Early Detection of Treatments Side Effect: A Sequential Approach

TL;DR

This paper develops an $(\alpha,\beta)$-optimal non-randomized sequential testing framework for early detection of treatment side effects, oriented to large-scale vaccination campaigns. It casts the problem as sequential testing of a binomial proportion with $H_0: \theta \leq \theta_0$ against $H_1: \theta > \theta_0$, deriving an optimal curtailed procedure $T^*_{seq}$ whose stopping time has a Negative Binomial distribution and whose power matches the fixed-sample UMP test via $\Pi_{T^*_{seq}}(\theta)=\mathcal{I}_\theta(k^*+1,N^*-k^*)$. The work provides exact ASN$^*(\theta)$ and Var$^*(\theta)$ expressions, post-test estimator properties, and asymptotic results under local alternatives, enabling precise confidence intervals after termination. An empirical illustration on COVID-19 side-effect data demonstrates rapid, interpretable inferences and potential practical impact for post-marketing surveillance and EUA settings.

Abstract

With the emergence and spread of infectious diseases with pandemic potential, such as COVID- 19, the urgency for vaccine development have led to unprecedented compressed and accelerated schedules that shortened the standard development timeline. In a relatively short time, the leading pharmaceutical companies1, received an Emergency Use Authorization (EUA) for vaccine\prime s en-mass deployment To monitor the potential side effect(s) of the vaccine during the (initial) vaccination campaign, we developed an optimal sequential test that allows for the early detection of potential side effect(s). This test employs a rule to stop the vaccination process once the observed number of side effect incidents exceeds a certain (pre-determined) threshold. The optimality of the proposed sequential test is justified when compared with the (α, β) optimality of the non-randomized fixed-sample Uniformly Most Powerful (UMP) test. In the case of a single side effect, we study the properties of the sequential test and derive the exact expressions of the Average Sample Number (ASN) curve of the stopping time (and its variance) via the regularized incomplete beta function. Additionally, we derive the asymptotic distribution of the relative savings in ASN as compared to maximal sample size. Moreover, we construct the post-test parameter estimate and studied its sampling properties, including its asymptotic behavior under local-type alternatives. These limiting behavior results are the consistency and asymptotic normality of the post-test parameter estimator. We conclude the paper with a small simulation study illustrating the asymptotic performance of the point and interval estimation and provide a detailed example, based on COVID-19 side effect data (see Beatty et al. (2021)) of our suggested testing procedure.

Figures (4)

• Figure 1: The curtailed sequential test $\operatorname{T^*_{seq}}$
• Figure 2: The plots of the $ASN$ curve and the power function with respect to $\theta$ for fixed $\alpha=0.05$, $\beta=0.1$, $\theta_0=0.065$, $\theta_1=0.0715$ with $N^*=12811$ and $k^*=878$.
• Figure 3: The plots of the relative 'savings' in the ASN with respect to $\alpha=0.05$, $\beta=0.1$, $\theta_0=0.065$ and different values of $\delta$: (a) $\delta=0.5$: $\theta_1=0.0975$, $N^*=584$ and $k^*=47$; (b) $\delta=0.25$, $\theta_1=0.08125$, $N^*=2162$ and $k^*=159$; (c) $\delta=0.1$, $\theta_1=0.0715$, $N^*=12811$ and $k^*=878$.
• Figure 4: The illustrations of the curtailed sequential test $\operatorname{T^*_{seq}}$ based on the beatty2021analysis data for two scenarios

Theorems & Definitions (10)

• Remark 1
• Theorem 1
• Remark 2
• Theorem 2
• Lemma 1
• Theorem 3
• Theorem 4
• Theorem 5
• Lemma 2
• Lemma 3: Rényi's adaptation of Anscombe’s theorem