Methods in Epidemiology. Medical statistics 02/11/2014. Estimation How large is the effect? At the end of the lecture students should be able

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1 Methods n Epdemology Estmaton How large s the effect? Medcal statstcs At the end of the lecture students should be able to llustrate the prncples of statstcal nference to nterpret confdence ntervals Methods n epdemology Medcal statstcs Estmaton 1

2 The structure of clncal research Plannng Implementaton queston protocol Actual study Target populaton object Parameter θ T populaton Varables to be measured conclusons θ = Methods n epdemology Medcal statstcs Estmaton ( ˆ ) S Eθ Random errors Inference Samplng dstrbuton sample Data Estmate θˆ Objectve. To assess effcacy and safety of olmesartan medoxoml vs ramprl n elderly patents wth essental hypertenson (J Hypertens 2010; 2: 232) Result. 12 weeks after randomzaton SBP was reduced more wth Olmesartan medoxoml than wth ramprl [17, (IC 95%: 1,-1,9) vs 15,7 (1,7-1,) mmhg]. Dfference was statstcally sgnfcant (p = 0,01) Objectve. To determne whether adjunctve dexamethasone treatment mproves the outcome n adults wth acute bacteral menngts (NEJM 2002; 37: 159) Result. Treatment wth dexamethasone was assocated wth a reducton n the rsk of an unfavorable outcome (relatve rsk, 0.59; 95 percent confdence nterval, 0.37 to 0.9; P=0.03). 2

3 The structure of clncal research Implementaton protocol Actual study Inference Estmaton (confdence ntervals) Hypothess testng (statstcal sgnfcance) Inference s based on samplng dstrbuton populaton Varables to be measured conclusons θ = Methods n epdemology Medcal statstcs Estmaton ( ˆ ) S Eθ Random errors Inference Samplng dstrbuton sample Data Estmate θˆ Pont and nterval estmaton Estmate θˆ s our best nformaton on the parameter ( ) E θˆ The sngle value θˆ (pont estmate) gves no nformaton on the varablty of estmates ES E( θˆ ) Samplng dstrbuton s the probablty lnk between the estmate and the parameter θˆ ( ) E θˆ SE measures how much the sample estmates θˆ spread around the mean E( ) θˆ and s a measure of the precson of our estmate, that s how relable are our conclusons θˆ Pont estmates are qute nvarably wrong; thus we estmate the populaton mean to le somewhere n a gven nterval around the pont estmate (confdence nterval) 3

4 Confdence nterval Is constructed around the observed effect and provdes an nterval of values that straddle the true value (parameter) wth a gven probablty (usually 95%) The wdth of the nterval s a measure of the precson of the estmate Objectve. To determne whether adjunctve dexamethasone treatment mproves the outcome n adults wth acute bacteral menngts (NEJM 2002; 37: 159) Result. Treatment wth dexamethasone was assocated wth a reducton n the rsk of an unfavorable outcome (relatve rsk, 0.59; 95 percent confdence nterval, 0.37 to 0.9; P=0.03). Confdence nterval (95%) The mean of the samplng dstrbuton s the true value of the dfference δ = E(δˆ). The observed dfferences δˆ are spread around δ mm Hg Observed effect δ δˆ 0-2 -

5 Confdence nterval (95%) The mean of the samplng dstrbuton s the true value of the dfference δ = E(δˆ). The observed dfferences δˆ are spread around δ mm Hg Observed effect δ 0 δˆ -2 - Confdence nterval (95%) The mean of the samplng dstrbuton s the true value of the dfference δ = E(δˆ). The observed dfferences δˆ are spread around δ mm Hg Observed effect δˆ δ

6 Confdence nterval (95%) The mean of the samplng dstrbuton s the true value of the dfference δ = E(δˆ). The observed dfferences δˆ are spread around δ mm Hg Observed effect δˆ δ In 95% of all samples the true value δ s straddled wthn the confdence nterval How to calculate confdence ntervals? ˆ θ ± z ES ˆ θ The general formula s ( ) where z s the standard normal value assocated to the wdth of the nterval as long as the samples are large enough (n>0) I.C. 90% 95% 99% z P(z > z) Two taled P(z > z) o P(-z < -z) 1,5 0,05 0,10 1,9 0,025 0,05 2,57 0,005 0,01 f the number of subjects s low (n<0) we should use the Student s t dstrbuton (varable wth DoF)

7 How large s the heght dfference between male and female students? We are lookng for 95% C.I. of a mean dfference n u = 3 n d = 22 µˆ u = 177,3 µˆ d = 15, δˆ = 11,9 σˆ =,5 p z = 1,9 Lower lmt ( ) = = 7. Upper lmt ( ) = = 1. Data are ndependent ˆ µ ˆ µ = ˆ δ A B ES( ˆ) δ = ˆ σ p + na nb How large s the heght dfference between male and female students? We are lookng for 95% C.I. of a mean dfference n u = n d = 12 µˆ u = 177,3 µˆ d δˆ = 15, = 11,9 σˆ p =,5 t 1 = 2,10 Lower lmt 1 12 ( ) = = 3. Upper lmt 1 12 ( ) = = 20.0 Sample sze s lower thus CI s larger and precson of the estmate s lower (n s at the denomnator of the SE) 7

8 Confdence nterval Propertes 1. Greater the wdth of the CI less precse the estmate of the effect 2. The wdth of the CI depends on the study sze and the requred precson Greater the sample sze smaller the wdth and more precse the estmate Larger the confdence requred (e.g. 99% rather than 95%) greater the wdth and less precse the estmate Objectve. To assess effcacy and safety of olmesartan medoxoml vs ramprl n elderly patents wth essental hypertenson (J Hypertens 2010; 2: 232) Result. 12 weeks after randomzaton SBP was reduced more wth Olmesartan medoxoml than wth ramprl [17, (IC 95%: 1,-1,9) vs 15,7 (1,7-1,) mmhg]. Dfference was statstcally sgnfcant (p = 0,01) Actually we should read the confdence nterval of the mean dfference between the groups!

9 Ths study amed to nvestgate the prevalence of metabolc syndrome among a Korean workng populaton and determne whether the prevalence dffered accordng to occupaton, age and gender. A stratfed multstage clustered probablty desgn was used to select representatve samples of nonnsttutonalzed Korean cvlans for the survey. For readers t would be better to report Cs rather than SE, but we may calculate them [eg for 3] 35.%±1.9 (2.3) Methods n epdemology Medcal statstcs Estmaton? SE o CI? 9