Cumulative Geographic Residual Test

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Cumulative Geographic Residual Test

• Example
• Taiwan Petrochemical Study
• Andrea Cook

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Outline

• 1. Motivation
• Petrochemical exposure in relation to childhood
  brain and leukemia cancers
• 2. Cumulative Geographic Residuals
• Unconditional
• Conditional
• 3. Application
• Childhood Leukemia
• Childhood Brain Cancer

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Taiwan Petrochemical Study

• Matched Case-Control Study
• 3 controls per case
• Matched on Age and Gender
• Resided in one of 26 of the overall 38
  administrative districts of Kaohsiung County,
  Taiwan
• Controls selected using national identity numbers
  (not dependent on location).

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Study Population

• Due to dropout approximately 50 3 to 1 matching,
  40 2 to 1 matching, and 10 1 to 1 matching.

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Map of Kaohsiung
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Cumulative Residuals

• Unconditional (Independence)
• Model definition using logistic regression
• Extension to Cluster Detection
• Conditional (Matched Design)
• Model definition using conditional logistic
  regression
• Extension to Cluster Detection

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Logistic Model

• Assume the logistic model where,
• and the link function,

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Residual Formulation

• Then define a residual as,
• Assuming the model is correctly specified would
  imply there is no pattern in residuals.
• gt Use Residuals to test for misspecification.

Cumulative Residuals for Model Checking Lin,
Wei, Ying 2002
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Hypothesis Test

• Hypothesis of interest,
• Geographic Location, (ri, ti )
• Independent
• of Outcome, YiXi
• ?
• Cumulative Geographic Residual
• Moving Block Process is Patternless

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Unconditional Cluster Detection

• Define the Cumulative Geographic Residual Moving
  Block Process as,

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Asymptotic Distribution

• However, the distribution of,
• is hard to define analytically, but we have found
  another distribution that is asymptotically
  equivalent,
• which consists of a fixed component of data and
  random variables

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Significance Test

• Testing the NULL
• Simulate N realizations of
• by repeatedly simulating , while
  fixing the data at their observed values.
• Calculate P-value

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Conditional Logistic Model

• Type of Matching 1 case to Ms controls
• Data Structure
• Assume that conditional on , an unobserved
  stratum-specific intercept, and given the logit
  link, implies,
• The conditional likelihood, conditioning on
  is,

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Conditional Residual

• Then define a residual as,
• gt Use these correlated Residuals to test for
  patterns based on location.

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Conditional Cumulative Residual

• However, the distribution of,
• is hard to define analytically, but we have found
  another distribution that is asymptotically
  equivalent,
• which consists of a fixed component of data and
  random variables

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Significance Test

• Testing the NULL
• Simulate N realizations of
• by repeatedly simulating , while
  fixing the data at their observed values.
• Calculate P-value

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Application

• Study
• Kaohsiung, Taiwan Matched Case-Control Study
• Method
• Conditional Cumulative Geographic Residual Test
  (Normal and Mixed Discrete)

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Results

• Odds Ratio (p-values)
• Marginally Significant Clustering for both
  outcomes without adjusting for smoking history.

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Childhood Leukemia
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Childhood Brain Cancer
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Discussion

• Cumulative Geographic Residuals
• Unconditional and Conditional Methods for Binary
  Outcomes
• Can find multiple significant hotspots holding
  type I error at appropriate levels.
• Not computer intensive compared to other cluster
  detection methods
• Taiwan Study
• Found a possible relationship between Childhood
  Leukemia and Petrochemical Exposure, but not with
  the outcome Childhood Brain Cancer.