COLFORD ET AL. RESPOND

In his letter, Hunter raises interesting issues: treatment-period interaction and carry-over effects in an AB–BA crossover trial.1 The treatment effect (active versus sham water filtration devices), stratified by sequence, suggests interaction: sequence active–sham (relative risk [RR] = 1.23; 95% confidence interval [CI] = 1.03, 1.48) and sequence sham–active (RR = 0.61; 95% CI = 0.50, 0.74). These estimates, however, are confounded by a strong period effect: highly credible gastrointestinal illness (HCGI) incidence declines in both study arms with time (Figure 1). An observed secular decline over time in incidence and prevalence (that is, a period effect) of self-reported outcome has been noted in studies of gastrointestinal illness.2–6 The cause remains unknown; hypotheses are that the decline is caused by genuine health improvement over time simply from participation (“Hawthorne Effects”) or by bias in self-reported outcomes. The decline due to bias could result from over-reporting early, under-reporting late (because of respondent fatigue), or both. Irrespective of the cause, the active filtration device appears harmful in sequence active–sham because incidence is higher in period 1 and lower in period 2. The device appears protective for sequence sham–active for this same reason. When a period effect is observed in an AB–BA cross-over trial, the only way to estimate an unbiased effect is to average treatment effects over the sequences.7 FIGURE 1 Decline of highly credible gastrointestinal illness (HCGI) over time, by study arm: Sonoma Water Evaluation Trial, Sonoma County, CA, 2001–2006. Hunter notes that the pattern in our study is consistent with a scenario in which participants randomized to sequence active–sham lose long-term immunity while using active water filtration and subsequently experience elevated levels of HCGI in period 2 while using sham water filtration (e.g., untreated water). This hypothesis merits consideration, but unfortunately we cannot test it directly. A carry-over effect results when the treatment in period 1 continues to influence the outcome in period 2. Indeed, with an AB–BA cross-over design it is impossible to distinguish carry-over effect from treatment-period interaction, and our results are also consistent with treatment-period interaction.7 A possible cause leading to a larger treatment effect in period 2 than in period 1 could be greater device use by participants remaining in the study. However, objective measures of device use based on our data suggest lower device use in period 2 (see supplemental Table A2 from the original study).1 Furthermore, parallel slopes of HCGI episodes per person-year observed in period 2 (Figure 1) do not support a carry-over effect. We suggest a rigorous alternative design to test carry-over effect: a 4-arm crossover trial (AA–AB–BA–BB) with participants rerandomized at crossover. If the treatment effect in single-treatment sequences mirrored the mixed-treatment sequences (majority of the protective effect in period 2) this would not support a carry-over effect. If the carry-over effect were observed, the specific cause would require further investigation, possibly measurement of participants' immunologic responses to specific putative pathogens.