Evidence Based Medicine MDCN 440

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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 MedicineMDCN 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
• I'm addicted to placebos. I'd give them up, but it wouldn't make any difference.
Types of Data
• Nominal
• Ordinal
• Ranked
• Discrete
• Continuous
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
• 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
• 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
• 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
• 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?
• Mathematical (biostatistical) analysis requires that we know the nature of the data.
• Reminds us about the nature of scoring systems.
e.g. Chi Square
• Cross-Sectional survey:
• Exercise Stress Test Status (counts)
• Sex (counts)
difference IS statistically significant
• may not use t-test for this situation.
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 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 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 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 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 Wright
• Boycott shampoo! Demand the REAL poo!
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

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)

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

Mode
• Most common value.

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

Mode = 4

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

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

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

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

Another method: Standard Dev / √ sample size

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?
• Confidence Interval
• the range over which the TRUE VALUE is covered 95% of the time.
Steven Wright
• Everyone has a photographic memory. Some just don't have film.
Expressing Our Results
• Outcome Measures
• Point Estimate
• Confidence Interval
Medical Outcomes
• Harm?
• Diagnosis?
• Therapy?
• Prognosis?
• Prevention?
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?

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 Wright
• Hard work pays off in the future. Laziness pays off now.
Graphs
• Box Plots
• Survival Curves
• There are others, which you are likely familiar with.
• pie, line, bar…
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
• Hypothesis Testing
• Sample Size Calculation
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 Wright
• The early bird gets the worm, but the second mouse gets the cheese.
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
• 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
• 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
• 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 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 Wright
• Support bacteria - they're the only culture some people have.
Statistical Tests
• As many as 400 statistical tests
• Which is the right test to use?
Comparing Means
• Student’s T-test
• Paired T-test
• Continuous Variables
• Null: mean value(1) – mean value (2) = 0
t-test Web Calculator
Typical t-test Input
• E.g. student scores from sample of front and back for Healthy Populations ;-)
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
• Chi – square Test
• Fisher’s Exact Test
• Discrete Data  Proportions
• Mathematics is fairly simple
• Web - calculator
Typical Output  Fisher’s Exact Test

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

Typical Chi Square Output

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

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

Correlation = 0.92

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

e.g.

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

Detksy & Goldman Perioperative Risk
• http://www.vasgbi.com/riskscores.htm
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 Wright
• I used to have an open mind but my brains kept falling out.
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 Wright
• A conclusion is the place where you got tired of thinking.
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 Wright
• Monday is an awful way to spend 1/7th of your life.
Critical Appraisal
• Articles and Instructions will be available at:
• dr.schaeferville.com
End of the Line…

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