Epidemiology And Biostatistics - Ask Mish

what does each study mean: 1.CASE REPORT or CASE SERIESREPORT report of one case or a small# of cases of a disease with lowprevalence 2.2.CROSS SECTIONAL disease vs nondisease one point in time 3.3.CASE CONTROL one diseasefollowed back in time to find associatedcauses and risk F 4.4.COHORT one risk F followed in thefuture to find associated disease(s) 5.5.RCT interventional study to verify ahypothesis vs all the above which areobservational ospective)cohort(prospective)

design of an observational studyDISEASENO DISEASEEXPOSEDABNONEXPOSEDCD*2 groups of people: exposed to arisk F vs non-exposedA,B,C,D number of people fromthe 2 groups above that have disease/not

hypothesis testing in observational studies if A C then A RISK FACTOR could be highlyprobable. A hypothesis is formulated but cannot be tested incase report and case series report also calledDESCRIPTIVE studies Hypothesis could be verified in cross sectional, casecontrol and cohort study. What we want to see is if A Cdue to hazard or the value is statistically significant ANALYTICAL studies Hypothesis testing : uses formulas for each study tosee if the association of risk F w/ disease is due tohazard or is statistically significant. Below are the nameof formulas used to test this association for each study. cross sectional: chi square case control: odds ratio cohort: relative/attributable riskDISEASENO DISEASEEXPOSEDABNONEXPOSEDCD

graphical representation of studiesstrong evidenceRCTcohortcase control analytical(hypothesis tested)cross sectionalweak evidencecase report, case series descriptive(hypothesis formulated)

Hypothesis testing in observational studies(1): conceptscase controlrisk factorscrosssectionalone diseaseodds ratio (OR)odds interested/uninterestedthis case: Exposed/Non exposedcohortone risk factorchi squaremany diseasesrelative risk, attributable risk (RR,AR)RRR* or RRI* relative risk reduction orrelative risk increase of the exposediseasenodiseaseexposedabnonexposedcd

Hypothesis testing in observational studies(2) formulascrosssectionalcase controloddsratioOR odds of exposure for casesdivided by odds of exposure for controlsa/c :b/d ad/bccohortrelative osedRR incidence among exposed vsincidence among unexposeddiseaseno diseaseaba/all :c/all a/c (DIVISION)dQuestion for RR:how much more likely?cRRR* or RRI* 1RR AR also called absolute risk reduction ARRAR incidence in the exposed -incidence in the controlQuestion for AR: how many more cases in E vs U?NNT *& NNH* 1/ ARR

How to interpret Relative Risk and Odds Ratio HOW TO INTERPRET RR AND ODDS RATIO 1 means no association disease-risk factor, 1 is increased risk for disease in exposed and 1 means decreased risk of disease in exposed. Calculation: RR 2.5 means 150% increasedrisk; RRI 1-RR x100 so RRI 1-2.5 x100 ;RRI 150% . RR 0.3 means 70% decreased risk;RRR 1-0.3 x100 70% Application of RR in clinical practice:Let’s suppose we have a study in which weused Estrogen/Progesterone to decrease the riskof CAD. Final result :RR 0.39 meaningRRR 61% equals 61% less risk of disease in theE/P group. If you have a woman with 20%Framingham CAD risk how much will be herrisk of CAD if she receives E/P? Multiply 0.39(RR)x 20%(Framingham.risk) approximative8% risk of CAD with E/P.How big should be RR or Odds ratio?Depends on study. RCT, least prone to bias, asmall variation is enough; in COHORT studyRR 3 , in CASE CONTROL study OR 4 (Casecontrol has a greater risk of bias)

NNT(number needed to treat) and NNH (number needed to harm)2.Total:100 people1.NNT/NNHrefer to# peopletreatedNNTNNHtreatmentas curetreatment w/side effectsto prevent 1 to prevent 1case(disease case(disease))diseaseno diseaseexposed:50545nonexposed:500501.NNT NNH :# people you need to treat/harm to prevent the appearance of 1 new case of disease (definition in table 1)2.Example : How to calculate NNT/NNH from table 2NNT/NNH : if you treat all 100 people you prevent the 5 cases of diseaseso you need to treat x NNT to prevent1 case of diseaseapply 3 simple rule: NNT 1x100/5 20meaning you need to treat 20 people in order to prevent 1 case of diseasealso calculate : NNT/NNH 1/ARR

Intervention studies: Clinical TrialsRCT design CLINICAL TRIAL intervention studies forthe benefit of patients usually involves the administration of a testregimen to evaluate its safety and efficacy study has 2 arms: people ondrug(intervention) and people on placebo(control) group RCT randomized controlled clinical trial :subjects randomly allocated into one group,intervention or control double blind: neither subject norresearchers know which group the subject is,intervention or control crossover study: switch arms of the studyone point in time, intervention groupbecomes control and control becomesintervention community trial: an entire communityreceives a regimen testing how the regimenworks in the real worldCROSSOVER in RCT

FDA approval for a drug : 3 Clinical Trial Phases For FDA approval 3 phases of theclinical trials must be passed: Phase 1: testing safety in healthyvolunteers Phase 2: testing efficacy ( doselevels) in small group of patientvolunteers Phase 3: testing efficacy and safetyin larger group of patient volunteers.Phase 3 is considered a definitive testfor FDA. Phase 4: not necessary for FDAapproval; is called post marketingsurvey and focuses on long termsafety (e.g. Vioxx)

Bias in researchType of BIASDEFINITIONImportant associationsSolutionsSELECTIONsample not representativeBerkson’s bias using hospital datanonrespondent bias p.included instudy are different than non-includrandom, independent sampleMEASUREMENTgathering information distorts itHawthorne effect people underobservation behave differentlycontrol group/placebo groupEXPERIMENTER EXPECTANCYresearcher’s beliefs affect outcomePygmalion effectdouble-blind designLEAD-TIMEearly detection confused w/increased survivalbenefits of screeningmeasure “back-end” survival(backend age of death for the disease)RECALLsubjects cannot remember accuratelyretrospective studiesconfirm association w/ othersourcesLATE-LOOKseverely diseased individuals arenot coveredearly mortalitystratify study by severityCONFOUNDINGA 3rd factor is involved in variousproportions in exposure-disease rel.affects resultrandom selection, multiple studies

Biostatistics STATISTICS means world expressed in numbers World includes: events action and categories structures that have names “this” or “that” and that’swhy they are called nominal/categorical data e.g. gender (onecategory with 2 groups: males and females) , population in a study(also 2 groups : on drug and on placebo) or categories with no groups(most of them)

2 events : probability to occur togethertype of event:1. Independent events: no connection Probability for ab/w them,blonde to catch ae.g. blond hair and catch a cold.cold (independentevents): multiply theprobability of eachevent expressed ashundredths.x and-2. Mutual exclusive events:one event excludes the possibilityof the other happeningin the same time,e.g. heads and tails for a coin flipProbability to have ahead or a tail whenflipping a coin : ADDtogether theprobability of eachevent3. Non-mutual exclusive events:one event does not excludethe possibility of the otherhappening in the same timee.g. obese and diabeticProbability for anobese patient toalso have diabetesis add the 2probabilities andsubtract theirproduct

categorical /nominal data measured in numbers1234512345678ORDINAL data rank orderINTERVALno similar intervals b/w rankingsany rank ordersimilar intervals on the scale w/ no 0height,weight, BP01234567RATIOsimilar intervals on the scale0 includedtemperature in KA nominal data can be measured using one of the three above scales:rank order, interval or ratio

Descriptive vs Inferential StatisticsDescriptive StatisticsInferential Statisticsmeasures groups/population(coz you can measure each memberof the group)takes a sample from a group anddraw conclusion about the wholegroup(coz you cannot measure all!)Result: distribution is a bell shapecurve symmetric to a central point(mean median mode)Result is expressed in confidenceintervals

Descriptive statistics: normal distribution Mean average add allquantities and divide by thenumber of quantities youadded (Xo) Median midpoint (Md) normal distribution examplemean median modeMode most frequentnumber (Mo)

Descriptive statistics:normal distribution example

Descriptive statistics: various distributionsXo Md MoMo Md Xo ASYMMETRIC DISTRIBUTIONS: have a hump and a tail. If the tail ison negative side there is a negativelyskewed distribution and if the tail ison positive side there is a positivelyskewed distribution. In both cases,mean is not equal to mode and isdifferent from median. KURTIC DISTRIBUTIONS: LEPTOKURTIC: peaked PLATYKURTIC: flattened

Inferential statistics : Standard Deviation If N sample size is too big to be measured wetake a number n of observations from it andmeasure them. Each measurement X is a number error. Eachtime, the next measurement contains less errorand is closer to the mean. This is called instatistics REGRESSION to the MEAN. Finally we obtain a normal distribution whereobservations are dispersed from min to maxaround a mean. One way to measureDISPERSION is using a unit calledSTANDARD DEVIATION (S) which is anaverage dispersion around the mean.STANDARD DEVIATION (S) average dispersion around the mean n-1 degree of freedom (observations- control)

Inferential statistics: standard deviation, variance,range DISPERSION IN STATISTICScan be measured not only usingS, but also variance and range: S standard deviation Variance Range max. value - min.value in the left, the extendedformulas for calculating S andvariance for a sample (in caseyou need) Standard deviation is used forcalculating confidence intervals

QUIZ: A standardized IQ test has amean of 100 and a standarddeviation of 15. A personwith IQ 115 is at whatpercentile of IQ? A.50th B.68th C.84th D.95th E.99th

answer: C (84th)

Inferential statistics - Confidence intervals: definition IN a NORMAL DISTRIBUTION68% of approximative:the data are within one SD (-1; 1) 95% are within 2 SD (-2; 2) 99.7% are within 3 SD (-3; 3) 0.3% are beyond 3 SD.CONFIDENCE INTERVALS: If you have a N sample size - you takeand measure n outcomes - you cancalculate the mean Xo from these noutcomes. However the result is adistribution of outcomes around thismean. Confidence intervals is about howfar from the mean you want to go to feelconfident with the result. It is generally accepted that a 95%interval around the mean (meaning 2 SDabove and 2 SD below the mean) wouldgive a good estimation of the sample. Thismeans that from 100 outcomes , based onthe 95% CI formula you will be able torecognize as good 95 outcomes. You willmake mistakes in 5 outcomes which youwill recognize as good when in realitythey are not.

Inferential statistics: 95% confidence interval, p value and type I (alfa) error P VALUE:When we chose a 95% confidence intervalwe accepted that we have a probability p ofmaking a mistake in 5% cases, meaning ap 0.05 also known as p valueTYPE I aka ALFA ERROR It is the error itself. When you recognize agood outcome when in reality is not youcommit an error aka TYPE I or ALFA error.In statistics where 95% confidence interval isgenerally accepted there is a 5%cases thatyou can make a type I (ALFA) error. p probability / 0.05 to make an error in astudy while type I (ALFA) is the error youactually make in 5% of outcomes at 95% C.I.

Inferential statistics: how to calculate confidence intervals CALCULATING CONFIDENCE INTERVAL: N sample size, you take n outcomes andcalculate the X average. Margin of errorincludes: standard error (SE) and Z score. As sample size N goes up you have a betterestimation from a larger N. So as N goes up, theerror goes down meaning standard error (SE) isless error than standard deviation (sigma) in theformula on the left. Z score or standard score tells you how farfrom the mean your C.I. goes and to calculatethe Z score use the formula on the left wheremean 0 and S 1. Z is actually how manystandard deviations far from the mean goes theC.I. you chose.For practical purpose,Z 2 for 95% c.iZ 2.5 for 99% c.i.

Inferential statistics: Calculating C.I. Quiz Compute a 95% C.I.knowing the following: mean Xo 67 standard deviation S 8 sample size N 16 consider Z 2 Answer: 95% CI : between63-71 including 63 and 71.

95% Confidence Interval plots & 95% confidence intervals for relative risk and odds ratioRELATIVE RISK95% ConfidenceIntervalINTERPRETATION1.48(1.10 - 2.20)statisticallysignificant1.69(0.80 - 2.43)not stat. significant0.73(0.55 - 0.94)statisticallysignificant Q: Assuming the graph in theleft presents 95%C.I. are the twoHIV detection methods differentfrom each other? A: When comparing 2 groupsany overlap of C.I. means thegroups are not statisticallydifferent. Therefore, method Aand method B are no different inHIV detection. Q: When are the C.I for RR orodds ratio not statisticallysignificant? (see table on left) A: If the given C.I contains 1.0then there is no statistically effectfor the exposure, meaning RISK isthe SAME. When C.I. contains no1.0 then there is a statisticallysignificant INCREASED RISK.

Hypothesis testing in statistical studies (1) TESTVARIABLES used intestInterval/ordinal data 2 interval(I) /2ordinalNominal datat test2 nominal (any number ofgroups)1N(max. 2 groups) 1ISTATISTIC FORMULAfor each of the tests Now the question is: what’s the link between allthese we described? I refer to categories,confidence intervals, p value, alfa error, etc? The link is this: imagine you want to compare 2or more categories and draw a conclusion. Firstyou need to DESIGN A STUDY. You need toknow what do you want to compare in yourstudy: only nominal data, interval data ornominal and interval data. If the categories are not identical you can findeither a correlation or a difference between themdepending on categories. Let’s assume you found a difference. The nextquestion : is this difference due to hazard or it issignificantly statistic? To know this you willapply for each study a specific STATISTICFORMULA specially designed for that study.You found a number and you want to know ifthis number is in your 95% confidence interval,that what you found is statistically significant.You take the number you obtained and check inthe tables for the p value related to your number.If the p found 0.05 then YES, your study resultshows a significant statistic difference. If pfound 0.05, your study result shows NOstatistically difference.Pearson(2I)/Spearman(2O)correlationchi squaret statisticANOVA one way1N (many groups) 1IF statisticANOVA two way2 N 1IF statisticp valuecannot tell if it isBIAS in studycannot tell if the resultis clinically significantit can only tell you if it isstatistically significantHYPOTHESIS in STATISTICS (1)

Hypothesis testing in statistical studies (2)REALITYDIFFERENCESTUDYRESULTDIFFERENCEPOWER When the study finds a difference when adifference truly exists (box1) and when thestudy finds no difference when no differenceexists (box4) everything is OK. (smiley) When the study finds a difference when ittruly exists then this is called THE POWER ofthe study (to see difference)- the first box. In TYPE I error or alfa error the study findsa difference when no difference really exists.This is a “false positive” study. It equals p. In TYPE II error or beta error the studyfinds no difference when one truly exists. It’sa “false negative” study. Usually:10-20% butno more than 20%. POWER 100 - beta error(%) or 1beta(decimal). You choose the power whenyou design the study. If the difference youneed to find is small you need an increasedpower and you need to increase the SAMPLESIZE which will also increase the costs. Youhave to find the optimum balance for all.Power 80%.NO DIFFERENCEType I errorerror“false positive”Type II errororNO DIFFERENCEerror“falsenegative”false negative”*NULL Hypothesis (Ho) no difference foundIf the study finds a difference : REJECT HoIf the study finds no difference : FAIL to reject Ho(H1)HYPOTHESIS in STATISTICS (2):

Hypothesis testing in statistical studies (3): Correlation Analysis A CORRELATION:means two measures are related not whythey are related. Does not mean one variablenecessarily causes the otherCORRELATION COEFFICIENT: indicates the DEGREE to which twomeasures are related. The further from 0 thestronger the relationship. Max. values 1 and-1 indicates a linear relationship. Whencoefficient 0 means the two variables haveno linear relation to one another (e.g. heightand exam scores). POSITIVE correlation: the 2 variables go thesame direction NEGATIVE correlation: the 2 variables goin opposite directions TYPES of correlation: PEARSON compares2 interval level variables and SPEARMAN - 2ordinal l.variables. SCATTER PLOT is a graphicalrepresentation of a correlation

Survival Analysis SURVIVALCURVE is a class of statistical procedures forestimating the proportion of people whosurvive (y axis) in relation to the lengthsurvival time A survival curve starts with 100% (1.0 ingraph) of the study population and showsthe percentage of population still surviving atsuccessive times for as long as information isavailable Median survival time is the time where50%(0.5 in graph) are still alive. Median survival time is also called LIFEEXPECTANCY Q: What is the life ex

why epidemiology & biostatistics?comparison: epidemiology biostatistics public health refer to study of DISEASES in a way that you can: application of STATISTICS application of theories from Epidemio & Biostat. action prevent and control disease (THEORY) to exclude events in medicine that a