Measures of Disease Association

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Measures of Disease Association
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From last time

• Three Important Epidemiologic Measures of Disease
  Frequency
• To describe prevalent cases of disease
• Prevalence
• To describe incident (or new) cases of disease
• Cumulative Incidence (CI)
• Incidence Density (ID)

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Recall

• One of the common applications of Epidemiology
  is
• to identify the causes of disease
• Measures described so far are descriptive
• They measure disease in only one group
• They also allow for crude comparisons of the same
  measures in other groups. However,
• What if the two groups differ on a number of
  characteristics (i.e. age and gender)?
• How can you judge the size of the difference? Is
  a 1 person differences rates (i.e. 4 per 1,000 in
  group a versus 5 per 1,000 in group B) a large
  increase?

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Measures of Association

• So, if we compare the occurrence of disease in
  two groups of people who
• Resemble each other in all respects but one
  factor (i.e. the intervention or exposure).
• We are in essence determining the relationship
  between that one factor and the disease

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Measures of Effect/Association

• Single summary parameters that estimates the
  association between an exposure and the risk of
  developing the outcome. Hennekens and Buring,
  1987
• Absolute Measures
• Difference in measures of disease frequency
• Relative Measures
• Ratio of measures of disease frequency

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The 2 x 2 Table
Disease (Outcome)
() (-)
Exposure
(-) ()
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The 2 x 2 Table (cont.)

• Both outcome and exposure must be dichotomous
  variables (e.g. yes vs. no, present vs. absent)
• Even if they are not, can we make them
  dichotomous?
• Multi-level exposures and outcomes can often be
  compressed
• But beware of the resulting loss of information!
• Must know overlap of exposure and outcome
• With limited information, the rest of the table
  can be derived

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EX Collapsing 2 x 2 Table-Loss of Information
Alzheimers Disease
() (-)
Marital Status
Not Married Married
Question What does it mean to be not married?
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Absolute Measures

• Differences in absolute rates or proportions
• Prevalence Difference (PD)
• Cumulative Incidence Difference
• AKA Risk Difference (RD)
• Incidence Density Difference (IDD)

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Prevalence Difference

• PD P exposed P unexposed
• The excess prevalence of the outcome that is
  associated with the exposure.
• For example, if PD5, then if we were to remove
  exposure x from the population we would decrease
  the prevalence of disease by 5.
• Or, there is a 5 excess prevalence of disease
  associated with exposure x.

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Cumulative Incidence (RISK) Difference

• RD CI exposed CI unexposed
• The excess risk of the outcome that is
  associated with the exposure.
• For example, if RD10, then if we were to remove
  exposure x from the population we would decrease
  the average risk of the disease in that
  population by 10.

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Incidence Rate Difference

• IRD IR exposed IR unexposed
• The excess rate of the outcome that is
  associated with the exposure.
• The difference between the exposed and the
  unexposed in the absolute number of cases per
  unit of person time
• For example, if IRD5 per 1000 p.years, then if
  we were to remove exposure x from the population
  we would decrease the number of cases per 1000
  p.years by 5.

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Relative Measures

• Ratios of disease measures including rates,
  proportions or odds
• Prevalence Ratio (PR)
• Cumulative Incidence Ratio (Relative Risk, Risk
  Ratio, RR)
• Incidence Rate Ratio (IRR)
• Odds Ratio (OR)
• Further introduction During Study Design Lecture

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Prevalence Ratio (PR)

• PR P exposed / P unexposed
• The relative increase or decrease in prevalence
  of the outcome in the exposed compared to the
  unexposed.
• For example, if PR1.1, then the exposed group
  was 1.1 times more likely (or 10 more likely) to
  have the outcome than the unexposed group
  (relative to the unexposed group).

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Cumulative Incidence Ratio (RR-Relative Risk)

• RR CI exposed / CI unexposed
• The relative increase or decrease in the risk
  of the outcome in the exposed compared to the
  unexposed.
• For example, if RR1.1, then the exposed group
  had a 1.1 greater risk (or 10 greater risk) of
  having the outcome than the unexposed group.

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Incidence Rate Ratio (IRR)

• IRR IR exposed / IR unexposed
• The relative increase or decrease in the rate of
  the outcome in the exposed compared to the
  unexposed.
• For example, if IRR1.1, then the exposed group
  had a 1.1 times greater rate (or 10 greater
  rate) of developing the outcome than the
  unexposed group.

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Relative vs. Absolute Measures?

• Depends on purpose of analysis
• Rate or Risk difference useful for public health
  research
• Magnitude of a public health problem attributable
  to an exposure.
• E.g. if we could eliminate smoking from the
  population, then we could also eliminate XXXX
  number of cases of lung cancer from the
  population
• Sometimes, there is no choice, you are limited by
  the data.
• i.e. Odds Ratios in case-control studies.more
  later in Study Design lecture

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Interpreting Relative Measures of Effect-Example
RR

• If RR 1, then there is no effect
• If RR gt 1, then there is an increased effect
• RR1.2, translates into a 20 increased
  likelihood
• If RR lt 1, then there is a decreased (or
  protective effect)
• RR0.6, translates into a 40 decreased likelihood

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Example Snow and Cholera in 1855
Water Company
SW/VX
LM
Cholera
(-) ()
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Example (continued)
3.2 per 2 years
0.4 per 2 years
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Example (continued)
8.4
In other words, persons receiving water from the
Southwark/Vauxhall water companies were 8.4 times
more likely to develop cholera than were persons
receiving water from the Lambeth water company.
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Number Needed to Treat (NNT)

• Typically, relative measures (i.e. RR, OR) are
  reported in modern study designs
• Yet, relative measures are not intuitive and
  the translation of a relative measure for an
  individual patients care is difficult
• For example, what does it mean to a physician
  when a study shows a 20 reduction in risk
  associated with a drug treatment? What is the
  patients baseline risk of an event to start
  with?

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NNT (cont.)

• As an alternative, statisticians have proposed
  the NNT methodology
• Calculated as the inverse of the absolute risk
  reduction
• Can be applied to many types of study designs and
  often to published data
• Formulas exist for
• Case-control studies
• Follow-up studies (both randomized and
  non-randomized studies)
• Time to event analyses

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NNT-2 Main Types

• NNTB
• Number Needed to Treat to Benefit
• The number of people that you hypothetically
  treat with a particular agent to prevent 1
  outcome.
• NNTH
• Number Needed to Treat to Harm
• The number of people you hypothetically treat
  with a particular agent to see 1 bad outcome

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NNT-Should be Interpreted Cautiously

• Errors do occur in calculation
• As with any measure, if the study is flawed, so
  are the results
• The NNT should not be extrapolated beyond the
  measured follow-up time
• A patients baseline risk needs to be considered
  in the application of such measures

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Example To Treat or Not to Treat
Source Quilliam et al. Stroke 2001 supplemented
with additional unpublished data