Analysing change based on two measures taken under different conditions.

Consider an analysis of change using two measurements on each individual taken from two periods of a longitudinal study, where the measurement conditions were different at each study period. In such situations, 'conditions effects' will necessarily be confounded with change between periods. An example of a conditions effect is a practice or learning effect, where a participant is tested at each period but learns to complete the test more effectively on the second occasion. If the conditions effect mechanism is associated with change and other factors in the analysis then biased model estimates will result. Unfortunately, as with classical age-period-cohort problems, estimating the conditions effect is impossible without modelling assumptions. In this paper, we show that the conditions effect is identifiable given empirically unverifiable assumptions about: (1) the sources of confounding bias in the study; (2) the functional form of age-related change; and (3) factors related to the conditions-effect. We develop the conditions-effect adjustment model (CEAM) for estimating change effects under different sets of assumptions. While none of these assumptions can be verified using the data alone, it is argued that assumptions 1 and 2 are always required when analysing change-even in the absence of conditions effects-and that robustness to all these assumptions can be assessed via sensitivity analysis. The CEAM is illustrated in an application to cognitive test data from the Whitehall II study of British civil servants.