【導讀】(.fracture,(somecells<5).sparsedata(somecells<5).insmokersvs.non-smokers.ratio…normaldistribution?Simulation…(exposure),p=.23(UNDERTHENULL!resulting2x2table.oftimes).thenullhypothesis.note. Normal!1111???Z. Confidenceinterval…eeOR. ;lnOR>0. lnOR=.288

　　

【正文】 ressants a risk factor for suicide attempts in children and adolescents? ?Example modified from: “Antidepressant Drug Therapy and Suicide in Severely Depressed Children and Adults ”。 Olfson et al. Arch Gen 。63:865872. Example 2: Difference in Proportions ? Design: Casecontrol study ? Methods: Researchers used Medicaid records to pare prescription histories between 263 children and teenagers (618 years) who had attempted suicide and 1241 controls who had never attempted suicide (all subjects suffered from depression). ? Statistical question: Is a history of use of antidepressants more mon among cases than controls? Example 2 ? Statistical question: Is a history of use of antidepressants more mon among heart disease cases than controls? What will we actually pare? ? Proportion of cases who used antidepressants in the past vs. proportion of controls who did No (%) of cases (n=263) No (%) of controls (n=1241) Any antidepressant drug ever 120 (46%) 448 (36%) 46% 36% Difference=10% Results Is the association statistically significant? ? This 10% difference could reflect a true association or it could be a fluke in this particular sample. ? The question: is 10% bigger or smaller than the expected sampling variability? Hypothesis testing Null hypothesis: There is no association between antidepressant use and suicide attempts in the target population (= the difference is 0%) Step 1: Assume the null hypothesis. Hypothesis Testing Step 2: Predict the sampling variability assuming the null hypothesis is true )033.=1241)15045681(1504568+263)15045681(1504568=σ,0(N~p?p? c o n t r o l sc a s e sAlso: Computer Simulation Results Standard error is about % Hypothesis Testing Step 3: Do an experiment We observed a difference of 10% between cases and controls. Hypothesis Testing Step 4: Calculate a pvalue 003.=p。=033.10.=ZWhen we ran this study 1000 times, we got 1 result as big or bigger than 10%. Pvalue from our simulation… We also got 3 results as small or smaller than –10%. Pvalue From our simulation, we estimate the pvalue to be: 4/1000 or .004 Here we reject the null. Alternative hypothesis: There is an association between antidepressant use and suicide in the target population. Hypothesis Testing Step 5: Reject or do not reject the null hypothesis. What would a lack of statistical significance mean? ? If this study had sampled only 50 cases and 50 controls, the sampling variability would have been much higher—as shown in this puter simulation… Standard error is about 10% 50 cases and 50 controls. Standard error is about % 263 cases and 1241 controls. With only 50 cases and 50 controls… Standard error is about 10% If we ran this study 1000 times, we would expect to get values of 10% or higher 170 times (or 17% of the time). Twotailed pvalue Twotailed pvalue = 17%x2=34% Practice problem… An August 2020 research article in Developmental and Behavioral Pediatrics reported the following about a sample of UK kids: when given a choice of a nonbranded chocolate cereal vs. CoCo Pops, 97% (36) of 37 girls and 71% (27) of 38 boys preferred the CoCo Pops. Is this evidence that girls are more likely to choose brandnamed products? Answer 1. Hypotheses: H0: p♂p♀= 0 Ha: p♂p♀≠ 0 [twosided] 2. Null distribution of difference of two proportions: 3. Observed difference in our experiment = .= .26 4. Calculate the pvalue of what you observed: 085.38)16(.84.37)16(.84.)38)75631(756337)75631(7563,0(~????????? ?Npp mfdata _null_。 pval=(1probnorm())*2。 put pval。 run。 5. pvalue is sufficiently low for us to reject the null。 there does appear to be a difference in gender preferences here. Null says p’s are equal so estimate standard error using overall observed p 5. 026. ???ZKey twosample Hypothesis Tests… Test for Ho: μx μy = 0 (σ2 unknown, but roughly equal): Test for Ho: p1 p2= 0: 2)1()1(。222222?????????nsnsnsnsnsyxtyyxxpypxpn2122112121 ??。)1)(()1)((??nnpnpnpnppnppppZ????????Corresponding confidence intervals… For a difference in means, 2 independent samples (σ2’s unknown but roughly equal): For a difference in proportions, 2 independent samples: ypxpn nsnstyx222/,2)( ???? ? ?212/21)1)(()1)(()??(nppnppZpp ???????Appendix: details of ranksum test… Wilcoxon Ranksum test ),m i n (12)1(2 Z 2)1(U,10 ,01f or