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This thesis covers the analysis of radix sort, radix select and the path length of digital trees under a stochastic input assumption known as the Markov model.
The main results are asymptotic expansions of mean and variance as well as a central limit theorem for the complexity of radix sort and the path length of tries, PATRICIA tries and digital search trees.
Concerning radix select, a variety of different models for ranks are discussed including a law of large numbers for the worst case behavior, a limit theorem for the grand averages model and the first order asymptotic of the average complexity in the quantile model.
Some of the results are achieved by moment transfer techniques, the limit laws are based on a novel use of the contraction method suited for systems of stochastic recurrences.
Background: Chronic hepatitis C is a major public health burden. With new interferon-free direct-acting agents (showing sustained viral response rates of more than 98%), elimination of HCV seems feasible for the first time. However, as HCV infection often remains undiagnosed, screening is crucial for improving health outcomes of HCV-patients. Our aim was to assess the long-term cost-effectiveness of a nationwide screening strategy in Germany.
Methods: We used a Markov cohort model to simulate disease progression and examine long-term population outcomes, HCV associated costs and cost-effectiveness of HCV screening. The model divides the total population into three subpopulations: general population (GEP), people who inject drugs (PWID) and HIV-infected men who have sex with men (MSM), with total infection numbers being highest in GEP, but new infections occurring only in PWIDs and MSM. The model compares four alternative screening strategies (no/basic/advanced/total screening) differing in participation and treatment rates.
Results: Total number of HCV-infected patients declined from 275,000 in 2015 to between 125,000 (no screening) and 14,000 (total screening) in 2040. Similarly, lost quality adjusted life years (QALYs) were 320,000 QALYs lower, while costs were 2.4 billion EUR higher in total screening compared to no screening. While incremental cost-effectiveness ratio (ICER) increased sharply in GEP and MSM with more comprehensive strategies (30,000 EUR per QALY for total vs. advanced screening), ICER decreased in PWIDs (30 EUR per QALY for total vs. advanced screening).
Conclusions: Screening is key to have an efficient decline of the HCV-infected population in Germany. Recommendation for an overall population screening is to screen the total PWID subpopulation, and to apply less comprehensive advanced screening for MSM and GEP.