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TWO-STAGE CASE-CONTROL STUDIES USING EXPOSURE ESTIMATES FROM A GEOGRAPHICAL INFORMATION SYSTEM. Jonas Björk 1 & Ulf Strömberg 2 1 Competence Center for Clinical Research 2 Occupational and Environmental Medicine Lund University Hospital. OUTLINE OF TALK.

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two stage case control studies using exposure estimates from a geographical information system

TWO-STAGE CASE-CONTROL STUDIES USING EXPOSURE ESTIMATES FROM A GEOGRAPHICAL INFORMATION SYSTEM

Jonas Björk1 & Ulf Strömberg2

1Competence Center for Clinical Research

2Occupational and Environmental Medicine Lund University Hospital

outline of talk
OUTLINE OF TALK
  • Previous project: What have we done? (Jonas Björk)
  • Ongoing project: What shall we do? (Ulf Strömberg)
two stage procedure for case control studies
Two-stage procedure for case-control studies

1st stage

Complete data obtained from registries

Disease status

General characteristics

Group affiliation

(e.g. occupation or residential area)

 Group-level exposure XG

2nd stage

Individual exposure data for a subset of the 1st stage sample

exposure database group level exposure
Exposure database group-level exposure
  • JEM = Job Exposure Matrix

Occupational group  proportion exposed

  • GIS

Residential group (area)  average concentration of an

air pollutant

jem proportion exposed
JEM - proportion exposed

Most data

typically in groups

with low XG

linear relation between proportion exposed and relative risk
Linear Relation between Proportion Exposed and Relative Risk
  • No confounding between/within groups Example: RR (exposed vs. unexposed) = 2.0
linear or model or x g 1 x g

Linear OR model: OR(XG) = 1 + β XG

XG = Exposure proportion

OR for exposed vs. unexposed = OR(1) = 1 + β

OR(1)

Most data

typically in groups

with low XG

1

XG

0

1

confounding between groups
Confounding between groups
  • General confounders (eg, gender and age) can normally be adjusted for
  • Assuming no confounding within groups and no effect modification in any stratum sk: OR(XG;s1, s2, ...sk) = (1 + β XG) exp(Σγksk)
combining 1 st and 2 nd stage data
Combining 1st and 2nd stage data
  • Assumption: 2nd stage data missing at random condition on disease status and 1st stage group affiliation
  • For subjects with missing 2nd stage data:

Use 1st stage data to calculate expected number of exposed/unexposed

  • Expectation-maximization (EM) algorithm
em algorithm wacholder weinberg 1994
EM-algorithm(Wacholder & Weinberg 1994)

1. Select a starting value, e.g. OR=1

2. E-step

Among the non-participants, calculate expected number of exposed/unexposed case and controls in each group

3. M-step

Maximize the likelihood for observed+expected cell frequencies using the chosen risk model for individual-level data

(not necessarily linear)

 New OR-estimate

4. Repeat 2. and 3. until convergence

e step in our situation str mberg bj rk submitted
E-step in our situation (Strömberg & Björk, submitted)

ÔR = Current OR-estimate

Complete the data in each group G:

  • m0 controls with missing 2nd stage data

m0 * XG = expected number of exposed

  • m1 cases with missing 2nd stage data

 m1 * XG * ÔR / [1+(ÔR-1)* XG]

simulated case control studies
Simulated case-control studies
  • 400 cases, 1200 controls in the 1st stage
  • 2nd stage participation

75% of the cases

25% of the controls

  • Selective participation of 2nd stage controls

Corr(Participation, XG) =0, > 0, <0

  • 1000 replications in each scenario
  • True OR = 3
simulations results
Simulations - Results

SD = Empirical standard deviation of the ln(OR) estimates

Coverage = Coverage of 95% confidence intervals

simulations conclusions
Simulations - Conclusions
  • Combining 1st and 2nd stage data,
  • using the EM method can:
  • 1. Improve precision
  • 2. Remove bias from selective participation
  • Method is sensitive to errors in the
  • (1st stage) external exposure data!
simulations conclusions ii
Simulations – Conclusions II
  • EM-method is sensitive to
  • Violations of the MAR-assumption
  • (condition on on disease status and 1st stage group affiliation)
  • 2. Errors in the (1st stage) external exposure data
ongoing methodological research project
Ongoing methodological research project
  • Focus on exposure estimates from a GIS
two stage exposure assessment procedure
Two-stage exposure assessment procedure

1st stage:XG represents mean exposure levels rather than proportion exposed

XG = 4.8 XG = 10.1 XG = 20.1 ...

xi

xi

xi

2nd stage:xi is a continuous, rather than a dichotomous, exposure variable

slide19

Assume a linear relation between and xi and disease odds (cf. radon exposure and lung cancer [Weinberg et al., 1996]).

Odds

xi

For the ”only 1st stage” subjects: no bias expected by using their XG:s (Berkson errors) provided MAR in each group – independent of disease status.

EM method? Exposure variation in each group?

two stage exposure assessment procedure related work
Two-stage exposure assessment procedure – related work
  • Multilevel studies with applications to a study of air pollution [Navidi et al., 1994]: pooling exposure effect estimates based on individual-level and group-level models, respectively
collecting data on confounders or effect modifiers at 2 nd stage
Collecting data on confounders or effect modifiers at 2nd stage

1st stage:XG = mean exposure levels

XG = 4.8 XG = 10.1 XG = 20.1 ...

ci

ci

ci

2nd stage:ci is a covariate, e.g. smoking history

data on confounders or effect modifiers at 2 nd stage estimation of exposure effect
Data on confounders or effect modifiers at 2nd stage – estimation of exposure effect
  • Confounder adjustment based on logistic regression: pseudo-likelihood approach [Cain & Breslow, 1988]
  • More general approach: EM method [Wacholder & Weinberg, 1994]
design stage stage 0
Design stage (“stage 0”)

1st stage: How many geographical areas (groups)?

Group1 Group 2 Group 3 ...

Subjects?

?

?

2nd stage: Fractions of the 1st stage cases and controls?

design stage related work
Design stage – related work
  • Two-stage exposure assessment: power depends more strongly on the number of groups than on the number of subjects per group [Navidi et al., 1994]
references i
References I
  • Björk & Strömberg. Int J Epidemiol 2002;31:154-60.
  • Strömberg & Björk. “Incorporating group-level exposure information in case-control studies with missing data on dichotomous exposures”. Submitted.
references ii
References II
  • Cain & Breslow. Am J Epidemiol 1988;128:1198-1206.
  • Navidi et al. Environ Health Perspect 1994;102(Suppl 8):25-32.
  • Wacholder & Weinberg. Biometrics 1994;50:350-7.
  • Weinberg et al. Epidemiology 1996;7:190-7.