rank Healthy MAT Pre-Tran MAT 14 5 5.36 2.64 11 13 4.35 4.84 4 2.5 2.61 2.42 10 7 3.78 2.92 6 8 2.78 2.94 12 2.5 4.51 2.42 9 16 3.43 15.08 1 15 1.66 11.04 67 69 Since both T1 (67) and T2 (69) are above 49, do not conclude population means (or medians) differ. 15. 9.3 10.73 2.6 / 9 0.87 t.05,8 1.860 TS : t obs RR : t obs 9.3 P : P(t 10.73) 0 16. a. Extensive : t obs 3.7 3.30 Poor : t obs 1.8 1.99 RR : t obs t.05, 4 2.132 2.51 / 5 2.02 / 5 Since extensive metabolizers are significant, may be evidence that codeine is cause b. 664 558 Codeine : TS : t obs Morphine : TS : t obs (95) 2 (114) 2 5 5 13.9 0.68 106 1.60 RR :| t obs | t.05 / 2,552 t.025,8 2.306 66.4 (10.5) 2 (0.15) 2 5 5 13.22 2.82 RR :| t obs | t.05 / 2,55 2 t.025,8 2.306 4.70 Codeine not significantly different. Morphine is significantly different 17. a. T + = 1+2+4+5+3+7+9 = 31 T - = 11+8+12+10+6 = 47 Fail to reject H0 (47>17) b. TS : t obs 0.053 0.285 / 20 0.053 0.83 RR : t obs t.05,19 1.729 0.064 c. No evidence that Orlistat increases levels of leutenizing hormones. 18. H0: D = 0 (No placebo effect) HA: D > 0 (Placebo effect) TS : z obs 8.2 9.0 / 169 8.2 11.8 0.69 RR : z obs z.05 1.645 P P( Z 11.8) 0 Strong evidence of placebo effect 19. For each test, conclude decrease if tobs < -t.05, 6-1 = -2.015 High Fat : t obs 443 854.6 / 6 1.27 Mixed : t obs 313 851.7 / 6 0.90 No Fat : t obs 760 859.0 / 6 2.17 20. di |di| -0.1 2.8 -5.2 0.35 -2.55 -5.25 0.55 5.85 -1.5 -2.4 2.05 5.85 1.88 -1.85 -4.2 0.1 2.8 5.2 0.35 2.55 5.25 0.55 5.85 1.5 2.4 2.05 5.85 1.88 1.85 4.2 rank(|di|) T1 10 12 2 9 13 3 14.5 4 8 7 14.5 6 5 11 T+ 1 10 12 2 9 13 3 14.5 4 8 7 14.5 6 5 11 63 57 Since 63 and 57 > 25, Don’t conclude differences exist in maximum concentrations by fasting and fed states. 21. a) Within regimen: Paired t-test, Signed Rank test (Before/After) b) Across regimens: Independent sample t-test, Rank Sum test (Compare Mean Before/After changes for dosing regimens) Chapter 4 22. 95%CI for Problem 12: (30.6 38.6) 1.96 (7.54) 2 (12.43) 2 8.0 (1.96)( 2.41) 8.0 4.73 (12.73,3.27) 37 36 23. 95%CI for Problem 13: (40.31 44.89) 2.086 (5.07) 2 (8.67) 2 4.58 (2.086)(3.21) 4.58 6.70 (11.28,2.12) 13 9 24. 95%CI for Problem 15: 2.6 9.3 2.306 9.3 2.306(0.87) 9.3 2.0 (7.3 , 11.3) 9 Chapter 5 23. (Bad automated numbering) a), b) , c) ^ E ^ 4 16 .0156 0.0156 E 0.0615 RR 0.2537 257 260 .0615 d) v 1 .0156 1 .0615 0.2461 0.0587 0.3048 4 16 CI : 0.2537e 1.96 0.3048 ,0.2537e1.96 0.3048 (0.2357(0.5502),0.2357(1.8174)) (0.1297,0..4284) Entire interval < 1, conclude antiplatelet trt reduces risk of primary cardiac event e) (RR-1)100% = (0.2357-1)100% = -76.43% , Reduction of 76% due to antiplatelet trt 24. Trt \ Outcome Xenical Placebo Total ^ ^ X 0.57 95%CI : >5% Reduction 1140 620 1760 1.96(.0386) Total 2000 2000 4000 0.57 1 0.57 1 0.31 1.84 v .0015 0.31 1140 620 , 1.84e1.96(.0386) (1.84(0.93) , 1.84(1.08)) (1.71 , 1.99) P 0.31 1.84e <5% Reduction 860 1380 2240 RR Entire CI > 1, Conclude that Xenical increases likelihood of >5% Reduction in body weight. 25. OR 80(395) 31600 1 1 1 1 1.62 v 0.0311 230(85) 19550 80 230 85 395 95%CI : 1.62e 1.96(.1765) v 0.1765 , 1.62e1.96(.1765) (1.62(0.71) , 1.62(1.41)) (1.15 , 2.29) Entire CI > 1, conclude odds of MI is higher for patients on CC Blockers. Cannot conclude causation. 26. ^ 174 248 0.0527 0.0527 PLAC 0.0753 RR 0.70 3302 3293 0.0753 1 .0527 1 .0753 v 0.0039 v 0.0621 174 248 95%CI : 0.70e 1.96(.0621) , 0.70e1.96(.0621) (0.70(0.89) , 0.70(1.13)) (0.62 , 0.79) ^ PRAV Entire CI < 1, conclude Pravastatin reduces risk of cardiac events. v .0386 27. Death Antisep Control Total Survive 1 6 7 Total Death 11 6 17 12 12 24 Antisep Control Total Survive 0 7 7 Total 12 5 17 28. McNemar’s Test: TS : z obs 19 10 19 10 9 1.67 5.39 RR : | z obs | 1.96 Don’t conclude detection rates differ. 29. Scandinavian/Cancer: Expected = 134(195)/410 = 63.7 2 = (63-63.7)2/63.7 = 0.008 Scandinavian/No Cancer: Expected = 134(215)/410 = 70.3 2 = (71-70.3)2/70.3 = 0.007 TS: 2obs = .017+.015+.360+.325+.533+.484+.211+.191+.006+.006+.133+.123+.008+.007=2.419 RR: 2obs 2.05,(7-1)(2-1) = 2.05,6 = 12.592 among cancer rates Don’t conclude ethnic differences exist 30. Note: Column marginal totals are reversed, should be 74 and 75, respectively. Experience <=15 <=15 >=16 >=16 OTC Switch No Yes No Yes obs exp 28 50 46 25 38.7 39.3 35.3 35.7 obs-exp -10.7 10.7 10.7 -10.7 chi-square 2.958398 2.913232 3.243343 3.207003 12.32198 Test Statistic: 2obs = 12.32 RR: 2obs 2.05,(2-1)(2-1) = 2.05,1 = 3.841 Conclude that attitudes toward switch differ by experience. 12 12 24 31. 22550 32565 10015 0.1817 22550 32565 55115 0.1817 b) TS : z obs 1.91 RR : | z obs | z.025 1.96 Don' t reject, but P 0.05 0.095 c) 0.049 1.96(0.025) 0.049 0.049) (0.098 , 0) ^ a) Borderline significan t negative associatio n 32. a) C=33(58+73+37+82)+18(58+73)+86(58+37)+82(58) = 8250+2358+8170+4756 = 23534 D=18(5+73+18+82)+86(5+18)+37(5+73)+82(5) = 3204+1978+2886+410 = 8478 ^ b) 23534 8478 15056 0.47 23534 8478 32012 RR: zobs z.05 = 1.645 Yes, Positive association c) TS: zobs = 0.47/0.059 = 7.97 d ) n 2 ni2. 410 2 136 2 137 2 137 2 168100 56034 112066 n 2 n.2j 410 2 113 2 244 2 56 2 168100 75441 92659 ^ B 15056 0.5 (112066)(92659) 15056 0.296 50951 e) 0.296 1.96(0.039) 0.296 0.076 (0.220 , 0.372) Conclude Positive assoc. 33. T1 = 23(16)+98(102)+98(249.5)+58(369.5)+40(436.5)+10(471)+7(486.5) = 81821.5 T2 = 8(16)+43(102)+56(249.5)+28(369.5)+8(436.5)+11(471)+3(486.5) = 38964.5 (81821.5) 2 (38964.5) 2 12 TS : H 491(492) 334 157 3(492) 1476.1 1476 0.1 RR : H .205,( 21)( 7 1) .205, 6 12.592 Absolutely no evidence of fatigue differences among two drugs. 34. Under independence, expect the following proportion of agreements (by chance): p11 (.301)(.390) .117 p 22 (.154)(.260) .040 p33 (.545)(.350) .191 p11 p 22 p33 .117 .040 .191 .348 Observed agrreement: .179+.057+.228 = .457 .457 .348 .109 .167 Fairly low level of agreement between the reviewers. 1 .348 .652 Chapter 6 35. 305.9 6.29 RR : Fobs F.05,3, 43 2.84 Conclude means not all equal 48.6 b) PCA has lower means than others (all CI’s completely negative) c) Tukey’s method gives narrower intervals (but Bonferroni is applicable to more situations) a) TS : Fobs 36. a) Drug (i) n_i Buproprion(1) Fluoxetine(2) Paroxetine(3) Sertraline(4) Total 22 37 21 27 107 ybar_i s_i 0.46 -0.49 -0.90 -0.49 0.80 0.97 0.73 1.25 n_i(ybar_i-ybar)^2 (n_i-1)s_i^2 15.5232 13.44 0.4477 33.8724 5.6784 10.658 0.3267 40.625 21.976 98.5954 SST SSE b) Source Trt (Drugs) Err (Subjects) df 4-1=3 107-4=103 SS 21.98 98.60 MS 21.98/3=7.33 98.6/103=0.96 F 7.33/0.96=7.64 107-1=106 Total 120.58 c) TS: Fobs =7.64 RR: Fobs F.05.3.103 2.70 exist) Conclude means not all equal (Drug effects d) Trts (i,j) (1,2) (1,3) (1,4) (2,3) (2.4) (3,4) ybar_i-ybar_j 0.46-(-0.49)=0.95 0.46-(-0.90)=1.36 0.46-(-0.49)=0.95 (-0.49-(-0.90))=0.41 (-0.49-(-0.49))=0 (-0.90-(-0.49))=-0.41 CV 0.624 0.708 0.666 0.634 0.587 0.675 Conclude 1 > 2 1 > 3 1 > 4 NSD* NSD* NSD* NSD* = Not significantly different e) Bupropion has higher mean than all others 37. i n_i 1 2 3 ybar_i 185 185 169 s_i 11.0 12.0 8.2 10.1 10.1 9.0 Sum ybar= 10.46531 z.05/2(3) = z.0083 = 2.40 n_i(ybar_i-ybar)^2 52.8910454 435.7277801 867.242399 1355.861224 SST=1355.86 dfT=3-1=2 MST=677.93 F_obs=7.10 F(.05,2,536)=3.0 (n_i-1)s_i^2 18769.84 18769.84 13608 51147.68 SSE=51147.68 dfE=539-3=536 MSE=95.42 1 1 1v 2 : (11.0 12.0) 2.40 95.42 1.0 2.40(1.02) 1.0 2.44 (3.44 , 1.44) 185 185 1 1 1v3 : (11.0 8.2) 2.40 95.42 2.8 2.40(1.04) 2.8 2.50 (0.30 , 5.30) 185 169 1 1 1v3 : (12.0 8.2) 2.40 95.42 3.8 2.40(1.04) 3.8 2.50 (1.30 , 6.30) 185 169 38. a. T .S : H 12 (2166.0 1700.2 682.7 73.5) 3(25) 92.448 75 17.448 24(25) RR : H .205, 41 7.815 Conclude Means are not all equal. b. Conclude: Placebo > 0.5, Placebo > 2.5 0.2 > 2.5 0.5 > 2.5 2.5 0.5 0.2 Placebo Treatments connected by a line are not significantly different. 39. TS : Fobs 1.38 0.19 7.17 RR : Fobs F.05, 4, 28 2.71 No evidence of formulation differences Much more variation in subjects 40. Note that the rank for form 5 is incorrect for subject 4 in table in notes. Subject Rank1 1 2 3 4 5 6 7 8 Rank2 2 4 2 1 1 3 2 2 17 Total Rank3 4 5 4 5 3 4 5 3 33 Rank4 5 1 5 3 4 5 4 4 31 Rank5 3 3 3 4 5 2 3 5 28 1 2 1 2 2 1 1 1 11 b=8 Subjects (blocks) k=5 Formulations (Treatments) 12 TS : Fr (17) 2 (33) 2 (31) 2 (28) 2 (11) 2 3(8)6 162.2 144 18.2 8(5)(6) RR : Fr .205,51 9.488 Conclude formulations are not all equal. Conclude: 1<2, 2>5, 3>5, 4>5 5 1 4 3 No others are significantly different. 2 41. a. TS : Fobs 44.70 2.73 16.40 RR : Fobs F.05, 2,92 3.10 Do not conclude interactio n exists b. Zidovudine : 77.71 4.74 16.40 52.76 3.22 16.40 TS : Fobs Disease State : TS : Fobs RR : Fobs F.05,1,92 3.95 AZT effect exists RR : Fobs F.05, 2,92 3.10 Disease state effects exist 42. TS : Fobs 0.0867 2.44 0.0356 RR : Fobs F.05,1, 22 4.30 No evidence of formulatio n difference s 43. TS : Fobs 64872.1 24.21 2680.1 RR : Fobs F.05,5, 24 2.62 Dose effects not all equal. Chapter 7 44. a. ^ 1 2.79 0.3233 8.63 ^ y 0.0536 0.3233 x ^ 0 14.682 41.27 0.3233 0.5873 0.5337 0.0536 25 25 s2 (2.79) 2 8.63 0.42 0.018 25 2 23 1.32 s 0.018 0.134 b. 0.134 0.046 t.05 / 2, 25 2 t.025, 23 2.069 2.94 8.63 95%CI : 0.3233 2.069(0.046) 0.3233 0.0952 (.2281, .4185) ^ ^ 0.134 1 Entire CI is positive, conclude positive association. c. S yy 1.32 SSE 0.42 SSR 1.32 0.42 0.90 Source Model Error Total df 1 23 24 SS 0.90 0.42 1.32 MS 0.90 0.0183 --- F 49.29 d. r 2.79 (8.63)(1.32) 2.79 0.8266 3.375 r2 0.90 0.6818 1.32 45. a. r 202.48 (22.47)( 2078.19) 202.48 0.94 216.095 b. ^ 1 202.48 9.01 22.47 c. Yes 46. z.025 = 1.96. Note that low Y values mean higher severity. The conclusions are associations, not necessarily causes. Variable Body Temp Sex (Male) Prev Stroke Atrial Fib Leucocytosis Infections Est S.E. -3.70 4.68 -4.56 -5.07 -1.21 -10.74 t=Est/SE Conclusion 1.40 -2.64286 Severity increases with temp 1.66 2.819277 Males have lower severity 1.91 -2.38743 Previous stroke increases sev 2.05 -2.47317 Atrial Fib increases sev 0.28 -4.32143 Leucocytosis increases sev 2.43 -4.41975 Infections increase sev 47. a. ^ y 1.2619 0.5623(3.25) 0.3896(1) 1.2619 1.8275 0.3896 3.4790 b. 0.3896 c. 0.2804 d. SSR = 0.2804(12.4146) = 3.4811 Source Model Error Total SSE = 12.4146-3.4811 = 8.9335 SS 3.4811 8.9335 12.4146 df 2 112 114 MS 1.7406 0.0798 F 21.81 Chapter 8 48. a. 2 TS : X 2 obs 0.0694 15.20 0.0178 2 RR : X obs .205,1 3.841 Positive association b. e0.0694 = 1.072 (7.2% increase in odds of seizure per unit increase in dose) c. 4.0733 0.0694 ED50 0 ED50 4.0733 58.7 0.0694 49. a. ^ y 3.8307 93.9809(3.8307) 46.99 3.8307 3.8307 ^ y 10 67.95 ^ y 50 87.29 ^ y 100 90.51 b. 3.8307 1.96(0.2038) 3.8307 0.3994 (3.43 , 4.23) c. Not good: The curve is very flat at top...small range of %ACE inhib covers a wide range of Enalaprilat concentrations 50. a. ^ y 50 6.115 27.620(50) 6.115 7.907 14.022 124.656 50 ^ y 100 18.409 b. Large amount of subject-to-subject variation. Chapter 9 51. a. Methylcholanthrene i t(i) 1 2 3 4 5 6 7 8 9 10 11 12 ni 14 15 16 17 18 19 20 21 22 23 28 31 di 46 45 43 37 33 28 18 15 9 8 7 6 1 2 6 4 5 10 3 6 1 1 1 1 lhat_i 0.021739 0.044444 0.139535 0.108108 0.151515 0.357143 0.166667 0.4 0.111111 0.125 0.142857 0.166667 S(t(i)) 0.978261 0.934783 0.804348 0.717391 0.608696 0.391304 0.326087 0.195652 0.173913 0.152174 0.130435 0.108696 ^ y 200 23.130 ^ y 400 27.173 Dibenzanthracene i t(i) ni 1 2 3 4 5 6 7 8 9 10 11 21 23 24 25 26 28 29 31 32 33 38 di 26 25 22 20 18 17 16 15 11 9 8 1 3 2 2 1 1 1 4 2 1 4 lhat_i 0.038462 0.12 0.090909 0.1 0.055556 0.058824 0.0625 0.266667 0.181818 0.111111 0.5 S(t(i)) 0.961538 0.846154 0.769231 0.692308 0.653846 0.615385 0.576923 0.423077 0.346154 0.307692 0.153846 n2i e1i 0.638889 1.267606 3.73913 2.349206 2.79661 5.185185 1.227273 2.560976 0.264706 0.969697 0.482759 0.518519 0.28 0.583333 0.272727 1.428571 0.625 0.357143 1.538462 27.08579 b. squares= M circles=D c. time (i) 14(1) 15(2) 16(3) 17(4) 18(5) 19(6) 20(7) 21(8) 22(9) 23(10) 24(11) 25(12) 26(13) 28(14) 29(15) 31(16) 32(17) 33(18) 38(19) Sum d1i n1i 1 2 6 4 5 10 3 6 1 1 0 0 0 1 0 1 0 0 0 41 O1-E1 = 41-27.09 = 13.91 TS : TMH groups. 13.91 12.74 d2i 46 45 43 37 33 28 18 15 9 8 7 7 7 7 6 6 5 5 5 0 0 0 0 0 0 0 1 0 3 2 2 1 1 1 4 2 1 4 26 26 26 26 26 26 26 26 25 25 22 20 18 17 16 15 11 9 8 v1i 0.23071 0.457562 1.305349 0.922602 1.147411 2.072625 0.691476 1.380428 0.194637 0.665748 0.353151 0.369315 0.2016 0.395229 0.198347 0.816327 0.401042 0.229592 0.710059 12.74321 V1 = 12.74 13.91 3.90 3.57 RR : | TMH | z.025 1.96 Conclude differences in 52. a. Bottom of Continuous Table: ni 7 5 5 2 i 2/7=.2857 0 3/5=.6000 0 di 2 0 3 0 S(t(i)) .2114(1-.2857)=.1510 .1510 .1510(1-.6)=.0604 .0604 b. circles=Intermittent squares=Continuous c. Similar to t=8, then better survival for Continuous 53. a. Increased age leads to higher risk of death (CI for RR > 1) Presence of Nausea/Vomiting leads to higher risk of death Presence of Biliary disease not associated with risk of death (CI contains 1) Low CD4 count associated with higher risk of death b. 4.1 times higher (Point estimate) 1.72 to 9.76 times higher (Interval estimate) c. No 54. a. age<35, Male, IDU behavior, date=1984-1987, Infection=PCP, CD4<50, No ZDV, No PCP Prophylaxis b. Age>35, Male, IDU behavior, Date=1984-1987, infection=CMV, CD4<50, Yes ZDV, Yes PCP prophylaxis c. Age<35, Female, Ex-IDU behavior, Date=1988-1990, infection=KS, CD4>100, No ZDV, No PCP prophylaxis d. CI for RR (0.87,1.22) contains 1, no association after controlling for other factors e. Same conclusion as d. (0.80,1.29) f. b : e 0.231000.53100.0300.058 e 0.85 2.34 c : e 00.0830.1510.2230.1390.69300 e 1.289 0.28