Risk Set Sampling for Case-Crossover Designs

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Abstract
In the case-crossover design, only cases are sampled, and effect estimates are based on within-subject comparisons of exposures at failure times with exposures at control times. Sampling control times appropriately can provide some control for unmeasured confounding, but may introduce bias owing to time trends in the exposure of interest. The theory of risk set sampling (Borgan Ø, Goldstein L, Langholz B. Ann Stat 1995;23:1749–1778) can be used to develop effect estimates in these situations that are free from bias caused by time trends. Through simulation, we compared four sampling schemes: the full-stratum bidirectional design, a matched pair design, the symmetric bidirectional design of Bateson and Schwartz (Bateson T, Schwartz J. Epidemiology 1999;10:539–544), and the semi-symmetric bidirectional design. We also studied a quasi-likelihood extension of Poisson regression with overdispersion. We used daily mean particulate matter less than 10 μm in aerodynamic diameter levels in Denver as the exposure of interest, simulated confounding with linear and seasonal trends, and simulated mortality counts using a log relative risk of 1.1. Neither the matched pair, the full-stratum design, or Poisson regression with overdispersion provided control for seasonal confounding. The symmetric bidirectional design controlled for seasonal confounding but exhibited bias from time trends in exposure. The semi-symmetric bidirectional design provided control of seasonal confounding equal to that of the symmetric bidirectional design, without any time-trend bias.