Epidemiology As A Liberal Art
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Cited References
Deductive Reasoning
Given a set of assumptions, deductive reasoning can lead to conclusions that are particularly firm because of the logical structure in which they are imbedded. Of course, the truth of the assumptions may be challenged, but in some cases that can be tested empirically. A stiffer limitation is often the need to restrict consideration to relatively simple problems, for the solving of which logical reasoning can be made clear and convincing.
Deductive reasoning has proved useful in estimating the efficacy of pneumococcal vaccine in the United States (Ref. 9). Efforts to develop a vaccine against pneumococcal disease began more than 40 years ago because of the importance of the pneumococcus as a cause of pneumonia, meningitis, and other life-threatening infections in adults and children. It has been estimated that some 10 percent of the approximately 3 million cases of pneumonia that occur in the United States each year are caused by the pneumococcus, making it the most common cause of bacterial pneumonia. Early studies showed that antibody to the polysaccharide capsule of some types of pneumococcus could protect against infection, so a vaccine composed of those polysaccharides seemed the most promising candidate. Unfortunately, 83 capsular types of pneumococci have been identified, and the prospect of making 83 different vaccines was daunting. However, the 14 most common types caused about 80 percent of all pneumococcal disease, and several other types had capsular polysaccharides chemically related to the 14, so vaccine development focused on these most common capsular types. Placebo-controlled, randomized prospective trials of vaccines against multiple pneumococcal capsular serotypes were conducted in South Africa among healthy young gold miners, who have a particularly high rate of pneumococcal disease. Estimates of vaccine efficacy in that population against serotypes included in the vaccine ranged from 76 to 100 percent. Subsequent prospective trials in this country in nursing-home residents and alcoholics -- two groups at relatively high risk of pneumococcal disease here -- showed no convincing evidence of efficacy, but the small size of the trials may have obscured efficacy.
In 1977, a pneumococcal vaccine designed to be effective against 14 capsular types was licensed for use in the United States. Continuing questions about the efficacy of the vaccine in groups at high risk of pneumococcal disease in the United States limited its use. The fact that the vaccine was licensed, however, made it unfeasible and probably unethical -- because the control group would be denied the vaccine -- to conduct further randomized clinical trials to determine whether the vaccine was effective in the groups for which it was recommended in this country. This quandary called for a method other than a vaccine trial -- one that would permit a vaccine's efficacy to be estimated after licensure.
The creation of such a method by deduction took advantage of the fact that more pneumococcal serotypes existed than were in the vaccine. Let us call the ratio of vaccine-type to nonvaccine-type pneumococcal cases in the vaccinated group a/b and that in the unvaccinated group c/d. If the vaccine were ineffective in preventing nonvaccine-type cases, then the ratio of vaccine type to nonvaccine-type cases in the vaccinated group (a/b) would be equal to c(1 - E)/d, where E is the best estimate of the efficacy of the vaccine against vaccine-type cases. This implies that E = 1 - ad/bc. The validity of the assumption that the vaccine is ineffective against nonvaccine types was confirmed by comparing the risk of pneumococcal disease caused by nonvaccine types in vaccinated and unvaccinated people enrolled in three pneumococcal vaccine trials. Little difference was seen in two trials, (Ref. 10,11) and in the third the difference was not statistically significant (Ref. 12).
To estimate the vaccine's efficacy against types in the vaccine, the serotypes of pneumococcal isolates from vaccinated persons all over the United States were compared with those of unvaccinated persons from specially selected sentinel hospitals in various locations throughout the United States. From vaccinated persons, 92 isolates were vaccine types and 58 were nonvaccine types, whereas from unvaccinated persons, 974 were vaccine types and 229 were nonvaccine types (Ref. 13). This gives an overall estimate of efficacy of 63 percent against vaccine types. This demonstration by deduction of the reasonably good efficacy of pneumococcal vaccine in groups at high risk in this country has encouraged the U.S. Public Health Service Advisory Committee on Immunization Practices to strengthen its recommendations for the use of the vaccine. At the same time, the vaccine has been reformulated to improve its efficacy against problematic types as well as to increase (to 23) the number of types it includes.
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