Principles of Epidemiology Lecture 8 CaseControl Studies I

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Principles of EpidemiologyLecture 8Case-Control
Studies (I)

• Wei J. Chen, MD, ScD
• Institute of Epidemiology
• College of Public Health
• National Taiwan University

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Outlines

• I. Rationale
• I-1. Sampling from a fixed cohort
• I-2. Sampling from a dynamic cohort (density
  sampling)
• II. Source of controls
• III. Comparability
• IV. Variants of the case-control design

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I. Rationale
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Basic Elements of Case-Control Studies

• Natures
• Select cases and controls
• Assess their exposure experience retrospectively
• Estimates
• Odds
• Odds for exposure in cases Pr (E D) / Pr (E-
  D)
• Odds for exposure in controls Pr (E D-) / Pr
  (E- D-)
• Odds ratio
• OR Pr (E D) / Pr (E- D) / Pr (E
  D-) / Pr (E- D-)

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Rationales

• Early
• Rare disease assumption
• Sampling from a fixed cohort
• Recent
• Sampling from a dynamic cohort
• Density sampling or sampling from person-time pool

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I-1. Sampling from a Fixed Cohort

• Cumulative incidence ratio (CIR)
• (X1/N1)/(X0/N0) (X1/X0)/(N1/N0)
• If X1 N1 and X0 N0,, then Z1? N1, Z0? N0
• CIR ? (X1/X0)/(Z1/Z0) , exposure odds among
  cases/exposure odds among non-cases
• Noncases sampled among the population of noncases
• F sampling fraction among noncases
• CIR ? (X1/X0)/(fZ1/fZ0) (X1/X0)/(Y1/Y0)

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Example of Controls Selected from a Fixed Cohort

• Breslow and Day (1980)
• A true cohort
• N 10,000, exposure rate30
• IR (exposed) 0.02 / year IR (unexposed) 0.01
  / year
• For 3 years
• Exposed cases 3000 x (1 - e-IRD) 3000 x (1 -
  e-0.06) 175
• Unexposed cases 7000 x (1 - e-0.03) 207

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(1) Analyzed as a Case-control Study

• Calculate OR instead of IRR

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(2) A Case-Control Study

• All patients were ascertained as cases
• Along with a 10 sample of controls
• Sampling fraction for cases and controls must be
  the same regardless of exposure category

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I-2. Density Sampling in Control Selection

• Density case-control study design
• I1A1/T1, I0A0/T0
• Goal of case-control design
• Use a control series in place of complete
  assessment of the T1 and T0
• Density sampling controls selected in such a way
  that the relative sizes of the T1 and T0 can be
  validly estimated
• Nested within a source population
• A description of the source population correspond
  to the ideal eligibility criteria for both cases
  and controls to be in the study

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Pseudo-Rates and Odds Ratio

• Goal of control sampling
• The exposure distribution among controls is the
  same as it is in the source population of cases
• Control sampling rate
• B1/T1 B0/T0 r, if controls are selected
  independently of exposure
• Pseudo-rate
• (A1/B1) / (A0/B0) (A1/T1) / (A0/T0)
• Ratio of pseudo-rates is an estimate of the IR
  ratio
• Penalty
• precision

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Features of Density Sampling

• A clear definition of source population needed
• Sampling of controls and cases should be
  independent of exposure
• Main advantage
• Easy to see the equivalence of odds ratio to IR
  ratio
• No rare disease assumption needed

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A Hypothetical Scenario for Sampling from
Person-time Pool

• Select a date at random from the case accrual
  period
• Select a person at random from the population
  list
• Was the subject resident within the predetermined
  area as of the random date chosen?
• Repeat 1-3 until the desired number
• Asking exposure information reference point
• cases onset of illness
• control the random point in time

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Guidelines of Density Sampling in Control
Selection

• From the same population that give rise to cases
• Independent of exposure status
• Probability of selecting proportional to person
  time
• Risk-set sampling
• Eligible time for a control is the time when one
  is eligible to become a case
• Risk set the set of individuals in the source
  population who are at risk of becoming a case at
  the time that the case is diagnosed
• Controls are matched to the case with respect to
  sampling

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Special Situation for Control Selection

• An individual selected as control who later
  develop the disease and is selected as a case
• Counted both as a control and a case
• The same person may appear in the control group
  two or more times
• The same person at different times may provide
  different exposure (or confounder) information

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Previous Guidelines on the Selection of Controls

• Schlesselman (1982)
• the control series is intended to provide an
  estimate of the exposure rate that would be
  expected to occur in the cases if there were no
  association between the study disease and
  exposure
• Miettinen (1976)
• the controls should be selected in an unbiased
  manner from those individuals who would have been
  included in the case series, had they developed
  the disease under study

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II. Source of Controls
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Source of Control Series

• Population controls
• Cases are a representative sample of all cases in
  a precisely defined and identified population
• Control
• A random sampling from registry
• Selecting probability is proportional to the
  individuals person-time at risk
• Neighborhood controls
• Controls are matched to the cases on neighborhood
• Neighborhood may be related to exposure should
  be accounted for in the analysis
• Random digital dialing
• Matched to cases on area code and prefix

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Source of Control Series (cont.)

• Hospital- or clinic-based controls
• The source of population is often not
  identifiable
• Control selection
• Limited the diagnoses for controls to those not
  related to the exposure of interest
• Other diseases
• In populations with established registries or
  insurance-claims databases
• Friend controls
• May be related in exposure
• List provision dependent on the cases
• Overlapping
• Dead controls
• Proxy respondents if cases are dead

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Methods for Obtaining Population-based Controls

• Random Digit Dialing (RDD)
• A two-stage sampling method to minimize the
  chances of calling telephone numbers that are not
  assigned to households (Waksberg, 1978)
• Any household with kgt1 residential telephone
  numbers was subsampled with probability 1/k
• Screener question How many people living in
  this household (including yourself) are X to Y
  years old?
• After enumberation, select a sample randomly
  (Kishs sampling tables)
• Area Probability Sampling (APS)
• Typically multi-stage
• Block groups
• Segments (one or more blocks)
• Listing of housing units
• Random sample of housing units

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• Steps for RDD
• Obtaining a list of all telephone area codes and
  existing prefix numbers (first 6 digits)
• Add all possible choices for the next two digits
  the 8-digit numbers as Primary Sampling Units
  (PSUs)
• Randomly select an 8-digit number and also
  randomly select the final 2 digits
• Dial the number
• If a residential address, select more additional
  2 digits until the desired number k conduct
  interviews on k1 numbers
• If not residential, reject the PSU
• Repeat steps 1-4 until the desired number of
  PSUs, m, is reached
• Total sample size m (k1), m and k are chosen to
  satisfy criteria for an optimal sampling design

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Example of One Kish Selection Table
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12 Kish Selection Tables to be used in order
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III. Comparability
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Misconception about Control Selection

• Representativeness
• Wrong
• Of all person with diseases
• Of the entire nondiseased population
• Correct
• the source population for the cases is the one
  that the controls should represent
• Exposure opportunity
• Not needed, as in a real follow-up study

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Comparability of Information

• Comparable or nondifferential error in exposure
  measurement tends to bias the observed odds ratio
  toward the null
• Not always true
• Unless exposure errors are also independent of
  errors in other variables
• Efforts to insure comparable exposure information
  lead to comparable information on other variables

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Number of Control Groups

• The value of using more than one control group is
  quite limited
• A lack of difference between the groups only
  tells us that both groups incorporate similar net
  bias
• A difference only tells us that at least one is
  biased but does not tell us which is best or
  which is worse

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Timing of Classification and Diagnosis

• For cases
• A lag period before diagnosis for exposure
  assessment
• For controls
• Selection time
• Natural event analogous to the case diagnosis
  time, e.g., time of hospitalization for hospital
  control
• Actual time of selection

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IV. Variants of the Case-control Design
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Variants of the Case-control Design

• Case-cohort studies
• Nested case-control studies
• Cumulative (Epidemic) case-control studies
• Controls are selected from those who remain free
  of disease at the end of epidemic
• Case-only studies
• In studies of gene-environment interaction
• Case-crossover studies
• Analogue to classical crossover study for
  interventions without carry-over effect
• For each case
• Pre-disease time periods selected as control
  period
• Exposure at onset vs. exposure during control
  period
• Example sexual activity and myocardial infarction

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Variants of the Case-control Design (cont.)

• Two-stage sampling
• The control series comprises a large number of
  individuals with a limited information (e.g.,
  exposure status)
• A subsample of the controls were investigated for
  more detailed information (e.g., covariates)
• Case-control studies with prevalent cases
• In studies
• Congenital malformations
• Chronic conditions with ill-defined onset times
  and limited effect on mortality (e.g., obesity)

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Case-Cohort Study

• For a fixed cohort
• Cases all incident cases in a given risk period
• Controls a random sample from the population at
  risk at the start of the risk period
• Rationale
• Risk ratio (exposure odds in cases) / (exposure
  odds in the total cohort at risk)

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Example of Case-Cohort Study

• An existing cohort
• Blood drawn on 10,000 individuals
• Control 400 sampled from original 10000
• Typing results 40 , 360 -
• Follow-up
• 200 with rheumatoid arthritis
• Typing results 80 , 120
• OR 80x360/40x120 6
• 150 with ankylosing spondylitis
• Typing results 15 , 135
• OR 1

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Example of Nested Case-control Studies

• Risk-set sampling (Sahl et al., 1993)
• Mortality from various cancers and exposure to
  electromagnetic fields
• Case cancer case from the worker cohort
• Control
• Individuals in the worker cohort who were alive
  on the date of death of the case
• Who had the same birth year, sex, and ethnicity
  as the case
• Randomly select 10 matching controls for each case

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Further Readings on Control Selection

• Potthoff RF (1994) Telephone sampling in
  epidemiologic research to reap the benefits,
  avoid the pittfalls. American Journal of
  Epidemiology, 139, 967-978
• Reilly M (1996) Optimal sampling strategies for
  two-stage studies. American Journal of
  Epidemiology, 143, 92-100
• Brogan DJ et al. (2001) Comparison of Telephone
  Sampling and Area Sampling Response Rates and
  Within-Household Coverage. American Journal of
  Epidemiology, 153, 1119-1127.
• DiGaetano R Waksberg J (2002) Commentary
  trade-offs in the development of a sample design
  for case-control studies. American Journal of
  Epidemiology, 155, 771-775