Questo 7. Cse Cotrol Expose 50 ( ( 7 ( Uexpose 38 ( 54 ( 76 ( 88 ( 545 ( 833 ( OR ˆ / (50(54/((38 5.4 log ( OR ˆ.657 Vˆ r (log( OR ˆ / / / / /50 / /38 /54.0737 95% ofee tervl for log OR: log ( OR ˆ Z α ( Vˆ r (log( OR ˆ.657.96 (.0737 (.49,.89 95% ofee tervl for OR: (e.49, e.89 (3.08, 8.93 Smll smple justmet: OR ˆ /(( (50(54/((39 4.98 log( O Rˆ log((.5(.5/(.5(.5 log((50.5(54.5/(.5(38.5.64 Vˆ r ( log( O Rˆ /(.5 /(.5 /(.5 /(.5 /50.5 /.5 /38.5 /54.5.074 Smll smple 95% ofee tervl for log OR: log( O Rˆ Z α ( Vˆ r ( log( O Rˆ.64.96 (.074 (.46,.694 Smll smple 95% ofee tervl for OR: (e.46, e.694 (3.05, 8.75 From the ofee tervl, whh oes NOT lue the ull vlue OR, we my fer tht there s some evee of ssoto etwee omss fuel exposure TB se sttus. The os rto of TB for expose ompre to uexpose vuls ws estmte s 5.4 (3.08, 8.93. The fferee ssote wth the smll smple justmet s eglgle.
STATA. put se fuel out se fuel out. 50. 0 38 3. 0 4. 0 0 54 5. e se fuel [freqout], wo (The wo (short for Woolf opto s eee here to get Stt to o the omprle lultos to ove fuel Proporto Expose Uexpose Totl Expose Cses 50 38 88 0.736 Cotrols 54 545 0.0385 Totl 7 76 833 0.085 Pot estmte [95% Cof. Itervl] ---------------------------------------------- Os rto 5.4097 3.07877 8.95503 (Woolf Attr. fr. ex..809366.67595.887965 (Woolf Attr. fr. pop.40495 ----------------------------------------------- h( 44.0 Pr>h 0.0000 Wthout the wo opto, Stt proves ext ofee tervls. se fuel [freqout] Proporto Expose Uexpose Totl Expose Cses 50 38 88 0.736 Cotrols 54 545 0.0385 Totl 7 76 833 0.085 Pot estmte [95% Cof. Itervl] ---------------------------------------------- Os rto 5.4097 3.004807 9.386937 (ext
Attr. fr. ex..809366.667999.893469 (ext Attr. fr. pop.40495 ----------------------------------------------- h( 44.0 Pr>h 0.0000 Questo 7.3 Alohol Cosumpto (gms/y Cses Cotrols >80 96 09 05 <80 04 666 770 00 775 995 ORˆ (96(666 (09(04 5.640 logorˆ log(5.640.730 Vr ˆ (logorˆ 96 09 04 666 0.03 95% Cofee Itervl for OR : logorˆ ± Z 0. 975 Vr( ˆ logor ˆ.730 ±.96 0.03 (.39,.07 ( e.39, e.07 (4.00,7.95 H 0 : OR,.e., there s o ssoto etwee oesophgel er lohol osumpto (epeee H A : OR,.e., there s ssoto etwee oesophgel er lohol osumpto. χ os ( (995(96 666 09 04 ( ( ( ( (05(770(00(775 0.6 Ρ( χ > 0.6 < 0.000
So there s evee to suggest ssoto etwee lohol osumpto ee of oesophgel er. The OR for oesophgel er omprg hevy lohol osumers (>80 gms/y to lght lohol osumers (<80 gms/y ws estmte s 5.64 (3.97,7.9. ORˆ ( ( (96(666 (0(05 5.536 (logorˆ ( ( (96.5(666.5 log log.76 ( ( (09.5(04.5 Vr ˆ (logorˆ 96.5 09.5 95% Cofee Itervl for OR : 04.5 666.5 0.03 (logorˆ ± Z 0. 975 Vr( ˆ log OR ˆ.76 ±.96 0.03 (.38,.07 ( e.38, e.07 (3.97,7.9 The smll smple justmets re less th % the pot estmte of OR, mke o hge to the seo eml ple the ssote 95% ofee tervl. Here, the smple szes of ses otrols re lrge eough to gore smll smple justmets. STATA:. sply hpro(,0.6 8.595e-6. 96 04 09 666, wo Proporto Expose Uexpose Totl Expose Cses 96 04 00 0.4800 Cotrols 09 666 775 0.406 Totl 05 770 975 0.03 Pot estmte [95% Cof. Itervl] ---------------------------------------------- Os rto 5.640085 4.000589 7.95467 (Woolf Attr. fr. ex..86977.7500368.87437 (Woolf Attr. fr. pop.3948949 ----------------------------------------------- h( 0.6 Pr>h 0.0000
. put se lohol out se lohol out. 96. 0 09 3. 0 04 4. 0 0 666 5. e. se lohol [freqout], wo lohol Proporto Expose Uexpose Totl Expose Cses 96 04 00 0.4800 Cotrols 09 666 775 0.406 Totl 05 770 975 0.03 Pot estmte [95% Cof. Itervl] ---------------------------------------------- Os rto 5.640085 4.000589 7.95467 (Woolf Attr. fr. ex..86977.7500368.87437 (Woolf Attr. fr. pop.3948949 ----------------------------------------------- h( 0.6 Pr>h 0.0000 Questo 9. Low Iome Exposure Cse Cotrol Yes 38 50 No 0 4 43 40 53 93 Hgh Iome Exposure Cse Cotrol Yes 9 No 36 383 59 48 39 540 Iome OR / / Low 4.38 8.87 4.77 Hgh 3.75 8.5.67 Totl 6.798 6.444 The Os Rto for the low ome ssote wth omss fuel exposure s 4.38 for the low ome strtum, 3.75 for the hgh ome strtum. The
Mtel-Heszel estmtor ssote wth omss fuel exposure, otrollg for the two ome levels s OR^ 6.798/6.444 4.6. Comprg ths juste estmte to the rue Os Rto (5.4 there oes pper to e pprele mout of ofoug of the exposure-sese reltoshp y ome. The rue juste os rtos ffer y pproxmtely 0%. Uer the ssumptos of the followg usl grph, the ome vrle fulflls rter requre for vrle to e ofouer (ome s ommo use of oth exposure sese. Iome Exposure Dsese The os rto of. reporte y the uthors fter justmet for ge, sex other vrles tes tht the rue os rto ws strogly ofoue y the presee of these other vrles (5.4. ffer y ~ 60%. STATA. put se expose ome out se expose ome out. 0 38. 0 0 0 3. 0 0 4. 0 0 0 4 5. 6. 0 36 7. 0 9 8. 0 0 383 9. e. se expose [freqout], y(ome wo ome OR [95% Cof. Itervl] M-H Weght ------------------------------------------------------------------ 0 4.37745.7985 8.790648 4.77474 (Woolf 3.75490.54795 9.08355.66667 (Woolf ------------------------------------------------------------------ Crue 5.4097 3.07877 8.95503 (Woolf M-H ome 4.58475.40977 7.9945 ------------------------------------------------------------------- Test of homogeety (M-H h( 0.07 Pr>h 0.7887
Test tht ome OR : Mtel-Heszel h( 8.76 Pr>h 0.0000 Questo 9. Alohol Age 5-54 yers Cosumpto (gms/y Cses Cotrol >80 30 64 94 <80 6 408 434 56 47 58 Alohol Age 55-75 yers Cosumpto (gms/y Cses Cotrol >80 66 45 <80 78 58 336 44 303 447 H 0 : Alohol osumpto oesophgel er re epeet, otrollg for ge. H A : Alohol osumpto oesophgel er re ot epeet, otrollg for ge. Cohr-Mtel-Heszel Test: Age 5--54 yers ol 30 9.970 7.340 55 75 yers ol 66 35.758 8.6 Totl 96 45.78 5.60 A V
χ (96 45.78 5.60 98.7 P( χ ( > 98.7 < 0.000 There s suffet evee to suggest ssoto etwee lohol osumpto oesophgel er, outg for the ofoug effet of ge. Summry Estmtes of the Os Rto: Woolf's Metho : log ORˆ log ( ( ( ( w Vr(log ORˆ log ORˆ W w w log ORˆ
Mtel - Heszel Metho : ORˆ w ORˆ w ORˆ w Woolf Mtel-Heszel Age logor w w logor OR I / I / 5 54.986.303.447 7.356 3.8 3.5 55 75.57 8.649 9.97 4.85 38.094 7.85 Totl 9.95 5.744 6.76.004 log( O Rˆ W 5.744 9.95.78 ORˆ W 5.67 Vr ˆ (log ORˆ W w 9.95 0.033
± ± W W OR Vr OR e e OR Vr Z OR ˆ (log 5.569.004 6.76 ˆ (3.943,8.037, ( OR : for Itervl 95% Cofee (.37,.084 0.033.96.78 ˆ (log ˆ ˆ log log OR : for Itervl 95% Cofee.084.37 0.975
Age ( ( 5--54 3.8 3.5 0.830 0.70 55 75 38.094 7.85 0.75 0.75 Totl 6.76.004 ( ( ( ( 9.4 0.536 6.557 7.68.59 6.69 54.8.695.76 Vr ˆ (logorˆ 54. 8 (6.76.695 (.004 7.76 (6.76(.004 0.035 95% Cofee Itervlfor log OR : logorˆ ± Z 0.975 Vr ˆ (logorˆ log 5.569±.96 0.035 (.348,.086 95% Cofee Itervlfor OR : ( e.348, e.086 (3.850,8.053 Both methos gve very smlr estmtes of the OR very smlr ofee tervls. The results re lso smlr to those fou Questo 7.3, suggestg tht ge my hve lttle ofoug effet of the reltoshp etwee lohol osumpto ee of oesophgel er.
STATA:. put ge lohol ses out ge lohol ses out. 30. 0 64 3. 0 6 4. 0 0 408 5. 0 66 6. 0 0 45 7. 0 0 78 8. 0 0 0 58 9. e. ses lohol [freqout], y(ge wo ge OR [95% Cof. Itervl] M-H Weght ------------------------------------------------------------------ 0 4.858 3.075577 7.650 7.85349 (Woolf 7.355769 4.087436 3.3748 3.555 (Woolf ------------------------------------------------------------------ Crue 5.640085 4.000589 7.95467 (Woolf M-H ome 5.568569 3.874674 8.00985 ------------------------------------------------------------------- Test of homogeety (M-H h(. Pr>h 0.706 Test tht ome OR : Mtel-Heszel h( 98.7 Pr>h 0.0000