Browsing by Author "Kulldorff, Martin"

Now showing 1 - 9 of 9
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    An early warning system for space-time cluster detection.
    (2003) Assunção, Renato Martins; Tavares, Andréa Iabrudi; Kulldorff, Martin
    A new topic of great relevance and concern has been the design of efficient early warning systems to detect as soon as possible the emergence of spatial clusters. In particular, many applications involving spatial events recorded as they occur sequentially in time require this kind of analysis, such as fire spots in forest areas as in the Amazon, crimes occurring in urban centers, locations of new disease cases to prevent epidemics, etc. We propose a statistical method to test for the presence of space-time clusters in point processes data, when the goal is to identify and evaluate the statistical significance of localized clusters. It is based on scanning the three dimensional space with a score test statistic under the null hypothesis that the point process is an inhomogeneous Poisson point process with space and time separable first order intensity. We discuss an algorithm to carry out the test and we illustrate our method with space-time crime data from Belo Horizonte, a large Brazilian city.
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    Border analysis for spatial clusters.
    (2018) Oliveira, Fernando L. P.; Cançado, André Luiz Fernandes; Souza, Gustavo Henrique Costa de; Moreira, Gladston Juliano Prates; Kulldorff, Martin
    Background: The spatial scan statistic is widely used by public health professionals in the detection of spatial clusters in inhomogeneous point process. The most popular version of the spatial scan statistic uses a circular-shaped scanning window. Several other variants, using other parametric or non-parametric shapes, are also available. However, none of them offer information about the uncertainty on the borders of the detected clusters. Method: We propose a new method to evaluate uncertainty on the boundaries of spatial clusters identified through the spatial scan statistic for Poisson data. For each spatial data location i, a function F(i) is calculated. While not a probability, this function takes values in the [0, 1] interval, with a higher value indicating more evidence that the location belongs to the true cluster. Results: Through a set of simulation studies, we show that the F function provides a way to define, measure and visualize the certainty or uncertainty of each specific location belonging to the true cluster. The method can be applied whether there are one or multiple detected clusters on the map. We illustrate the new method on a data set concerning Chagas disease in Minas Gerais, Brazil. Conclusions: The higher the intensity given to an area, the higher the plausibility of that particular area to belong to the true cluster in case it exists. This way, the F function provides information from which the public health practitioner can perform a border analysis of the detected spatial scan statistic clusters. We have implemented and illustrated the border analysis F function in the context of the circular spatial scan statistic for spatially aggregated Poisson data. The definition is clearly independent of both the shape of the scanning window and the probability model under which the data is generated. To make the new method widely available to users, it has been implemented in the freely available SaTScanTM software www.satscan.org.
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    Confidence intervals for spatial scan statistic.
    (2021) Silva, Ivair Ramos; Duczmal, Luiz Henrique; Kulldorff, Martin
    The spatial scan statistic is a popular statistical tool to detect geographical clusters of diseases. The basic problem of constructing confidence intervals for the relative risk of the most likely cluster has remained an open question. To cover this lack, a Monte Carlo based interval estimator for the relative risk of the primary cluster is derived. The method works for the circular spatial scan statistic applied to binomial data, and it ensures, by construction, an analytical control of the coverage probability under the nominal confidence coefficient. In addition, its performance is illustrated on simulated and real data of birth defects in New York State.
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    Continuous post-market sequential safety surveillance with minimum events to signal.
    (2017) Kulldorff, Martin; Silva, Ivair Ramos
    Continuous sequential analysis is increasingly used for near real-time post-market drug and vaccine safety surveillance. We explore continuous sequential monitoring when the null cannot be rejected until a minimum number of adverse events have occurred. For fixed alpha, one can simultaneously increase the statistical power and reduce the expected time to signal. We also evaluate continuous sequential analysis with a delayed start until a certain sample size has been attained. This is only useful if the start of the surveillance is delayed for logistical reasons. Tables with exact critical values, statistical power and the average times to signal are provided.
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    Continuous versus group sequential analysis for post-market drug and vaccine safety surveillance.
    (2015) Silva, Ivair Ramos; Kulldorff, Martin
    The use of sequential statistical analysis for post-market drug safety surveillance is quickly emerging. Bothcontinuous and group sequential analysis have been used, but consensus is lacking as to when to use which approach. Wecompare the statistical performance of continuous and group sequential analysis in terms of type I error probability; statisticalpower; expected time to signal when the null hypothesis is rejected; and the sample size required to end surveillance withoutrejecting the null. We present a mathematical proposition to show that for any group sequential design there always existsa continuous sequential design that is uniformly better. As a consequence, it is shown that more frequent testing is alwaysbetter. Additionally, for a Poisson based probability model and a flat rejection boundary in terms of the log likelihood ratio,we compare the performance of various continuous and group sequential designs. Using exact calculations, we found that, forthe parameter settings used, there is always a continuous design with shorter expected time to signal than t he best groupdesign. The two key conclusions from this article are (i) that any post-market safety surveillance system should attempt toobtain data as frequently as possible, and (ii) that sequential testing should always be performed when new data arriveswithout deliberately waiting for additional data.
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    Exact conditional maximized sequential probability ratio test adjusted for covariates.
    (2019) Silva, Ivair Ramos; Lingling, Li; Kulldorff, Martin
    Sequential analysis is now commonly used for post-market drug and vaccine safety surveillance, and a Poisson stochastic process is typically used for rare adverse events. The conditional maximized sequential probability ratio test, CMaxSPRT, is a powerful tool when there is uncertainty in the estimated expected counts under the null hypothesis. This paper derives exact critical values for CMaxSPRT, as well as statistical power and expected time to signal. This is done for both continuous and group sequential analysis, and for different rejection boundaries. It is also shown how to adjust for covariates in the sequential design. A table of critical values is provided for selected parameters and rejection boundaries, while new functions in the R Sequential package can be used for other calculations. In addition, the method is illustrated for monitoring adverse events after pediarix vaccination data.
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    Exact sequential analysis for multiple weighted binomial end points.
    (2019) Silva, Ivair Ramos; Gagne, Joshua J.; Najafzadeh, Mehdi; Kulldorff, Martin
    Sequential analysis is used in clinical trials and postmarket drug safety surveillance to prospectively monitor efficacy and safety to quickly detect benefits and problems, while taking the multiple testing of repeated analyses into account. When there are multiple outcomes, each one may be given a weight corresponding to its severity. This paper introduces an exact sequential analysis procedure for multiple weighted binomial end points; the analysis incorporates a drug's combined benefit and safety profile. It works with a variety of alpha spending functions for continuous, group, or mixed group-continuous sequential analysis. The binomial probabilities may vary over time and do not need to be known a priori. The new method was implemented in the free R Sequential package for both one- and two-tailed sequential analysis. An example is given examining myocardial infarction and major bleeding events in patients who initiated non-steroidal antiinflammatory drugs.
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    Exact sequential test for clinical trials and post-market drug and vaccine safety surveillance with Poisson and binary data.
    (2021) Silva, Ivair Ramos; Maro, Judith; Kulldorff, Martin
    In sequential analysis, hypothesis testing is performed repeatedly in a prospective manner as data accrue over time to quickly arrive at an accurate conclusion or decision. In this tutorial paper, detailed explanations are given for both designing and operating sequential testing. We describe the calculation of exact thresholds for stopping or signaling, statistical power, expected time to signal, and expected sample sizes for sequential analysis with Poisson and binary type data. The calculations are run using the package Sequential, constructed in R language. Real data examples are inspired on clinical trials practice, such as the current efforts to develop treatments to face the COVID-19 pandemic, and the comparison of treatments of osteoporosis. In addition, we mimic the monitoring of adverse events following influenza vaccination and Pediarix vaccination.
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    Optimal alpha spending for sequential analysis with binomial data.
    (2020) Silva, Ivair Ramos; Kulldorff, Martin; Yih, W. Katherine
    For sequential analysis hypothesis testing, various alpha spending functions have been proposed. Given a prespecified overall alpha level and power, we derive the optimal alpha spending function that minimizes the expected time to signal for continuous as well as group sequential analysis. If there is also a restriction on the maximum sample size or on the expected sample size, we do the same. Alternatively, for fixed overall alpha, power and expected time to signal, we derive the optimal alpha spending function that minimizes the expected sample size. The method constructs alpha spending functions that are uniformly better than any other method, such as the classical Wald, Pocock or O’Brien–Fleming methods.The results are based on exact calculations using linear programming. All numerical examples were run by using the R Sequential package.