Defining Relevant Product Markets for Pharmaceuticals

To identify the relevant product markets for Swedish pharmaceuticals, a spatial econometrics approach is employed. First, we calculate Moran’s Is for different market definitions and then we use a spatial Durbin model to determine the effect of price changes on quantity sold off own and competing products. As expected, the results show that competition is strongest between close substitutes; however, the relevant product markets for Swedish pharmaceuticals extend beyond close substitutes down to products included in the same class on the four-digit level of the Anatomic Therapeutic Chemical system as defined by the World Health Organization. The spatial regression model further indicates that increases in the price of a product significantly lower the quantity sold of that product and in the same time increase the quantity sold of competing products. For close substitutes (products belonging to the same class on the seven-digit level of the Anatomic Therapeutic Chemical system), as well as for products that, without being close substitutes, belong to the same therapeutic/pharmacological/chemical subgroup (the same class on the five-digit level of the Anatomic Therapeutic Chemical system), a significant change towards increased competition is also visible after 1 July 2009 when the latest policy changes with regards to pharmaceuticals have been implemented in Sweden.

A pharmacokinetic-pharmacodynamic model for duodenal levodopa infusion

Objective Levodopa in presence of decarboxylase inhibitors is following two-compartment kinetics and its effect is typically modelled using sigmoid Emax models. Pharmacokinetic modelling of the absorption phase of oral distributions is problematic because of irregular gastric emptying. The purpose of this work was to identify and estimate a population pharmacokinetic- pharmacodynamic model for duodenal infusion of levodopa/carbidopa (Duodopa®) that can be used for in numero simulation of treatment strategies. Methods The modelling involved pooling data from two studies and fixing some parameters to values found in literature (Chan et al. J Pharmacokinet Pharmacodyn. 2005 Aug;32(3-4):307-31). The first study involved 12 patients on 3 occasions and is described in Nyholm et al. Clinical Neuropharmacology 2003:26:156-63. The second study, PEDAL, involved 3 patients on 2 occasions. A bolus dose (normal morning dose plus 50%) was given after a washout during night. Plasma samples and motor ratings (clinical assessment of motor function from video recordings on a treatment response scale between -3 and 3, where -3 represents severe parkinsonism and 3 represents severe dyskinesia.) were repeatedly collected until the clinical effect was back at baseline. At this point, the usual infusion rate was started and sampling continued for another two hours. Different structural absorption models and effect models were evaluated using the value of the objective function in the NONMEM package. Population mean parameter values, standard error of estimates (SE) and if possible, interindividual/interoccasion variability (IIV/IOV) were estimated. Results Our results indicate that Duodopa absorption can be modelled with an absorption compartment with an added bioavailability fraction and a lag time. The most successful effect model was of sigmoid Emax type with a steep Hill coefficient and an effect compartment delay. Estimated parameter values are presented in the table. Conclusions The absorption and effect models were reasonably successful in fitting observed data and can be used in simulation experiments.

Short Communication: A compelling argument for the gravity p-median model

The p-median model is used to locate P facilities to serve a geographically distributed population. Conventionally, it is assumed that the population always travels to the nearest facility. Drezner and Drezner (2006, 2007) provide three arguments on why this assumption might be incorrect, and they introduce the extended the gravity p-median model to relax the assumption. We favour the gravity p-median model, but we note that in an applied setting, Drezner and Drezner’s arguments are incomplete. In this communication, we point at the existence of a fourth compelling argument for the gravity p-median model.

Fitting spatial models in the R package: hglm

We present a new version of the hglm package for fittinghierarchical generalized linear models (HGLM) with spatially correlated random effects. A CAR family for conditional autoregressive random effects was implemented. Eigen decomposition of the matrix describing the spatial structure (e.g. the neighborhood matrix) was used to transform the CAR random effectsinto an independent, but heteroscedastic, gaussian random effect. A linear predictor is fitted for the random effect variance to estimate the parameters in the CAR model.This gives a computationally efficient algorithm for moderately sized problems (e.g. n<5000).

Spatial modeling of data with excessive zeros applied to reindeer pellet-group counts

We analyze a real data set pertaining to reindeer fecal pellet-group counts obtained from a survey conducted in a forest area in northern Sweden. In the data set, over 70% of counts are zeros, and there is high spatial correlation. We use conditionally autoregressive random effects for modeling of spatial correlation in a Poisson generalized linear mixed model (GLMM), quasi-Poisson hierarchical generalized linear model (HGLM), zero-inflated Poisson (ZIP), and hurdle models. The quasi-Poisson HGLM allows for both under- and overdispersion with excessive zeros, while the ZIP and hurdle models allow only for overdispersion. In analyzing the real data set, we see that the quasi-Poisson HGLMs can perform better than the other commonly used models, for example, ordinary Poisson HGLMs, spatial ZIP, and spatial hurdle models, and that the underdispersed Poisson HGLMs with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLMs. Spatial count response with an extremely high proportion of zeros, and underdispersion can be successfully modeled using the quasi-Poisson HGLM with spatial random effects.