Estimation of small probabilities with applications to forensic genetics

When determining kinship relations based on genetic material, there is a need to quantify the probability for doing errors. These probabilities are typically very small, but nonetheless important, and needs to be controlled. It is no trivial task to estimate such small probabilities, and so the main purpose of this thesis has been to explore how they can best and most accurately be estimated. The applications in this thesis has been kinship cases in forensic genetics, but the methods are relevant also for other areas where calculations rely on the values of small probabilities. To estimate these probabilities, the simulation method of importance sampling was used. This method works by sampling from a more beneficiary distribution than the one of original interest, and then correcting for it. The precision of the estimates has also been of interest in this thesis, and is quantified in terms of the variance and MSE. These measures were used to evaluate different possible sampling distributions. The importance sampling method worked better for smaller probabilities than the straightforward simulation, but there are some trade-offs; there seems to be a difference between which distribution gives the best estimates, and which ones manage to make non-zero estimates for the smallest probabilities. As is intuitively understood, using more markers when genotyping makes it easier to correctly determine relationships, but it does however also make it harder to estimate the probabilities involved. In conclusion, we have found that relevant estimates can be found, and that these estimates can be used to add understanding to conventionally used verbal statements when evidence is presented in court. It is possible to accompany such verbal statements, like "extremely strong evidence", to tangible probabilities.Når slektskapsforhold skal bestemmes på grunnlag av genetisk materiale er det et behov for å tallfeste sannsynligheten for å gjøre feil. Disse sannsynlighetene er typisk veldig små, men likevel viktige, og må kontrolleres. Det er ingen triviell oppgave å estimere slike små sannsynligheter, og hensikten i denne avhandlingen har hovedsakelig vært å undersøke hvordan disse kan estimeres på beste og mest presise måte. For å estimere disse sannsynlighetene har simuleringsmetoden importance sampling blitt brukt. Denne metoden virker ved å trekke utvaget fra en mer gunstig fordeling enn den som opprinnelig er av interesse, for så å korrigere for dette. Presisjonen til estimatene har også vært av interesse i denne oppgaven, og har blitt tallfestet gjennom varianse og MSE. Disse målene ble brukt til å evaluere forskjellige alternative fordelinger. Metoden importance sampling virket bedre for mindre sannsynligheter enn direkte simulering, men noen avveininger må gjøress; det ser ut til å være en forskjell mellom hvilken fordeling som gir det beste estimatet, og hvilken som får til å produsere et resultat som ikke er null for de aller minste sannsynlighetene. Som man intuitivt kan forstå så blir det enklere å bestemme slektskap på en korrekt måte når flere markører tas i bruk, men samtidig blir det vanskeligere å estimere de involverte sannsynlighetene. For å konkludere, så har vi funnet at de relevante estimatene kan bestemmes, og at disse estimatene videre kan bli brukt til å øke forståelsen for konvensjonelt brukte verbale uttalelser ved presentasjon av bevis i retten. Det gir en mulighet for at slike verbale uttalelser som "ekstremt sterkt bevis" kan ledsages av håndfaste sannsynligheter.M-BIA

Silver release from dentine treated with combinations of silver diamine fluoride, potassium iodide and etching

AbstractFor individuals with very high to extremely high caries activity and poor control of daily oral hygiene, a simple treatment for arresting their caries activity is necessary. Silver Diamine Fluoride (SDF) has become increasingly common for this purpose due to its efficacy and ease of application. To avoid or reduce tooth discoloration after SDF treatment potassium iodide (KI) may be applied. However, the release of silver from SDF-treated tooth surfaces may be of concern. Thus, the aim of the present study was to quantify the amount of silver leached in both a short- and long-term perspective. In this in vitro experiment we measured the cumulative release of silver from SDF-treated dentin surfaces with and without imminent application of KI, and with and without phosphoric acid etching as pre-treatment, after 24 h and weekly for four weeks. The release of silver was highest after 24 h for all treatment groups, with a significant drop after this point. When etching was not used, the use of KI did not affect the release of silver. However, when etching was used, there was a significantly lower silver release when KI was also used compared to when KI was not used. This effect was largest for the first two weeks, after which the difference was smaller as all groups released low amounts of silver

Reduced heart rate variability is related to the number of metabolic syndrome components and manifest diabetes in the sixth Tromsø study 2007–2008

Both diabetes mellitus (DM) and the metabolic syndrome (MetS) are associated with autonomic neuropathy, which predisposes to cardiac events and death. Measures of heart rate variability (HRV) can be used to monitor the activity of the autonomic nervous system (ANS), and there are strong indications that HRV can be used to study the progression of ANS-related diabetes complications. This study aims to investigate diferences in HRV in healthy, MetS and diabetic populations. Based on 7880 participants from the sixth health survey in Tromsø (Tromsø 6, 2007–2008), we found a signifcant negative association between the number of MetS components and HRV as estimated from short-term pulse wave signals (PRV). This decrease in PRV did not appear to be linear, instead it leveled of after the third component, with no signifcant diference in PRV between the MetS and DM populations. There was a signifcant negative association between HbA1c and PRV, showing a decrease in PRV occurring already within the normal HbA1c range. The MetS and DM populations are diferent from healthy controls with respect to PRV, indicating impaired ANS in both conditions. In the future, a study with assessment of PRV measurements in relation to prospective cardiovascular events seems justifed

Estimation of heart rate variability from finger photoplethysmography during rest, mild exercise and mild mental stress

Abstract Due to the possibilities in miniaturization and wearability, photoplethysmography (PPG) has recently gained a large interest not only for heart rate measurement, but also for estimating heart rate variability, which is derived from ECG by convention. The agreement between PPG and ECG-based HRV has been assessed in several studies, but the feasibility of PPG-based HRV estimation is still largely unknown for many conditions. In this study, we assess the feasibility of HRV estimation based on finger PPG during rest, mild physical exercise and mild mental stress. In addition, we compare different variants of signal processing methods including selection of fiducial point and outlier correction. Based on five minutes synchronous recordings of PPG and ECG from 15 healthy participants during each of these three conditions, the PPG-based HRV estimation was assessed for the SDNN and RMSSD parameters, calculated based on two different fiducial points (foot point and maximum slope), with and without outlier correction. The results show that HRV estimation based on finger PPG is feasible during rest and mild mental stress, but can give large errors during mild physical exercise. A good estimation is very dependent on outlier correction and fiducial point selection, and SDNN seems to be a more robust parameter compared to RMSSD for PPG-based HRV estimation