The focus of this research is to develop statistical approaches and methods suitable for predicting occurrence of decompression sickness (DCS) among astronauts and other aviators under hypobaric decompression conditions. The DCS risk assessment is an important technical problem for the NASA and USAF researchers who have been conducting experimental studies to obtain information deemed necessary to evaluate the DCS risk in terms of both environmental and physiological variables. Scientists at Johnson Space Center have developed a measure of decompression stress, called tissue ratio (TR), which is indicative of the relative change in atmosphere that the human body can sustain. Empirical studies of decompression physiology have been made on the usefulness of TR using simulated extravehicular activity (EVA) data.[1,2,3] The analysis reported in these and other more recent studies undertaken by the researchers at Johnson Space Center focus on the selection of a probabilistic model that statistically provides the best-fit for the observed DCS occurrences. The methodology of survival analysis is applied to investigate suitability of a model; the method of maximum likelihood is used for estimation of model parameters.
The tissue ratio is shown to be a statistically significant predictor for DCS occurrence. However, it only accounts for a small portion of the variability seen in the DCS occurrence times. There are other important factors such as occurrence of different grades of circulating microbubbles (CMBs) in the venous return (tissues), prebreathing of oxygen, exercise, time spent at altitude, etc. that can cause significant variability in the time for DCS to occur.[4] As part of this research, statistical models utilized in the NASA and USAF empirical studies are reviewed and their performances evaluated, taking into considerations the various factors as predictors of DCS occurrence.
NASA experimental data consisted of a total of 1322 observations on DCS occurrence or censored time along with values for TR360, altitude time and different grades of CMBs, among other variables. The mean time of DCS occurrence was linearly expressed in terms of one or more of these variables. The three models chosen for evaluation are: (1) log logistic, (2) lognormal, and (3) inverse Gaussian. The first two models are pretty standard and known to be useful as survival models. Both NASA and USAF researchers have begun to use them in the analyses of their data. The third model, the inverse Gaussian behaves similarly to the lognormal; yet data analysis using the inverse Gaussian model is conducted for the observations in their original scale rather than for their transformations in logarithmic scale which may create difficulty in interpretation of the analysis results in cases of the first two models. Another advantage the inverse Gaussian has over the other two models is its basis as a first passage time distribution for an inherently Gaussian process underlying decompression physiology.[5]
Statistical analyses carried out here comprised an application of survival analysis method to determine statistical models that provide best fit to the NASA data using different sets of predictors. The maximum likelihood estimates of model parameters were obtained in each case of the three statistical models. The estimates of distribution functions of all three models were contrasted and compared with the nonparametric Kaplan-Meier estimate.
These estimates are listed in the appendix corresponding to the best-fitted model obtained for each of three distributions, log logistic, lognormal, and inverse Gaussian. Among the three distributions, the log logistic and lognormal performed equally well and provided better modelfits than the inverse Gaussian. It is, however, unclear why the performance of inverse Gaussian was poorer than lognormal. One major difficulty involved in the use of inverse Gaussian is the computation of its survival function, which is subject to instability whenever its shape parametric value is substantially small as is the case here. The computational aspects of fitting inverse Gaussian model are being further investigated.
The ISSO research team of University of Houston Clear Lake actively participated with NASA/JSC and USAF San Antonio researchers in a workshop held at KRUG Life Sciences Division, Houston during July 10-11, 1996. It featured several technical presentations on the survival analysis. The research work carried out by us enhances the scope of their statistical modeling and analysis for risk assessment of decompression sickness.
References
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2J. Conkin, B. F. Edwards, J. M. Waligora, J. Stanford Jr, J. H. Gilbert III,
and D. J. Horrigan Jr. "Updating Empirical Models That Predict the Incidence
of Aviator Decompression Sickness and Venous Gas Emboli for Shuttle and Space
Station Extravehicular Operations," Houston, TX: Johnson Space Center; NASA
Technical Memorandum 100456, 1990, update.
3K. V. Kumar, D. S. Calkins, J. H. Waligora Jr., M. R. Powell (1992). Time to
Detection of Circulating Microbubbles as a Risk for Symptoms of Altitude
Decompression Sickness," Aviat. Space Environ. Med. 63 (1992): 961-64.
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5R. S. Chhikara and J. L. Folks. Inverse Gaussian Distribution. N.Y.: Marcel
Dekkar, 1989.