A selection from Stockholm University publication database

• Mortality related to methadone maintenance treatment in Stockholm, Sweden, during 2006–2013

  2017. Anders Ledberg. Journal of Substance Abuse Treatment 74, 35-41

  Article

  Background: Methadone maintenance treatment (MMT) of opiate addiction was introduced in Sweden 50years ago. The first Swedish programs were modeled after the original Dole and Nyswander program, with strict criteria for admittance into treatment, and have been shown to have positive effects on social andhealth variables, including mortality. During the last 11 years, there have been a number of changes in the regulations controlling MMT-programs in Sweden, and the criteria for admittance are now much less strict compared to previous ones. This study aims to characterize the current MMT-programs with respect to mortality and to compare the results to those obtained in earlier periods.

  Methods: Persons entering into treatment in Stockholm county, between 2006 and 2011, were followed until September 2013 or until death occurred. Death rates for periods in treatment and out of treatment were determined and compared to rates for the general population. Proportional hazards models with treatment status as time-varying covariate were fitted to the data. A competing risk analysis was made to investigate the effects of MMT on drug-related mortality as compared to mortality from other causes. Mortality data for earlier periods were retrieved from the literature.

  Results: A total of 441 persons entered MMT during the time period. Of these 67 died during follow-up, the death rate being almost twenty times higher than in the general population. Not being in treatment was associated with a significantly increased hazard of dying (hazard ratio: 2.1, 95% confidence interval: 1.3–3.4). The hazard ratio was mainly increased for drug-related deaths (hazard ratio: 4.4 (2.1–9.2).

  Conclusions: Mortality rates among persons who entered MMT-programs in Stockholm during 2006–2011 were not increased compared to persons in treatment twenty years ago. The mortality was significantly increased during periods off treatment. Changes in regulations that minimizes the time off treatment are therefore likely to reduce the mortality rates among clients of MMT-programs.

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• Estimating the size of hidden populations from register data

  2014. Anders Ledberg, Peter Wennberg. BMC Medical Research Methodology 14, 58

  Article

  Background: Prevalence estimates of drug use, or of its consequences, are considered important in many contexts and may have substantial influence over public policy. However, it is rarely possible to simply count the relevant individuals, in particular when the defining characteristics might be illegal, as in the drug use case. Consequently methods are needed to estimate the size of such partly 'hidden' populations, and many such methods have been developed and used within epidemiology including studies of alcohol and drug use. Here we introduce a method appropriate for estimating the size of human populations given a single source of data, for example entries in a health-care registry. Methods: The setup is the following: during a fixed time-period, e. g. a year, individuals belonging to the target population have a non-zero probability of being registered. Each individual might be registered multiple times and the time-points of the registrations are recorded. Assuming that the population is closed and that the probability of being registered at least once is constant, we derive a family of maximum likelihood (ML) estimators of total population size. We study the ML estimator using Monte Carlo simulations and delimit the range of cases where it is useful. In particular we investigate the effect of making the population heterogeneous with respect to probability of being registered. Results: The new estimator is asymptotically unbiased and we show that high precision estimates can be obtained for samples covering as little as 25% of the total population size. However, if the total population size is small (say in the order of 500) a larger fraction needs to be sampled to achieve reliable estimates. Further we show that the estimator give reliable estimates even when individuals differ in the probability of being registered. We also compare the ML estimator to an estimator known as Chao's estimator and show that the latter can have a substantial bias when applied to epidemiological data. Conclusions: The population size estimator suggested herein complements existing methods and is less sensitive to certain types of dependencies typical in epidemiological data.

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• Framework to study dynamic dependencies in networks of interacting processes

  2012. Daniel Chicharro, Anders Ledberg. Physical Review E. Statistical, Nonlinear, and Soft Matter Physics 86 (4)

  Article

  The analysis of dynamic dependencies in complex systems such as the brain helps to understand how emerging properties arise from interactions. Here we propose an information-theoretic framework to analyze the dynamic dependencies in multivariate time-evolving systems. This framework constitutes a fully multivariate extension and unification of previous approaches based on bivariate or conditional mutual information and Granger causality or transfer entropy. We define multi-information measures that allow us to study the global statistical structure of the system as a whole, the total dependence between subsystems, and the temporal statistical structure of each subsystem. We develop a stationary and a nonstationary formulation of the framework. We then examine different decompositions of these multi-information measures. The transfer entropy naturally appears as a term in some of these decompositions. This allows us to examine its properties not as an isolated measure of interdependence but in the context of the complete framework. More generally we use causal graphs to study the specificity and sensitivity of all the measures appearing in these decompositions to different sources of statistical dependence arising from the causal connections between the subsystems. We illustrate that there is no straightforward relation between the strength of specific connections and specific terms in the decompositions. Furthermore, causal and noncausal statistical dependencies are not separable. In particular, the transfer entropy can be nonmonotonic in dependence on the connectivity strength between subsystems and is also sensitive to internal changes of the subsystems, so it should not be interpreted as a measure of connectivity strength. Altogether, in comparison to an analysis based on single isolated measures of interdependence, this framework is more powerful to analyze emergent properties in multivariate systems and to characterize functionally relevant changes in the dynamics.

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