Louisa Smith

SER: June 14, 2023

Department of Health Sciences

The Roux Institute

Northeastern University

Frailty is a syndrome of vulnerability more common in older adults

A frailty index is a quantitative measure of the aggregate burden of age-related health deficits

FI = # of deficits / # of possible deficits

- Large-scale NIH study to gather health data from 1 million+ Americans
- Focus on those underrepresented in biomedical research
- Multimodal data collection includes surveys, electronic health records, biospecimens, and more

- 33 deficits based on items from multiple surveys
- Cover multiple domains, including comorbidities, function, cognition, mental health, and geriatric syndromes
- Cannot be weighted to heavily toward one domain (or it would be, e.g., a comorbidity index)

**9.8% of 200,000+ participants had complete data**

**38% had data for >80% of deficits (>27/33)**

**Complete-case**

Exclude those with any missing items

**Proration**

Adjust denominator (person-mean imputation)

**Multiple imputation**

Of individual items / total score

Throwing away *a lot* of data, strong assumptions

Different weighting across domains

Computationally intensive, still requires assumptions

Model how the distribution of missing data depends on missingness pattern

For example, a missingness pattern in which a given deficit is missing may be associated with a

*higher*probability of that deficitCan’t tell from the observed data – by definition we are missing the item in that missingness pattern

A simple model for a single variable with missingness:

\[ E[Y \mid R, X] = \beta_0 + \beta_1X + \color{IndianRed}{\delta} I(R = \color{SlateBlue}{r_0}) \]

where \(\color{IndianRed}{\delta}\) parameterizes how much different the distribution (expectation) of \(Y\) is in observations with missing data patterns where it is missing (\(\color{SlateBlue}{r_0}\))

The delta adjustment approach can be done in the context of multiple imputation, e.g., with MICE

- Fit a model for the conditional expectation of \(Y\) as usual
- Add \(\delta\) to the modeled expectation and draw values of \(Y\)
- Analyze multiple datasets as usual

With multiple missing variables, interpretation of sensitivity parameter \(\delta\) is different

- conditional on the missingness pattern of the other variables
- D. M. Tompsett et al. (2018) proposed a solution which involves eliciting more interpretable \(\delta\)-like parameters and searching the solution space for the \(\delta\)s they correspond to
- computationally infeasible with 33 missing items without further assumptions

For a given item \(Y\), we collapsed missingness patterns into:

- data on \(Y\) and all surveys completed (group A)
- data on \(Y\) but missing some surveys (group B)
- missing data on \(Y\) but completed survey (group C)
- missing survey on which \(Y\) is collected (group D)
^{1}

Most items are binary

- Parameters on odds ratio scale suggested in literature
- “Non-respondents may have up to 1.3 times the odds of
*item*compared to respondents who are similar in other ways”

- “Non-respondents may have up to 1.3 times the odds of
- Even differences in means not particularly intuitive
- “Non-respondents may have up to 10 percentage points higher prevalence of
*item*compared to respondents who are similar in other ways”

- “Non-respondents may have up to 10 percentage points higher prevalence of

Standardized means seem more interpretable

- Fit a model for item among participants with complete data (group A), conditional on demographics, etc.
- Predict item prevalence among participants with other missing surveys, but complete item of interest (group B)
- Compare observed and predicted item prevalence in group B: differences are not accounted by demographics, instead by missing data pattern

*Synthetic AoU dataset*

- complete case
- proration > 80% complete
- proration > 50% complete
- MAR (MICE with no delta-adjustment)
- MNAR, drawing sensitivity parameters from various distributions taking in account possible correlations
- draw from triangle distribution, individually
- compute rank within all draws
- draw across all items by rank to allow for correlation

**Observations with missing data are quite different, but it’s not clear that reasonable non-random missingness makes any difference**

- Deal with computational challenges
- Is it necessary to recompute frailty index in between every item?

- At what point is this necessary?
- “Tipping point” analysis

*Thanks to Chelsea Wong MD, Ariela Orkaby MD, Brianne Olivieri-Mui PhD*

Buuren, Stef van. 2012. *Flexible Imputation of Missing Data*. Chapman & Hall/CRC Interdisciplinary Statistics Series. Boca Raton, FL: CRC Press.

Little, Roderick J. A. 1993. “Pattern-Mixture Models for Multivariate Incomplete Data.” *Journal of the American Statistical Association* 88 (421): 125–34. https://doi.org/10.2307/2290705.

Mason, Alexina J, Manuel Gomes, Richard Grieve, Pinar Ulug, Janet T Powell, and James Carpenter. 2017. “Development of a Practical Approach to Expert Elicitation for Randomised Controlled Trials with Missing Health Outcomes: Application to the IMPROVE Trial.” *Clinical Trials* 14 (4): 357–67. https://doi.org/10.1177/1740774517711442.

Rubin, Donald B. 1987. *Multiple Imputation for Nonresponse in Surveys*. New York: John Wiley & Sons. https://doi.org/10.1002/9780470316696.

Tompsett, Daniel Mark, Finbarr Leacy, Margarita Moreno-Betancur, Jon Heron, and Ian R. White. 2018. “On the Use of the Not-at-Random Fully Conditional Specification (NARFCS) Procedure in Practice.” *Statistics in Medicine* 37 (15): 2338–53. https://doi.org/10.1002/sim.7643.

Tompsett, Daniel, Stephen Sutton, Shaun R. Seaman, and Ian R. White. 2020. “A General Method for Elicitation, Imputation, and Sensitivity Analysis for Incomplete Repeated Binary Data.” *Statistics in Medicine* 39 (22): 2921–35. https://doi.org/10.1002/sim.8584.

Van Buuren, Stef, and Karin Groothuis-Oudshoorn. 2011. “Mice: Multivariate Imputation by Chained Equations in R.” *Journal Of Statistical Software* 45 (3): 1–67. https://doi.org/10.1177/0962280206074463.

Wong, Chelsea, Michael P. Wilczek, Louisa H. Smith, Jordon D. Bosse, Erin L. Richard, Robert Cavanaugh, Justin Manjourides, Ariela R. Orkaby, and Brianne Olivieri-Mui. 2023. “Frailty Among Sexual and Gender Minority Older Adults: The All of Us Database.” *Journal of Gerontology: Medical Sciences*, in press.