A non linear parabolic equation with noise : a reduction method

In this paper we study a class of parabolic equations with a non-linear gradient term. The system is disturbed by white noise in time. We show that the solution of this problem can be represented as the Wick product between a normalized random variable of exponential form and the solution of a nonlinear parabolic equation. We allow random initial data which might be anticipating. A relation between the Wick product with a normalized exponential and translation is proved in order to establish our results

Svangerskapsdatering

SAMMENDRAG Svangerskapsdatering er et komplekst felt med mange aspekter. Minst tre svært forskjellige metoder for datering er i bruk: siste menstruasjon, ultralyd samt tidspunkt for fertilisering eller overføring av embryo ved in vitro-fertilisering. Bare innenfor ultralyddatering finnes en stor mengde forskjellige “formler” for datering. Jeg gir her en kort oversikt over de forskjellige tilnærmingene til svangerskapsdatering og viser noen av prinsippene bak populasjonsbasert ultralyddatering. ENGLISH ABSTRACT Pregnancy dating is a complex and multifaceted field. At least three very different methods for dating are commonly used: last menstrual period, ultrasound, and date of fertilization or embryo transfer during in vitro fertilization. Within ultrasound dating alone there is a wide range of different “formulas” for dating. I present a short overview over the different approaches to pregnancy dating and show some of the principles behind population-based ultrasound dating

MinLinMo: a minimalist approach to variable selection and linear model prediction

Generating prediction models from high dimensional data often result in large models with many predictors. Causal inference for such models can therefore be difficult or even impossible in practice. The stand-alone software package MinLinMo emphasizes small linear prediction models over highest possible predictability with a particular focus on including variables correlated with the outcome, minimal memory usage and speed. MinLinMo is demonstrated on large epigenetic datasets with prediction models for chronological age, gestational age, and birth weight comprising, respectively, 15, 14 and 10 predictors. The parsimonious MinLinMo models perform comparably to established prediction models requiring hundreds of predictors.publishedVersio

Biparietal diameter vs crown–rump length as standard parameter for late first-trimester pregnancy dating

Objective: To compare the precision of biparietal diameter (BPD) and crown–rump length (CRL) as predictors of gestational age in the human fetus in the late first and early second trimesters, using a population-based approach. Methods: We constructed term and gestational-age prediction curves for first-trimester dating, based on 11 041 pregnancies with 12 260 measurements of CRL and/or BPD from a population-based Norwegian clinical database. We used a population-based approach with local linear quantile regression, combined with a time-to-event strategy that compensates for induced births. Term prediction precision was assessed by estimating and comparing the prediction residual curves using a time-to-event analysis. Individual differences in gestational-age predictions from CRL and BPD were assessed using measurements performed on the same fetus on the same day. A sensitivity analysis was performed to evaluate the effect of not distinguishing between non-spontaneous and spontaneous births. Results: CRL and BPD provided almost identical term prediction precision judged from the residual distribution. In about 51% of examinations, the difference in predicted gestational age was 1 day or less; 24% of examinations had a difference of 2 days, 14% had a difference of 3 days, 7% had a difference of 4 days and only 5% of all examinations had a difference of 5 days or more. Incorrectly removing induced births from the analysis, or treating them as spontaneous, would cause a substantial systematic prediction bias of about 2 days. Conclusions: Based on population data, using comparisons at an individual level, our study found that BPD is as precise as CRL when used for first-trimester dating. BPD has advantages from a clinical point of view, since it is technically less challenging and less time-consuming to measure compared with CRL, and can be measured and assessed throughout the entire pregnancy.publishedVersio

A fast wavelet-based functional association analysis replicates several susceptibility loci for birth weight in a Norwegian population

Background Birth weight (BW) is one of the most widely studied anthropometric traits in humans because of its role in various adult-onset diseases. The number of loci associated with BW has increased dramatically since the advent of whole-genome screening approaches such as genome-wide association studies (GWASes) and meta-analyses of GWASes (GWAMAs). To further contribute to elucidating the genetic architecture of BW, we analyzed a genotyped Norwegian dataset with information on child’s BW (N=9,063) using a slightly modified version of a wavelet-based method by Shim and Stephens (2015) called WaveQTL. Results WaveQTL uses wavelet regression for regional testing and offers a more flexible functional modeling framework compared to conventional GWAS methods. To further improve WaveQTL, we added a novel feature termed “zooming strategy” to enhance the detection of associations in typically small regions. The modified WaveQTL replicated five out of the 133 loci previously identified by the largest GWAMA of BW to date by Warrington et al. (2019), even though our sample size was 26 times smaller than that study and 18 times smaller than the second largest GWAMA of BW by Horikoshi et al. (2016). In addition, the modified WaveQTL performed better in regions of high LD between SNPs. Conclusions This study is the first adaptation of the original WaveQTL method to the analysis of genome-wide genotypic data. Our results highlight the utility of the modified WaveQTL as a complementary tool for identifying loci that might escape detection by conventional genome-wide screening methods due to power issues. An attractive application of the modified WaveQTL would be to select traits from various public GWAS repositories to investigate whether they might benefit from a second analysis.publishedVersio

Parent-of-origin-environment interactions in case-parent triads with or without independent controls

With case–parent triad data, one can frequently deduce parent of origin of the child's alleles. This allows a parent‐of‐origin (PoO) effect to be estimated as the ratio of relative risks associated with the alleles inherited from the mother and the father, respectively. A possible cause of PoO effects is DNA methylation, leading to genomic imprinting. Because environmental exposures may influence methylation patterns, gene–environment interaction studies should be extended to allow for interactions between PoO effects and environmental exposures (i.e., PoOxE). One should thus search for loci where the environmental exposure modifies the PoO effect. We have developed an extensive framework to analyze PoOxE effects in genome‐wide association studies (GWAS), based on complete or incomplete case–parent triads with or without independent control triads. The interaction approach is based on analyzing triads in each exposure stratum using maximum likelihood estimation in a log‐linear model. Interactions are then tested applying a Wald‐based posttest of parameters across strata. Our framework includes a complete setup for power calculations. We have implemented the models in the R software package Haplin. To illustrate our PoOxE test, we applied the new methodology to top hits from our previous GWAS, assessing whether smoking during the periconceptional period modifies PoO effects on cleft palate only.publishedVersio

Estimation of fetal weight in pregnancies past term

Introduction: The aim of the study was to investigate the accuracy of estimating fetal weight with ultrasound in pregnancies past term, using the eSnurra algorithm. Material and methods: In all, 419 women with pregnancy length of 290 days, attending a specialist consultation at Stavanger University Hospital, Norway, were included in a prospective observational study. Fetal weight was estimated using biparietal diameter (BPD) and abdominal circumference (AC). The algorithm implemented in an electronic calculation (eSnurra) was used to compute estimated fetal weight (EFW). Results were compared with birthweight (BW). Results: The mean interval between the ultrasound examination and birth was 2 days (SD 1.4). The median difference between BW and EFW was −6 g (CI −40 to +25 g) and the median percentage error was –0.1% (95% CI −1.0 to 0.6%). The median absolute difference was 190 g (95% CI 170–207 g). The BW was within 10% of EFW in 83% (95% CI 79–87%) of cases and within 15% of EFW in 94% (95% CI 92–96%) of cases. Limits of agreement (95%) were from −553 g to +556 g. Using 5% false‐positive rates, the sensitivity in detecting macrosomic and small for gestational age fetuses was 54% (95% CI 35–72%) and 49% (95% CI 35–63%), respectively. Conclusion: The accuracy of fetal weight estimation was good. Clinicians should be aware of limitations related to prediction at the upper and lower end, and the importance of choosing appropriate cut‐off levels.publishedVersio

Effect of polygenic scores of telomere length alleles on telomere length in newborns and parents

In adults, polygenic scores (PGSs) of telomere length (TL) alleles explain about 4.5% of the variance in TL, as measured by quantitative polymerase chain reaction (qPCR). Yet, these PGSs strongly infer a causal role of telomeres in aging-related diseases. To better understand the determinants of TL through the lifespan, it is essential to examine to what extent these PGSs explain TL in newborns. This study investigates the effect of PGSs on TL in both newborns and their parents, with TL measured by Southern blotting and expressed in base-pairs (bp). Additionally, the study explores the impact of PGSs related to transmitted or non-transmitted alleles on TL in newborns. For parents and newborns, the PGS effects on TL were 172 bp (p =  2.03 × 10−15) and 161 bp (p =  3.06 × 10−8), explaining 6.6% and 5.2% of the TL variance, respectively. The strongest PGS effect was shown for maternally transmitted alleles in newborn girls, amounting to 214 bp (p =  3.77 × 10−6) and explaining 7.8% of the TL variance. The PGS effect of non-transmitted alleles was 56 bp (p = 0.0593) and explained 0.6% of the TL variance. Our findings highlight the importance of TL genetics in understanding early-life determinants of TL. They point to the potential utility of PGSs composed of TL alleles in identifying susceptibility to aging-related diseases from birth and reveal the presence of sexual dimorphism in the effect of TL alleles on TL in newborns. Finally, we attribute the higher TL variance explained by PGSs in our study to TL measurement by Southern blotting.publishedVersio