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Evidence Based Medicine MDCN 440. Epidemiology Unit Biostatistics April 13, 2010 Jeffrey P Schaefer MSc MD FRCPC. The peril of teaching biostatistics…. Section 1. Types of Data Measures of Central Tendency Measures of Dispersion Expressing Results. Steven Wright.

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Evidence based medicine mdcn 440

Evidence Based MedicineMDCN 440

Epidemiology Unit

Biostatistics

April 13, 2010

Jeffrey P Schaefer MSc MD FRCPC


The peril of teaching

biostatistics…


Section 1
Section 1

  • Types of Data

  • Measures of Central Tendency

  • Measures of Dispersion

  • Expressing Results


Steven wright
Steven Wright

  • I'm addicted to placebos. I'd give them up, but it wouldn't make any difference.


Types of data
Types of Data

  • Nominal

  • Ordinal

  • Ranked

  • Discrete

  • Continuous


Nominal data
Nominal Data

  • Data is placed into ‘named’ categories.

  • E.g.

    • 1 = pneumonia

    • 2 = heart disease

    • 3 = abdominal pain

      Mathematical analysis usually inappropriate.

      (exception might be 0 = male, 1 = female)


Ordinal data
Ordinal Data

  • Data relates to a logical order.

  • Example:

    • 5 = fatal

    • 4 = severe

    • 3 = moderate

    • 2 = mild

    • 1 = none

  • Mathematical analysis usually inappropriate. Does mild + moderate = fatal?


Ranked data
Ranked Data

  • Data relates to position within a sequence.

    E.g. Causes of death…

    • 1 = cardiovascular disease

    • 2 = neoplasm

  • Mathematical analysis usually inappropriate. However, information is usually useful and often quoted.


Discrete data
Discrete Data

  • Data represents ‘counts’.

  • E.g.

    • number of children

    • number of accidents

    • number dying of heart failure

  • Mathematics are appropriate although result may not be. e.g. 2.4 children / family


Continuous data
Continuous Data

  • Data has any numerical value (ratio data)

  • E.g.

    • cholesterol values

    • blood pressures

  • Mathematics is usually appropriate. e.g. Average hemoglobin was 120 g/l


Who cares
Who cares?

  • Mathematical (biostatistical) analysis requires that we know the nature of the data.

  • Reminds us about the nature of scoring systems.


E g chi square
e.g. Chi Square

  • Cross-Sectional survey:

    • Exercise Stress Test Status (counts)

    • Sex (counts)



Staging of heart failure
Staging of Heart Failure

NYHA Cardiac Status

  • Class I: uncompromised

  • Class II: slightly compromised

  • Class III: moderately compromised

  • Class IV: severely compromised

    • updated from old NYHA Classification

      • ‘usual activities’ ‘minimal exertion’


Specific activity scale goldman circulation 64 1227 1981
Specific Activity ScaleGoldman Circulation 64:1227, 1981

Stage I

  • patients can perform to completion any activity requiring 7 metabolic equivalents

    • can carry 24 lb up eight steps

    • carry objects that weigh 80 lb

    • do outdoor work [shovel snow, spade soil]

    • do recreational activities [skiing, basketball, squash, handball, jog/walk 5 mph]


Specific activity scale goldman circulation 64 1227 19811
Specific Activity ScaleGoldman Circulation 64:1227, 1981

Stage II

  • patients can perform to completion any activity requiring 5 metabolic equivalents

    • have sexual intercourse without stopping

    • garden, rake, weed, roller skate

    • dance fox trot, walk at 4 mph on level ground

    • but cannot and do not perform to completion activities requiring 7 metabolic equivalents


Specific activity scale goldman circulation 64 1227 19812
Specific Activity ScaleGoldman Circulation 64:1227, 1981

Stage III

  • patients can perform to completion any activity requiring 2 metabolic equivalents

    • dress, shower without stopping, strip and make bed, clean windows

    • walk 2.5 mph, bowl, play golf, dress without stopping

    • but cannot and do not perform to completion any activities requiring 5 metabolic equivalents


Specific activity scale goldman circulation 64 1227 19813
Specific Activity ScaleGoldman Circulation 64:1227, 1981

Stage IV

  • patients cannot or do not perform to completion activities requiring 2 metabolic equivalents

    • CAN’T:

      • dress without stopping

      • shower without stopping

      • strip and make bed

      • walk 2.5 mph

      • bowl, play golf


Prognosis varies with class stage iv not 4 x more serious than stage i heart failure
Prognosis varies with ClassStage IV NOT 4 X more serious than stage I heart failure.


Steven wright1
Steven Wright

  • Boycott shampoo! Demand the REAL poo!


Measures of central tendency
Measures of Central Tendency

  • Mean

  • Median

  • Mode

  • others exist

    • truncated mean

    • geometric mean

    • weighted mean


Mean

  • Average

    sum of all observations

    --------------------------------------

    number of observations

    2, 3, 6, 8, 10, 12

    41 / 6 = 6.83333


Truncated mean
Truncated Mean

  • Truncated Mean

    sum of all observations (restricted in some way)

    ---------------------------------------------------------------

    number of permitted observations

    42, 56, 69, 43, 53, 55, 56, 99 (mean = 59.1)

    e.g. remove highest and lowest number

    56, 69, 43, 53, 55, 56 (truncated mean = 55.3)



Median
Median are doctors; we have our own code!

  • The 50th percentile (or ‘middlemost’ value).

    3, 6, 7, 19, 10, 13, 2, 1, 21, 4, 22

    1, 2, 3, 4, 6, 7, 10, 13, 19, 21, 22

    Median = 7

    (Use Average of the Two Middle Values

    if Even Number of Observations)

    1, 2, 3, 4, 6, 6, 7, 10, 13, 19, 21, 22

    Median = (6 + 7)/2 = 6.5


Mode are doctors; we have our own code!

  • Most common value.

    3, 6, 7, 4, 19, 4, 10, 13, 10, 2, 1, 21, 4, 22

    Mode = 4


Measures of central tendency1
Measures of Central Tendency are doctors; we have our own code!

  • Medicine and Health

    • mainly mean and median

  • Mean:

    • sensitive to outliers

    • does not convey multimodal distributions

  • Median:

    • less intuitive

    • less suitable for mathematical analysis


Hospital Length of Stay: typical example of where a few patients

(e.g. complication of surgery) requires longer stays


Same mean age
same mean age patients


Normal distribution
Normal Distribution patients

  • mean = median = mode

  • bell shaped (single peak) and symmetrical


Steven wright2
Steven Wright patients

  • If at first you don't succeed, destroy all evidence that you tried.


Measures of dispersion variability
Measures of Dispersion (variability) patients

  • Range

  • Variance

  • Standard Deviation

  • Standard Error

  • Confidence Intervals


Range
Range patients

  • The difference between largest and smallest values. (Usually expressed as smallest to largest)

    2, 4, 6, 10, 12, 14, 17, 20

    range = 18

    The range was 2 to 20.


Interquartile range
Interquartile Range patients

  • the distance between the 25th percentile and the 75th percentile

    1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

    IQR = 4 to 9


Box plots
Box Plots patients


Variance sample
Variance (sample) patients

115, 116, 118, 114, 117  mean = 116

 range = 3

44, 80, 110, 180, 166  mean = 116

 range = 136

Range is helpful but depends only on two numbers.


Variance sample1
Variance (sample) patients

115, 116, 118, 114, 117  mean = 116

 range = 3

observations 115 116 118 114 117

mean 116 116 116 116 116

difference - 1 0 2 -2 1 sum = 0

diff squared 1 0 4 4 1 sum = 10

divide by obs 10 / (5-1) = 2.5 = variance

take square root of variance = √2.5 = 1.58  std dev


Variance sample2
Variance (sample) patients

44, 80, 110, 180, 166  mean = 116

 range = 3

observations 44 80 110 180 166

mean 116 116 116 116 116

difference -72 -36 -6 64 50 sum = 0

diff squared 5184 1296 36 4096 2500 sum=13,112

divide by obs 13,112 / (5-1) = 3,278 = variance

take square root of variance = √3,278 = 57.3  std dev


Normal distribution1
Normal Distribution patients

  • +/- 1 sd  66% +/- 2 sd  95% +/- 3 sd 99.7%


Variance population
Variance (Population) patients

  • Variance of a Population

    • population is where everyone is measured

    • denominator = number of observations

  • Variance of a Sample

    • a sample of the population is selected

    • denominator = number of observations - 1


Standard error
Standard Error patients

  • Imagine a data set with 1,000 values

    • Select 100 values, calculate mean

    • Select 100 values, calculate mean

    • Select 100 values, calculate mean

    • Select 100 values, calculate mean

    • and so on, and so on…

    • Plot the means

    • Calculate the standard deviation of these means


Standard error1
Standard Error patients

Another method: Standard Dev / √ sample size


Confidence interval
Confidence Interval patients

  • General Formula:

    95% Confidence Interval =

    mean – (1.96 x Standard Error)

    to

    mean + (1.96 x Standard Error)


So what does this actually mean
So what does this actually mean? patients

  • Confidence Interval

    • the range over which the TRUE VALUE is covered 95% of the time.


Steven wright3
Steven Wright patients

  • Everyone has a photographic memory. Some just don't have film.


Expressing our results
Expressing Our Results patients

  • Outcome Measures

    • Point Estimate

    • Confidence Interval


Medical outcomes
Medical Outcomes patients

  • Harm?

  • Diagnosis?

  • Therapy?

  • Prognosis?

  • Prevention?



Diagnosis
Diagnosis patients



Rales trial nejm 1999 341 709 17
Rales Trial patients NEJM 1999;341:709-17

placebo: 753 / 841 = 0.895

spirono: 515 / 822 = 0.625

(0.625) / 0.895 = 70%

Relative Risk 0.7  Point Estimate

95% CI (0.59 to 0.82)  Measure of Precision

What if C.I. included 1.0?


Sensitivity and Specificity of the Individual CT Signs of Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Journal of Computer Assisted Tomography: September/October 1997 - Volume 21 - Issue 5 - pp 686-692 Rao, Patrick M.; Rhea, James T.; Novelline, Robert A.

  • Purpose: Our goal was to determine the sensitivity, specificity, and diagnostic value of individual signs at helical appendiceal CT.

  • Method: Two hundred helical appendiceal CT scans (100 appendicitis and 100 normal appendix cases) were interpreted for individual signs of appendicitis. Scan findings were correlated with appendectomy or clinical follow-up results.

  • Results: Individual CT signs identified and their sensitivity and specificity, respectively, included fat stranding (100%, 80%), enlarged (>6 mm) unopacified appendix (93%, 100%), focal cecal apical thickening (69%, 100%), adenopathy (62%, 66%), appendolith(s) (44%, 100%), arrowhead sign (23%, 100%), paracolic gutter fluid (18%, 86%), abscess (11%, 100%), cecal bar (10%, 100%), extraluminal air (8%, 97%), phlegmon (7%, 99%), ileal (3%, 86%) or sigmoid (3%, 95%) wall thickening, and diffuse cecal wall thickening (0%, 91%).

  • Conclusion: Individual appendiceal CT signs of appendicitis vary in sensitivity, specificity, and thus diagnostic value…


Steven wright4
Steven Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Hard work pays off in the future. Laziness pays off now.


Graphs
Graphs Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Box Plots

  • Survival Curves

  • There are others, which you are likely familiar with.

    • pie, line, bar…


Box plots1
Box Plots Appendicitis: Experience with 200 Helical Appendiceal CT Examinations


Survival kaplan meier curve
Survival (Kaplan – Meier Curve) Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

- plots events over time (not nec. death)

  • takes into consideration losses to follow-up

    - be able to identify this graph type


Section 2
Section 2 Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Hypothesis Testing

  • Sample Size Calculation


  • Independent and Dependent Variables Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Hypothesis testing

  • Error Types

  • Comparing

    • means

      • independent samples versus paired samples

    • proportions

  • Parametric versus Non-Parametrics

  • Correlation

  • Modeling

  • Sample Size


Steven wright5
Steven Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • The early bird gets the worm, but the second mouse gets the cheese.


Independent versus dependent variables
Independent versus Dependent Variables Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Independent Variables

    • those that are manipulated

    • includes the ‘populations’ of interest

    • e.g. experimental drug vs placebo

    • e.g. population with diabetes vs controls

  • Dependent Variables

    • those that are only measured or registered

    • includes the ‘outcome’ of interest

    • e.g. mortality, morbidity

    • e.g. health related quality of life


Hypothesis testing
Hypothesis Testing Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Is there an association between an independent and dependent variable?

  • Generate a null hypothesis

    There is no association between these variables.

  • Reject the Null Hypothesis or

  • Do Not Reject the Null Hypothesis


Implications
Implications Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • We do not ‘accept’ the null hypothesis…

    • Failing to demonstrate an association does not ensure that an association does not exist!

    • Equivalency trials


Errors two possibilities
Errors Appendicitis: Experience with 200 Helical Appendiceal CT Examinations two possibilities

  • Type 1

    • alpha error or rejection error

    • ‘rejecting the null hypothesis when in truth there is no association’

  • Possible Reasons

    • bias

    • confounding

    • play of chance

      • P-value  accept a probability of Type 1 = 0.05 (5%)


Errors two possibilities1
Errors Appendicitis: Experience with 200 Helical Appendiceal CT Examinations two possibilities

  • Type 2 Error

    • beta error

    • ‘error of missed opportunity’

    • inter-related reasons

      • high variance among the outcomes

        • population attributes

      • small sample size relative to variance

      • intervention was insufficient (too low a dose)

      • intervention was too brief (too short a trial)

    • Power = 1 – Beta

    • ‘The power to detect a difference was … values typically vary from 80% to 95%


Steven wright6
Steven Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Support bacteria - they're the only culture some people have.


Statistical tests
Statistical Tests Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • As many as 400 statistical tests

  • Which is the right test to use?


So many study designs so many tests
So many study designs, so many tests! Appendicitis: Experience with 200 Helical Appendiceal CT Examinations


More tests
More tests… Appendicitis: Experience with 200 Helical Appendiceal CT Examinations


Comparing means
Comparing Means Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Student’s T-test

  • Paired T-test

  • Continuous Variables

  • Null: mean value(1) – mean value (2) = 0


T test web calculator
t-test Web Calculator Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • http://www.graphpad.com/quickcalcs/ttest1.cfm


Typical t test input
Typical t-test Input Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • E.g. student scores from sample of front and back for Healthy Populations ;-)


Typical t test output
Typical t-test Output Appendicitis: Experience with 200 Helical Appendiceal CT Examinations


Dissect the results
Dissect the results… Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • p < 0.0325

    • the probability that a difference as large as the one observed, or larger, was due to the play of chance alone 0.0325 or 3.25% or < 5%

    • Yup… statistically significant

    • but is a 5% difference important?

    • from 85 to 90  not really

    • from 58 to 63 (if MPL is 60)  maybe

    • moreover, the 95%CI included 0.46 to 9.34


Comparing proportions
Comparing Proportions Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Chi – square Test

  • Fisher’s Exact Test

  • Discrete Data  Proportions

  • Mathematics is fairly simple

  • Web - calculator


Typical output fisher s exact test
Typical Output Appendicitis: Experience with 200 Helical Appendiceal CT Examinations Fisher’s Exact Test

http://www.matforsk.no/ola/fisher.htm


Chi square input
Chi Square Input Appendicitis: Experience with 200 Helical Appendiceal CT Examinations


Typical chi square output
Typical Chi Square Output Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

http://schnoodles.com/cgi-bin/web_chi_form.cgi


Steven wright7
Steven Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Eagles may soar, but weasels don't get sucked into jet engines.


Correlation
Correlation Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Pearson’s Correlation

  • http://www.wessa.net/corr.wasp


Typical input output
Typical Input / Output Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

Correlation = 0.92


+ 1 Appendicitis: Experience with 200 Helical Appendiceal CT Examinations


0 Appendicitis: Experience with 200 Helical Appendiceal CT Examinations


- 1 Appendicitis: Experience with 200 Helical Appendiceal CT Examinations


Steven wright8
Steven Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • When I'm not in my right mind, my left mind gets pretty crowded.


Modeling
Modeling Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Linear Regression Analysis

    • what ‘vector’ best describes a relationship

  • Logistic Regression Analysis

    • what ‘odds ratio’ best describes a relationship

    • http://www.wessa.net/esteq.wasp



Multiple regression can evaluate several variables
Multiple Regression can Appendicitis: Experience with 200 Helical Appendiceal CT Examinationsevaluate several variables

e.g.

periop MI = a + age*x1 + gender*x2+prevMI*x3 ….


Detksy goldman perioperative risk
Detksy & Goldman Perioperative Risk Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • http://www.vasgbi.com/riskscores.htm


Framingham risk score
Framingham Risk Score Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • http://chealth.canoe.ca/health_tools.asp?relation_id=3233

  • Ahh… but don’t get sucked in too often….

  • e.g. ? does the calculator consider family history…


Reading the fine print cmaj 2003
Reading the Fine Print (CMAJ 2003) Appendicitis: Experience with 200 Helical Appendiceal CT Examinations


Steven wright9
Steven Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • I used to have an open mind but my brains kept falling out.


Parametric and non parametric data
Parametric and Non-Parametric Data Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • refers to underlying distribution of the data

  • In general:

    • non-parametric analyses are more conservative

      • lower Type 1 error

      • higher Type 2 error


Steven wright10
Steven Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • A conclusion is the place where you got tired of thinking.


Sample size calculations
Sample Size Calculations Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Context

    • the least number of subjects that result in a statistically significant difference.

    • What are the factors?

      • Minimum Important Difference

      • Variability of response


Steven wright11
Steven Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Monday is an awful way to spend 1/7th of your life.


Critical appraisal
Critical Appraisal Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

  • Articles and Instructions will be available at:

    • dr.schaeferville.com


End of the line
End of the Line… Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

http://www.thiswebsiteisajoke.com/index.html


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