| 1. |
- Garmo, Hans
(författare)
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Random railways and cycles in random regular graphs
- 1998
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In a cubic multigraph certain restrictions on the paths are made to define what is called a railway. Due to these restrictions a special kind of connectivity is defined. As the number of vertices tends to infinity, the asymptotic probability of obtaining an, in this sense, connected random cubic multigraph is shown to be 1/3.An equivalence relation on the tracks in the railway (edges in the multigraph) is defined in order to further study the properties of railways. The number of equivalence classes induced by this relation - the connectivity number - is investigated for a random railway achieved from a random cubic multigraph.As a result we obtain the asymptotic distribution of this connectivity number.In recent years the asymptotic distribution of Hamiltonian cycles in random r-regular graphs has been derived. As a generalization we investigate the asymptotic distribution of the number of cycles of length l in a random r-regular graph. The length of the cycles is defined as a function of the number of vertices n in the graph, thus, l = l(n), where l(n) → ∞ as n → ∞. The resulting limiting distribution turns out to depend on whetherl(n)/n → 0 or l(n)/n> → q, for 0 < q < 1.In the first case the limit distribution is a weighted sum of Poisson variables while in the other case the limit distribution is similar to the limit distribution of Hamiltonian cycles in a random r-regular graph.
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| 2. |
- Hoppe, Sabina, et al.
(författare)
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Soft and sour : The challenge of setting environmental quality standards for bioavailable metal concentration in Fennoscandinavian freshwaters
- 2015
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Ingår i: Environmental Science and Policy. - : Elsevier BV. - 1462-9011 .- 1873-6416. ; 54, s. 210-217
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Tidskriftsartikel (refereegranskat)abstract
- The European Union Water Framework Directive (WFD) requires member states to ensure that all inland and coastal waters achieve 'good' water quality status. To this end, the WFD has set environmental quality standards (EQS) or Water quality criteria (WQC) for priority pollutants that include the four metals Cd, Ni, Pb and Hg. Many states have also chosen to set EQS for Cu and Zn. The use of bioavailability models to set EQS, paves the way for accepting higher local metal concentrations in waters where metal bioavailability is deemed low. The Biotic Ligand Model (BLM) concept has been proposed as a tool for estimating metal bioavailability and for calculating local EQS in the EU guidance document. The BLM estimates metal bioavailability based on the dissolved metal concentration and key ancillary water chemistry parameters (acidity, hardness and organic carbon content). The BLMs developed so far, have only been validated for water chemistry input parameters typical of Central Europe. However, the pH, alkalinity and dissolved organic carbon levels of a significant fraction of Fennoscandinavian (Finland, Norway and Sweden) freshwaters are outside the calibration range of currently available BLMs. The levels of Ca2+, alkalinity and pH in 75%, 29% and 22%, respectively, of the ca. 2500 Fennoscandinavian freshwater bodies investigated in this survey were outside the calibration range of tested BLMs. Moreover, a comparison of the ability of the tested BLMs to predict the acute and chronic copper toxicity to Daphnia magma and Rainbow trout indicated that the BLMs should be used with caution outside their current validation range. We conclude that more work is needed to extend the application of BLMs in the practical risk assessment to encompass a broader range of European freshwater bodies.
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| 3. |
- Westerberg, Marcus, et al.
(författare)
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Different assumptions about missingness in registration of metastatic status have important implications for following trends in cancer presentation
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Objectives: We assessed approaches for handling missing M stage when estimating incidence trends of metastatic prostate cancer at diagnosis (M1) in Sweden. Study design and setting: We used different implementations of deterministic- and multiple imputation to handle missing M stage and estimate the age-standardized incidence of M1. Each method was assessed by studying adjusted survival of men with known and imputed M stage.Results: Missing data in M stage was high (66%) and varied over calendar time and risk groups. The estimated incidence of M1 differed greatly depending on the method of imputation, however all indicated a downward trend. A combination of deterministic imputation and multiple imputation produced adjusted survival curves for men with imputed M stage that best resembled the survival curves for men with known M stage. Conclusions: Deterministic imputation of missing M stage to M0 among men with low risk of metastatic disease in combination with multiple imputation appeared to the best method to estimate incidence of metastatic prostate cancer. Simply substituting missing M stage with M0 most likely underestimates the true incidence of M1. Inclusion of key clinical variables is important to generate plausible imputations. It is important to include data on use of imaging to handle missing M stage appropriately and assess potential bias of a chosen imputation method.
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| 4. |
- Westerberg, Marcus
(författare)
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Modelling short and long term consequences of changes in diagnostic activity and treatment
- 2020
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Since the late 90’s the diagnostic activity for prostate cancer has increased in Sweden, primarily due to increased use of PSA testing, and this has led to a large increase in diagnoses. Simultaneously, there have been changes in treatment strategies, and more effective treatments have been introduced. This thesis aims to increase the understanding of short and long term consequences of these changes by use of high quality data on virtually all men diagnosed with prostate cancer in Sweden.In paper I, the survival of men with metastatic prostate cancer at diagnosis was investigatedby use of survival models, including Kaplan-Meier analyses and Cox proportional hazards regression.The median survival from diagnosis increased with 6 months when comparing mendiagnosed 1998-2001 with men diagnosed 2010-2015, and the risk of death decreased with 13%, while median levels of prostate specific antigen at diagnosis dropped with up to 50%.In paper II, the interplay between diagnostic activity, incidence and risk of death by prostate cancer was modelled using a discrete time model. Data on diagnostic activity, e.g. in termsof testing frequencies, was not available and therefore a proxy for the diagnostic activity wasused. The hazards were estimated within the framework of generalized additive models. Two simulations were performed, assuming low and high diagnostic activity respectively, to compare incidence and mortality from 2017-2060. Higher diagnostic activity, compared to lower, led to more men being diagnosed, primarily with lower risk prostate cancer, but in the long run it led to fewer men diagnosed with metastatic disease and fewer prostate cancer deaths.
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| 5. |
- Westerberg, Marcus, 1990-
(författare)
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Prostate cancer incidence, treatment and mortality : Empirical longitudinal register-based studies and methods for handling missing data
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The diagnostic activity for prostate cancer has increased substantially in Sweden, primarily due to increased use of prostate-specific antigen (PSA) testing in asymptomatic men, and this has led to a large increase in diagnoses. There have also been changes in the diagnostic workup, guidelines, treatment strategies, and more effective treatments have been introduced in different phases of the disease. This thesis aims to increase the understanding of consequences of changes in diagnostic activity and treatment, with a focus on empirical studies, methodological development, and handling of missing data.In paper I, the survival of men with metastatic prostate cancer was investigated across calendar time periods by use of Kaplan-Meier analyses and Cox regression. The median survival from diagnosis increased with six months comparing men diagnosed 1998-2001 with men diagnosed 2010-2015, while median PSA decreased.In paper II, a discrete time multivariate longitudinal model was combined with a proxy for the unobserved level of diagnostic activity to produce prognoses of incidence and mortality. Simulations indicated that a higher diagnostic activity was associated with fewer men diagnosed with metastatic disease and fewer prostate cancer deaths.In paper III, we looked for clinical variables predictive of the survival of men with castration-resistant prostate cancer (CRPC). A new data base was created including longitudinal data on prescriptions of hormonal treatment, PSA, and cause of death. We found that PSA doubling time and PSA at time of CRCP were highly predictive and could be used for treatment decision.In paper IV, we estimated annual incidence of metastatic prostate cancer using different methods for handling missing data in metastatic status (M stage). Missing data in M stage was high and varied over calendar time and risk groups, yet each method indicated a downward trend in incidence. Although men with unknown metastatic status cannot be assumed to have nonmetastatic disease in general, this may be reasonable among those with tumour characteristics that indicate a low risk of metastases.In paper V, the estimation of multivariate longitudinal models was considered in a context where some events are observed on a coarser level (e.g. grouped) at some time points, causing gaps in the data. The likelihood function, score and observed information were derived under an independent coarsening mechanism. A simulation study was conducted comparing properties of several estimators including direct maximum likelihood and Monte Carlo Expectation Maximisation.
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| 6. |
- Westerberg, Marcus, et al.
(författare)
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Simulation model of disease incidence driven by diagnostic activity
- 2021
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Ingår i: Statistics in Medicine. - : John Wiley & Sons. - 0277-6715 .- 1097-0258. ; 40:5, s. 1172-1188
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Tidskriftsartikel (refereegranskat)abstract
- It is imperative to understand the effects of early detection and treatment of chronic diseases, such as prostate cancer, regarding incidence, overtreatment and mortality. Previous simulation models have emulated clinical trials, and relied on extensive assumptions on the natural history of the disease. In addition, model parameters were typically calibrated to a variety of data sources. We propose a model designed to emulate real-life scenarios of chronic disease using a proxy for the diagnostic activity without explicitly modeling the natural history of the disease and properties of clinical tests. Our model was applied to Swedish nation-wide population-based prostate cancer data, and demonstrated good performance in terms of reconstructing observed incidence and mortality. The model was used to predict the number of prostate cancer diagnoses with a high or limited diagnostic activity between 2017 and 2060. In the long term, high diagnostic activity resulted in a substantial increase in the number of men diagnosed with lower risk disease, fewer men with metastatic disease, and decreased prostate cancer mortality. The model can be used for prediction of outcome, to guide decision-making, and to evaluate diagnostic activity in real-life settings with respect to overdiagnosis and prostate cancer mortality.
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