Browsing by Author "Petzold, Max"

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A comprative study of some approaches for constructing tolerance limits
(2000) Petzold, Max; Department of Statistics
In a dose finding study the aim is to come up with a safe and efficient drug administration. By comparing the obtained tolerance limits with predetermined desired concentration limits, i.e. the therapeutic window, one may be able to adjust the drug dosage. For drugs with a therapeutic window situated at high concentrations close to toxic levels, one has to balance between attaining a high proportion of the population at efficient high levels on one hand and the risks of an overdose on the other hand. In such cases it is important to use the proper estimation approach for the upper tolerance limit. Here a conservative estimation approach intended for a drug with potentially adverse side effects with minor overdoses is compared with an approach intended for a drug with harmless side effects. It is shown that the conservative approach can be considerably less efficient when used in the latter case, a disadvantage that is rarely discussed when proposing conservative estimators. The properties of the two approaches are evaluated using well-known parametric and non-parametric estimators in a simulation study for small and moderate sample sizes.
A note on the first moment of extreme order statistics from the normal distribution
(2000) Petzold, Max; Department of Statistics
In this note some well known asymptotic results for moments of order statistics from the normal distribution are treated. The results originates from the work of Cramér. A bias correction for finite sample sizes is proposed for the expected value of the largest observation.
A small sample limitation for estimators based on order statistics
(2000) Petzold, Max; Department of Statistics
Aspects on tolerance limit estimation - some common approaches and flexible modeling
(University of Gothenburg, 2000-02-01) Petzold, Max
In a dose finding study the aim is to attain a safe and efficient drug therapy in a certain population. By a dose finding study we generally refer to a study where the dosage is successively adjusted after analyzing the responding concentration in e.g. the blood. Measurements of interest are e.g. area under curve, time to peak, peak value, time to zero and tolerance limits. The estimates obtained from the pharmacokinetical data are compared with the known safety and efficiency profiles of the drug, and the dosage may be adjusted to attain a satisfactory result. Different estimation approaches have to be used depending on the safety and efficiency profiles of the drug. When estimating tolerance limits there are roughly two different approaches, one intended for drugs with severe side effects and one intended for drugs with harmless side effects. However, sometimes the approaches are used as interchangeable resulting in misleading estimates. It is also important to consider the data utilization. A variety of estimation techniques are used in pharmacokinetics. Some of the proposed estimators use cross sectional data and the more advanced ones use the longitudinal structure of the data to different extents. The benefits of the latter are often considerable, especially for small sample sizes common in pharmacokinetics. For crude data where we can not assume fixed regression parameters flexible regression models tend to be superior. In Report I two different estimation approaches for tolerance limits are considered: the conservative approach intended for drugs with severe side effects and the closeness approach intended for drugs with harmless side effects. It is obvious, but rarely discussed, that the conservative approach tends to result in less efficient drug therapies than the closeness approach. In the case with severe side effects this disadvantage may be well motivated by safety aspects. However, this approach is sometimes also proposed for drugs with harmless side effects. In Report I it is shown in a simulation study that the conservative approach can be considerably less efficient and some examples are given. Both parametric and non-parametric cross sectional estimators are used in the study. In many applications data is based on repeated observations over time. In Report II this longitudinal structure of the data is taken into consideration. A flexible model which after linearization has a random intercept and a fixed slope is proposed. The model is flexible in the sense that the time dependence is modeled by tP where t is the time value and p is an unknown parameter. A two-step estimation approach is proposed where p is estimated in the first step, and the rest of the parameters are estimated in the second step by using standard regression techniques. The effects of first estimating p upon the rest of the estimators are demonstrated by a simulation study. It is concluded that bias and precision of estimators of the variance components and the dependent variable remain quite unaffected by the two-step procedure, as well as bias of the slope and intercept parameters. However, the precision of the latter estimators may be poor for small values of p, provided that the variance of the measurement errors is large. ii
Detection of intra-uterine growth restriction
(University of Gothenburg, 2003-03-01) Petzold, Max; Sonesson, Christian; Bergman, Eva; Kieler, Helle
A new methodology for on-line detection of intrauterine growth restriction (IUGR) is proposed where traditional methods for statistical surveillance are applied. Here, deficient growth rate is used to detect IUGR instead of the common surrogate measure "small for gestational age" (SGA). Foetal growth is estimated by repeated measurements of symphysis-fundus (SF) height. At each time point the new method, based on the Shiryaev-Roberts method, is used to evaluate the growth in SF height. We use Swedish data to model a normal growth pattern, which is used to evaluate the capability of the new method to detect IUGR in comparison with a method used in practice today. Results from simulations indicate that the new method performs considerably better than the method used today. We also illustrate the effect of some important factors, which influence the detection ability and illuminate the tendency of the method used today to misclassify SGA cases as IUGR.
Evaluation of Information in Longitudinal Data
(2003) Petzold, Max
Maximum Likelihood Ratio based small-sample tests for random coefficients in linear regression
(2003) Jonsson, Robert; Petzold, Max; Department of Economics
Two small-sample tests for random coefficients in linear regression are derived from the Maximum Likelihood Ratio. The first test has previously been proposed for testing equality of fixed effects, but is here shown to be suitable also for random coefficients. The second test is based on the multiple coefficient of determination from regressing the observed subject means on the estimated slopes. The properties and relations of the tests are examined in detail, followed by a simulation study of the power functions. The two tests are found to complement each other depending on the study design: The first test is preferred for a large number of observations from a small number of subjects, and the second test is preferred for the opposite situation. Finally, the robustness of the tests to violations of the distributional assumptions is examined.
Maximum Likelihood Ratio based small-sample tests for random coefficients in linear regression
(2003-08-01) Petzold, Max; Jonsson, Robert
Two small-sample tests for random coefficients in linear regression are derived from the Maximum Likelihood Ratio. The first test has previously been proposed for testing equality of fixed effects, but is here shown to be suitable also for random coefficients. The second test is based on the multiple coefficient of determination from regressing the observed subject means on the estimated slopes. The properties and relations of the tests are examined in detail, followed by a simulation study of the power functions. The two tests are found to complement each other depending on the study design: The first test is preferred for a large number of observations from a small number of subjects, and the second test is preferred for the opposite situation. Finally, the robustness of the tests to violations of the distributional assumptions is examined.
Preliminary testing in a class of simple non-linear mixed models to improve estimation accuracy
(2003-09-02) Petzold, Max
In applied research hypothetical information about the parameters in a stochastic model sometimes can be generated from theory or previous studies. Replacing unknown parameters by constants might increase the estimation accuracy. This is especially apparent when replacing parameters in non-linear expressions. The problem is how to handle the uncertainty of the hypothetical information. Here, a pretest procedure will be examined for an unknown exponent of the explanatory variable in a simple non-linear mixed model. The optimal pretest sizes for some parameter settings are found for a minimax regret criterion based on Mean-Squared-Error. The optimal test sizes were found to be approximately valid also for the case where no subject specific components are present. The examined class of models is useful for modelling concentration-time data for drugs with rapid absorption, and a small-sample example is given to illustrate the potential gain in estimation accuracy of the pretest approach in pharmacokinetics.