In most clinical trials the group of patients (or sample) who participate is just a small portion of a heterogeneous patient population with the intended disease. As indicated earlier, a well-controlled randomized clinical trial is necessary to provide an unbiased and valid assessment of the study medicine. A well-controlled randomized trial is conducted under well-controlled experimental conditions, which are usually very different from a physician's best clinical practice. Therefore it is a concern whether the clinical results observed from the well-controlled randomized clinical trial can be applied on the patient population with the disease. As a result the feasibility and generalization of well-controlled randomized trials have become an important issue in public health (Rubins, 1994). For illustration purposes, consider the following two examples.
In early 1970s, a high cholesterol level was known to be a risk factor for developing coronary heart disease. To confirm this, a trial known as the Lipids Research Clinics Coronary Primary Prevention Trials (CPPT) was initiated by the National Heart, Lung, and Blood Institute to test the hypothesis whether lowering cholesterol can prevent the development of coronary heart disease. In the CPPT trial, a total of 4000 healthy, middle-age males were randomized to receive either the cholesterol-lowering agent cholestyramine or its matching placebo (Lipids Research Clinics Program, 1984). The primary endpoint was the incidence of coronary heart disease after a seven-year follow-up. A statistically significant reduction of 1.7% in 7-year incidence of coronary heart diseases was observed for the cholestyramine group as compared to the placebo (8.1% versus 9.8%). An expert panel recommended to extrapolate the results for the treatment of high cholesterol in populations that had never been studied and whose benefit has not yet been demonstrated (The Expert Panel, 1989; Recommendations for the Treatment of Hypercholesterolemia, 1984). Moore (1989), however, raises a serious doubt regarding the expert panel's recommendation for the treatment of patients with high cholesterol levels. Moore points out that the CPPT trial was conducted on middle-age males which cannot be applied to a general patient population with hypercholesterolemia. Another example concerning the generation of controlled randomized trials is the U.S. Physician's Health Study described earlier. The question is whether the benefit regarding fatal and nonfatal coronary heart disease, which was observed using 22,000 highly educated males aged over 40 years old, can also be observed in an average individual regardless of gender, race education, and socioeconomic background. This question is indeed a tough one to answer. We can address the question in part by performing a subgroup analysis with respect to the composition of the patients in the trial. This study led to the United States Congress passing legislation (National Institute of Health Reauthorization Bill, 1993) which requires the specification of the composition of any human studies sponsored by the NIH. More detail can be found in Wittes (1994).
One way to ensure the generalization of controlled randomized trials is to understand the process for drawing statistical and clinical inference. Basically statistical and clinical inference for the generalization of results obtained from clinical trials to other patients is a two-step process. The first step is to internally apply the statistical and clinical inference on the targeted population to other patients within the population. The second step is to externally generalize the statistical/clinical inference made on the targeted population to another patient population with different characteristics. These steps involve the concept of population efficacy (or safety), individual efficacy (or safety), reproducibility and general-izability which will be illustrated below.
Note that the current conduct of clinical trials is to compare the difference in distributions of the clinical responses observed from patients under a test therapy and a standard (or reference) therapy or a placebo. This concept is referred to as population efficacy (or safety). Suppose that the distribution of a clinical response can be adequately described by a normal probability distribution. Then the population efficacy can be assessed through the comparison of the first two moments of the distributions between the test and the reference therapies. This is because a normal distribution is uniquely determined by its first two moments. The comparison of the first moment of the efficacy endpoints for the two therapies is usually referred to as average efficacy, while the comparison of the second moments is called the variability of efficacy. To provide a better understanding of average efficacy and variability of efficacy, the comparison in averages and variabilities are illustrated in Figures 4.5.1 through 4.5.3. For example, to compare the reduction in diastolic blood pressure for evaluation of a new antihypertensive agent against a placebo, Figure 4.5.1 shows that the two distributions are very close in both average and variability, which indicates that there is no difference in average and variability of the reduction of diastolic blood pressure. Therefore the new agent may not be efficacious. On the other hand, Figure 4.5.2 demonstrates that the new agent is more effective in reducing blood pressure. Note that in most clinical trials with continuous primary endpoints, the objectives are often formulated as hypotheses for testing the average efficacy. As a result, the population efficacy of the new therapy is often
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