When possible, report a Fisher-exact P value and display its underlying null randomization distribution.

In randomized experiments, Fisher-exact P values are available and should be used to help evaluate results rather than the more commonly reported asymptotic P values. One reason is that using the latter can effectively alter the question being addressed by including irrelevant distributional assumptions. The Fisherian statistical framework, proposed in 1925, calculates a P value in a randomized experiment by using the actual randomization procedure that led to the observed data. Here, we illustrate this Fisherian framework in a crossover randomized experiment. First, we consider the first period of the experiment and analyze its data as a completely randomized experiment, ignoring the second period; then, we consider both periods. For each analysis, we focus on 10 outcomes that illustrate important differences between the asymptotic and Fisher tests for the null hypothesis of no ozone effect. For some outcomes, the traditional P value based on the approximating asymptotic Student's t distribution substantially subceeded the minimum attainable Fisher-exact P value. For the other outcomes, the Fisher-exact null randomization distribution substantially differed from the bell-shaped one assumed by the asymptotic t test. Our conclusions: When researchers choose to report P values in randomized experiments, 1) Fisher-exact P values should be used, especially in studies with small sample sizes, and 2) the shape of the actual null randomization distribution should be examined for the recondite scientific insights it may reveal.

Causal mediation analysis for longitudinal data with exogenous exposure.

Mediation analysis is a valuable approach to examine pathways in epidemiological research. Prospective cohort studies are often conducted to study biological mechanisms and often collect longitudinal measurements on each participant. Mediation formulae for longitudinal data have been developed. Here, we formalize the natural direct and indirect effects using a causal framework with potential outcomes that allows for an interaction between the exposure and the mediator. To allow different types of longitudinal measures of the mediator and outcome, we assume two generalized mixed-effects models for both the mediator and the outcome. The model for the mediator has subject-specific random intercepts and random exposure slopes for each cluster, and the outcome model has random intercepts and random slopes for the exposure, the mediator, and their interaction. We also expand our approach to settings with multiple mediators and derive the mediated effects, jointly through all mediators. Our method requires the absence of time-varying confounding with respect to the exposure and the mediator. This assumption is achieved in settings with exogenous exposure and mediator, especially when exposure and mediator are not affected by variables measured at earlier time points. We apply the methodology to data from the Normative Aging Study and estimate the direct and indirect effects, via DNA methylation, of air pollution, and temperature on intercellular adhesion molecule 1 (ICAM-1) protein levels. Our results suggest that air pollution and temperature have a direct effect on ICAM-1 protein levels (i.e. not through a change in ICAM-1 DNA methylation) and that temperature has an indirect effect via a change in ICAM-1 DNA methylation.

The importance of having a conceptual stage when reporting non-randomized studies.

Formal guidelines for statistical reporting of non-randomized studies are important for journals that publish results of such studies. Although it is gratifying to see some journals providing guidelines for statistical reporting, we feel that the current guidelines that we have seen are not entirely adequate when the study is used to draw causal conclusions. We therefore offer some comments on ways to improve these studies. In particular, we discuss and illustrate what we regard as the need for an essential initial stage of any such statistical analysis, the conceptual stage, which formally describes the embedding of a non-randomized study within a hypothetical randomized experiment.

Heterogeneous ozone effects on the DNA methylome of bronchial cells observed in a crossover study.

We used a randomized crossover experiment to estimate the effects of ozone (vs. clean air) exposure on genome-wide DNA methylation of target bronchial epithelial cells, using 17 volunteers, each randomly exposed on two separated occasions to clean air or 0.3-ppm ozone for two hours. Twenty-four hours after exposure, participants underwent bronchoscopy to collect epithelial cells whose DNA methylation was measured using the Illumina 450 K platform. We performed global and regional tests examining the ozone versus clean air effect on the DNA methylome and calculated Fisher-exact p-values for a series of univariate tests. We found little evidence of an overall effect of ozone on the DNA methylome but some suggestive changes in PLSCR1, HCAR1, and LINC00336 DNA methylation after ozone exposure relative to clean air. We observed some participant-to-participant heterogeneity in ozone responses.