流行病學(xué) (第5版)：5病例對(duì)照之計(jì)算和偏倚

1、病例對(duì)照研究(2)Case-Control Study病例對(duì)照研究Case-Control StudyData AnalysisPower CalculationBias病例對(duì)照研究Case-Control StudyFigure. Design of a case-control studyExposedNotExposedExposedNotExposedDiseaseNoDiseaseCASESCONTROLS病例對(duì)照研究Case-Control StudyIDDiseaseExposureCaseGroup1YesYes2YesNo3YesYes4YesYes5YesYes YesNo

2、ControlGroup1NoNo2NoNo3NoYes4NoNo5NoYesNoNo數(shù)據(jù)分析Data Analysis(1) First SelectCaseControls(2) Then MeasurePast ExposureExposedabNot exposedcdTotalsa+cb+dAnalysis of Case-Control Study數(shù)據(jù)分析Data Analysis(1) First SelectCaseControls(2) Then MeasurePast ExposureExposedabNot exposedcdTotalsa+cb+dProportions

3、exposedCalculation of Proportion Exposed in a Case-Control Study復(fù)習(xí)：隊(duì)列研究 Cohort StudyDefined PopulationExposedNon-ExposedDiseaseNo DiseaseNON-RANDOMIZEDDiseaseNo DiseaseFigure. Design of a cohort study復(fù)習(xí)：隊(duì)列研究 Cohort StudyAnalysis of Cohort Study(2) Then Follow to See WhetherTotalsDiseaseDevelopsDisea

4、se DoesNot Develop(1) FirstSelectExposedaba+bNot exposedcdc+d復(fù)習(xí)：隊(duì)列研究 Cohort StudyRisk Calculation in a Cohort Study(2) Then Follow to See WhetherTotalsIncidenceRatesof DiseaseDiseaseDevelopsDisease DoesNot Develop(1) FirstSelectExposedaba+bNot exposedcdc+d病例對(duì)照研究Case-Control Study(1) First SelectCase

5、Controls(2) Then MeasurePast ExposureExposedabNot exposedcdTotalsa+cb+dProportionsexposedCalculation of Proportion Exposed in a Case-Control StudyCOMPARESampling Error Statistical Significance TestingAll comparative statements, stated or implied, based on survey data, must be supported by statistica

6、l testing卡方檢驗(yàn)Chi-Square TestQuestion 1: Is there a relationship (association) between exposure and disease? Or: Is there statistical significant difference between cases and controls regarding the proportion of exposed people?Bivariate tabular analysis is good for asking the following kinds of quest

7、ions: Is there a relationship between any two variables IN THE DATA? How strong is the relationship IN THE DATA? What is the direction and shape of the relationship IN THE DATA? Is the relationship due to some intervening variable(s) IN THE DATA? Chi-square allows you to make decisions about whether

8、 there is a relationship netween two or more variables; if the null hypothesis is rejected, we conclude that there is a statistically significant relationship between the variables. But we frequently want a measure of the strength of that relationship-an index of degree oof correlation, a measure of

9、 the degree of association between the variables represented in our table (and data). Luckily, several related measures of association can be derived from a tables chi square value. 卡方檢驗(yàn)Chi-Square TestResultNo Association: STOP HEREHave Association: GO ON 關(guān)聯(lián)強(qiáng)度Strength of AssociationQuestion 2: How s

10、trong is the relationship (association) between exposure and disease?How strong is the relationship IN THE DATA? What is the direction and shape of the relationship IN THE DATA? Is the relationship due to some intervening variable(s) IN THE DATA? Strength of Association: Is the exposure associated w

11、ith a high relative risk of acquiring the disease? 復(fù)習(xí)：隊(duì)列研究 Cohort StudyRisk Calculation in a Cohort Study(2) Then Follow to See WhetherTotalsIncidenceRatesof DiseaseDiseaseDevelopsDisease DoesNot Develop(1) FirstSelectExposedaba+bNot exposedcdc+d復(fù)習(xí)：隊(duì)列研究 Cohort StudyExposed people is ? times more lik

12、ely to develop a disease than non-exposed people.病例對(duì)照研究Case-Control StudyCannot calculate the RR directlyEven though we cannot calculate a relative risk from a case-control study, under many conditions, we can obtain a very good estimate of the relative risk from a case-control study using the odds

13、ratio比值OddsProbability that the event will occur divided by the probability that the event will not occur比值OddsExample:If both of your parents have an Aa genotype, the probability that you have an AA genotype is ? The odds would be ?If both parents are Aa, then the probability that you will be Aa is

14、 ? In this case, the odds would be ?no particular advantage to thinking about odds or probabilities a. most people more comfortable thinking about probabilities, but some advantage to odds比值OddsExample:If both of your parents have an Aa genotype, the probability that you have an AA genotype is 0.25.

15、 The odds would beIf both parents are Aa, then the probability that you will be Aa is 0.50. In this case, the odds would be病例對(duì)照研究Case-Control Study(1) First SelectCaseControls(2) Then MeasurePast ExposureExposedabNot exposedcdCalculation of Proportion Exposed in a Case-Control StudyWhat are the odds

16、 that a case was exposed?What are the odds that a control was exposed?病例對(duì)照研究Case-Control Study(1) First SelectCaseControls(2) Then MeasurePast ExposureExposedabNot exposedcdCalculation of Proportion Exposed in a Case-Control StudyWhat are the odds that a case was exposed?What are the odds that a con

17、trol was exposed?比值比Odds Ratio, ORThe ratio of the odds that the cases were exposed to the odds that the controls were exposed.比值比Odds Ratio, OR(1) First SelectCaseControls(2) Then MeasurePast ExposureExposedabNot exposedcdAnalysis of Case-Control StudyCross-products ratioOR=Support hypothesis of an

18、 association: a, d diseased people who were exposed and non-diseased people who were not exposedNegate hypothesis of an association: b, c non-diseased people who were exposed and diseased people who were not exposedAs Dr. Lechaim Naggan has pointed out, the odds ratio or the cross-products ratio can

19、 be viewed as the ratio of the two cells that support the hypothesis of an association (cells a and d diseased people who were exposed and non-diseased people who were not exposed), to the product of the two cells that negate the hypothesis of an association (cells b and c non-diseased people who we

20、re exposed and diseased people who were not exposed).可信區(qū)間Confidence Interval, C.I.Woolfs methodA confidence interval provides a range of values that is expected to include the true value of the parameter being estimated.比值比Odds Ratio, ORQuestion 3: What is the direction of the association and how to

21、 interpret it?OR = 1OR 1OR 1OR & RRQuestion 4: How well the OR approximates the RR? When is the OR a good estimate of the RR?Answer: When the disease being studied does not occur frequently.Why? (Self learning)Leon Gordis. Epidemiology, 3rd edition. Philadelphia: W.B. Saunders. 2004. REMEMBERThe rar

22、e-disease assumption applies only to situations in which the OR is used to estimate the RR.When the OR is used as a measure of association in itself, this assumption is obviously not needed.The rare-disease assumption does not apply to situations in which the control group is a sample of the total p

23、opulation, which is the usual strategy in case-control studies within a defined cohort.匹配病例對(duì)照研究Matched Case-Control StudyPair NoExposureCaseControl1YesNo2YesYes3YesYes4NoNo5NoYes6YesNo7YesNo8YesNo匹配病例對(duì)照研究Matched Case-Control StudyControlExposedNot ExposedCaseExposedabNot ExposedcdAnalysis of Matched

24、 Case-Control StudyPAIRSStep 1: Chi-Square TestCalculation of the odds ratio in such a matched pair study is based on the discordant pairs only (b and c). The concordant pairs (a and d, in which cases and controls were either both exposed or both not exposed) are ignored, because they do not contrib

25、ute to our knowledge of how cases and controls differ in regard to past history of exposure.上面公式：適用于較大樣本下面校正公式：對(duì)子數(shù)較少匹配病例對(duì)照研究Matched Case-Control StudyControlExposedNot ExposedCaseExposedabNot ExposedcdAnalysis of Matched Case-Control StudyConcordantpairs1. Pairs in which both the case and the contro

26、l were exposed a2. Pairs in which neither the case nor the control was exposed dDiscordantpairs3. Pairs in which the case was exposed but the control was not b4. Pairs in which the control was exposed and the case was not cPAIRSCalculation of the odds ratio in such a matched pair study is based on t

27、he discordant pairs only (b and c). The concordant pairs (a and d, in which cases and controls were either both exposed or both not exposed) are ignored, because they do not contribute to our knowledge of how cases and controls differ in regard to past history of exposure.匹配病例對(duì)照研究Matched Case-Contro

28、l StudyControlExposedNot ExposedCaseExposedabNot ExposedcdAnalysis of Matched Case-Control StudyPAIRSStep 2: Calculating OR匹配病例對(duì)照研究Matched Case-Control StudyControlExposedNot ExposedCaseExposedabNot ExposedcdAnalysis of Matched Case-Control StudyPAIRSOR=Support hypothesis of an association: b the nu

29、mber of pairs in which the case was exposed and the control was notNegate hypothesis of an association: c the number of pairs in which the control was exposed and the case was not匹配病例對(duì)照研究Matched Case-Control StudyControlExposedNot ExposedCaseExposedabNot ExposedcdAnalysis of Matched Case-Control Stu

30、dyPAIRSStep 3: 95% C.I.分級(jí)暴露資料的分析Dose Response: Test for TrendWhen exposure is categorized into multiple ordinal categories, it may be of interest to assess whether the observed relation between increasing (or decreasing) levels of exposure and the risk (or odds) of disease follows a linear dose-resp

31、onse pattern.分級(jí)暴露資料的分析Dose Response: Test for TrendStratum(i)Score(xi)No. of Cases(ai)No. of controls(bi)Total(ni)ORi1x1a1b1n11.02x2a2b2n2.kxkakbknkTotalABN分級(jí)暴露資料的分析Dose Response: Test for TrendStep 1: 2 by k chi-square independence testStep 2: calculating stratum-specific OR and their 95% C.I.Step

32、3: chi-square test for linear trend病例對(duì)照研究中的歸因分值A(chǔ)R% in Case-Control Studies復(fù)習(xí)：隊(duì)列研究 Cohort StudyUnexposedExposedFigure. Attributable risk in the exposedARexpIncidence (per 1000)復(fù)習(xí)：隊(duì)列研究 Cohort StudyFigure. Population attributable risk and its dependence on the population prevalence of the exposureUnexp

33、osedExposedARexpIncidence (per 1000)Pop ARPopulationAExposure is rareAs the population is composed of exposed and unexposed individuals, the incidence in the population is similar to the incidence in the unexposed when the exposure is rare (A) and is closer to that in the exposed when the exposure i

34、s common (B). Thus, a fixed relative risk, the population attributable risk is heavily dependent on the prevalence of exposure.復(fù)習(xí)：隊(duì)列研究 Cohort StudyExposure is commonUnexposedExposedARexpIncidence (per 1000)Pop ARPopulationB病例對(duì)照研究中的歸因分值A(chǔ)R% in Case-Control StudiesWhen the odds ratio is a reasonable es

35、timate of the RR, then病例對(duì)照研究Case-Control StudyData AnalysisPower CalculationBias功效PowerStage of the WorldH0: TrueH1: FalseResearchFindingsH0: True1- Type II Error(p=)H1: FalseType I Error(p=)1- Ideally, power analysis is carried out a priori, that is during the design stage of the study. 功效PowerPrio

36、ri AnalysisPost Hoc AnalysisSample sizeEffect sizeExposure proportion of control groupIdeally, power analysis is carried out a priori, that is during the design stage of the study. 給定樣本量的情況下（例如，有時(shí)就只能有這么多樣本，確定成功的希望大不大）A power analysis program can be used to determine power given the values of a, samp

37、le size and effect size. If the power is deemed to be insufficient, steps can be taken to increase the power, (most commonly, but not exclusively, by increasing the sample size.) Whereas a priori analysis is done before a study has been carried out, post-hoc analysis is done after a study has been c

38、arried out to help to explain the results if a study which did not find any significant effects. 病例對(duì)照研究Case-Control StudyData AnalysisPower CalculationBias偏倚Bias, Systematic ErrorWhy considering bias? That results in a mistaken estimate of an exposures effect on the risk of disease. When considering

39、 bias?Before a study: avoid and controlAfter a study: control and explain偏倚是研究設(shè)計(jì)、實(shí)施或分析過程中發(fā)生的系統(tǒng)誤差，導(dǎo)致錯(cuò)誤的估計(jì)暴露對(duì)疾病危險(xiǎn)性的效應(yīng)。偏倚Bias, Systematic ErrorSelection biasInformation biasConfounding bias選擇偏倚Selection BiasDifferentiatingSelecting subjects for a studyGeneralizability, external validitySelection biasIn

40、ternal validity注意區(qū)分研究對(duì)象的選擇和選擇偏倚。實(shí)際上，每項(xiàng)在人群中開展的研究都會(huì)從一個(gè)大的人群中選擇部分作研究對(duì)象。這種選擇可能會(huì)影響到結(jié)果的外部真實(shí)性（external validity）、外推（generalizability），但是不一定會(huì)影響到研究中進(jìn)行的比較的真實(shí)性，或說(shuō)內(nèi)部真實(shí)性（internal validity）。選擇偏倚會(huì)導(dǎo)致OR或RR非正確的估計(jì)值，因此使得推論的暴露和疾病間的關(guān)聯(lián)大小和方向可能是錯(cuò)誤的。選擇偏倚是在選擇研究中一個(gè)或多個(gè)研究組的研究對(duì)象時(shí)發(fā)生的系統(tǒng)誤差，對(duì)研究的內(nèi)部真實(shí)性有重要的影響。 選擇偏倚Selection BiasTechnical

41、 definitionBias that is caused when individuals have different probabilities of being included in the study according to relevant study characteristics: namely, the exposure and the outcome of interest.In a case-control study of smoking andchronic lung disease, the association ofexposure with diseas

42、e will tend to beweaker if controls are selected from ahospital population (because smokingcauses many diseases resulting inhospitalization) than if controls areselected from the community.In this example, hospital controls do notrepresent the prevalence of exposure(smoking) in the community from wh

43、ichcases of chronic lung disease arise. Theexposure-disease association has beendistorted by selection of hospital controls.選擇偏倚Selection BiasUnbiasedBiased入院率偏倚Berkson BiasCancer of the pancreas and their uses of tobacco, alcohol, tea, and coffeeCases: Patients with histologically proved cancer of

44、the pancreasControls: Other patients under the care of the same physician of the cases with pancreatic cancer.Patients with diseases known to be associated with smoking or alcohol consumption were excluded.This is what the authors did. For controls, they choose patients under the care of the same ph

45、ysician of a case patient at the same time the case patient was diagnosedThey also excluded patients with diseases known to be associated with smoking or alcohol consumption.What do you think of this control selection? Any problems with this?(best approach: limit to cases who were were residents of

46、the area when they were diagnosed. Then assume that all panc cancer gets diagnosed in the region. Sample controls using a pop-based sample of persons. Incidence density in a free living population)tobacco, alcohol, tea, and coffee入院率偏倚Berkson BiasCasesControlsCoffee 1cup/day207275No coffee 9 32 OR=

47、(207/9) / (275/32) = 2.7 (95% C.I., 1.2-6.5)Do you believe?入院率偏倚Berkson BiasThere are many reasons to believe that this odds ratio is biased. Controls who were examined were:Other patients under the care of the same physician at the time of an interview with a patient with pancreatic cancerMost of t

48、he MDs were gastroenterologists whose other patients were likely advised to stop using coffeePatients with diseases known to be associated with smoking or alcohol consumption were excludedSmoking and alcohol use are correlated with coffee use; therefore, sample is relatively depleted of coffee users

49、N Engl J Med. 1981 Mar 12;304(11):630-3.Related Articles, Links Coffee and cancer of the pancreas.MacMahon B, Yen S, Trichopoulos D, Warren K, Nardi G.We questioned 369 patients with histologically proved cancer of the pancreas and 644 control patients about their use of tobacco, alcohol, tea, and c

50、offee. There was a weak positive association between pancreatic cancer and cigarette smoking, but we found no association with use of cigars, pipe tobacco, alcoholic beverages, or tea. A strong association between coffee consumption and pancreatic cancer was evident in both sexes. The association wa

51、s not affected by controlling for cigarette use. For the sexes combined, there was a significant dose-response relation (P approximately 0.001); after adjustment for cigarette smoking, the relative risk associated with drinking up to two cups of coffee per day was 1.8 (95% confidence limits, 1.0 to

52、3.0), and that with three or more cups per day was 2.7 (1.6 to 4.7). This association should be evaluated with other data; if it reflects a causal relation between coffee drinking and pancreatic cancer, coffee use might account for a substantial proportion of the cases of this disease in the United

53、States.入院率偏倚Berkson Bias多個(gè)醫(yī)院多病種Alternatively, knowledge of the exposure ofinterest might lead to an increased rate of admission tohospital. For example, doctors who care for women withsalpingitis were more likely to recommend hospitaladmission for those using an intrauterine device (IUD)than for tho

54、se using a hormonal method ofcontraception.18,19 In a hospital-based case-control study,this would stack the deck (or gynaecology ward) with ahigh proportion of IUD-exposed cases, spuriouslyincreasing the odds ratio.Schwartzbaum J, Ahlbom A, Feychting M. Berksons bias reviewed. Eur J Epidemiol 2003;

55、18(12):1109-12.Sadetzki S, Bensal D, Novikov I, Modan B. The limitations of using hospital controls in cancer etiology-one more example for Berksons bias. Eur J Epidemiol 2003;18(12):1127-31. 入院率偏倚Berkson BiasRecommended References1. Schwartzbaum J, Ahlbom A, Feychting M. Berksons bias reviewed. Eur

56、 J Epidemiol 2003;18(12):1109-12.2. Sadetzki S, Bensal D, Novikov I, Modan B. The limitations of using hospital controls in cancer etiology-one more example for Berksons bias. Eur J Epidemiol 2003;18(12):1127-31.現(xiàn)患新發(fā)病例偏倚Neyman BiasUp: How rarely the patients with short survival times appear among th

57、e prevalent cases. Down” Notice that the incident cases include a fair number of patients with short survival times. 現(xiàn)患新發(fā)病例偏倚Neyman Bias現(xiàn)患新發(fā)病例偏倚Neyman BiasThis can make a critical difference for a case control design where you have risk factors that are associated not with the disease itself, but wi

58、th mortality. Any risk factor that makes a person die quickly is going to be underrepresented among prevalent cases and could lead to a spurious finding.現(xiàn)患新發(fā)病例偏倚Neyman BiasNeyman bias is an incidence-prevalence bias. It ariseswhen a gap in time occurs between exposure andselection of study participa

59、nts. This bias crops up instudies of diseases that are quickly fatal, transient, orsubclinical. Neyman bias creates a case group notrepresentative of cases in the community. For example, ahospital-based case-control study of myocardialinfarction and snow shovelling (the exposure of interest)would mi

60、ss individuals who died in their driveways andthus never reached a hospital; this eventuality mightgreatly lower the odds ratio of infarction associated withthis strenuous activity.檢出征候偏倚Detection signal biasThe often quoted example is that of oestrogen administered as.hormone replacement therapy (H