Statistical Modeling and Analysis for Risk Assessment of Decompression Sickness

Raj S. Chhikara, Ph.D., Professor, UHCL
Floyd M. Spears, Ph.D., Associate Professor, UHCL
Michael R. Powell, Ph.D., JSC
Kallappa M. Koti, Ph.D., Post-Doctoral Fellow, UHCL

DECOMPRESSION SICKNESS (DCS) may be attributed to acute environment pressure reduction in divers, aviators and astronauts. In the space program, DCS is likely to occur when crew members perform extra-vehicular activities or when there is damage or loss of cabin pressure or space suit pressure. Scientists at USAF, NASA-JSC and KRUG Life Sciences, Houston, TX, among many others, have investigated a wide range of problems associated with hypobaric decompression sickness.[1]

Tests conducted at NASA involving simulated extravehicular activities determine the incidence and the time of DCS onset for a number of test-subjects. One such test monitored each subject for Doppler detectable bubbles and also recorded a number of physiological measurements. Testing was terminated either upon incidence of a DCS onset symptom or at the abortion of the test. In either case, the test duration in hours was recorded. Another response recorded is VGETIME, the failure time for the first VGE detection. Other explanatory variables taken into consideration are TR360, P2, ALTTIME, PN2360, EXERCISE, ASCENTS and ASCTIME1.[1,2]

Dr. Raj Chhikara (standing) reviews data describing the onset of decompression sickness during space travel and its effects with Dr. Norman Richert.

The main objectives of the research are (1) to estimate the risk of incidence of DCS onset symptom and (2) to model, for example, the "decompression sickness onset time." Meeting these objectives may involve identifying the covariates that cause or prevent an occurrence of a DCS symptom. Obviously, one also needs to assess the effect of these covariates on the DCS onset time.

The data set discussed in this report is a subset of the "Hypobaric Decompression Sickness Databank,"[3] accumulated from literature sources, which contains information on 130,000 person-exposure in altitude chambers. Some of the data were derived from NASA-sponsored tests at the Johnson Space Center and from the Brooks Air Force Base. We abbreviate the decompression sickness onset time as DCSTIME. The data set has 1322 observations of which 1154 are right-censored. The smallest of the uncensored measurements is .2 hrs and the largest is 5.43 hrs. There are 604 right-censored observations exceeding 5.43 hrs, the largest uncensored observation; the largest censored observation is 12.75 hrs.

In the analysis of these data, a complicating factor is that the exact values of the response DCSTIME are not known in 87 percent of the cases, as they are the right-censored cases. For example, because of the high percentage of censoring, the widely used product-limit (Kaplan-Meier) estimator becomes practically useless. According to the product-limit estimator, every test-subject experiences decompression sickness by 5.43 hours. Available data, however, consist of 604 censored measurements out of 1322 that are larger than 5.43 (Fig. 1).

Figure 1. Kaplan-Meier Estimate and EDF.

The next alternative is to use parametric models which, though efficient, are too restrictive in nature. Probability plots can be quite helpful in checking the validity of fitted parametric models. For example, if DCSTIME has a Weibull distribution and if regressor variables do not severely dominate, the plot in Fig. 2 should be linear.[4]

Figure 2. Probability Plot: Weibull

In general, a statistical model used to analyze the censored data consists of two components: (1) a model specification in a functional form that facilitates prediction and (2) a set of assumptions that validates prediction and statistical inference. An analysis without verification of the validity of assumptions is considered incomplete. It is possible that the inference made from such an analysis is incorrect.

Conkin et al.[5] consider a variety of accelerated failure time log-logistic models to describe DCSTIME using this particular data set. We try the accelerated failure time lognormal model for the DCSTIME with P2, ALTTIME, and PN2360 as covariates. The SAS/LIFEREG Procedure shows every covariate to be highly significant. That is, the model is usable. We construct a residual plot using the procedure in Lawless.[4] Unfortunately, the residual plot in Fig. 3 suggests that the model may not be adequate. This observation is also true in the case of the log-logistic model.

Figure 3. Residual Plot

When data are Type II or singly Type I censored, simple modifications can be made to the EDF goodness-of-fit statistics, such as the Kolmogorov-Smirnov statistic, Cramer-Von Mises statistic, and the Anderson-Darling statistic.[4] With arbitrary censoring, things are more difficult. No analytic goodness-of-fit tests are available for accelerated failure time models. Residual plot and cross-validation methods are used to examine the adequacy of a model. A number of papers are available on goodness-of-fit tests for parametric models.[6,7] Computing is, however, extremely difficult and no computer packages are available to implement them.

We review the Akritas'[6] A-test and the Hollander and Peņa's[7] Q-test and apply them to our decompression sickness onset time data set. The A-test and the Q-test are constructed for the Weibull, lognormal, and log-logistic distributions. The results of these tests are summarized in Table I.

Table I. Summary of Chi-square Tests

In each case, the observed significance level (p-value) is nearly zero, thus indicating that none of these models provides an adequate fit.

References
[1]J. Conkin, K. V. Kumar, M. R. Powell, P. P. Foster, and J. M. Waligora. "A Probabilistic Model of Hypobaric Decompression Sickness Based on 66 Chamber Tests," Aviation Space and Environmental Medicine 67.2 (1996): 176-83.
[2]H. D. Van Liew, M. E. Burkard, and J. Conkin. Testing of Hypotheses About Altitude Decompression Sickness by Statistical Analyses. N.Y.: Undersea and Hyperbaric Medical Society, Inc., 1996. 225-33.
[3]J. Conkin, R. S. Bedahl, and H. D. Van Liew. "A Computerized Databank of Decompression Sickness Incidence in Altitude Chambers," Aviation Space and Environmental Medicine 63 (1992): 819-24.
[4]J. F. Lawless. Statistical Models and Methods for Lifetime Data. John Wiley & Sons, New York, 1982.
[5]J. Conkin, M. R. Powell, P. P. Foster, and J. M. Waligora. "Information About Venous Gas Emboli Improves Prediction of Hypobaric Decompression Sickness," Technical Report, Life Sciences Research Laboratories, NASA-JSC, Houston, TX, 1997.
[6]M. Akritas. "Pearson-Type Goodness-of-Fit Tests: The Univariate Case," J. of the American Statistical Association 83 (1988): 222-30.
7[M]. Hollander and E. A. Peņa. "A Chi-Squared Goodness-of-Fit Test for Randomly Censored Data," J. of the American Statistical Association 87 (1992): 458-63.

Contents
ISSO -- Institute for Space Systems Operations
1996-1997 Annual Report