Case Cross-Over Design

1. By Carracedo-Mart�nez et al Case-Crossover Analysis of Air Pollution Health Effects: A Systematic Review of Methodology and Application. Environ Health Perspect 118:1173�1182 (2010). Case Cross-Over Design 1

2. Previous approaches Assume that the dependent variable is distributed normally dynamic regression models include lagged values of x on the right hand side of the regression equation autoregressive integrated moving-average models (ARIMA) to control for residual auto-correlation Poisson regression 2

3.  Poisson regression aka a log-linear model the dependent variable is a count does not require knowledge of the denominator (the entire population) as long as population flux is in steady state when cases can be enumerated the dependent variable is a rate, where the rate is a count of events occurring to a particular unit of observation an offset 3

4. Limitation of Poisson Regression the parametric functions of time or of its sinusoidal transforms cannot be easily �adapted� the cyclical component of varying frequency nonparametric Poisson regression d.f. of the smoothed nonparametric function must be specified by the researcher Poisson regression with the application of generalized additive models (GAMs) 4

5.  Case-crossover (CCO) design proposed by Maclure (1991) to identify risk factors of acute events each subject serves as his or her own control by assessing referent exposure at a point in time prior to the event initially used to assess the effect of exposures measured at an individual level not applicable to exposures with a time trend, such as air pollution 5

6. bidirectional CCO developed by Navidi (1998) having control time periods before and after the event appropriate for ecologic-type exposures such as air pollution, because the existence of registries means that the values of such exposure can be ascertained even after the event pollution values are not affected by the presence of prior morbidity and mortality events 6

7. Other Varients for control of biases full-stratum bidirectional proposed by Navidi symmetric bidirectional case-crossover proposed by Bateson & Schwartz semisymmetric bidirectional case-crossover proposed by Navidi & Weinhandl time-stratified case-crossover proposed by Lumley & Levy 7

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9. Bias and Power (Figueiras et al. 2005) full semisymmetric design the least bias together with the best coverage and statistical power but unstable when the beta value varied with respect to the usual values. semisymmetric CCO fewer biases than did symmetric or time-stratified CCO (both of which yielded similar results) but a lower statistical power 9

10. Advantages of CCO Studies no confounding by time-fixed characteristics (self-matching) control of time-varying confounders (short-interval reference-window) directly estimate the effect of personal exposures, and assess effect modification of exposure by individual attributes no concurvity as in Poisson GAM models (the nonparametric analogue of multicollinearity) 10

11. Problems fails to appropriately account for fluctuations in time (assumption that confound the exposure, the effect estimate is biased) perform model-checking Discuss this later on Arbitrariness in the selection of reference periods or sampling method 11

12. Comparisons of varied CCO designs Most popular Symmetric bidirectional CCO Time-stratified CCO Conclusions about semi-symmetric CCO are contradictory But statistical power is no good 12

13. Steps of Applying CCO Designs to Study the Relationship between Air Pollution and Health 13

14. Steps of Applying CCO Designs to Study the Relationship between Air Pollution and Health 14

15. Steps of Applying CCO Designs to Study the Relationship between Air Pollution and Health 15

16. Steps of Applying CCO Designs to Study the Relationship between Air Pollution and Health 16

17. Log-Linear Time Series Models log-linear regression model (Lu et al. 2008) Yt is the number of events with , where ? is the over-dispersion parameter, Xt is the exposure such as air pollution, and St is the value of a smooth function of time at time t Most case-crossover analyses rely on conditional logistic regression and assume that all subjects are independent the CCO approach is equivalent to a log-linear time-series model without over-dispersion 17

18. Model Checking Standardized Residuals use residual plot to reveal outliers, autocorrelation, or cyclic effects Q-Q plots of can be used to check the assumption Q-Q plot: a graphical method for comparing two probability distributions by plotting their quantiles against each other 18

19. Example: Model Checking before (top) and after (bottom) removing influential points Method A is a time-stratified case-crossover design Method D is a time-series method using a natural spline with 8 degrees of freedom 19

20. Model Checking Dffits (large|Dffits|? influential) check for highly influential events in case-crossover studies where and are the predicted outcomes at time t with or without the observation in the regression, is the SE estimated without ; the leverage statistic for time t, which is the tth diagonal elements of the projection matrix H 20

21. Example: Model Checking before (top) and after (bottom) removing influential points Method A is a time-stratified case-crossover design Method D is a time-series method using a natural spline with 8 degrees of freedom 21

22. Simulations of Statistical Power Analyze statistical power (Symons et al. 2006) Estimated results from 500 simulations each for three fixed values of b (beta coefficient from conditional logistic regression model). sufficient power to detect statistically significant effects for odds ratios greater than 1.20 for an IQR difference (i.e. OR=exp(9.2*0.02)=1.2) in 24-hour averaged PM2.5 uncertainty increased for detecting a smaller ?=0.01 (OR=1.10) 22