The case-crossover design extends this methodology to observational studies. Only cases are sampled, and each subject's exposure at the time of failure is compared with past exposures. The great advantage of the case-crossover design is that confounding factors such as age, sex, and general condition of health are automatically controlled for. The case-crossover design has weakness, however, in that time trends in exposure can cause bias. This is particularly true for environmental exposures such as air pollutants, which typically exhibit strong time trends.
Studies involving environmental exposures have certain advantages, however.
One is that exposure levels are not affected by failures. Thus we can determine the exposure that a subject would have had at any given time post-failure. We present a variant of the case-crossover design that takes advantage of this fact to produce estimates of risk that are insensitive to time trends in exposure. This method can prove useful for assessing risks of environmental exposures. Methods of two-dimensional smoothers usually involve kernels or locally weighted regression, sometimes constructed adaptively depending upon the apparent behavior of the function and the density of data points in local neighborhoods.