Predicting the time of occurrence of decompression sickness. J. Appl. Physiol. 72(4): [1541][1542][1543][1544][1545][1546][1547][1548]1992.-Probabilistic models and maximum likelihood estimation have been used to predict the occurrence of decompression sickness (DCS). We indicate a means of extending the maximum likelihood parameter estimation procedure to make use of knowledge of the time at which DCS occurs. Two models were compared in fitting a data set of nearly 1,000 exposures, in which MO

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... cases of DCS have known times of symptom onset. The additional information provided by the time at which DCS occurred gave us better estimates of model parameters. It was also possible to discriminate between good models, which predict both the occurrence of DCS and the time at which symptoms occur, and poorer models, which may predict only the overall occurrence. The refined models may be useful in new applications for customizing decompression strategies during complex dives involving various times at several different depths. Conditional probabilities of DCS for such dives may be reckoned as the dive is taking place and the decompression strategy adjusted to circumstance. Some of the mechanistic implications and the assumptions needed for safe application of decompression strategies on the basis of conditional probabilities are discussed. bends; mathematical models; risk management; inert gas exchange EXPERIENCE has shown that decompression sickness (DCS) becomes more common, but seldom becomes a certainty, when certain limits are exceeded. Rapid ascents from long stays at great depths are more apt to give rise to DCS than slower ascents from short stays at more shallow depths. However, sometimes the risky dive and decompression may be undertaken with no untoward results, and occasionally symptoms of DCS are seen in usually safe dives. Accordingly, probabilistic models have been used to predict the probability of DCS in various circumstances (10, 13, 14, 16, 18, 19). In the probabilistic models used so far, the probability of the occurrence of DCS for the entire dive was calculated without regard for the time at which the symptoms occurred. We now have data for which the time of onset of symptoms of DCS is known at least approximately. We wish to introduce this additional information in a likelihood estimation procedure, with the expectation that this refinement will provide sounder estimates of the unknown parameters of the model. In addition, we hope that some insights may be gained into plausible mechanisms leading to symptoms when information about the time of the symptoms is used. The models we use have functional forms suggested by notations commonly used in survival or failure time analysis (3). At any time T, during or after the dive, the probability P(s), for an individual to be free of DCS symptoms is related to the probability of his having suffered DCS by that time Pi is sometimes called the survivor function. If no DCS has occurred, then we define the probability of suffering DCS during a short ensuing time interval, dt, as r X dt, where r is the risk function or hazard function (3). Because r X dt is a probability, r cannot be negative. Freedom from DCS symptoms until time T requires surviving (integrating) all DCS risk incurred up to that time. The survival function is the probability of not experiencing DCS before time T (2) The instantaneous risk is determined by the mechanisms giving rise to the terminal event of the probabilistic process. For the decay of a radioactive isotope, for example, r is a constant that is characteristic of the particular isotope. Patient survival after surgery often is characterized by an r that is large immediately after surgery (immediate postoperative mortality), declines gradually, and then follows a course that will vary with the nature of the risks at those later times. Aging corresponds to a function r that increases with time. So if the greatest risk of DCS occurs immediately after a decompression step, r should be at its highest level at that time and then decline with time until the next decompression step. Such a risk function might be expected if DCS were triggered immediately after the occurrence of bubble nucleation, because bubble nucleation depends on instantaneous supersaturation even more strongly than a linear function (15). If, on the other hand, it takes a long time for the risk to develop after a decompression step, then r might rise, reach a peak, and then decline. If DCS depended on bubble growth to a certain size, r might have such a shape (11). In the long run, we expect to find more occurrences of DCS at times when r is large than at times when it is small. If r provides a satisfactory summary of the hazard process, then DCS should not occur at all when r is zero. The probability of not developing DCS sometime during or after the dive is expressed as the integration of the risk over the entire history of the dive and recovery. 1541