Week 2 An overview

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Week 2An overview

• Exposure and outcome (dependent and independent
  variables)
• Reliability and validity
• What is statistical significance?
• Relationships between variables-continuous
  variables (t-tests and z-tests)-continuous
  variables (correlations)
• -the normal (gaussian) distribution-categorical
  variables (chi-square tests)
• Two by two tables and confidence intervals
• Review of the articles
• Example 1 Children crossing streets
• Measures of association between variables
• For next week

2

• A somewhat advanced society has figured how to
  package basic knowledge in pill form. A student,
  needing some learning, goes to the pharmacy and
  asks what kind of knowledge pills are available.
  The pharmacist says "Here's a pill for English
  literature." The student takes the pill and
  swallows it and has new knowledge about English
  literature!
• "What else do you have?" asks the student. "Well,
  I have pills for art history, biology, and world
  history, "replies the pharmacist. The student
  asks for these, and swallows them and has new
  knowledge about those subjects!
• Then the student asks, "Do you have a pill for
  statistics? "The pharmacist says "Wait just a
  moment", and goes back into the storeroom and
  brings back a whopper of a pill that is about
  twice the size of a jawbreaker and plunks it on
  the counter. "I have to take that huge pill for
  statistics?" inquires the student.
• The pharmacist understandingly nods his head and
  replies "Well, you know statistics always was a
  little hard to swallow."

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Epidemiologic study designs

• Randomized controlled trial
• Considered the gold standard
• Exposure is assigned randomly
• Participants followed over time to assess outcome
• Analytic comparison of risk or benefit in exposed
  vs. not exposed
• Can be applied to program evaluation

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Epidemiologic study design 2

• 2. Cohort study
• One group exposed
• Other group unexposed
• Participants followed over time to assess outcome
• Analytic comparison of risk in exposed vs. not
  exposed
• Can be applied to program evaluation

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Epidemiologic study designs 3

• 3. Case-control study
• Based on outcome
• Exposure is compared in those with and without
  outcome
• Analytic comparison of risk in exposed vs. not
  exposed
• 4. Descriptive study
• Provides descriptive statistics of problem under
  study
• No analytic comparison of risk / benefit
• Often precedes analytic studies

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Dependent vs independent variables

• Remember the exposure/outcome relationship
• Another way to describe it is to attribute
  dependent and independent variables-the outcome
  depends on the independent exposure variables
• It is the association between these variables
  that leads us to statistical tests
• The test we use depends on the type of variable

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Statistical significance

• What is statistical significance?
• The probability that the observed relationship
  could have happed by chance
• The p-value and confidence interval are the usual
  measures of significance
• Set by tradition at 0.05 or 95
• The higher the p value, the more likely it could
  have happened by chance
• The wider the confidence interval, the more
  likely it could have happened by chance
• Both driven by variability in the data and sample
  size

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Types of variables

• Continuous variables
• -variables for which there is a range of
  responses
• e.g., age, blood pressure, weight
• Categorical variables
• Variables that fall into categories
• e.g, gender, smoking status

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Hypothesis testing for continuous variables

• Mean (the average number)
• -calculated by summing all the numbers and
  dividing by n
• -Hypothesis testing usually done using a t-test
  to compare the 2 means
• -Significance of t-test based on sample size and
  variability within the data
• Median (the number in the middle)
• -not usually tested
• Mode (the most frequent response)
• -not usually tested

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Hypothesis testing for categorical variables

• Counts (how many fall within each category)
  Compare using 2X2 table
• Proportions (what percentage fall within each
  category)
• Compare 2 proportions
• Frequency distributions (comparing counts and
  percentages between categories)
• Compare using chi-square test

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2X2 tables the foundation
Disease or other outcome No disease or other outcome
Exposed a b
Not exposed c d
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2X2 tables estimating associations
Disease or other outcome No disease or other outcome
Exposed a b ab
Not exposed c d cd
ac bd abcd
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Odds ratios and relative risks

• Odds ratios (ad/bc) calculate the odds of an
  outcome given an exposure
• Relative risk (a/ab)/c/cd) calculates the
  relative risk of an outcome in exposed compared
  to non-exposed group
• Statistical packages calculate confidence
  intervals

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Confidence intervals

• Confidence intervals are used for hypothesis
  testing in 2X2 tables (and others)
• The width of a confidence interval is based on
  the variablility within the data and the sample
  size
• An OR or RR of 1 no association
• A confidence interval that crosses 1 is NOT
  statistically significant

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Regression lines and correlation

• Correlation is the measure of the way one
  variable is associated with another
• Can be done with 2 continuous variables
• The regression line is the best fit between 2
  variables
• Ranges from -1 to 1

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Article review

• Questions to consider
• What is the research question?
• What is their study design?
• What is the exposure variable(s)?
• What is the outcome variable?
• What are the strengths and limitations?
• Who funded the study?
• How compelling are the findings?

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• Example 1
• Statistical associations of the number of streets
  crossed by children and
• -socio-economic indicators-child pedestrian
  injury rate

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Background

• Child pedestrian injury rate has been declining
  in many countries, including Canada
• Concern has been expressed that the decline is
  due to a reduction in exposure to traffic (i.e.,
  children are driven or bussed rather than walking)

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Objective

• The objective of this study was to measure the
  number of streets children cross on one day
• To see if the number of streets crossed varies by
  socio-economic status
• To see if the child pedestrian injury rate is
  associated with the number of streets crossed

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Variables

• Number of streets crossed as reported by parents
  from a random sample of schools in Montreal
• Socio-economic status measured by-car
  ownership-parental education-home ownership
• Injury rate in police district as reported by the
  police

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Methods

• Frequency distribution of average of streets
  crossed presented by age and SES
• Statistical testing for the differences between
  means for categorical variables
• Scatterplot generated and regression line
  calculated

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Table 1 Number of Streets Crossed by Age and
Socio-economic Indicators
Age N Mean SD
5 6 487 3.8 4.2
7 730 4.2 5.0
8 9 519 4.8 5.3
10 657 5.5 5.8
11 12 108 6.6 6.3
Number of cars
0 467 5.9 5.8
1 1191 4.8 5.3
2 815 3.8 4.8
Home Ownership
Rent home 1213 5.5 5.6
Own home 1210 3.8 4.7
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Comparing average streets crossed by car ownership
No car 1 car
Average streets crossed (Mean) 5.9 4.8
Standard deviation 5.8 5.3
Sample size 467 1171
Z Test for difference between means 13.8, plt0.001
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Measures of association between variables

• Tied in to the concept of reliability and
  validity
• Sometimes we need to test a new variable in
  relation to an old one
• For example, a new questionnaire, faster blood
  test, etc.
• Several ways to measure association
• Cronbachs alpha, kappa, sensitivity,
  specificity, positive predictive value, negative
  predictive value

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Cronbachs alpha

• Measures the reliability of a psychometric
  instrument
• Assesses the extent to which a set of test items
  can be treated as measuring a single latent
  variable
• Mean correlation between a set of items with the
  mean of all the other items
• Looks at variation between individuals compared
  to variation due to items
• Can be between infinity and 1 (although usually
  only between 0 and 1)
• Usually considered good if gt 0.8

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Kappa

• Measures the extent to which ratings given by 2
  raters agree
• Often used when experts are assigning scores
  based on opinions (e.g., medication errors)
• Gives credit when scores match exactly, takes
  away agreement when they dont
• Can be between 0 and 1
• Usually considered good if gt 0.7

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Sensitivity and specificity

• Sensitivity
• Measures the extent to which a test agrees with a
  gold standard
• Often used when trying out a new diagnostic test
• Reports how often the new test agrees with the
  old when positive
• Captures the false negatives
• Calculated using a 2 X 2 table
• Acceptability of score depends on test qualities

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Sensitivity and specificity

• Specificity
• Measures the extent to which a test agrees with a
  gold standard
• Often used when trying out a new diagnostic test
• Captures the false positives
• Reports how often the new test agrees with the
  old when negative (eg accurately reports the
  absence of the condition)
• Calculated using a 2 X 2 table
• Acceptability of score depends on test qualities

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2X2 tables revisited
Gold standard (has condition) Gold standard (does not have condition)
New test a b
New test - c d
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Calculating sensitivity and specificity

• Sensitivity number who are both disease positive
  and test positive/number who are disease positive
• a/ac
• Specificity number who are both disease
  negative and test negative/number who are disease
  negative
• d/db

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Understanding sensitivity and specificity

• Sensitivity is high when the test picks up a lot
  of the true disease (has few false negatives)
  High sensitivity is important for infectious
  diseases (e.g., HIV)
• Specificity is high when the test does not have
  false positives. This is important when the
  consequences of treating the disease are
  significant (e.g., cancer)

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Positive and negative predictive value

• Tells you how good a test is at predicting
  whether a patient actually has the disease
• Positive predictive value is the probability that
  the patient has the disease given a positive test
  
• Depends on sensitivity, specificity and the
  prevalence of the disease

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Overview

• Different types of variables are measured and
  presented differently
• P values and confidence intervals are the measure
  of statistical significance
• Tell us the probability that these results could
  have happened by chance
• Cronbachs alpha, kappa, sensitivity and
  specificity tell us about relationships between
  measurements

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For next week 1

• Read Chapter 3 in the text
• Read the ICES privacy document (www.ices.on.ca)
• Think about privacy and confidentiality
• What issues are relevant to you in your current
  research?

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For next week 2

• Identify your data set
• Where did it come from?
• How was it collected?
• What type of variables does it include?
• What is your research question?
• What are your exposure variables?
• What is your outcome variable?
• If you are not familiar with SPSS it is STRONGLY
  recommended that you complete the tutorial