Documents
Resources
Learning Center
Upload
Plans & pricing Sign in
Sign Out
Your Federal Quarterly Tax Payments are due April 15th Get Help Now >>

Principles of Epidemiology

VIEWS: 150 PAGES: 35

									Principles of Epidemiology
Lecture 8

Case-Control Studies (I)
     Wei J. Chen, MD, ScD
     Institute of Epidemiology
     College of Public Health
     National Taiwan University

                                  1
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

                                                       2
I. Rationale




               3
    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-)]


                                                                                 4
Rationales
   Early
       Rare disease assumption
       Sampling from a fixed cohort
   Recent
       Sampling from a dynamic cohort
           Density sampling or sampling from person-time
            pool



                                                            5
I-1. Sampling from a Fixed Cohort
                                  Disease
                             1                0           Total
    Exposure      1         X1               Z1            N1
                  0         X0               Z0            N0

    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)/(f·Z1/f·Z0) = (X1/X0)/(Y1/Y0)
                                                                         6
Example of Controls Selected
from a Fixed Cohort
   Breslow and Day (1980)
   A true cohort
       N= 10,000, exposure rate=30%
       IR (exposed) = 0.02 / year; IR (unexposed) = 0.01 /
        year
   For 3 years
       Exposed cases: 3000 x (1 - e-IR•D) = 3000 x (1 - e-0.06)
        = 175
       Unexposed cases: 7000 x (1 - e-0.03) = 207

                                                                   7
(1) Analyzed as a Case-control
Study
   Calculate OR instead
    of IRR
                                            Exposed       Unexposed


                           Diseased           175             207        382


                           Disease-free       2825           6793        9618


                                              3000           7000        10000

                             Odds ratio = (175x6793)/(207x2825) = 2.03




                                                                                 8
(2) A Case-Control Study
   All patients were
    ascertained as cases
   Along with a 10%                          Exposed       Unexposed


    sample of controls      Diseased            175            207      382


   Sampling fraction for   Disease-free        282            679      961


    cases and controls                          457            886      1343


    must be the same          Odds ratio = (175x679)/(207x282) = 2.04


    regardless of
    exposure category
                                                                               9
I-2. Density Sampling in
Control Selection
   Density case-control study design
       I1=A1/T1, I0=A0/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

                                                                          10
    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


                                                                11
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

                                                       12
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

                                                          13
    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
                                                               14
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
                                                     15
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”

                                                                 16
II. Source of Controls




                         17
    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 individual’s
            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
                                                                        18
    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
                                                                             19
    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 k>1 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 (Kish’s 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
                                                                            20
   Steps for RDD
    1)   Obtaining a list of all telephone area codes and
         existing prefix numbers (first 6 digits)
    2)   Add all possible choices for the next two digits; the
         8-digit numbers as Primary Sampling Units (PSUs)
    3)   Randomly select an 8-digit number and also
         randomly select the final 2 digits
    4)   Dial the number
         1)   If a residential address, select more additional 2 digits until
              the desired number k; conduct interviews on k+1 numbers
         2)   If not residential, reject the PSU
    5)   Repeat steps 1-4 until the desired number of PSUs,
         m, is reached;
    6)   Total sample size: m (k+1), m and k are chosen to
         satisfy criteria for an optimal sampling design
                                                                                21
Example of One Kish
Selection Table
Selection Table A

If the Number of       Interview the
                                          1. Count the Number of Eligible Persons
Eligible Persons is:   Person Numbered:      in the Household
1                                   1

2                                   1     2. Locate Number in Left-Hand Column:
3                                   1        Place a check in that Row
4                                   1

5                                   1     3. Place a Check in the Corresponding
6+                                  1        Right-Hand Column

                                          4. The Number Next to the Check
                                             Corresponds to the Person
                                             Selected as the Respondent

                                          5. Go to Col. 11I and Place an “R” in the
                                             Row Which Corresponds to the
                                             Selected Respondent


                                                                                      22
12 Kish Selection Tables: to
be used in order
 Selection Table A                         Selection Table E                         Selection Table I
 If the Number of       Interview the      If the Number of       Interview the      If the Number of       Interview the
 Eligible Persons is:   Person Numbered:   Eligible Persons is:   Person Numbered:   Eligible Persons is:   Person Numbered:
 1                                    1    1                                    1    1                                    1
 2                                    1    2                                    1    2                                    2
 3                                    1    3                                    2    3                                    3
 4                                    1    4                                    2    4                                    3
 5                                    1    5                                    3    5                                    3
 6+                                   1    6+                                   3    6+                                   5

 Selection Table B                         Selection Table F                         Selection Table J
 If the Number of       Interview the      If the Number of       Interview the      If the Number of       Interview the
 Eligible Persons is:   Person Numbered:   Eligible Persons is:   Person Numbered:   Eligible Persons is:   Person Numbered:
 1                                    1    1                                    1    1                                    1
 2                                    1    2                                    1    2                                    2
 3                                    1    3                                    2    3                                    3
 4                                    1    4                                    2    4                                    4
 5                                    1    5                                    3    5                                    5
 6+                                   1    6+                                   3    6+                                   5

 Selection Table C                         Selection Table G                         Selection Table K
 If the Number of       Interview the      If the Number of       Interview the      If the Number of       Interview the
 Eligible Persons is:   Person Numbered:   Eligible Persons is:   Person Numbered:   Eligible Persons is:   Person Numbered:
 1                                    1    1                                    1    1                                    1
 2                                    1    2                                    2    2                                    2
 3                                    1    3                                    2    3                                    3
 4                                    1    4                                    3    4                                    4
 5                                    2    5                                    4    5                                    5
 6+                                   2    6+                                   4    6+                                   6

 Selection Table D                         Selection Table H                         Selection Table L
 If the Number of       Interview the      If the Number of       Interview the      If the Number of       Interview the
 Eligible Persons is:   Person Numbered:   Eligible Persons is:   Person Numbered:   Eligible Persons is:   Person Numbered:
 1                                    1    1                                    1    1                                    1
 2                                    1    2                                    2    2                                    2
 3                                    1    3                                    2    3                                    3
 4                                    2    4                                    3    4                                    4
 5                                    2    5                                    4    5                                    5
 6+                                   2    6+                                   4    6+                                   6




                                                                                                                               23
III. Comparability




                     24
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

                                                                   25
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

                                                      26
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

                                                          27
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



                                                            28
IV. Variants of the Case-control
Design




                               29
    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
                                                                   30
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)

                                                                          31
    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
                               P(E|D)  P(D)
                  P(D| E)                          (1)
                                   P(E)
                               P(E | D)  P(D)
                  P(D| E )                           (2)
                                    P(E )
                                              P(E|D)
                 (1) P(D|E) P(E| D) P(E ) P(E | D)
                                                  P(E)
                 (2) P(D| E ) P(E | D) P(E)
                                                     P(E )

        Risk ratio = (exposure odds in cases) / (exposure odds in the total
         cohort at risk)

                                                                               32
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

                                                   33
    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
                                                               34
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
                                                                    35

								
To top