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Statistics Bootcamp 101 for HLABC MembersPenny Brasher, PhDVancouver, BCJune 14, 2013c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 2 / 57Statistics are everywhereAngus Reid Public Opinion surveyed 808 randomly selected B.C. residents from May 1 to 2. Itclaims a margin of error of +/-3.5c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 3 / 57
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What is Statistics?c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 4 / 57What is Biostatistics?Biostatistics = statistics applied to biomedical problemsdesign and analysis of experimentsdesign and analysis of observational studiesmeasurement, data analysis (description, inference), statistical graphicsdetective workmaking decisions in the face of uncertainty (variability)inference from a sample (speciﬁc) to a population (general)c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 5 / 57
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Basic ConceptsDescriptive Statisticsusing numerical summaries and ﬁgures to summarize or characterize a set of data.mean, median, variance, range, etc.histograms, scatterplots, boxplots, etc.no assumptions are made.⇒ If the data are a random sample from a certain population, the sample represents thepopulation in minature.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 10 / 57Part IITypes of Datac PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 12 / 57
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Types of DataCategorical DataNominal variables assume values that fall into unordered categories. Nominal datamay be binary (dichotomous) or polychotomous (polytomous). Examples: admissionstatus (admitted, not admitted), survival status (alive, dead), race (caucasian, asian,black, ...).Ordinal variables assume values that fall into ordered categories but diﬀerencesbetween values are not meaningful. Examples: response to treatment (worse, same,improved), degress of illness (none, mild, moderate, severe), likert-item (stronglydisagree, disagree, neutral, agree, strongly agree).Numerical (Metric, Quantitative) DataNumerical discrete variables assume a countable number of values. There can begaps in its possible values. Examples: number of comorbidities, number of falls in ayear.Numerical continuous variables assume, in theory, iniﬁnite values in a given range;there are no gaps in its possible values. Examples: age, weight, etc.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 13 / 57Grip strength of health librariansData collected:Cohort HLABCID 1Year of birth 1952 numerical discreteHeight (cm) 161.3 numerical continuousSex F nominalGrip position 2 ordinalDominant hand R nominalOrder RL nominalGrip strength, Right (kg) 31.8 numerical continuousScrunchy face (R) 1 nominalGrip strength, Left (kg) 24.6 numerical continuousScrunchy face (L) 1 nominalc PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 14 / 57
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Descriptive StatisticsTypes of DataNota beneThere is no such thing as”nonparametric data”.⇒ Parameters belong to models.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 15 / 57Part IIIDescriptive Statisticsc PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 16 / 57
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Grip strength of health librariansDescriptive StatisticsHow would you summarize the characteristics of this sample of librarians?The characteristics we have collected include:Year of birthHeight (cm)SexDominant handGrip strengthc PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 17 / 57Descriptive StatisticsData SummariesFor categorical variables - frequencies & percentages. 1For numerical continuous variables, typically, one wants to describe the central tendency(central location) of the data, and the degree to which the data is, or is not, spread out(dispersion).Why are mean and standard deviation often used to describe continuous variables?1Don’t report percentages if the sample size is small.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 18 / 57
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The Normal (Gaussian) DistributionNormal distributions are completely determined by only two values – the mean, µ, andthe standard deviation, σ.−8 −6 −4 −2 0 2 4 6 8(0,1) (3,1)(0,2)Gaussian (normal) distributionsThe mean, µ, determinesthe center.The standard deviation, σdetermines the spread(variability).c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 19 / 57The Normal (Gaussian) DistributionNormal distributions are completely determined by only two values – the mean, µ, andthe standard deviation, σ.µ−4σ µ−2σ µ µ+2σ µ+4σN(µ,σ)95%95% of observations will lie in theinterval (µ − 1.96σ, , µ + 1.96σ).∼70% of observations will lie in theinterval (µ − σ , µ + σ).50% of observations will lie in theinterval (µ − 0.675σ , µ + 0.675σ).c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 20 / 57
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Describing DataData SummariesFor continuous variables that are approximately normally distributed the sampledistribution may be summarized with the sample mean, ¯x, and the sample standarddeviation, sd.For continuous variables with skewed distributions other summary statistics should beused. If the distribution is unimodal the median and P25 & P75 (Q1 & Q3) or themedian and P10 & P90 could be used.– Altman DG, Bland JM. Quartiles, quintiles, centiles, and other quantiles. BMJ 1994;309:996.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 21 / 57Descriptive StatisticsPart of Table 1 from a randomized trial in patients undergoing CABG.20Table 1. Anthropometric, baseline and procedural characteristics (intent-to-treat and safety population)ClevidipineN=49NitroglycerinN=51Age, years; mean (SD) 65.8 (11.3) 63.2 (12.3)SexMale, n (%) 40 (81.6) 43 (84.3)Female, n (%) 9 (18.4) 8 (15.7)Weight, kg; mean (SD) 79.7 (15.9) 82.1 (18.5)Height, cm; mean (SD) 170.4 (9.0) 170.5 (12.4)ASA Physical Status*, n (%)I 0 (0.0) 0 (0.0)II 0 (0.0) 1 (2.0)III 29 (59.2) 33 (64.7)IV 19 (38.8) 16 (31.4)V 1 (2.0) 0 (0.0)Body Mass Index, kg/m2; mean (SD) 27.4 (5.1) 28.2 (5.2)Index Procedure, n (%)CABG 43 (87.8) 45 (88.2)CABG plus valve surgery 6 (12.2) 6 (11.8)Target MAP, pre-CPB, mmHg; mean (SD) 76.1 (7.0) 76.4 (7.9)Target MAP, aortic cannulation, mmHg; mean (SD);CLV n=49, NTG n=4964.6 (11.9) 63.6 (10.4)Duration of bypass, min; mean (SD); CLV n=47,NTG n=51102.5 (37.1) 99.2 (35.8)Duration of aortic cannulation (min) mean (SD); CLVn=35, NTG n=3818.9 (40.3) 13.3 (26.1)IABP used, mean (SD) 2 (4.1) 0 (0.0)Number of grafts, mean (SD) 3.1 (0.8) 3.0 (1.0)Abbreviations: kg = kilograms, cm = centimeters. ASA = American Society of Anesthesiologists.IABP = intra-aortic balloon pump.SD=standard deviation. CLV=clevidipine. NTG=nitroglycerin.*ASA physical status unknown for 1 NTG-treated patient.1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465What changes would you make to this table?c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 22 / 57
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Descriptive Statistics20CABG 43 (87.8) 45 (88.2)CABG plus valve surgery 6 (12.2) 6 (11.8)Target MAP, pre-CPB, mmHg; mean (SD) 76.1 (7.0) 76.4 (7.9)Target MAP, aortic cannulation, mmHg; mean (SD);CLV n=49, NTG n=4964.6 (11.9) 63.6 (10.4)Duration of bypass, min; mean (SD); CLV n=47,NTG n=51102.5 (37.1) 99.2 (35.8)Duration of aortic cannulation (min) mean (SD); CLVn=35, NTG n=3818.9 (40.3) 13.3 (26.1)IABP used, mean (SD) 2 (4.1) 0 (0.0)Number of grafts, mean (SD) 3.1 (0.8) 3.0 (1.0)Abbreviations: kg = kilograms, cm = centimeters. ASA = American Society of Anesthesiologists.IABP = intra-aortic balloon pump.SD=standard deviation. CLV=clevidipine. NTG=nitroglycerin.*ASA physical status unknown for 1 NTG-treated patient.3435363738394041424344454647484950515253545556575859606162636465⇒ For skewed (asymmetric) data use percentiles.⇒ For nominal and ordinal variables and for numerical discrete variables with a limitedrange use a table of frequencies.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 23 / 57Describing dataData SummariesSometimes you don’t need to summarize data:Times to circulatory collapse(s) were10,35,42,42,43,70; 5,46,50,50,54,64 in IG and C groups, respectively.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 24 / 57
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Part VInferential Statisticsc PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 25 / 57Basic ConceptsInferential Statisticsmaking inferences about a population from a sample.estimation and hypothesis testing.some assumptions are made.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 26 / 57
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Quantifying the role of chanceA very simple example.We wish to know if a coin is ”fair”. By ”fair” we mean that the probability of getting ahead on any ﬂip is 1/2.To determine if the coin is ”fair” we could take it to the laboratory and:determine the weight distribution throughout the coin,determine the aerodynamics of the coin,etc.In this way we would discover the ”truth”.ORWe could conduct an experiment, compute some statistics and try to get close to thetruth.⇒ Statistical inference.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 27 / 57Signiﬁcance TestingQuantifying the role of chanceReturning to our very simple example.We decide to ﬂip the coin 15 times.We observe 4 heads in 15 ﬂips.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 28 / 57
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Signiﬁcance TestingQuantifying the role of chanceN Observed Expected Assumed p Observed p---------------------------------------------------15 4 7.5 0.50000 0.26667Pr(k <= 4) = 0.059 (one-sided test)Pr(k <= 4 or k >= 11) = 0.118 (two-sided test)What does this mean?c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 29 / 57Signiﬁcance TestingSir Ronald A. FisherIn general, tests of signiﬁcance arebased on hypothetical probabilitiescalculated from their nullhypotheses. They do not generallylead to any probability statementsabout the real world, but to arational and well-deﬁned measureof reluctance to the acceptance ofthe hypotheses they test”.– Fisher RA. Statistical Methods and ScientiﬁcInference (1956)c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 30 / 57
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Signiﬁcance TestingA very simple exampleStudy design: ﬂip coin 15 times.Test statistic: number of heads.Evidence against: too many or too few heads.Probability model: Binomial (n=15,π = 0.5)Theoretical distribution of the number of heads if the coin is fair.number of headsprobability0.000.050.100.150 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15If the coin was fairFisher would ask us to consider if 4heads (plus more extreme results)is unlikely under the nullhypothesis, i.e. fair coin.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 31 / 57Signiﬁcance TestingThe P-valuePr(k <= 4 or k >= 11 | if coin is fair) = 0.118The more interesting question is . . .What is the probablity that the coin is fair? i.e. What is the probability that the nullhypothesis is true?I have no idea.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 32 / 57
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Quantifying the role of chanceThe P-valueIn signiﬁcance testing, the P-value is the probability of obtaining a result (i.e. teststatistic) at least as extreme as the one that was actually observed, when the nullhypothesis is true.It is Pr(data|H0 is true).An ”unlikely” event suggests that H0 is unlikely but the P-value provides no measure ofjust how unlikely H0 is.Akin to proof by contradiction.We have a model and we examine the extent to which the data contradict the model.The basis for suggesting a contradiction is observing data that are highly improbableunder the model.⇒ In health research involving human subjects, P-values are next to useless.And yet they’re everywhere.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 33 / 57Inferential StatisticsP-values vs Conﬁdence IntervalsIn a randomized trial comparing two treatments the following mortality results werereported by the authors.Std Exp Std Expnumber percentdied 19 12 31.7 20.7survived 41 46 68.3 79.3total 60 58P = 0.21, Fisher’s exact test.The authors concluded ”there is no diﬀerence in mortality”.What do you think?c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 34 / 57
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Inferential StatisticsConﬁdence IntervalsA P-value tells you nothing about the size of the treatement eﬀect.The estimate of the true treatment eﬀect is:31.7% - 20.7% = 11.0%, 95% CI: -4.9% to 26.1%, 80% CI: 0.6% to 21.0%.What does the conﬁdence interval represent?statistical deﬁnition: If the study were to be repeated 1000 times and a 95% CI wasconstructed each time, we would expect 950 of those intervals to include the populationparameter. A reported conﬁdence interval from a particular study may or may not include the actualpopulation value.working deﬁnition: Values of the population parameter that are conistent with thesample data.⇒ The conﬁdence interval gives a plausible range of values for the unknown populationparameter.Would you want to receive standard treatment?c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 35 / 57Angus Reid Public Opinion surveyed 808 randomly selected B.C. residents from May 1 to2. It claims a margin of error of +/-3.5For a proportion the maximum variance is when p = 0.50.. cii 808 404-- Binomial Exact --Obs Mean Std. Err. [95% Conf. Interval]----------------------------------------------------808 0.5 0.01759 0.46496 .535042*.01759 = 0.03518Angus Reid is providing the width of the largest possible 95% conﬁdence interval.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 36 / 57
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Conﬁdence Intervals vs P-valuesInterpreting ResultsOveremphasis on hypothesis testing — and the use of P-values to dichotomizesigniﬁcant or non-signiﬁcant results — has detracted from more usefulapproaches to interpreting study results, such as estimation and conﬁdenceintervals. In medical studies investigators should usually be interested indetermining the size of diﬀerence of a measured outcome between groups,rather than a simple indication of whether or not it is statistically signiﬁcant.Gardner MJ, Altman DG. Statistics with Conﬁdence”’The 0.05 syndrome’, a severe, debilitating statistical illness.”– Palmer CR. 2002c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 37 / 57Inferential StatisticsP-values Conﬁdence intervalsc PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 38 / 57
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Part VIThe other big problem - useless graphics.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 39 / 57Graphical DisplaysCommon pitfalls in statisticsEvaluating research articlesOtherWhat to look for in a clinical trialRed larger than yellow or yellow larger than red?c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 40 / 57
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Graphical Displays0 2 4 6 8 10frequencyWhat to look for in a clinical trialOtherCommon pitfalls in statisticsEvaluating research articlesc PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 41 / 57Graphical Displays”Any data that can be encoded by one of the pop charts [pie charts, divided barcharts, area charts] can also be encoded by either a dot plot or a multiway dotplot that typically provides far more eﬃcient pattern perception and tablelook-up than the pop-chart encoding.”– WS Cleveland, The Elements of Graphing Data (rev. Ed) 1994.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 42 / 57
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Graphical DisplaysDynamite plots020406080100posttreatmentscoremean+sdsham acupuncture020406080100Posttreatmentscoresham acupuncturec PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 45 / 57Graphical DisplaysTufte’s list of nine ”shoulds”The Visual Display of Quantitative Information, 1983Graphical displays should:show the data,induce the viewer to think about the substance rather than about methodology,graphic design, the technology of graphic production, or something else,avoid distorting what the data have to say,present many numbers in a small space,make a large data set coherent,encourage the eye to compare diﬀerent pieces of data,reveal the data at several levels of detail, from a broad overview to the ﬁne structure,serve a reasonably clear purpose: description, exploration, tabulation, or decoration,andbe closely integrated with the statistical and verbal descriptions of a data set.c PMA Brasher (UBC) Biostats Bootcamp 14.Jun.2013 46 / 57
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