Time‐period effects in longitudinal studies measuring average rates of change

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Abstract
Random time‐period effects are unexplained increases or decreases in the observed value for all individuals measured at a particular time point in a longitudinal study. They can be caused by learning effects, changes in equipment, personnel and overall subject co‐operation. We investigate the consequences of time‐period effects in random coefficient regression models, where interest is in the average rate of change (slope) of a continuous outcome. In a study with a single group of subjects, they can lead to conditionally biased estimates of the mean slope and its variance (conditional on the time‐period effects). Calculations suggest that the increase in sample size required to maintain a specified precision of the mean slope estimate over repeated studies may be substantial. In a study with a concurrent control group, however, time‐period effects do not distort the expectation, estimated variance or the distribution of the difference between the mean slopes. With missing data, in addition to time‐period effects, an unbaised estimate of a single mean slope remains problematic, but one can use standard maximum likelihood techniques to obtain consistent estimators of the difference in mean slopes and its variance. This suggests the importance of a concurrent control group when potential time‐period effects are of concern.