Multiple imputation using chained equations: Issues and guidance for practice

Key takeaways

content: "@whiteMultipleImputationUsing2011" -file:@whiteMultipleImputationUsing2011

Reading notes

Imported on 2025-04-27 17:52

⭐ Important

• & So far we have not explained how we choose the number of imputations. Standard texts on multiple imputation suggest that small numbers of imputed data sets (m = 3 or 5) are adequate. We first review this argument, then explain why we usually prefer larger values of m, and suggest a rule of thumb. (p. 11)
• & The standard argument is based on the statistical efficiency of the estimates [7]. The (true) variance of a parameter estimate based on m imputations is W +(1+1/m)B, where as before W is the average within-imputation variance and B is the between-imputations variance. Therefore the relative efficiency of infinitely many imputations compared to m imputations is {W +(1+1/m)B}/(W + B) = 1+FMI/m where FMI = B/(W + B) is the fraction of missing information. If we can accept 5 per cent loss of efficiency, then we need FMI/m 0.05, hence m = 5 is adequate if FMI 0.25. Graham et al. argued that we should instead choose the number of imputations to limit the loss in power for testing an association of interest [35]. To limit the loss in power to no more than 1 per cent, they needed m 20 when the FMI was between 0.1 and 0.3. (p. 11)
• Son't use MCMC then...:
  • & We believe that statistical efficiency and power are not enough. Instead, as data analysts, we want to be confident that a repeat analysis of the same data would produce essentially the same results [13, 36]. This means that we must consider the Monte Carlo error of our results, defined as their standard deviation across repeated runs of the same imputation procedure with the same data. Clearly, Monte Carlo error tends to zero as m increases. (p. 11)
• & TheFMIis about 0.17, hence MI with m = 5 loses about FMI/m = 3 per cent precision: conventionally, this would be adequate (p. 11)
• & Bodner performed a simulation study to explore the Monte Carlo variability of three quantities: the width of the 95 per cent confidence interval, the P-value, and the estimated FMI [38]. He chose as a key criterion that the width of the 95 per cent confidence interval should be within 10 per cent of its true value in 95 per cent of imputation runs. This led to the requirement m 3, 6, 12, 24, 59 for FMI = 0.05, 0.1, 0.2, 0.3, 0.5, respectively. Bodner proposed conservatively estimating the FMI as the fraction of incomplete cases. This work has been summarized by ‘the number of imputations should be similar to the percentage of cases that are incomplete’ [34], at least with FMI 0.5. (p. 12)
• I don't:
  • & prefer the following simpler argument that leads to the same rule of thumb, using results in Appendix C that give simple approximations to Monte Carlo errors. We start by considering a particular parameter .Ifm is chosen so that FMI/m ≈ 0.01, where FMI is the fraction of missing information for , we get the following properties: (1) The Monte Carlo error of ̂ is approximately 10 per cent of its standard error. (2) The Monte Carlo error of the test statistic ̂/se( ̂) is approximately 0.1. (3) The Monte Carlo error of the P-value is approximately 0.01 when the true P-value is 0.05, and 0.02 when the true P-value is 0.1. (p. 12)
• & Recall that MICE repeatedly samples from conditional distributions: for example, with three variables X , Y , Z , it draws X from the conditional posterior [X |Y, Z ], then Y from the conditional posterior [Y |X, Z ], and so on. This is somewhat similar to a Monte Carlo Markov Chain procedure [47], but its properties are not proven in general (e.g. [48]). Thus, justification of the MICE procedure has rested on empirical studies [10, 49] rather than theoretical arguments. (p. 17)
• & MI, like all missing data procedures that are based around an MAR assumption, is sensitive to departures from MAR, especially with larger fractions of missing data. One way to deal with this is to include many variables in the imputation model in an effort to make MAR more plausible. (p. 18)
• & As MICE is an iterative procedure, it is important that convergence is achieved. This may be checked by computing, at each cycle, the means of imputed values and/or the values of regression coefficients, and seeing if they are stable. For the example in Section 9, these values appeared stable from the very first cycle. We have never found 10 cycles inadequate, but larger numbers of cycles might in principle be required when incomplete variables are very strongly associated. (p. 18)