A bootstrapped sequential probability ratio test for signal processing applications

Gölz, Martin; Fauß, Michael; Zoubir, Abdelhak M.

doi:10.1109/camsap.2017.8313175

Cited by 2 publications

(6 citation statements)

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“…Appropriate implementation of SPRTs requires an understanding of the behavior of the SPRT statistic so its variance under null conditions can be used to inform the creation of thresholds which, if the SPRT statistic crosses, can in turn be used to determine if H 1 : slope for the response variable/time relationship = 0.0 vs. H 2 : slope > some value of interest should be accepted. Naively using an SPRT that does not consider the noise in the behavior of the SPRT statistic attributed to the estimation of the nontarget-slope 'nuisance parameters' would lead to tests resulting in false positive and false negative findings (Cox, 1963;(Gölz et al, 2017).…”

Section: Quickest Single-subject Outcome Determination Studiesmentioning

confidence: 99%

“…Working out the thresholds used to determine if H 1 or H 2 should be accepted analytically can be complicated (Gölz et al, 2017). However, bootstrap methods can be used to characterize the behavior of the SPRT statistic and create approximate thresholds for an SPRT, including an SPRT for testing a single regression coefficient as considered here.…”

Section: Quickest Single-subject Outcome Determination Studiesmentioning

confidence: 99%

“…However, bootstrap methods can be used to characterize the behavior of the SPRT statistic and create approximate thresholds for an SPRT, including an SPRT for testing a single regression coefficient as considered here. This strategy simply estimates confidence limits of the SPRT statistic using bootstrap sampling at each time a measurement is made in the study (Gölz et al, 2017). Basically, after an evaluation of the SPRT statistic under an assumed pair of H 1 and H 2 values for the slope (e.g., H 1 : slope=0.0 and H 2 : slope=0.05), bootstrap samples are drawn with replacement from the current accumulated set of measurements and measurement times.…”

Section: Quickest Single-subject Outcome Determination Studiesmentioning

confidence: 99%

“…Fixed upper and lower percentiles of the estimated SPRT statistic distribution from the bootstrapped SPRT statistics are then obtained (e.g., the 5th and 95th percentiles) depending on desired type I and type II error rates for the SPRT. If the threshold for accepting H 1 (positing a value lower than H 2 ), as determined in a standard nonbootstrapped SPRT (Cox, 1963;(Gölz et al, 2017), is crossed by the upper confidence limit of the estimated SPRT distribution, or if the threshold for accepting H 2 (positing a value higher than H 1 ) is crossed by the lower confidence limit of the estimated SPRT distribution, the SPRT is terminated. The upper right panel of Figure 6 depicts this phenomenon.…”

Section: Quickest Single-subject Outcome Determination Studiesmentioning

confidence: 99%

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Accommodating Serial Correlation and Sequential Design Elements in Personalized Studies and Aggregated Personalized Studies

Schork

2022

Harvard Data Science Review

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Single subject, or 'N-of-1,' studies are receiving a great deal of attention from both theoretical and applied researchers. This is consistent with the growing acceptance of 'personalized' approaches to health care and the need to prove that personalized interventions tailored to an individual's likely unique physiological profile and other characteristics work as they should. In fact, the preferred way of referring to N-of-1 studies in contemporary settings is as 'personalized studies.' Designing efficient personalized studies and analyzing data from them in ways that ensure statistically valid inferences are not trivial, however. I briefly discuss some of the more complex issues surrounding the design and analysis of personalized studies, such as the use of washout periods, the frequency with which measures associated with the efficacy of an intervention are collected during a study, and the serious effect that serial correlation can have on the analysis and interpretation of personalized study data and results if not accounted for explicitly. I point out that more efficient sequential designs for personalized and aggregated personalized studies can be developed, and I explore the properties of sequential personalized studies in a few settings via simulation studies. Finally, I comment on contexts within which personalized studies will likely be pursued in the future.

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Section: Quickest Single-subject Outcome Determination Studiesmentioning

confidence: 99%

Section: Quickest Single-subject Outcome Determination Studiesmentioning

confidence: 99%

Section: Quickest Single-subject Outcome Determination Studiesmentioning

confidence: 99%

Section: Quickest Single-subject Outcome Determination Studiesmentioning

confidence: 99%

See 2 more Smart Citations

Accommodating Serial Correlation and Sequential Design Elements in Personalized Studies and Aggregated Personalized Studies

Schork

2022

Harvard Data Science Review

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“…Although there exist sequential tests which deal with composite hypotheses and that include an estimation part (Li et al, 2014;Gölz et al, 2017), estimation is usually of secondary interest. The joint solution of sequential detection and estimation has attained little attention in the literature.…”

Section: Introductionmentioning

confidence: 99%

Bayesian sequential joint detection and estimation

Reinhard

Fauß

Zoubir

2018

Sequential Analysis

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Joint detection and estimation refers to deciding between two or more hypotheses and, depending on the test outcome, simultaneously estimating the unknown parameters of the underlying distribution. This problem is investigated in a sequential framework under mild assumptions on the underlying random process. We formulate an unconstrained sequential decision problem, whose cost function is the weighted sum of the expected run-length and the detection/estimation errors. Then, a strong connection between the derivatives of the cost function with respect to the weights, which can be interpreted as Lagrange multipliers, and the detection/estimation errors of the underlying scheme is shown. This property is used to characterize the solution of a closely related sequential decision problem, whose objective function is the expected run-length under constraints on the average detection/estimation errors. We show that the solution of the constrained problem coincides with the solution of the unconstrained problem with suitably chosen weights. These weights are characterized as the solution of a linear program, which can be solved using efficient off-the-shelf solvers. The theoretical results are illustrated with two example problems, for which optimal sequential schemes are designed numerically and whose performance is validated via Monte Carlo simulations.2. The hypothesis H i , i = 0, 1, as well as the random parameter Θ i do not change during the observation period of X N .3. A sufficient static t n (x n ) in a state space (E t , E t ) exists such thatThe sufficient statistic has a transition kernel of the formand some initial statistic t 0 .4. The two hypotheses are separable, i.e.,5. The second order moment of the random parameter Θ exists and is finite, i.e., E[Θ 2 ] <∞ .Note that this implies, that the conditional second order moment E[Θ 2 | A] exist and is finite for all events A with non-zero probability.

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A bootstrapped sequential probability ratio test for signal processing applications

Cited by 2 publications

References 4 publications

Accommodating Serial Correlation and Sequential Design Elements in Personalized Studies and Aggregated Personalized Studies

Accommodating Serial Correlation and Sequential Design Elements in Personalized Studies and Aggregated Personalized Studies

Bayesian sequential joint detection and estimation

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