12.4. Simple Methods and MCAR
We will briefly review a number of relatively simple methods that have been and are still in extensive use. They have been discussed in some detail in Dmitrienko et al. (2005, Chapter 5). We will focus on complete case analysis (CC) and last observation carried forward (LOCF). The latter is a single or simple imputation method, which shares a certain number of pitfalls with the other methods. Multiple imputation, on the other hand (Section 12.5.2) is valid under MAR and therefore is discussed in Section 12.5.
12.4.1.
12.4.1.1. Complete Case Analysis
A complete case (CC) analysis considers only those cases for which all ni measurements were recorded. The method is simple since it restores balance, in the sense that a rectangular data matrix is obtained. However, the drawbacks surpass the advantages. Apart from considerable information loss, leading to inefficient estimates and tests with less than optimal power, often severe bias is to be expected. The method is, therefore, not recommended. See Dmitrienko et al. (2005, Chapter 5) for details.
12.4.1.2. Last Observation Carried Forward
Alternatively, balance can be restored by substituting the last obtained measurement for the missing ones. This technique is termed last observation carried forward (LOCF) or last value carried forward. The practical advantages are the same as with CC, but the issues are manifold. The technique has been discussed in detail in Dmitrienko et al. (2005, Chapter 5) and insightful illustrations of the issues are provided in Molenberghs et al. (2004). An important issue is that filled-in values are treated as actual data. Further, Molenberghs et al. (2004) have illustrated that the bias resulting from this method can be both conservative and liberal, contradicting common belief that the appeal of the method lies in it being conservative for the assessment of treatment effect in superiority trials.
Moreover, since direct likelihood is perfectly feasible in the sense that it is valid under MAR and easy to implement in standard software (Section 12.5), there is generally very little reason to apply LOCF. See also Mallinckrodt et al. (2003ab).
12.4.1.3. Available Case Methods
Available case methods (Little and Rubin, 1987) use as much of the data as possible. In a multivariate normal setting, means and variances are estimated based on the information available for individual outcomes, while covariances are estimated using pairs of outcomes. While this is a simple solution in this setting, the method is difficult to extend to other settings, such as continuous data to which regression models or linear mixed models are applied, or categorical data. Moreover, the method is still valid only under MCAR. The reason is that the method uses moments only; in our setting, these are the first and second moments of the multivariate normal. As such, it is a frequentist method. In the following section, We will show that using the available information in a likelihood framework extends validity to MAR.