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THE PROBLEM OF SAMPLING

Events happen quickly in critical care medicine. This can be beneficial in that it forces thoughtful practitioners to reevaluate their diagnostic hypotheses constantly. In general, however, it is destructive because of a problem described by an area of information theory called the sampling theorem.[228] The sampling theorem says that monitoring a process requires that the process be sampled twice as fast as the measured variable changes. For example, assume that a 1 cycle per second (hertz) wave is being sampled. If the wave is sampled once a second, every sample might be a peak. To the experimenter, the 1 hertz cycle looks like a steady pressure. If the wave is sampled every 30 seconds or less, then its wave nature will be obvious.

The sampling theorem haunts critical care medicine in two ways. The more obvious is in serial measurements of physiologic variables. It is not unusual to monitor a dozen variables on a patient in the CCU. These variables may have vastly different periods, ranging from minutes to days. It is also not unusual to follow these variables with isolated snapshots. This hides the periodicity of the variables and can lead the physician to miss important phenomena that are driven by the transient extremes of a variable rather than its average or randomly chosen value. Thus, it is more important to know that a patient's blood pressure has transients of 300/120 than to know that at 10:00 p.m. the pressure was 130/80.

The problem of sampling is exacerbated by the continuity heuristic: once a therapy has been chosen, it biases the decision maker in favor of continuing that treatment rather than trying another. This bias can be profound when a CCU patient's therapy is constantly modified based on measurements of a physiologic variable. If this variable is measured less frequently than twice the rate at which it is affected by the intervention, the intervention can appear to have a paradoxical effect.

For example, assume that a severely hypotensive patient is treated with a very short-acting pressor agent. This hypothetical pressor agent is given in a bolus. It takes 1 hour to act and wears off in 4 hours. The patient's blood pressure is taken every 4 hours. The first measurement is taken 30 minutes after injection and shows the pressure to be low. Four hours later (30 minutes after the second dose), the pressure is again measured as low. The dose is now increased. The third measurement, taken 4 hours later (30 minutes after the increased dose has been given), is now normal. The patient, however, is severely hypertensive in the intervals between the measurements.

Few physicians would make this simple mistake. However, as the number of drugs and variables increases and the drugs interact with each other, it becomes difficult to ensure that a measured variable truly represents the effect of a given drug or the indirect effect of a drug given to affect a different organ system. Unlike office practice internal medicine, the intensivist cannot tell the patient to add one new drug each week and see what happens.

[228]Pierce JR: An Introduction to Information Theory: Symbols, Signals, and Noise. 2d ed. 1980.


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