A population-based method to determine the time-integrated activity in molecular radiotherapy

Background The calculation of time-integrated activities (TIAs) for tumours and organs is required for dosimetry in molecular radiotherapy. The accuracy of the calculated TIAs is highly dependent on the chosen fit function. Selection of an adequate function is therefore of high importance. However, model (i.e. function) selection works more accurately when more biokinetic data are available than are usually obtained in a single patient. In this retrospective analysis, we therefore developed a method for population-based model selection that can be used for the determination of individual time-integrated activities (TIAs). The method is demonstrated at an example of [177Lu]Lu-PSMA-I&T kidneys biokinetics. It is based on population fitting and is specifically advantageous for cases with a low number of available biokinetic data per patient. Methods Renal biokinetics of [177Lu]Lu-PSMA-I&T from thirteen patients with metastatic castration-resistant prostate cancer acquired by planar imaging were used. Twenty exponential functions were derived from various parameterizations of mono- and bi-exponential functions. The parameters of the functions were fitted (with different combinations of shared and individual parameters) to the biokinetic data of all patients. The goodness of fits were assumed as acceptable based on visual inspection of the fitted curves and coefficients of variation CVs < 50%. The Akaike weight (based on the corrected Akaike Information Criterion) was used to select the fit function most supported by the data from the set of functions with acceptable goodness of fit. Results The function $$A_{1} { }\beta { }e^{{ - \left( {\lambda_{1} + \lambda_{{{\text{phys}}}} } \right)t}} + A_{1} { }\left( {1 - \beta } \right){ }e^{{ - \left( {\lambda_{{{\text{phys}}}} } \right)t}}$$ A 1 β e - λ 1 + λ phys t + A 1 1 - β e - λ phys t with shared parameter $$\beta$$ β was selected as the function most supported by the data with an Akaike weight of 97%. Parameters $$A_{1}$$ A 1 and $$\lambda_{1}$$ λ 1 were fitted individually for every patient while parameter $$\beta { }$$ β was fitted as a shared parameter in the population yielding a value of 0.9632 ± 0.0037. Conclusions The presented population-based model selection allows for a higher number of parameters of investigated fit functions which leads to better fits. It also reduces the uncertainty of the obtained Akaike weights and the selected best fit function based on them. The use of the population-determined shared parameter for future patients allows the fitting of more appropriate functions also for patients for whom only a low number of individual data are available.

Towards a pragmatic use of statistics in ecology

Although null hypothesis testing (NHT) is the primary method for analyzing data in many natural sciences, it has been increasingly criticized. Recently, approaches based on information theory (IT) have become popular and were held by many to be superior because it enables researchers to properly assess the strength of the evidence that data provide for competing hypotheses. Many studies have compared IT and NHT in the context of model selection and stepwise regression, but a systematic comparison of the most basic uses of statistics by ecologists is still lacking. We used computer simulations to compare how both approaches perform in four basic test designs (t-test, ANOVA, correlation tests, and multiple linear regression). Performance was measured by the proportion of simulated samples for which each method provided the correct conclusion (power), the proportion of detected effects with a wrong sign (S-error), and the mean ratio of the estimated effect to the true effect (M-error). We also checked if the p-value from significance tests correlated to a measure of strength of evidence, the Akaike weight. In general both methods performed equally well. The concordance is explained by the monotonic relationship between p-values and evidence weights in simple designs, which agree with analytic results. Our results show that researchers can agree on the conclusions drawn from a data set even when they are using different statistical approaches. By focusing on the practical consequences of inferences, such a pragmatic view of statistics can promote insightful dialogue among researchers on how to find a common ground from different pieces of evidence. A less dogmatic view of statistical inference can also help to broaden the debate about the role of statistics in science to the entire path that leads from a research hypothesis to a statistical hypothesis.

The Markets of Green Cars of Three Countries: Analysis Using Lotka–Volterra and Bertalanffy–Pütter Models

Did the diesel scandal of 2015 affect the market for cars? We consider this question in relation to Germany, Austria, and Switzerland. Starting with historical registration data of cars with different drivetrain technologies, we considered each technology in isolation and fitted a five-parameter Bertalanffy–Pütter (BP) growth model to the stocks of cars. We used this model as it generalizes several well-known three-parameter models, which are distinguished by their exponent pair, e.g., Brody model BP (0, 1), West model BP (0.75, 1), and logistic growth BP (1, 2). We then used these models to derive a Lotka–Volterra (LV) model for the co-evolution of the (annual) market shares of the different drivetrain technologies. We augmented this model by a consideration of model uncertainty and found that initially all technologies were in a state of competition, except for Austria, which changed in 2015 to a predator–prey situation with diesel as the sole prey. This analysis of model uncertainty compared the best-fitting growth curve with the growth trajectories of other likely (Akaike weight 5% or higher) models of BP type. We conclude with remarks about open innovation.

Preprint Glautier (2017) Revised Non-local influences on associative learning: new data and further model evaluation

Revised preprintPrevious work (Glautier, 2013) showed that the responses made by humans on trial n insimple associative learning tasks were influenced by events that took place on trial n−1and a simple extension of the Rescorla-Wagner Model (RWM Rescorla &amp; Wagner,1972), the Memory Environment Cue Array (MECA) model, was presented to accountfor those results. In the current work further evidence of non-local influences onresponding during associative learning tasks is presented. The Rescorla-Wagner modeland the MECA model are evaluated as models for the observed data using qualitative,näive maximum likelihood, and Akaike weight analyses. In two experiments the Akaikeweight analyses strongly supported the simpler Rescorla-Wagner model over the MECAmodel but the qualitive and näive maximum likelihood analyses strongly supported theMECA model model over the simpler Rescorla-Wagner model. In Experiment 2 thisapparent conflict was resolved using a generalisation criterion test (Ahn, Busemeyer,Wagenmakers, &amp; Stout, 2008; Busemeyer &amp; Wang, 2000) which gave clear support tothe MECA model over the Rescorla-Wagner model. These results demonstrate thesuperiority of model selection using predictive validity, where possible, over selectionusing statistical adjustments for model complexity.

Preprint Glautier (2017) Non-local influences on associative learning: new data and further model evaluation

There is a revised version at: https://osf.io/4nx2vPrevious work (Glautier, 2013) showed that the responses made by humans on trial n insimple associative learning tasks were influenced by events that took place on trial n−1and a simple extension of the Rescorla-Wagner Model (RWM Rescorla &amp; Wagner,1972), the Memory Environment Cue Array (MECA) model, was presented to accountfor those results. In the current work further evidence of non-local influences onresponding during associative learning tasks is presented. The Rescorla-Wagner modeland the MECA model are evaluated as models for the observed data using qualitative,näive maximum likelihood, and Akaike weight analyses. In two experiments the Akaikeweight analyses strongly supported the simpler Rescorla-Wagner model over the MECAmodel but the qualitive and näive maximum likelihood analyses strongly supported theMECA model model over the simpler Rescorla-Wagner model. In Experiment 2 thisapparent conflict was resolved using a generalisation criterion test (Ahn, Busemeyer,Wagenmakers, &amp; Stout, 2008; Busemeyer &amp; Wang, 2000) which gave clear support tothe MECA model over the Rescorla-Wagner model. These results demonstrate thesuperiority of model selection using predictive validity, where possible, over selectionusing statistical adjustments for model complexity. Data and code available at Glautier(2017).