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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

slide2
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)
slide13
difference IS statistically significant
  • may not use t-test for this situation.
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
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
slide22
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)

slide24
Note: I hate this nomenclature and will avoid its use. We are doctors; we have our own code!
median
Median
  • 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

slide26
Mode
  • 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
  • Medicine and Health
    • mainly mean and median
  • Mean:
    • sensitive to outliers
    • does not convey multimodal distributions
  • Median:
    • less intuitive
    • less suitable for mathematical analysis
slide28
Hospital Length of Stay: typical example of where a few patients

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

normal distribution
Normal Distribution
  • mean = median = mode
  • bell shaped (single peak) and symmetrical
steven wright2
Steven Wright
  • If at first you don't succeed, destroy all evidence that you tried.
measures of dispersion variability
Measures of Dispersion (variability)
  • Range
  • Variance
  • Standard Deviation
  • Standard Error
  • Confidence Intervals
range
Range
  • 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
  • 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

variance sample
Variance (sample)

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)

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)

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
  • +/- 1 sd  66% +/- 2 sd  95% +/- 3 sd 99.7%
variance population
Variance (Population)
  • 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
  • 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

Another method: Standard Dev / √ sample size

confidence interval
Confidence Interval
  • 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?
  • Confidence Interval
    • the range over which the TRUE VALUE is covered 95% of the time.
steven wright3
Steven Wright
  • Everyone has a photographic memory. Some just don't have film.
expressing our results
Expressing Our Results
  • Outcome Measures
    • Point Estimate
    • Confidence Interval
medical outcomes
Medical Outcomes
  • Harm?
  • Diagnosis?
  • Therapy?
  • Prognosis?
  • Prevention?
rales trial nejm 1999 341 709 17
Rales Trial 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?

slide53
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
  • Hard work pays off in the future. Laziness pays off now.
graphs
Graphs
  • Box Plots
  • Survival Curves
  • There are others, which you are likely familiar with.
    • pie, line, bar…
survival kaplan meier curve
Survival (Kaplan – Meier Curve)

- 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
  • Hypothesis Testing
  • Sample Size Calculation
slide60
Independent and Dependent Variables
  • Hypothesis testing
  • Error Types
  • Comparing
    • means
      • independent samples versus paired samples
    • proportions
  • Parametric versus Non-Parametrics
  • Correlation
  • Modeling
  • Sample Size
steven wright5
Steven Wright
  • The early bird gets the worm, but the second mouse gets the cheese.
independent versus dependent variables
Independent versus Dependent Variables
  • 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
  • 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
  • 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  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  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
  • Support bacteria - they're the only culture some people have.
statistical tests
Statistical Tests
  • As many as 400 statistical tests
  • Which is the right test to use?
comparing means
Comparing Means
  • 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
  • http://www.graphpad.com/quickcalcs/ttest1.cfm
typical t test input
Typical t-test Input
  • E.g. student scores from sample of front and back for Healthy Populations ;-)
dissect the results
Dissect the results…
  • 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
  • Chi – square Test
  • Fisher’s Exact Test
  • Discrete Data  Proportions
  • Mathematics is fairly simple
  • Web - calculator
typical output fisher s exact test
Typical Output  Fisher’s Exact Test

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

typical chi square output
Typical Chi Square Output

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

steven wright7
Steven Wright
  • Eagles may soar, but weasels don't get sucked into jet engines.
correlation
Correlation
  • Pearson’s Correlation
  • http://www.wessa.net/corr.wasp
typical input output
Typical Input / Output

Correlation = 0.92

steven wright8
Steven Wright
  • When I'm not in my right mind, my left mind gets pretty crowded.
modeling
Modeling
  • 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 evaluate several variables

e.g.

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

detksy goldman perioperative risk
Detksy & Goldman Perioperative Risk
  • http://www.vasgbi.com/riskscores.htm
framingham risk score
Framingham Risk Score
  • 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…
steven wright9
Steven Wright
  • I used to have an open mind but my brains kept falling out.
parametric and non parametric data
Parametric and Non-Parametric Data
  • 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
  • A conclusion is the place where you got tired of thinking.
sample size calculations
Sample Size Calculations
  • 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
  • Monday is an awful way to spend 1/7th of your life.
critical appraisal
Critical Appraisal
  • Articles and Instructions will be available at:
    • dr.schaeferville.com
end of the line
End of the Line…

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

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