Because of rare but serious adverse events, pharmaceutical drugs and vaccines are sometimes withdrawn from the market, either by a government agency such as the Food and Drug Administration (FDA) in the United States or by the manufacturing pharmaceutical company. In other cases, a drug may be generally safe but increase the risk for serious adverse events for certain subpopulations such as pregnant women or people with heart problems. Due to limited sample size and selected study populations, rare adverse events are often impossible to detect during phase 3 trials conducted before the drug is approved for general use. It is then important to conduct post-approval drug safety surveillance, using, for example, health insurance claims data. In such surveillance, the goal should be to detect serious adverse events as early as possible without too many false alarms, and it is then natural to use a continuous or near-continuous sequential test procedure that reevaluates the data on a daily or weekly b...

A maximized sequential probability ratio test for drug and vaccine safety surveillance

Ecological and environmental monitoring has become increasingly impor- tant, with increasing threats from human disturbances. Monitoring usually involves sam- pling from several sites of a similar habitat at regular (or irregular) intervals through time. The purpose of monitoring is to determine where and when an impact may have occurred or, once detected, may still be occurring. Sequential statistical methods, including control charts, as developed for industrial applications, offer some promise in this regard. These provide a way of identifying when a system (e.g., in a factory) is going "out of control," so as to trigger an alarm to stop the system and employ appropriate remedial measures. Such techniques clearly would be useful in the context of environmental monitoring. Tra- ditional control charts, however, cannot be used for many ecological applications because they do not handle multivariate data, and individual counts of species abundances do not generally fulfill the necessary statistical assumptions. A distance-based multivariate control chart method is described here, with some examples of its use in monitoring coral reef fish assemblages of the Great Barrier Reef, Australia. The method is flexible, as it can be based on any dissimilarity measure of choice, and useful, as it does not require any specific assumptions regarding distributions of variables. Bootstrapping techniques are used to pro- vide control-chart limits for an appropriate multivariate distance-based criterion through time. The method is designed to identify impacts at individual sites as quickly as possible, thus triggering an "alarm bell" in the context of ecological monitoring. It can also be applied at several spatial scales in hierarchical designs.

Multivariate control charts for ecological and environmental monitoring

In environmental monitoring the quality assessment is essentially one-sided. For example quality of air decreases as one or more air pollutants increase. Statistical multivariate monitoring is then concerned with the problem of detecting some non-random one-sided shifts of one or more among various pollutant levels. In this paper, after discussing some change models useful in environmental monitoring, a generalized likelihood ratio test statistic is proposed both for retrospective testing and for on-line change detection. The test is then compared to the approach based on union-intersection of one-sided univariate tests.

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One-sided Multivariate Testing and Environmental Monitoring

Environmental monitoring data are collected successively in time. Therefore, it is self evident to think about analyzing the data sequentially. We propose the use of a sequential probability ratio test (SPRT), developed to test against a simple hypothesis, to test against a minimal relevant trend 01 (i.e., a composite hypothesis). Three refinements are introduced: the boundaries An and Bn are made funnel shaped, 01 is replaced by 0 if the norm of 0 exceeds the norm of 01, and observation is stopped as soon as a predescribed accuracy is attained. Simulation studies show that these refinements generalize the SPRT for testing against a composite hypothesis and improve the performance in terms of power and expected sample size of the test. The robustness of the adjusted SPRT against spatial and serial correlation is studied. We demonstrate that the test is robust against serial correlation between -.5 and +.5 and spatial correlation between -.5 and +.2. The use of the SPRT is illustrated with filed data on three Tern species-the Sandwich Tern, the Arctic Tern, and the Common Tern.

Sequential Analysis of Environmental Monitoring Data: Refined SPRT's for Testing against a Minimal Relevant Trend

As environmental monitoring data are collected successively in time, the data are suitable for sequential analysis. An earlier article proposed a refined sequential probability ratio test (SPRT) to test against a minimal relevanttrend, assuming no serial correlations and without modeling the spatial covariance matrix. As the model parameters are unknown in advance, a minimal number of observations(n
 min) is required for estimation prior to analysis. Leaving the spatial covariance matrix unstructured, n
 min increases if the number of sampling locations increases. Therefore, assumptions on the spatial covariance matrix are proposed, thereby reducing the number of nuisance parameters, thus reducingn
 min. This article studies. three simple types of spatial covariance matrix structures and derives an adjusted SPRT for each of these types. Furthermore, we examine the robustness against deviations from the assumed spatial covariance matrix structure. Simulation studies show that adjusted SPRTs can be derived rather easily and that they are in general robust against deviations from the assumed type of spatial covariance matrix. Sequential analysis of simulated data, which are based on monitoring data of bats in the Netherlands, illustrates the use of one of the derived SPRTs.

Making sequential analysis of environmental monitoring data feasible by simplifying the covariance matrix structure

Data provided by an environmental monitoring system are sampled successively. We propose to analyse such data by means of the sequential probability ratio test (SPRT) which is especially designed to analyse data which are sampled consecutively. We present a method, the minimax method, that can be used to select an SPRT which is optimal in testing the null hypothesis θ = θ0 against the composite alternative hypothesis θ ≠ θ0 for three monitoring systems, namely a system consisting of one sampling location with known mean and variance, a system consisting of one sampling location with unknown mean and variance and a system consisting of two sampling locations with unknown mean and covariance matrix. The latter test is applied to field data of the mallard. © 1997 by John Wiley & Sons, Ltd.

Jolanda Den Hartog

Papers

SEQUENTIAL ANALYSIS OF ENVIRONMENTAL MONITORING DATA: OPTIMAL SPRTs