### Trang Le

#math graduate. Postdoc fellow with Jason Moore.

- 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)

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

\(f(t_i)\) 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

mask one result per analyte per patient

n_{GP}= [n_{MICE}\times \frac{\sigma_{MICE}}{\sigma_{GP}}] = [100 \times \frac{\sigma_{MICE}}{\sigma_{GP}}]

x_n = \frac{x-min(x)}{max(x) - min(x)}

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}}}

patient \(p\)

analyte \(a\)

time index \(i\)

correlation between analytes and

between current and prior values for each analyte

- Amelia II
- https://www.ieee-ichi.org/2019/challenge.html

- > 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

- 3DMICE is competitive in imputing missing data, especially when both inter-variable and within-variable correlation are present

By Trang Le