TWO AUTHORS REPLY
Moran Ki1,2 and
Taesung Park3
1 Department of Preventive Medicine, Eulji University School of Medicine, Jung-gu, Taejon 301-726, Korea
2 Department of Epidemiology, University of Michigan School of Public Health, Ann Arbor, MI 48109
3 Department of Statistics, Seoul National University, Seoul 151-747, Korea
We appreciate Dr. Farringtons letter (1) and his interest in our paper (2). Dr. Farrington raised quite an important fundamental issue regarding the case-crossover design. The case-crossover design compares the probability of exposure between the control period and the hazard period (figure 1). If the probability of exposure is time dependent, the control period and the hazard period cannot be comparable, and the analysis by case-crossover design may have time-trend bias (3).
However, we do not agree that the case-crossover design should not be recommended for investigating the association between adverse events and childhood immunizations. The reasons are as follows.
In general, "time dependent" is totally different from "age dependent." "Time" has the same meaning as "age" only for the specific instance when the observation ages of all cases are the same as the observation time period (figure 2).

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FIGURE 2. Hypothetical examples of when the ages of cases are all the same, illustrating time-trend bias in case-crossover analysis. The probablility of exposure, measles-mumps-rubella vaccination, is higher at 1215 months of age.
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It is true that, in the study by Ki et al. (2), the probability of vaccination is not constant over age. Rather, the probability of vaccination is constant over calendar time. The aseptic meningitis incidence rates based on symptom criteria were not significantly different among those under 3 years of age (<12 months, 21.6; 1223 months, 26.0; and 2435 months, 27.0 per 100,000, respectively; p > 0.05) (2). If the event (aseptic meningitis) occurs randomly between 6 and 36 months of age, then the observation ages of all cases are different. The exposure age (i.e., 1215 months of age) was regarded as randomly located during the observation time periods (1 year before onset of aseptic meningitis). Eventually, the exposure is age dependent but not time dependent. Thus, the hazard period and the control period are comparable without the time-trend bias. Figure 3 shows the structure of the data by Ki et al. more clearly.

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FIGURE 3. Hypothetical examples of when the ages of cases are different, illustrating no time-trend bias in case-crossover analysis. The probability of exposure, measles-mumps-rubella vaccination, is higher at 1215 months of age.
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Most of the case-crossover studies followed the matched case-control study frame that compares the frequency, "counts," of exposure between the hazard period and the control period and uses conditional logistic regression analysis. On the other hand, Ki et al. (2) used the Cochran-Mantel approach to compare person-times that were the average incidence rate ratios. In this instance, the analysis of a case-crossover study with 100 cases may be viewed as a pooled analysis of 100 retrospective cohort studies, each with a sample size of one (4).
In their related work, Park et al. (5) further investigated the adequacy of the Cochran-Mantel approach to find out whether application of the case-crossover design to vaccine studies is valid or not. Through a limited simulation study, it was shown that the Mantel-Haenszel odds ratio is valid as long as the events happen randomly over the observation period. Park et al. also considered alternative approaches, such as Poisson regression, using offset and a simple uniformity test. The Poisson regression model yielded results quite similar to the Mantel-Haenszel odds ratio. The uniformity test is for testing whether or not the time interval between aseptic meningitis (AM) and measles-mumps-rubella (MMR) vaccination, t = MMR AM, is uniform. The results of the uniformity test were statistically significant.
We think the self-controlled case-series method (6) that uses the conditional Poisson regression model can also be used to investigate the association between adverse events and any age-dependent exposures. It also has some advantages, such as full adjustment for age and time effects. On the other hand, the case-crossover design of Ki et al. (2) can still be used for investigating the association between adverse events and any age-dependent exposures including childhood immunizations. Analysis of a case-crossover study is much simpler than the conditional Poisson regression model in a self-controlled case-series study.
REFERENCES
REFERENCES
- Farrington CP. Re: "Risk analysis of aseptic meningitis after measles-mumps-rubella vaccination in Korean children by using a case-crossover design." (Letter). Am J Epidemiol 2004;159:71718.
- Ki M, Park T, Yi SG, et al. Risk analysis of aseptic meningitis after measles-mumps-rubella vaccination in Korean children by using a case-crossover design. Am J Epidemiol 2003;157:15865.[Abstract/Free Full Text]
- Greenland S. Confounding and exposure trends in case-crossover and case-time-control designs. Epidemiology 1996;7:2319.[ISI][Medline]
- Maclure M. The case-crossover design: a method for studying transient effects on the risk of acute events. Am J Epidemiol 1991;133:14453.[Abstract]
- Park T, Ki M, Yi SG. Statistical analysis of MMR vaccine adverse events on aseptic meningitis using the case-crossover design. Stat Med (in press).
- Farrington CP. Relative incidence estimation from case series for vaccine safety evaluation. Biometrics 1995;51:22835.[ISI][Medline]