Analysis of correlated continuous repeated observations: modelling the effect of ketosis on milk yield in dairy cows

Abstract

This study used mixed models analysis to demonstrate the advantages of a repeated measures technique for a continuous variable over a single measure technique. As an illustration, the loss of milk yield due to ketosis was studied in 2604 multiparous New York State Holstein cows belonging to eight herds, calving between 1991 and 1993. Two methods of analysis were presented: The first treated milk yield as a continuous, summary measure (projected 305-day milk yield); the second treated milk yield as repeated measurements (test-day milk yields). In the first example, with 305-day milk yield as the outcome, ketosis was treated as a binary covariate. Ketosis had no effect on the 305-day milk yield. In the second example, with monthly test-day milk yields as the outcome, four different covariance structures (simple, compound symmetry, autoregressive, and unstructured) to model the association among the repeated measurements were compared. With this approach, ketotic cows yielded significantly less milk per day both before and immediately after diagnosis than did non-ketotic cows. Based on the goodness-of-fit statistics, it was unclear whether an autoregressive or unstructured covariance structure was best. However, an autoregressive structure, in which the previous and current test-day milk yields are assumed to be correlated, was considered more suitable in this study; it is a simpler and more appropriate covariance structure for this particular problem than is an unstructured covariance structure. Nevertheless, with the test-day approach, any of these correlation structures could be used to estimate milk loss after disease. Based on these findings, it is recommended that a repeated measures approach, rather than a single measure approach, be used to study the short-term effect of disease on milk yield.