Conditional Probability and Screening Tests

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Conditional Probability and Screening Tests

• Clinical topics
• Mammography and Pap smear
• (screening for cancer)

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What factors determine the effectiveness of
screening?

• The prevalence (risk) of disease.
• The effectiveness of screening in preventing
  illness or death.
• Is the test any good at detecting
  disease/precursor (sensitivity of the test)?
• Is the test detecting a clinically relevant
  condition?
• Is there anything we can do if disease (or
  pre-disease) is detected (cures, treatments)?
• Does detecting and treating disease at an earlier
  stage really result in a better outcome?
• The risks of screening, such as false positives
  and radiation.

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Cumulative risk of disease
(from your course reader)
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To assess your cumulative risk

• http//bcra.nci.nih.gov/brc/

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Mammography

• Mammography utilizes ionizing radiation to image
  breast tissue.
• The examination is performed by compressing the
  breast firmly between a plastic plate and an
  x-ray cassette that contains special x-ray film.
• Mammography can identify breast cancers too small
  to detect on physical examination, and can also
  find ductal carcinoma in situ (DCIS), a
  noninvasive condition that may or may not
  progress to cancer.
• Early detection and treatment of breast cancer
  (before metastasis) can improve a womans chances
  of survival.
• Studies show that, among 50-69 year-old women,
  screening results in 20-35 reductions in
  mortality from breast cancer.

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Mammography

• Controversy exists over the efficacy of
  mammography in reducing mortality from breast
  cancer in 40-49 year old women.
• Mammography has a high rate of false positive
  tests that cause anxiety and necessitate further
  costly diagnostic procedures.
• Mammography exposes a woman to some radiation,
  which may slightly increase the risk of mutations
  in breast tissue.

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Pap Smear

• In a pap test, a sample of cells from a womans
  cervix is collected and spread on a microscope
  slide. The cells are examined under a microscope
  in order to look for pre-malignant
  (before-cancer) or malignant (cancer) changes.
• Cellular changes are almost always a result of
  infection with high-risk strains of human
  papillomavirus (HPV), a common sexually
  transmitted infection.
• Most cellular abnormalities are not cancer and
  will regress spontaneously, but a small percent
  will progress to cancer.
• It takes an average of 10 years for HPV infection
  to lead to invasive cancer early detection and
  removal of pre-cancerous lesions prevents cancer
  from ever developing.

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Progression to cervical cancer
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Pap smear

• Widespread use of Pap test in the U.S. has been
  linked to dramatic reductions in the countrys
  incidence of cervical cancer.
• However, cervical cancer is the leading cause of
  death from cancer among women in developing
  countries, because of lack of access to screening
  tests and treatment.
• However, as with mammography, false positives,
  detection of abnormalities of unknown
  significance, or detection of low-grade lesions
  that are not likely to progress to cancer can
  cause anxiety and unnecessary follow-up tests

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Thought Question 1

• A 54-year old woman has an abnormal mammogram
  what is the chance that she has breast cancer?
• Guesses?

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Thought Question 2

• A 35-year old woman has an abnormal pap smear
  what is the chance that she has HSIL or cervical
  cancer?
• Guesses?

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Key Concepts

• -Independence
• -Conditional probability
• -Sensitivity
• -Specificity
• -Positive Predictive Value

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Independence

• Example if a mother and father both carry one
  copy of a recessive disease-causing mutation (d),
  there are three possible outcomes for the child
  (the sample space)
• P(genotypeDD).25
• P(genotypeDd).50
• P(genotypedd).25

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Using a probability tree
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Independence

• Formal definition A and B are independent iff
  P(AB)P(A)P(B)
• The mothers and fathers alleles are segregating
  independently.
• P(?D/?D).5 and P(?D/?d).5

Note the conditional probability

• Fathers gamete does not depend on the
  mothersdoes not depend on which branch you
  start on.
• Formally, P(DD).25P(D?)P(D?)

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Characteristics of a diagnostic test

• Sensitivity Probability that, if you truly have
  the disease, the diagnostic test will catch it.
  P(test/D)
• SpecificityProbability that, if you truly do not
  have the disease, the test will register
  negative. P(test-/D)

Note the conditional probabilities! P(test/D)?P(
test/D)) not independent!
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Thought Question 1

• A 54-year old woman has an abnormal mammogram
  what is the chance that she has breast cancer?

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Hypothetical example Mammography
P(BC/test).0027/(.0027.10967)2.4
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Thought Question 1

• The probability that she has cancer given that
  she tested abnormal is just 2.4!
• This is called the positive predictive value,
  or PPV.
• The PPV depends on both the characteristics of
  the test (sensitivity, specificity) and the
  prevalence of the disease.

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Thought Question 2

• A 35-year old woman has an abnormal pap smear
  what is the chance that she has HSIL or cervical
  cancer?

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Hypothetical example Pap Test
P(CC or HSIL/test).0044/(.0044.10945)3.8
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Thought Question 2

• A 35-year old woman has an abnormal pap smear
  what is the chance that she has HSIL or cervical
  cancer?
• Just 3.8!

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Part II

• Epidemiology is the study of patterns of diseases
  in populations.

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Assumptions and aims of epidemiologic studies

• 1) Disease does not occur at random but is
  related to environmental and/or personal
  characteristics.
• 2) Causal and preventive factors for disease can
  be identified.
• 3) Knowledge of these factors can then be used to
  improve health of populations.

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Correlation studies

• Using differences in the rate of diseases between
  populations to gather clues as to the cause of
  disease is called a correlation study or an
  ecologic study.

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Example Patterns of disease and cervical cancer

• Initial examination of the patterns of cervical
  cancer gave strong etiologic clues
• -high rates among prostitutes
• -absence of cases among nuns
• -higher rates among married and highest rates
  among widowed women
• ? Suggested sexually transmitted cause

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Problems with correlation studies

• Hypothesis-generating, not hypothesis-testing
• Ecologic fallacy Cannot infer causation
  association may not exist at the individual
  level.
• - Making observations of risk factor and
  diseases status on individual subjects is called
  analytic epidemiology

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Introduction to Case-Control studies
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Case-Control Studies

• Sample on disease status and ask retrospectively
  about exposures (for rare diseases)
• Marginal probabilities of exposure for cases and
  controls are valid.
• Doesnt require knowledge of the absolute risks
  of disease
• For rare diseases, can approximate relative risk

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Case-Control Studies
Exposed in past

• Disease
• (Cases)

Not exposed
Target population
Exposed
No Disease (Controls)
Not Exposed
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Case-Control Studies in History

• In 1843, Guy compared occupations of men with
  pulmonary consumption to those of men with other
  diseases (Lilienfeld and Lilienfeld 1979).
• Case-control studies identified associations
  between lip cancer and pipe smoking (Broders
  1920), breast cancer and reproductive history
  (Lane-Claypon 1926) and between oral cancer and
  pipe smoking (Lombard and Doering 1928). All
  rare diseases.
• Case-control studies identified an association
  between smoking and lung cancer in the 1950s.
• You read about two historical case-control
  studies for homework.

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Frequency Distributions

• Refer to figure 4, p. 144 of Bimodal age
  distributions of mammary cancer.
• Histograms, or frequency distributions, plot the
  frequency of disease according to categories of a
  predictor (such as age).