Hightower A W, Orenstein W A, Martin S M
Bull World Health Organ. 1988;66(1):99-105.
A simple formula for calculating confidence intervals by means of a Taylor series variance approximation has been recommended for gauging the precision of estimates of vaccine efficacy. To evaluate the performance of Taylor series 95% confidence intervals for vaccine efficacy, we conducted a simulation study for commonly expected values of vaccine efficacy, risk of disease in the unvaccinated population, and sample sizes of the vaccinated and unvaccinated groups. In the first simulation, the sample size in the vaccinated group was 500 or 1000, whereas that in the unvaccinated group ranged from 10 to 1000. The confidence intervals were accurate when the sample size in the unvaccinated group was >/=50 and the risk of disease was 0.3-0.9. In contrast, the intervals were too narrow when all three of the following situations occurred: the number of unvaccinated was small (10 or 20), the true vaccine efficacy was relatively low (60% or 80%), and the risk of disease was 0.5-0.9. Furthermore, when the true vaccine efficacy was high (90% or 95%) and the disease risk in the unvaccinated was low (0.1 and 0.2), the confidence intervals were too broad, especially when the unvaccinated sample size was <50. Additional simulations with a sample size in the vaccinated group of 200 gave broad intervals for 95% vaccine efficacy (for all values of disease risk) and for 90% vaccine efficacy when the disease risk was </=0.3.
一种通过泰勒级数方差近似来计算置信区间的简单公式已被推荐用于衡量疫苗效力估计值的精度。为了评估泰勒级数95%疫苗效力置信区间的性能，我们针对疫苗效力的常见预期值、未接种人群的疾病风险以及接种和未接种组的样本量进行了一项模拟研究。在第一次模拟中，接种组的样本量为500或1000，而未接种组的样本量范围为10至1000。当未接种组的样本量≥50且疾病风险为0.3 - 0.9时，置信区间是准确的。相比之下，当出现以下所有三种情况时，区间会过窄：未接种人数较少（10或20）、真实疫苗效力相对较低（60%或80%）以及疾病风险为0.5 - 0.9。此外，当真实疫苗效力较高（90%或95%）且未接种人群中的疾病风险较低（0.1和0.2）时，置信区间会过宽，尤其是当未接种样本量<50时。接种组样本量为200的额外模拟显示，对于95%的疫苗效力（对于所有疾病风险值）以及疾病风险≤0.3时的90%疫苗效力，区间都很宽。
