1 / 100

# Evidence Based Medicine MDCN 440 - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Evidence Based Medicine MDCN 440' - waneta

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Evidence Based MedicineMDCN 440

Epidemiology Unit

Biostatistics

April 13, 2010

Jeffrey P Schaefer MSc MD FRCPC

biostatistics…

• Types of Data

• Measures of Central Tendency

• Measures of Dispersion

• Expressing Results

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

• Nominal

• Ordinal

• Ranked

• Discrete

• Continuous

• 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)

• 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?

• 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.

• 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

• 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

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

• Reminds us about the nature of scoring systems.

• Cross-Sectional survey:

• Exercise Stress Test Status (counts)

• Sex (counts)

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.

• Boycott shampoo! Demand the REAL poo!

• Mean

• Median

• Mode

• others exist

• truncated mean

• geometric mean

• weighted mean

• Average

sum of all observations

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

number of observations

2, 3, 6, 8, 10, 12

41 / 6 = 6.83333

• 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 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 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

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

same mean age patients

Normal Distribution patients

• mean = median = mode

• bell shaped (single peak) and symmetrical

Steven Wright patients

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

• Range

• Variance

• Standard Deviation

• Standard Error

• Confidence Intervals

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 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 patients

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 (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 (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 Distribution patients

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

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 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 Error patients

Another method: Standard Dev / √ sample size

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? patients

• Confidence Interval

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

Steven Wright patients

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

Expressing Our Results patients

• Outcome Measures

• Point Estimate

• Confidence Interval

Medical Outcomes patients

• Harm?

• Diagnosis?

• Therapy?

• Prognosis?

• Prevention?

Diagnosis patients

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 Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

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

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 Plots Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

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 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 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 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 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 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 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 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 Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

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

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! Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

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

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 Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

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 Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

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 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 Appendicitis: Experience with 200 Helical Appendiceal CT Examinations Fisher’s Exact Test

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

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

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

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

Steven Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

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

Correlation Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

• Pearson’s Correlation

• http://www.wessa.net/corr.wasp

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 Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

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

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 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 Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

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

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) Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

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 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 Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

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

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 Wright Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

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

Critical Appraisal Appendicitis: Experience with 200 Helical Appendiceal CT Examinations

• Articles and Instructions will be available at:

• dr.schaeferville.com

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

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