Fitting additive risk models using auxiliary information.

There has been a growing interest in incorporating auxiliary summary information from external studies into the analysis of internal individual-level data. In this paper, we propose an adaptive estimation procedure for an additive risk model to integrate auxiliary subgroup survival information via a penalized method of moments technique. Our approach can accommodate information from heterogeneous data. Parameters to quantify the magnitude of potential incomparability between internal data and external auxiliary information are introduced in our framework while nonzero components of these parameters suggest a violation of the homogeneity assumption. We further develop an efficient computational algorithm to solve the numerical optimization problem by profiling out the nuisance parameters. In an asymptotic sense, our method can be as efficient as if all the incomparable auxiliary information is accurately acknowledged and has been automatically excluded from consideration. The asymptotic normality of the proposed estimator of the regression coefficients is established, with an explicit formula for the asymptotic variance-covariance matrix that can be consistently estimated from the data. Simulation studies show that the proposed method yields a substantial gain in statistical efficiency over the conventional method using the internal data only, and reduces estimation biases when the given auxiliary survival information is incomparable. We illustrate the proposed method with a lung cancer survival study.

EFFICIENT ESTIMATION OF THE MAXIMAL ASSOCIATION BETWEEN MULTIPLE PREDICTORS AND A SURVIVAL OUTCOME.

This paper develops a new approach to post-selection inference for screening high-dimensional predictors of survival outcomes. Post-selection inference for right-censored outcome data has been investigated in the literature, but much remains to be done to make the methods both reliable and computationally-scalable in high-dimensions. Machine learning tools are commonly used to provide predictions of survival outcomes, but the estimated effect of a selected predictor suffers from confirmation bias unless the selection is taken into account. The new approach involves the construction of semi-parametrically efficient estimators of the linear association between the predictors and the survival outcome, which are used to build a test statistic for detecting the presence of an association between any of the predictors and the outcome. Further, a stabilization technique reminiscent of bagging allows a normal calibration for the resulting test statistic, which enables the construction of confidence intervals for the maximal association between predictors and the outcome and also greatly reduces computational cost. Theoretical results show that this testing procedure is valid even when the number of predictors grows superpolynomially with sample size, and our simulations support this asymptotic guarantee at moderate sample sizes. The new approach is applied to the problem of identifying patterns in viral gene expression associated with the potency of an antiviral drug.

Examining the Role of Aging Perceptions in Subjective Cognitive Decline.

OBJECTIVE: While subjective cognitive decline (SCD) is gaining ground as a "preclinical" risk state for Alzheimer disease, its utility depends on our understanding of the factors linked to SCD. Rarely examined sociocultural factors including perceptions of aging may relate to the subjective experience of cognitive aging. Identifying such associations will help to refine the utility of SCD as an early marker of AD while setting the stage for addressing modifiable factors contributing to SCD. METHODS: The study consisted of N=136 participants (68% female; 73% White; 22% Black race, age mean =74.72; education mean =16.01). Questionnaires assessed SCD, depressive symptoms, and age perceptions (essentialist aging beliefs, subjective age, age group identification, and explicit/implicit age stereotypes). Cognitive functioning was measured with a semantic interference and learning task. RESULTS: SCD was correlated with essentialist aging beliefs, age identification, and depressive symptoms [ rrange =0.18 to 0.22, Prange =0.009 to 0.02, confidence interval (CI) range =0.00-0.39]. Essentialist aging beliefs were correlated with subjective age and age group identification ( rrange =0.22 to 0.42, Prange <0.001 to 0.003, CI range =0.08-0.57). Both age group identification and essentialism were correlated with depressive symptoms ( rrange =0.22, Prange =0.009 to 0.01, CI range =0.04-0.39). In the adjusted regression model including depressive symptoms, age perceptions, and SCD, only SCD was associated with cognition ( b =-0.31, P <0.001). CONCLUSION: Although correlated with SCD, perceptions of aging do not explain the relationship between SCD and performance on a sensitive cognitive test among older adults.

Maternal serum persistent organic pollutant exposure and offspring diagnosed ADHD in a national birth cohort.

BACKGROUND: Evidence implicates environmental factors in attention-deficit/hyperactivity disorder (ADHD) risk. Prenatal exposures to polychlorinated biphenyls (PCBs) and the pesticide metabolite p,p'-dichlorodiphenyl dichloroethylene (DDE) have been linked to lower cognitive ability, increased impulsivity, and attention related deficits in the offspring. However, information on the relationship of these exposures to the risk of clinically diagnosed ADHD is limited. OBJECTIVES: To determine whether prenatal maternal levels of PCBs or DDE are associated with ADHD diagnosis in the offspring. METHODS: The investigation was conducted in the Finnish Prenatal Study of ADHD (FIPS-ADHD), a case-control study nested in a national birth cohort. Cases were born in 1998 or 1999 and diagnosed with ADHD (ICD-9 314x or ICD-10 F90. x) according to the national Care Register for Health Care. Each case was individually matched to a control on sex, date, and place of birth. PCB congeners (PCB 74, 99, 118, 138, 153, 156, 170, 180, 183, 187) and DDE were quantified from archived prenatal maternal sera from 359 matched case-control pairs using gas chromatography - high triple quadrupole mass spectrometry. Maternal total PCBs were quantified as the sum of concentrations of the measured congeners. Associations with ADHD were examined using conditional logistic regression. RESULTS: Maternal PCB or DDE levels greater than the 75th percentiles of the control distributions showed no evidence of association with offspring ADHD (PCBs: adjusted odds ratio (aOR) = 1.01, 95% CI = 0.63, 1.60), p = 0.98; DDE: aOR = 1.13, 95% CI = 0.71, 1.81; p = 0.60). Maternal levels of either pollutant dichotomized at the 90th percentile or considered as a continuous variable also did not show evidence for association with offspring ADHD diagnosis. DISCUSSION: This study did not find evidence for association of maternal prenatal levels of PCBs or DDE with clinical diagnosis of offspring ADHD; however, this does not rule out the possibility of an impact on subclinical phenotypes.

Increased Risk of ADHD at Short and Long Interpregnancy Intervals in a National Birth Cohort.

BACKGROUND: Short or long interpregnancy interval (IPI) may adversely impact conditions for foetal development. Whether attention deficit hyperactivity disorder (ADHD) is related to IPI has been largely unexplored. OBJECTIVES: To examine the association between IPI and ADHD in a large, population-based Finnish study. METHODS: All children born in Finland between 1991 and 2005 and diagnosed with ADHD (ICD-9 314x or ICD-10 F90.x) from 1995 to 2011 were identified using data from linked national registers. Each subject with ADHD was matched to 4 controls based on sex, date of birth, and place of birth. A total of 9564 subjects with ADHD and 34,479 matched controls were included in analyses. IPI was calculated as the time interval between sibling birth dates minus the gestational age of the second sibling. The association between IPI and ADHD was determined using conditional logistic regression and adjusted for potential confounders. RESULTS: Relative to births with an IPI of 24 to 59 months, those with the shortest IPI (<6 months) had an increased risk of ADHD (odds ratio [OR] 1.30, 95% confidence interval (CI) 1.12, 1.51) and the ORs for the longer IPI births (60-119 months and ≥120 months) were 1.12 (95% CI 1.02, 1.24) and 1.25 (95% CI 1.08, 1.45), respectively. The association of longer IPI with ADHD was attenuated by adjustment for maternal age at the preceding birth, and comorbid autism spectrum disorders did not explain the associations with ADHD. CONCLUSIONS: The risk of ADHD is higher among children born following short or long IPIs although further studies are needed to explain this association.

Maternal serum Vitamin B12 and offspring attention-deficit/hyperactivity disorder (ADHD).

Maternal Vitamin B12 deficiency during pregnancy is associated with offspring neuropsychiatric disorders. Few previous studies examining this association with attention-deficit/hyperactivity disorder (ADHD) report inconsistent findings. The study examines the association between maternal serum Vitamin B12 levels and offsprings' risk of ADHD. This study is based on the Finnish Prenatal Study of ADHD with a nested case-control design. All the singleton children born in Finland between January 1998 and December 1999 and diagnosed with ADHD were included in the study. A total of 1026 cases were matched with an equal number of controls on sex, date of birth and place of birth. Maternal Vitamin B12 levels were assessed using a chemiluminescence microparticle immunoassay and archived from maternal serum banks, collected during the first and early second trimester of pregnancy. Lower maternal Vitamin B12 levels when analyzed as a continuous variable was not associated with offspring ADHD (aOR 0.97, 95% CI 0.79-1.18, p = 0.75). No significant associations were seen in the lowest quintile of Vitamin B12 levels (aOR 0.96, 95% CI 0.73-1.27, p = 0.80). This is the first study examining maternal sera Vitamin B12 levels during early pregnancy and offspring ADHD. The result suggests that Vitamin B12 deficiency during early pregnancy has specificity for some disorders but not with offspring ADHD.

Protocol for a family-centered behavioral intervention to reduce early childhood caries: the MySmileBuddy program efficacy trial.

BACKGROUND: Although largely preventable through diet management and topical fluoride use, early childhood caries (ECC) often progresses to severity that necessitates surgical repair. Yet repair often fails to mitigate caries progression. Needed is an effective behavioral intervention to address underlying behavioral causes. METHODS: This randomized controlled trial will evaluate the efficacy of a behaviorally focused, family-centered intervention, the MySmileBuddy Program (MSB Program), to reduce ECC progression in high-risk preschoolers in New York City. Recruitment will target 858 children ages 24-71 months with ECC and their parents from primary care medical and dental clinics. The study aims to assess the MSB Program's efficacy to: (1) decrease ECC progression measured 12-months post-randomization; and (2) enhance adoption of a low cariogenic diet and twice-daily fluoridated toothpaste use compared to control group. Potential causal pathways (mediators and moderators) will be explored. The MSB Program equips community health workers (CHWs) with an app that facilitates multilevel risk assessment and provides motivational interviewing-based counseling to inform parents about the caries process, develop personalized goals, and create family-level action plans to achieve targeted behaviors. Social support from CHWs (4 interactions during the 6-month intervention, supplemented by up to 4 in-person/remote contacts throughout the 12-month study period, based on need) is bolstered by automated text messages. Participants will be randomized to a Control Group (paper-based educational handout plus toothbrushes and fluoridated toothpaste for the child) or Intervention Group (MSB Program, two tooth-brushing observations with feedback and instruction, and toothbrushes and toothpaste for the entire family). All children will receive visual ICDAS dental examinations and parents will complete study measures at baseline and 12-months. An incentive up to $150 plus round-trip transit cards ($5.50 value) will be provided. DISCUSSION: This study hypothesizes that the MSB Program can reduce ECC progression in a high-risk population. Sufficient incentives and a focus on establishing rapport between participants and CHWs are anticipated to mitigate recruitment and retention challenges. If successful, this study will advance the long-term goal of reducing pediatric oral health disparities by demonstrating the efficacy of an acceptable and feasible intervention that shifts attention from dental repair to behavioral risk mitigation. TRIAL REGISTRATION: Trial registration was completed on 4/13/2021 through the U.S. National Library of Medicine ClinicalTrials.gov website (Identifier: NCT04845594).

Marginal screening of 2 × 2 tables in large-scale case-control studies.

Assessing the statistical significance of risk factors when screening large numbers of 2×2 tables that cross-classify disease status with each type of exposure poses a challenging multiple testing problem. The problem is especially acute in large-scale genomic case-control studies. We develop a potentially more powerful and computationally efficient approach (compared with existing methods, including Bonferroni and permutation testing) by taking into account the presence of complex dependencies between the 2×2 tables. Our approach gains its power by exploiting Monte Carlo simulation from the estimated null distribution of a maximally selected log-odds ratio. We apply the method to case-control data from a study of a large collection of genetic variants related to the risk of early onset stroke.

NONPARAMETRIC TESTING FOR MULTIPLE SURVIVAL FUNCTIONS WITH NON-INFERIORITY MARGINS.

New nonparametric tests for the ordering of multiple survival functions are developed with the possibility of right censorship taken into account. The motivation comes from non-inferiority trials with multiple treatments. The proposed tests are based on nonparametric likelihood ratio statistics, which are known to provide more powerful tests than Wald-type procedures, but in this setting have only been studied for pairs of survival functions or in the absence of censoring. We introduce a novel type of pool adjacent violator algorithm that leads to a complete solution of the problem. The limit distributions can be expressed as weighted sums of squares involving projections of certain Gaussian processes onto the given ordered alternative. A simulation study shows that the new procedures have superior power to a competing combined-pairwise Cox model approach. We illustrate the proposed methods using data from a three-arm non-inferiority trial.

Marginal screening for high-dimensional predictors of survival outcomes.

This study develops a marginal screening test to detect the presence of significant predictors for a right-censored time-to-event outcome under a high-dimensional accelerated failure time (AFT) model. Establishing a rigorous screening test in this setting is challenging, because of the right censoring and the post-selection inference. In the latter case, an implicit variable selection step needs to be included to avoid inflating the Type-I error. A prior study solved this problem by constructing an adaptive resampling test under an ordinary linear regression. To accommodate right censoring, we develop a new approach based on a maximally selected Koul-Susarla-Van Ryzin estimator from a marginal AFT working model. A regularized bootstrap method is used to calibrate the test. Our test is more powerful and less conservative than both a Bonferroni correction of the marginal tests and other competing methods. The proposed method is evaluated in simulation studies and applied to two real data sets.

Stein's method and approximating the quantum harmonic oscillator.

Hall et al. (2014) recently proposed that quantum theory can be understood as the continuum limit of a deterministic theory in which there is a large, but finite, number of classical "worlds." A resulting Gaussian limit theorem for particle positions in the ground state, agreeing with quantum theory, was conjectured in Hall et al. (2014) and proven by McKeague and Levin (2016) using Stein's method. In this article we show how quantum position probability densities for higher energy levels beyond the ground state may arise as distributional fixed points in a new generalization of Stein's method These are then used to obtain a rate of distributional convergence for conjectured particle positions in the first energy level above the ground state to the (two-sided) Maxwell distribution; new techniques must be developed for this setting where the usual "density approach" Stein solution (see Chatterjee and Shao (2011)) has a singularity.

Hybrid combinations of parametric and empirical likelihoods.

This paper develops a hybrid likelihood (HL) method based on a compromise between parametric and nonparametric likelihoods. Consider the setting of a parametric model for the distribution of an observation Y with parameter θ. Suppose there is also an estimating function m(·, µ) identifying another parameter µ via Em(Y, µ) = 0, at the outset defined independently of the parametric model. To borrow strength from the parametric model while obtaining a degree of robustness from the empirical likelihood method, we formulate inference about θ in terms of the hybrid likelihood function Hn (θ) = Ln (θ)1-a Rn (µ(θ)) a . Here a ∈ [0,1) represents the extent of the compromise, Ln is the ordinary parametric likelihood for θ, Rn is the empirical likelihood function, and µ is considered through the lens of the parametric model. We establish asymptotic normality of the corresponding HL estimator and a version of the Wilks theorem. We also examine extensions of these results under misspecification of the parametric model, and propose methods for selecting the balance parameter a.

Convergence of empirical distributions in an interpretation of quantum mechanics.

From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the interaction of finitely many classical "worlds." The wave function is then recovered (as a secondary object) from observations of particles in these worlds, without knowing the world from which any particular observation originates. Hall, Deckert and Wiseman [Physical Review X 4 (2014) 041013] have introduced an explicit many-interacting-worlds harmonic oscillator model to provide support for this approach. In this note we provide a proof of their claim that the particle configuration is asymptotically Gaussian, thus matching the stationary ground-state solution of Schrödinger's equation when the number of worlds goes to infinity. We also construct a Markov chain based on resampling from the particle configuration and show that it converges to an Ornstein-Uhlenbeck process, matching the time-dependent solution as well.

Central Limit Theorems under additive deformations.

Additive deformations of statistical systems arise in various areas of physics. Classical central limit theory is then no longer applicable, even when standard independence assumptions are preserved. This paper investigates ways in which deformed algebraic operations lead to distinctive central limit theory. We establish some general central limit results that are applicable to a range of examples arising in nonextensive statistical mechanics, including the addition of momenta and velocities via Kaniadakis addition, and Tsallis addition. We also investigate extensions to random additive deformations, and find evidence (based on simulation studies) for a universal limit specific to each statistical system.

Tests for stochastic ordering under biased sampling.

In two-sample comparison problems it is often of interest to examine whether one distribution function majorizes the other, i.e., for the presence of stochastic ordering. This paper develops a nonparametric test for stochastic ordering from size-biased data, allowing the pattern of the size bias to differ between the two samples. The test is formulated in terms of a maximally-selected local empirical likelihood statistic. A Gaussian multiplier bootstrap is devised to calibrate the test. Simulation results show that the proposed test outperforms an analogous Wald-type test, and that it provides substantially greater power over ignoring the size bias. The approach is illustrated using data on blood alcohol concentration of drivers involved in car accidents, where the size bias is due to drunker drivers being more likely to be involved in accidents. Further, younger drivers tend to be more affected by alcohol, so in making comparisons with older drivers the analysis is adjusted for differences in the patterns of size bias.

Central limit theorems under special relativity.

Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.

Estimation of treatment policies based on functional predictors.

Biosignatures such as brain scans, mass spectrometry, or gene expression profiles might one day be used to guide treatment selection and improve outcomes. This article develops a way of estimating optimal treatment policies based on data from randomized clinical trials by interpreting patient biosignatures as functional predictors. A flexible functional regression model is used to represent the treatment effect and construct the estimated policy. The effectiveness of the estimated policy is assessed by furnishing prediction intervals for the mean outcome when all patients follow the policy. The validity of these prediction intervals is established under mild regularity conditions on the functional regression model. The performance of the proposed approach is evaluated in numerical studies.

Finnish Prenatal Study of Bipolar Disorders (FIPS-B): overview, design and description of the sample.

BACKGROUND: Bipolar disorders (BPD) are chronic mental illnesses, the development of which involves genetic factors and environmental influences. AIMS: The aim of this paper is to provide an overall description of the Finnish Prenatal Study of Bipolar Disorders (FIPS-B), including the study design, national registers and linkage of the registers. METHODS: FIPS-B is a population-based prenatal epidemiological study of BPD with a nested case-control study design using several national registers. The registers used are: the Finnish Medical Birth Register (FMBR), the Finnish Hospital Discharge Register (FHDR), the Population Central Register and the Finnish Maternity Cohort (FMC), which are linked using the unique personal identity code (PIC). FIPS-B includes all children born from January 1, 1983 to December 31, 1998 and diagnosed with BPD in Finland by December 31, 2008. RESULTS: The total number of cases included in the FIPS-B is 1887. The age at first diagnosis ranged from 4 to 25 years. Half (50.4%) of the cases utilized only outpatient services, 12.7% only inpatient services and the rest (36.9%) utilized both services. Offspring of mothers with the lowest educational level had an increased odds of BPD (OR = 1.46, 95% CI 1.13-1.88). The cumulative incidence of BPD in the population aged 25 years or younger was 11.6/10,000 in 2008. CONCLUSIONS: FIPS-B has all the strengths of a register-based prenatal epidemiological study, along with the availability of maternal biomarkers, enabling it to examine several prenatal, perinatal and familial risk factors for BPD.

Maternal vitamin D levels during pregnancy and offspring schizophrenia.

BACKGROUND: Findings from previous studies on maternal 25(OH)D levels during pregnancy and offspring schizophrenia are limited and inconsistent. METHODS: We used nationwide population-based register data with a nested case-control design to examine the association between maternal 25(OH)D levels during pregnancy and offspring schizophrenia. The cases of schizophrenia (n = 1145) were born from 1987 to 1997, and received a diagnosis of schizophrenia by 2017, and were matched with equal number of controls. A quantitative immunoassay was used to measure maternal 25(OH)D in archived maternal serum in the national biobank of the Finnish Maternity Cohort, collected during the first and early second trimesters. Conditional logistic regression models examined the association between maternal 25(OH)D levels and offspring schizophrenia. RESULTS: No significant association was found between log-transformed maternal 25(OH)D levels and schizophrenia in unadjusted (OR 0.96, 95 % CI 0.78-1.17, p = 0.69) or adjusted analyses (aOR 0.98, 95 % CI 0.79-1.22, p = 0.89). Analyses by quintiles also revealed no association between the lowest quintile of maternal 25(OH)D levels and schizophrenia (OR 1.09, 95 % CI 0.81-1.45, p = 0.55; aOR 1.06, 95 % CI 0.78-1.45, p = 0.71). Maternal 25(OH)D levels, measured in categories, either in deficient category (OR 1.07 (0.85-1.35), p = 0.52; aOR 1.05 (0.81-1.34), p = 0.88) or insufficient category (OR 1.13, 95 % CI 0.92-1.40, p = 0.23; aOR 1.13, 95 % CI 0.90-1.41, p = 0.27) were also not associated with offspring schizophrenia. CONCLUSIONS: Maternal vitamin D levels in early pregnancy were not associated with offspring schizophrenia. Future studies measuring vitamin D during different stages of gestation are needed to draw firm conclusions.

Recovering gradients from sparsely observed functional data.

The recovery of gradients of sparsely observed functional data is a challenging ill-posed inverse problem. Given observations of smooth curves (e.g., growth curves) at isolated time points, the aim is to provide estimates of the underlying gradients (or growth velocities). To address this problem, we develop a Bayesian inversion approach that models the gradient in the gaps between the observation times by a tied-down Brownian motion, conditionally on its values at the observation times. The posterior mean and covariance kernel of the growth velocities are then found to have explicit and computationally tractable representations in terms of quadratic splines. The hyperparameters in the prior are specified via nonparametric empirical Bayes, with the prior precision matrix at the observation times estimated by constrained ℓ1 minimization. The infinitessimal variance of the Brownian motion prior is selected by cross-validation. The approach is illustrated using both simulated and real data examples.