Trang Le
#math graduate. Postdoc fellow with Jason Moore.
Kim Lab journal club
the problem
- EHR data are often available only at irregular intervals that vary among patients
- machine learning algorithms cannot directly accommodate
- "complete case" approach: biased, limited generalizability, few observations left
- existing imputation methods: cross-sectional data (same time point)
MICE
multiple imputation:
multiple copies of a data set
Step 1: Naively impute missing data points of each variable (e.g., with mean value)
Step 2: Put NAs back in the age variable where it was missing.
Step 3: Train age on income and gender (linear regression) with available data
Step 4 Use the fitted model to predict the missing age values.
Step 5: Repeat Steps 2–4 separately for each variable that has missing data, namely income and gender.
age, gender, income
for each cycle:
- focus on one variable at a time
- utilizes the correlation among the features
Gaussian processes
\(f(t_i)\) have a joint Gaussian distribution
P(f(t))
locality constraint
closer time points have more similar measurement values
cov(f(t_1), f(t_2)) = \alpha e^{-(t_1-t_2)^2/l}
Step 1: extract separate univariate time series for each patient and variable
Step 2: GPfit: MLE over \(\alpha\) and \(l\)
Step 3: infer values at unobserved time points
utilizes autocorrelation within each variable
dataset
mask one result per analyte per patient
n_{GP}= [n_{MICE}\times \frac{\sigma_{MICE}}{\sigma_{GP}}] = [100 \times \frac{\sigma_{MICE}}{\sigma_{GP}}]
sampling
x_n = \frac{x-min(x)}{max(x) - min(x)}
normalization
nRMSD(a) = \sqrt{\frac{\sum{_{p,i}}I_{p,a,i}\left(\frac{X_{p,a,i} - Y_{p,a,i}}{max(Y_{p,a}) - min(Y_{p,a})}\right)^2}{\sum_{p,i}I_{p,a,i}}}
evaluation
patient \(p\)
analyte \(a\)
time index \(i\)
correlation between analytes and
between current and prior values for each analyte
Other methods
- Amelia II
- https://www.ieee-ichi.org/2019/challenge.html
Limitations
- > 2/3 patients were excluded
- interpolations in place of GP for cases lacking sufficient temporal data to use 3D-MICE
- improvement over MICE or GP is small
- missing at random assumption
Conclusion
- 3DMICE is competitive in imputing missing data, especially when both inter-variable and within-variable correlation are present
3D-MICE
By Trang Le
