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  • 1.
    Magnúsdóttir, Bergrún Tinna
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Optimal designs for a multiresponse Emax model and efficient parameter estimation2016In: Biometrical Journal, ISSN 0323-3847, E-ISSN 1521-4036, Vol. 58, no 3, p. 518-534Article in journal (Refereed)
    Abstract [en]

    The aim of dose finding studies is sometimes to estimate parameters in a fitted model. The precision of the parameter estimates should be as high as possible. This can be obtained by increasing the number of subjects in the study, N, choosing a good and efficient estimation approach, and by designing the dose finding study in an optimal way. Increasing the number of subjects is not always feasible because of increasing cost, time limitations, etc. In this paper, we assume fixed N and consider estimation approaches and study designs for multiresponse dose finding studies. We work with diabetes dose-response data and compare a system estimation approach that fits a multiresponse Emax model to the data to equation-by-equation estimation that fits uniresponse Emax models to the data. We then derive some optimal designs for estimating the parameters in the multi- and uniresponse Emax model and study the efficiency of these designs.

  • 2. Neumann, André
    et al.
    Bodnar, Taras
    Stockholm University, Faculty of Science, Department of Mathematics.
    Pfeifer, Dietmar
    Dickhaus, Thorsten
    Multivariate multiple test procedures based on nonparametric copula estimation2019In: Biometrical Journal, ISSN 0323-3847, E-ISSN 1521-4036, Vol. 61, no 1, p. 40-61Article in journal (Refereed)
    Abstract [en]

    Multivariate multiple test procedures have received growing attention recently. This is due to the fact that data generated by modern applications typically are highdimensional, but possess pronounced dependencies due to the technical mechanisms involved in the experiments. Hence, it is possible and often necessary to exploit these dependencies in order to achieve reasonable power. In the present paper, we express dependency structures in the most general manner, namely, by means of copula functions. One class of nonparametric copula estimators is constituted by Bernstein copulae. We extend previous statistical results regarding bivariate Bernstein copulae to the multivariate case and study their impact on multiple tests. In particular, we utilize them to derive asymptotic confidence regions for the family-wise error rate (FWER) of multiple test procedures that are empirically calibrated by making use of Bernstein copulae approximations of the dependency structure among the test statistics. This extends a similar approach by Stange et al. (2015) in the parametric case. A simulation study quantifies the gain in FWER level exhaustion and, consequently, power that can be achieved by exploiting the dependencies, in comparison with common threshold calibrations like the Bonferroni or Šidák corrections. Finally, we demonstrate an application of the proposed methodology to real-life data from insurance.

  • 3.
    Nyimvua, Shaban
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Andersson, Mikael
    Stockholm University, Faculty of Science, Department of Mathematics.
    Svensson, Åke
    Stockholm University, Faculty of Science, Department of Mathematics.
    Britton, Tom
    Stockholm University, Faculty of Science, Department of Mathematics.
    Modelling household epidemics and early stage vaccination2009In: Biometrical Journal, ISSN 0323-3847, E-ISSN 1521-4036, Vol. 51, no 3, p. 408-419Article in journal (Refereed)
    Abstract [en]

    A Markovian susceptible → infectious → removed (SIR) epidemic model is considered in a community partitioned into households. A vaccination strategy, which is implemented during the early stages of the disease following the detection of infected individuals is proposed. In this strategy, the detection occurs while an individual is infectious and other susceptible household members are vaccinated without further delay. Expressions are derived for the influence on the reproduction numbers of this vaccination strategy for equal and unequal household sizes. We fit previously estimated parameters from influenza and use household distributions for Sweden and Tanzania census data. The results show that the reproduction number is much higher in Tanzania (6 compared with 2) due to larger households, and that infected individuals have to be detected (and household members vaccinated) after on average 5 days in Sweden and after 3.3 days in Tanzania, a much smaller difference.

  • 4. Salmon, Maelle
    et al.
    Schumacher, Dirk
    Stark, Klaus
    Höhle, Michael
    Stockholm University, Faculty of Science, Department of Mathematics.
    Bayesian outbreak detection in the presence of reporting delays2015In: Biometrical Journal, ISSN 0323-3847, E-ISSN 1521-4036, Vol. 57, no 6, p. 1051-1067Article in journal (Refereed)
    Abstract [en]

    One use of infectious disease surveillance systems is the statistical aberration detection performed on time series of counts resulting from the aggregation of individual case reports. However, inherent reporting delays in such surveillance systems make the considered time series incomplete, which can be an impediment to the timely detection and thus to the containment of emerging outbreaks. In this work, we synthesize the outbreak detection algorithms of Noufaily etal.(2013) and Manitz and Hohle(2013) while additionally addressing right truncation caused by reporting delays. We do so by considering the resulting time series as an incomplete two-way contingency table which we model using negative binomial regression. Our approach is defined in a Bayesian setting allowing a direct inclusion of all sources of uncertainty in the derivation of whether an observed case count is to be considered an aberration. The proposed algorithm is evaluated both on simulated data and on the time series of Salmonella Newport cases in Germany in 2011. Altogether, our method aims at allowing timely aberration detection in the presence of reporting delays and hence underlines the need for statistical modeling to address complications of reporting systems. An implementation of the proposed method is made available in the R package surveillance as the function bodaDelay.

  • 5. Stallard, Nigel
    et al.
    Miller, Frank
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Day, Simon
    Hee, Siew Wan
    Madan, Jason
    Zohar, Sarah
    Posch, Martin
    Determination of the optimal sample size for a clinical trial accounting for the population size2017In: Biometrical Journal, ISSN 0323-3847, E-ISSN 1521-4036, Vol. 59, no 4, p. 609-625Article in journal (Refereed)
    Abstract [en]

    The problem of choosing a sample size for a clinical trial is a very common one. In some settings, such as rare diseases or other small populations, the large sample sizes usually associated with the standard frequentist approach may be infeasible, suggesting that the sample size chosen should reflectthe size of the population under consideration. Incorporation of the population size is possible in adecision-theoretic approach either explicitly by assuming that the population size is fixed and known, or implicitly through geometric discounting of the gain from future patients reflecting the expected population size. This paper develops such approaches. Building on previous work, an asymptotic expression is derived for the sample size for single and two-arm clinical trials in the general case of a clinical trial with a primary endpoint with a distribution of one parameter exponential family form that optimizes a utility function that quantifies the cost and gain per patient as a continuous function of this parameter. It is shown that as the size of the population, N, or expected size, N∗ in the case of geometric discounting, becomes large, the optimal trial size is O(N^1/2) or O(N∗^1/2). The sample size obtained from the asymptotic expression is also compared with the exact optimal sample size in examples with responses with Bernoulli and Poisson distributions, showing that the asymptotic approximations can also be reasonable in relatively small sample sizes.

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