Analysis of covariance models for data from observational field studies

We outline the features of a general class of statistical models (i.e., analysis of covariance [ANCOVA] models) that has proven to be effective for the analysis of data from observational studies. In observational studies, treatments are assigned by Nature in a decidedly nonrandom manner; consequently, many of the crucial assumptions and safeguards of the classic experimental design either fail or are absent. Hence, inferences (causal or associative) are more difficult to justify. Typically, investigators can expect the primary factors of interest, which are usually called environmental exposures rather than treatments, to be involved in complex interactions with each other and with other factors, and these factors will be confounded with still other factors. We provide examples illustrating the application of ANCOVA models to adjust for confounding factors and complex interactions, thereby providing relatively clean estimates of association between exposure and response. We summarize information on available software and supporting literature for implementing ANCOVA models for the analysis of cross-sectional and longitudinal observational field data. We conclude with a brief discussion of critical model fitting issues, including proper specification of the functional form of continuous covariates and problems associated with overfitted models and misspecified models that lack important covariates.