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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

Prognosis varies with ClassStage IV NOT 4 X more serious than stage I heart failure.

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

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

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

(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

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

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

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