This paper concerns the construction of confidence intervals in standard seroprevalence surveys. In particular, we discuss methods for constructing confidence intervals for the proportion of individuals in a population infected with a disease using a sample of antibody test results and measurements of the test's false positive and false negative rates. We begin by documenting erratic behavior in the coverage probabilities of standard Wald and percentile bootstrap intervals when applied to this problem. We then consider two alternative sets of intervals constructed with test inversion. The first set of intervals are approximate, using either asymptotic or bootstrap approximation to the finite-sample distribution of a chosen test statistic. We consider several choices of test statistic, including maximum likelihood estimators and generalized likelihood ratio statistics. We show with simulation that, at empirically relevant parameter values and sample sizes, the coverage probabilities for these intervals are close to their nominal level and are approximately equi-tailed. The second set of intervals are shown to contain the true parameter value with probability at least equal to the nominal level, but can be conservative in finite samples.
翻译:本文涉及标准血清阳性反应率调查中建立信任间隔的构建。 特别是, 我们讨论使用抗体测试结果样本和测量测试的假正负负率和假负率来构建受疾病感染人口中个人比例信任间隔的方法。 我们首先记录标准Wald 和百分位靴带间隔覆盖面概率中的不规律行为, 当应用到这一问题时, 我们首先记录标准Wald 和百分位靴带间隔概率的覆盖概率中的不规律行为。 我们然后考虑用测试倒置来构建两套替代间隔。 第一套间隔是近似的, 使用随机或靴套近似于所选测试统计数据的有限抽样分布。 我们考虑几种测试统计选择, 包括最大概率估计器和普遍概率比率统计。 我们用模拟方法显示, 在实验相关的参数值和样本大小上, 这些间隔的覆盖概率接近其名义水平, 并且大致是等同的。 第二套间隔显示包含真实参数值, 概率至少等于名义值, 但对于定数样本来说是保守的。