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STIMA DI FUNZIONI NON-LINEARI DI RISPOSTA DIPENDENTI DAL TEMPO O DALLA DOSE QUANDO I PROFILI DI RISPOSTA NON POSSONO ESSERE INTERPOLATI SINGOLARMENTE
No full textStatistical models aiming to establish the relationship of a biological response (or effect) to increasing values of dose (or time) must take into account the differences in shape that such a relationship presents between individuals. These models involve two levels of variability: a within-individual level 1 including measurement errors and random deviations from the individual dose-response function, and a between-individuals level 2 expressing the biological differences between individuals belonging to the same population. At level 1, random terms usually have a simple covariance structure (i.e. are uncorrelated). The parameters of individual functions are regarded as random variables whose means are the parameters of the function at level 2 (or population level) and whose covariance may be expressed by any Gramian.
Since dose-response functions are typically nonlinear, two-stage models properly apply to this kind of problems. Unfortunately, in many situations the observed response profiles are so irregular that only mean profiles can be successfully fitted. This approach may result in a severe underestimation of the standard errors of parameters and in a confidence level by far lower than the nominal value. In addition, the estimate of one or more parameters may be biased.
The simulation studies presented in this thesis demonstrate that the first drawback can be avoided including the covariance matrix of residuals conditional on the dose into the estimate of the covariance matrix of the parameters estimates, whereas the extent of bias in the estimate of a given parameter may be derived from the structure of the model
FEV1% predicted in patients with at least one nonsense mutation and patients homozygous for F508del
No full textYear to year change in FEV1 in patients with cystic fibrosis and different mutation classes
No full textIn patients with cystic fibrosis, most treatments addressing the underlying basic defect are mutation or mutation class specific. These treatments are disease modifying if they lower the year to year change in lung function. We therefore calculated the current loss of lung function, measured by year to year change in forced expired volume in 1s in 11,417 patients included in the European Cystic Fibrosis Society Patient Registry. Whereas patients with at least one mutation of class IV or V have on average a lower year to year change, we did not find a difference between patients with a stop codon mutation, homozygous for F508del or at least one class III mutation. These data are useful background information to discuss the impact of different disease modifying treatments
ESTIMATING NONLINEAR TIME- OR DOSE-RESPONSE FUNCTIONS WHEN RESPONSE PROFILES CANNOT BE INDIVIDUALLY FITTED
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Introducing the Harmonic Mean Solving a Tourist’s Problem
Full text linkThis exercise can be given to a group of students with basic knowledge of mathematics and physics at the beginning of a lesson. We can imagine that there will be some students that will solve the exercise using the “common sense” solution recalling basic notions of physics and some students that will solve the exercise recalling basic notion of physics and computing a mean velocity using the arithmetic mean, the most common mean. At the end of the exercise, the teacher will compare the two solutions and will present the harmonic mean as the fastest solution for the students that solved the problem using the “common sense” solution and as the correct mean to be used for the students that solved the exercise computing a mean velocit
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