Center for Quantitative Methods
Erasmus Medical Center
31 October 2018
“Why can’t I just use MICE?”
Well, you can use MICE, …
… and in standard settings it usually works well, …
… but there are settings in which it doesn’t!
Then (naive) use of MICE leads to
- violation of assumptions
- invalid imputations
- biased results
Example: Quadratic effect
Consider an analysis model \(\quad y = \beta_0 + \beta_1 x + \boldsymbol{\beta_2 x^2} + \ldots\)
Example: Quadratic effect
MICE uses a linear relation when imputing \(x\): \(\quad x = \theta_{10} + \theta_{11} y + \ldots\)
Example: Quadratic effect
severely biased results
Example: Interaction Effects
Another example: non-linear relationship due to interaction term \[y = \beta_0 + \beta_x x + \beta_z z + \boldsymbol{\beta_{xz} xz} + \ldots\]
Example: Interaction Effects
Again: MICE assumes a linear relation between \(x\) and \(y\) in the imputation model \[x = \theta_{10} + \theta_{11} y + \theta_{12} z + \ldots\]
Example: Interaction Effects
severely biased estimates
Example: Longitudinal data
| ID | y | x1 | x2 | x3 | x4 | time |
|---|---|---|---|---|---|---|
| 5 | NA | |||||
| 5 | NA | |||||
| 5 | NA | |||||
| 5 | NA | |||||
| 6 | NA | NA | ||||
| 6 | NA | NA | ||||
| 6 | NA | NA | ||||
| 8 | NA | |||||
| 8 | NA | |||||
| 8 | NA | |||||
| 18 | NA | |||||
| 18 | NA | |||||
| 18 | NA | |||||
| 18 | NA | |||||
Here, \(x_1, \ldots, x_4\) are baseline covariates, i.e., not measured repeatedly.
Example: Longitudinal data
Imputation in long format
- regards each row as independent,
- may cause bias
- and inconsistent imputations.
| ID | y | x1 | x2 | x3 | x4 | time |
|---|---|---|---|---|---|---|
| 5 | boy | |||||
| 5 | girl | |||||
| 5 | girl | |||||
| 5 | girl | |||||
| 6 | girl | high | ||||
| 6 | girl | mid | ||||
| 6 | girl | high | ||||
| 8 | 37.22 | |||||
| 8 | 37.71 | |||||
| 8 | 41.37 | |||||
| 18 | boy | |||||
| 18 | boy | |||||
| 18 | boy | |||||
| 18 | boy | |||||
Example: Longitudinal data
Estimates can be severely biased.
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = ## control$checkConv, : Model failed to converge with max|grad| = 0.00609238 ## (tol = 0.002, component 1)
Example: Longitudinal data
Sometimes imputation in wide format may be possible. 
Example: Longitudinal data
| id | y.1 | y.3 | y.5 | y.7 | y.9 | time.1 | time.3 | time.5 | time.7 | time.9 | … |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 5 | NA | NA | … | ||||||||
| 6 | NA | NA | NA | NA | … | ||||||
| 8 | NA | NA | NA | NA | … | ||||||
| 18 | NA | NA | … | ||||||||
| \(\ddots\) |
In wide format:
- missing values in outcome and measurement times need to be imputed
(to be used as predictors in imputation of covariates) - Very inefficient in for unbalanced data!
Example: Longitudinal data
Better, but very large confidence intervals