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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS2014

Missing Data and Multiple Imputation: An Unbiased Approach

The default method of dealing with missing data in statistical analyses is to only use the complete observations (complete case analysis), which can lead to unexpected bias when data do not meet the assumption of missing completely at random (MCAR). For the assumption of MCAR to be met, missingness cannot be related to either the observed or unobserved variables. A less stringent assumption, missing at random (MAR), requires that missingness not be associated with the value of the missing variable itself, but can be associated with the other observed variables. When data are truly MAR as opposed to MCAR, the default complete case analysis method can lead to biased results. There are statistical options available to adjust for data that are MAR, including multiple imputation (MI) which is consistent and efficient at estimating effects. Multiple imputation uses informing variables to determine statistical distributions for each piece of missing data. Then multiple datasets are created by randomly drawing on the distributions for each piece of missing data. Since MI is efficient, only a limited number, usually less than 20, of imputed datasets are required to get stable estimates. Each imputed dataset is analyzed using standard statistical techniques, and then results are combined to get overall estimates of effect. A simulation study will be demonstrated to show the results of using the default complete case analysis, and MI in a linear regression of MCAR and MAR simulated data. Further, MI was successfully applied to the association study of CO2 levels and headaches when initial analysis showed there may be an underlying association between missing CO2 levels and reported headaches. Through MI, we were able to show that there is a strong association between average CO2 levels and the risk of headaches. Each unit increase in CO2 (mmHg) resulted in a doubling in the odds of reported headaches.

Foy, M.↗
NASA NTRS2015

Astronaut Preflight Cardiovascular Variables Associated with Vascular Compliance are Highly Correlated with Post-Flight Eye Outcome Measures in the Visual Impairment Intracranial Pressure (VIIP) Syndrome Following Long Duration Spaceflight

The detection of the first VIIP case occurred in 2005, and adequate eye outcome measures were available for 31 (67.4%) of the 46 long duration US crewmembers who had flown on the ISS since its first crewed mission in 2000. Therefore, this analysis is limited to a subgroup (22 males and 9 females). A "cardiovascular profile" for each astronaut was compiled by examining twelve individual parameters; eleven of these were preflight variables: systolic blood pressure, pulse pressure, body mass index, percentage body fat, LDL, HDL, triglycerides, use of anti‐lipid medication, fasting serum glucose, and maximal oxygen uptake in ml/kg. Each of these variables was averaged across three preflight annual physical exams. Astronaut age prior to the long duration mission, and inflight salt intake was also included in the analysis. The group of cardiovascular variables for each crew member was compared with seven VIIP eye outcome variables collected during the immediate post‐flight period: anterior-posterior axial length of the globe measured by ultrasound and optical biometry; optic nerve sheath diameter, optic nerve diameter, and optic nerve to sheath ratio‐ each measured by ultrasound and magnetic resonance imaging (MRI), intraocular pressure (IOP), change in manifest refraction, mean retinal nerve fiber layer (RNFL) on optical coherence tomography (OCT), and RNFL of the inferior and superior retinal quadrants. Since most of the VIIP eye outcome measures were added sequentially beginning in 2005, as knowledge of the syndrome improved, data were unavailable for 22.0% of the outcome measurements. To address the missing data, we employed multivariate multiple imputation techniques with predictive mean matching methods to accumulate 200 separate imputed datasets for analysis. We were able to impute data for the 22.0% of missing VIIP eye outcomes. We then applied Rubin's rules for collapsing the statistical results across our 200 multiply imputed data sets to assess the canonical correlation between the eye outcomes and the twelve astronaut cardiovascular variables available for all 31 subjects. Results: A highly significant canonical correlation was observed among the canonical solutions (p<.00001), with an average best canonical correlation of.97. The results suggest a strong association between astronauts' measures of cardiovascular health and the seven eye outcomes of the VIIP syndrome used in this analysis. Furthermore, the "joint test" revealed a significant difference in cardiovascular profile between male and female astronauts (Prob > F = 0.00001). Overall, female astronauts demonstrated a significantly healthier cardiovascular status. Individually, the female astronauts had significantly healthier profiles on seven of twelve cardiovascular variables than the men (p values ranging from <0.0001 to <0.05). Male astronauts did not demonstrate significantly healthier values on any of the twelve cardiovascular variables measured

Otto, Christian↗
NASA NTRS2016

Exploration Analysis of Carbon Dioxide Levels and Ultrasound Measures of the Eye During ISS Missions

Enhanced screening for the Visual Impairment/Intracranial Pressure (VIIP) Syndrome, including in-flight ultrasound, was implemented in 2010 to better characterize the changes in vision observed in some long-duration crewmembers. Suggested possible risk factors for VIIP include cardiovascular changes, diet, anatomical and genetic factors, and environmental conditions. As a potent vasodilator, carbon dioxide (CO (sub 2)), which is chronically elevated on the International Space Station (ISS) relative to typical indoor and outdoor ambient levels on Earth, seems a plausible contributor to VIIP. In an effort to understand the possible associations between CO (sub 2) and VIIP, this study analyzes the relationship between ambient CO (sub 2) levels on ISS and ultrasound measures of the eye obtained from ISS fliers. CO (sub 2) measurements will be pulled directly from Operational Data Reduction Complex for the Lab and Node 3 major constituent analyzers (MCAs) on ISS or from sensors located in the European Columbus module, as available. CO (sub 2) measures between ultrasound sessions will be summarized using standard time series class metrics in MATLAB including time-weighted means and variances. Cumulative CO (sub 2) exposure metrics will also be developed. Regression analyses will be used to quantify the relationships between the CO (sub 2) metrics and specific ultrasound measures. Generalized estimating equations will adjust for the repeated measures within individuals. Multiple imputation techniques will be used to adjust for any possible biases in missing data for either CO (sub 2) or ultrasound measures. These analyses will elucidate the possible relationship between CO (sub 2) and changes in vision and also inform future analysis of inflight VIIP data.

Young, M.↗
NASA NTRS2017

Relationship Between Carbon Dioxide Levels and Reported Congestion and Headaches on the International Space Station

Congestion is commonly reported during spaceflight, and most crewmembers have reported using medications for congestion during International Space Station (ISS) missions. Although congestion has been attributed to fluid shifts during spaceflight, fluid status reaches equilibrium during the first week after launch while congestion continues to be reported throughout long duration missions. Congestion complaints have anecdotally been reported in relation to ISS CO2 levels; this evaluation was undertaken to determine whether or not an association exists. METHODS: Reported headaches, congestion symptoms, and CO2 levels were obtained for ISS expeditions 2-31, and time-weighted means and single-point maxima were determined for 24-hour (24hr) and 7-day (7d) periods prior to each weekly private medical conference. Multiple imputation addressed missing data, and logistic regression modeled the relationship between probability of reported event of congestion or headache and CO2 levels, adjusted for possible confounding covariates. The first seven days of spaceflight were not included to control for fluid shifts. Data were evaluated to determine the concentration of CO2 required to maintain the risk of congestion below 1% to allow for direct comparison with a previously published evaluation of CO2 concentrations and headache. RESULTS: This study confirmed a previously identified significant association between CO2 and headache and also found a significant association between CO2 and congestion. For each 1-mm Hg increase in CO2, the odds of a crew member reporting congestion doubled. The average 7-day CO2 would need to be maintained below 1.5 mmHg to keep the risk of congestion below 1%. The predicted probability curves of ISS headache and congestion curves appear parallel when plotted against ppCO2 levels with congestion occurring at approximately 1mmHg lower than a headache would be reported. DISCUSSION: While the cause of congestion is multifactorial, this study showed congestion is associated with CO2 levels on ISS. Data from additional expeditions could be incorporated to further assess this finding. CO2 levels are also associated with reports of headaches on ISS. While it may be expected for astronauts with congestion to also complain of headaches, these two symptoms are commonly mutually exclusive. Furthermore, it is unknown if a temporal CO2 relationship exists between congestion and headache on ISS. CO2 levels were time-weighted for 24hr and 7d, and thus the time course of congestion leading to headache was not assessed; however, congestion could be an early CO2-related symptom when compared to headache. Future studies evaluating the association of CO2-related congestion leading to headache would be difficult due to the relatively stable daily CO2 levels on ISS currently, but a systematic study could be implemented on-orbit if desired.

Cole, Robert↗
NASA NTRS2017

Full-Coverage High-Resolution Daily PM(sub 2.5) Estimation using MAIAC AOD in the Yangtze River Delta of China

Satellite aerosol optical depth (AOD) has been used to assess population exposure to fine particulate matter (PM (sub 2.5)). The emerging high-resolution satellite aerosol product, Multi-Angle Implementation of Atmospheric Correction(MAIAC), provides a valuable opportunity to characterize local-scale PM(sub 2.5) at 1-km resolution. However, non-random missing AOD due to cloud snow cover or high surface reflectance makes this task challenging. Previous studies filled the data gap by spatially interpolating neighboring PM(sub 2.5) measurements or predictions. This strategy ignored the effect of cloud cover on aerosol loadings and has been shown to exhibit poor performance when monitoring stations are sparse or when there is seasonal large-scale missngness. Using the Yangtze River Delta of China as an example, we present a Multiple Imputation (MI) method that combines the MAIAC high-resolution satellite retrievals with chemical transport model (CTM) simulations to fill missing AOD. A two-stage statistical model driven by gap-filled AOD, meteorology and land use information was then fitted to estimate daily ground PM(sub 2.5) concentrations in 2013 and 2014 at 1 km resolution with complete coverage in space and time. The daily MI models have an average R(exp 2) of 0.77, with an inter-quartile range of 0.71 to 0.82 across days. The overall Ml model 10-fold cross-validation R(exp 2) (root mean square error) were 0.81 (25 gm(exp 3)) and 0.73 (18 gm(exp 3)) for year 2013 and 2014, respectively. Predictions with only observational AOD or only imputed AOD showed similar accuracy.Comparing with previous gap-filling methods, our MI method presented in this study performed bette rwith higher coverage, higher accuracy, and the ability to fill missing PM(sub 2.5) predictions without ground PM(sub 2.5) measurements. This method can provide reliable PM(sub 2.5)predictions with complete coverage that can reduce biasin exposure assessment in air pollution and health studies.

PM2.5↗
NASA NTRS2021

Salvaging Data Records with Missing Data: Data Imputation using the Multivariate t Distribution

When doing multivariate data analysis, one commonobstacle is the presence of incomplete observations, i.e., observationsfor which one or more key fields are blank. Missing datais often countered by deleting entire observations that containmissing data. The negative effects of deleting entire observationsare multiple: deleting observations reduces sample size andcan also result in biased inferences even if data is missing atrandom. In addition, knowledge contained within incompleteobservations is knowledge lost when they are deleted– and theeffort spent collecting that knowledge is effort wasted. Data imputationmethods, or methods of statistically “filling-in” missingdata, can help combat small sample sizes by using the existinginformation in partially complete observations with the end goalof producing less biased and higher confidence inferences. Whena sample from a multivariate normal population is only partiallycomplete, and the missing data meets appropriate assumptions(missing at random), robust data imputation of the missing datacan be implemented with monotone data augmentation (MDA)using the multivariate t distribution.Missing data imputation is applied to data from the NASA InstrumentCost Model (NICM) using the MDA algorithm underthe assumption of having a multivariate t distribution with fixeddegrees of freedom. A sensitivity analysis to the degrees offreedom parameter is presented to demonstrate robustness ofthe multivariate t distribution when dealing with small samplesas compared to the multivariate normal distribution.

DiNicola, Michael↗
NASA NTRS1988

Multiple input/output random vibration control system

A multi-input/output random vibration control algorithm was developed based on system identification concepts derived from random vibration spectral analysis theory. The unique features of the algorithm are: (1) the number of input excitors and the number of output control responses need not be identical; (2) the system inverse response matrix is obtained directly from the input/output spectral matrix; and (3) the system inverse response matrix is updated every control loop cycle to accommodate system amplitude nonlinearities. A laboratory demonstration case of two imputs with three outputs is presented to demonstrate the system capabilities.

Unruh, James F.↗
NASA NTRS2022

Bayesian Rules of Thumb: Robust Uncertainty Quantification in Early Project Cost Estimation

Systems engineers often make use of cost Rules ofThumb in order to estimate cost during early phases of projectformulation. These Rules of Thumb typically take the form ofa sequence of percentages over which a total cost is allocatedacross NASA WBS elements. Rules of Thumb can then be usedto extrapolate cost from one or more known WBS elements tothe remaining unknown WBS elements, assisting early projectformulation architecture studies (such as those in JPL’s Team Xand A Team).A number of issues can arise when generating and using costRules of Thumb. For example, many records of project costsconsist of incomplete data. Typical methods of dealing withincomplete cost allocation data include (a) ignoring missionswith incomplete data, or (b) taking averages of the non-zero percentagesacross missions, but both of these methods can result inbiased estimates if the existence of incomplete data correlateswith total mission cost or any particular WBS element. Anothercommon example is cost reported in one or more incorrect WBSelements. This is especially prevalent in smaller missions whereit is more common for engineers to perform tasks that fall underthe purview of multiple WBS elements.Furthermore, a Rule of Thumb estimate is typically reported asa point estimate; there is no reported uncertainty around thepercentages used to generate an allocation. Even in the rarecase in which confidence intervals around mean percentages areprovided, there may be positive or negative correlations betweenWBS elements which can skew estimates.Here we attempt to address these problems by formulatingprobabilistic Rules of Thumb in which a distribution of allocationschemes, rather than a single allocation scheme, is generated.We use a bootstrap imputation method to simultaneouslyaccount for uncertainty in the missing data while using allavailable information contained in the dataset. The imputeddatasets are then input into a multivariate Bayesian modelwhich accounts for correlations between WBS elements andproperly accounts for uncertainty in the final Rule of Thumbpercentages and predictions. We describe the mathematicalmodel and provides snippets of R code utilizing the brms(Bayesian Regression Models using Stan) package. To illustratethis model, we generate a Bayesian Level 2 WBS Cost Rule ofThumb for MIDEX (Medium-Class Explorers) missions withdata extracted from NASA’s CADRe. We then compare thismethod’s performance with the classical Rule of Thumb method.

Hooke, Melissa A↗