S tatistik fo r M P H : 5 F ra d en 4 . u g es statistik u n d erv isn in g : F ...
S tatistik fo r M P H : 5 F ra d en 4 . u g es statistik u n d erv isn in g : F ...
S tatistik fo r M P H : 5 F ra d en 4 . u g es statistik u n d erv isn in g : F ...
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The Mantel-Ha<strong>en</strong>szel <strong>es</strong>timator.A common odds <strong>ra</strong>tio <strong>fo</strong>r all st<strong>ra</strong>ta may be <strong>es</strong>timated by theMantel-Ha<strong>en</strong>szel <strong>es</strong>timator∑ a·d= OR MHn∑ b·cn(weighted ave<strong>ra</strong>ge of sepa<strong>ra</strong>te OR-<strong>es</strong>timat<strong>es</strong>)In the example:OR MH =0·23092431 + 72·238243211·1112431 + 48·20742432= 0.17011The Mantel-Ha<strong>en</strong>szel t<strong>es</strong>t.In each st<strong>ra</strong>tum, we can calculate:OBS<strong>erv</strong>ed = aEXPected = (a+b)(a+c)SD == E(a)√ n(a+b)(c+d)(a+c)(b+d)n 2 (n−1)= SD(a)The comb<strong>in</strong>ed Mantel-Ha<strong>en</strong>szel t<strong>es</strong>t statistic is( ∑ a − ∑ E(a)) 2∑ (SD(a))2= X 2 MH ∼ χ 2 1 under H 0In the example: X 2 MH =((0 + 72) −( 111·11)) 22431 + 2146·1202432111·11·2320·2420(2431) 2·2430 + 120·2146·286·2312(2432) 2·2431= (−34.39)212.32= 96.0, P < 0.001.12
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