Prenatal organochlorine pollutant exposure and risk of schizophrenia in a national birth cohort.

Non-genetic prenatal exposures have been associated with schizophrenia risk. However, the role of prenatal exposure to environmental neurotoxicants in offspring schizophrenia risk has been studied in only limited instances. Polychlorinated biphenyls (PCBs) and the pesticide metabolite p,p'-dichlorodiphenyl dichloroethylene (DDE) have been linked to neurodevelopmental outcomes, including impairments implicated in schizophrenia. To determine whether prenatal maternal levels of organochlorine pollutants including PCBs or DDE are associated with schizophrenia in the offspring, an investigation was conducted in the Finnish Prenatal Study of Schizophrenia (FIPS-S), a case-control study nested in a national birth cohort. Cases were born in 1987-1991 and had at least two diagnoses of schizophrenia (ICD-10 F20; ICD-9 295) or schizoaffective disorder (ICD-10 F25; ICD-9 295.7) recorded in the national Care Register for Health Care. Each case was individually matched to a control on sex, date of birth, and residence in Finland on the date of case diagnosis. In 500 case-control pairs, PCB congeners 74, 99, 118, 138, 153, 156, 170, 180, 183, 187, and some widespread organochlorine pesticides or their metabolites including DDE were measured in archived prenatal maternal sera using gas chromatography - high triple quadrupole mass spectrometry. Maternal total PCBs were quantified as the sum of concentrations of the measured congeners. Associations with schizophrenia were examined using conditional logistic regression. Maternal PCB or DDE levels greater than the 75th percentiles of the control distributions showed no evidence of association with offspring schizophrenia (PCBs: adjusted odds ratio (aOR) = 1.13, 95 % CI = 0.85-1.50), p = 0.41; DDE: aOR = 1.08, 95 % CI = 0.80-1.45; p = 0.63). 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 schizophrenia. This study found a lack of evidence that prenatal maternal levels of the organochlorine pollutants DDE and PCBs are associated with offspring risk of schizophrenia.

Maternal Serum Vitamin B12 during Pregnancy and Offspring Autism Spectrum Disorder.

This study examined the association between maternal serum vitamin B12 levels during early pregnancy and offspring autism spectrum disorders (ASD) and subtypes. Based on a Finnish national birth cohort, case offspring (n = 1558) born in 1987-2007 and diagnosed with ASD by 2015 were matched with one control on date of birth, sex and place of birth. Maternal vitamin B12 levels were measured during first and early second trimesters of pregnancy. High maternal vitamin B12 levels (≥81th percentile) was associated with increased risk for offspring childhood autism, adjusted odds ratio, 1.59, 95% confidence interval 1.06-2.41 (p = 0.026). No significant associations were observed between maternal vitamin B12 levels and offspring Asperger's or pervasive developmental disorder/NOS.

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.

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.

Significance testing for canonical correlation analysis in high dimensions.

We consider the problem of testing for the presence of linear relationships between large sets of random variables based on a post-selection inference approach to canonical correlation analysis. The challenge is to adjust for the selection of subsets of variables having linear combinations with maximal sample correlation. To this end, we construct a stabilized one-step estimator of the euclidean-norm of the canonical correlations maximized over subsets of variables of pre-specified cardinality. This estimator is shown to be consistent for its target parameter and asymptotically normal, provided the dimensions of the variables do not grow too quickly with sample size. We also develop a greedy search algorithm to accurately compute the estimator, leading to a computationally tractable omnibus test for the global null hypothesis that there are no linear relationships between any subsets of variables having the pre-specified cardinality. We further develop a confidence interval that takes the variable selection into account.

Maternal Vitamin D Levels During Pregnancy and Offspring Autism Spectrum Disorder.

BACKGROUND: Findings from previous studies on maternal 25-hydroxyvitamin D [25(OH)D] levels during pregnancy and autism spectrum disorder (ASD) in offspring are inconsistent. METHODS: The association between maternal 25(OH)D levels during pregnancy and offspring ASD was examined using data from a nationwide population-based register with a nested case-control study design. The ASD cases (n = 1558) were born between 1987 and 2004 and received a diagnosis of ASD by 2015; cases were matched with an equal number of controls. Maternal 25(OH)D levels during pregnancy were measured using quantitative immunoassay from maternal sera collected during the first and early second trimesters and archived in the national biobank of the Finnish Maternity Cohort. Conditional logistic regression examined the association between maternal 25(OH)D levels and offspring ASD. RESULTS: In the adjusted model, there was a significant association between increasing log-transformed maternal 25(OH)D levels and decreasing risk of offspring ASD (adjusted odds ratio [aOR] 0.75, 95% confidence interval [CI] 0.62-0.92, p = .005). Analyses by quintiles of maternal 25(OH)D levels revealed increased odds for ASD in the 2 lowest quintiles, <20 (aOR 1.36, 95% CI 1.03-1.79, p = .02) and 20-39 (aOR 1.31, 95% CI 1.01-1.70, p = .04), compared with the highest quintile. The increased risk of ASD was observed in association with deficient (<30 nmol/L) (aOR 1.44, 95% CI 1.15-1.81, p = .001) and insufficient (30-49.9 nmol/L) maternal 25(OH)D levels (aOR 1.26, 95% CI 1.04-1.52, p = .01) compared with sufficient levels. CONCLUSIONS: This finding has implications for understanding the role of maternal vitamin D during fetal brain development and increased risk of ASD.

A biomarker-based study of prenatal smoking exposure and autism in a Finnish national birth cohort.

Maternal exposure to tobacco smoke during pregnancy is a common and persistent exposure linked to adverse neurodevelopmental outcomes in the offspring. However, previous studies provide mixed evidence regarding the relationship between prenatal smoking and offspring autism. This study used cotinine level, a biomarker for nicotine, to investigate the relationship between prenatal smoking and autism. The authors conducted a population-based case-control study nested in a national cohort of all births in Finland from 1987 to 2005. Cases diagnosed with childhood autism (ICD-10/9 code F84.0/299.0) through 2007 were identified using data from linked national registers. Each case was matched with a control on date of birth (±30 days), sex, and place of birth (N = 962 pairs). Maternal serum cotinine levels were prospectively measured in first- to early second-trimester serum samples archived in a national biobank using a quantitative immunoassay. Data were analyzed using conditional logistic regression. Prenatal maternal levels of serum cotinine were not associated with the odds of autism, whether cotinine was classified continuously, by deciles, or using previously defined categories corresponding to probable maternal smoking status. After adjusting for maternal age, paternal age, previous births, and any history of parental psychiatric disorder, the odds ratio for categorical high versus low cotinine, using a 3-level exposure variable, was 0.98 (95% CI = 0.76, 1.26; p = 0.88). In conclusion, this national birth cohort-based study does not provide evidence for an association between maternal cotinine, a biomarker of maternal smoking, and risk of autism. LAY SUMMARY: This study explored whether prenatal exposure to tobacco smoke in mothers is related to the diagnosis of autism in their children, by measuring the levels of cotinine, a biomarker for tobacco exposure, in stored serum samples drawn from mothers during pregnancy. The levels of cotinine in the mothers of children diagnosed with autism were similar to those in the mothers of control children of similar age and gender distribution.

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.

Robust data-driven identification of risk factors and their interactions: A simulation and a study of parental and demographic risk factors for schizophrenia.

OBJECTIVES: Few interactions between risk factors for schizophrenia have been replicated, but fitting all such interactions is difficult due to high-dimensionality. Our aims are to examine significant main and interaction effects for schizophrenia and the performance of our approach using simulated data. METHODS: We apply the machine learning technique elastic net to a high-dimensional logistic regression model to produce a sparse set of predictors, and then assess the significance of odds ratios (OR) with Bonferroni-corrected p-values and confidence intervals (CI). We introduce a simulation model that resembles a Finnish nested case-control study of schizophrenia which uses national registers to identify cases (n = 1,468) and controls (n = 2,975). The predictors include nine sociodemographic factors and all interactions (31 predictors). RESULTS: In the simulation, interactions with OR = 3 and prevalence = 4% were identified with <5% false positive rate and ≥80% power. None of the studied interactions were significantly associated with schizophrenia, but main effects of parental psychosis (OR = 5.2, CI 2.9-9.7; p < .001), urbanicity (1.3, 1.1-1.7; p = .001), and paternal age ≥35 (1.3, 1.004-1.6; p = .04) were significant. CONCLUSIONS: We have provided an analytic pipeline for data-driven identification of main and interaction effects in case-control data. We identified highly replicated main effects for schizophrenia, but no interactions.

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.

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.

Proband and Familial Autoimmune Diseases Are Associated With Proband Diagnosis of Autism Spectrum Disorders.

OBJECTIVE: There is evidence that parental autoimmune diseases (ADs) are associated with autism spectrum disorders (ASD) in offspring. The association between offspring ASD and ADs diagnosed in siblings and probands remains less clear. We examined whether proband and familial diagnoses of ADs were associated with increased odds of ASD in probands. METHOD: The study is based on a nested case-control design that used data from a large national birth cohort (N = 1.2 million) in Finland. There were 4,600 cases of ASD and controls matched 1:4 on date of birth, sex, and residence. Data were accessed from national medical, birth, and central registries. RESULTS: Probands had a statistically significant increase in odds of ASD when they (adjusted odds ratio [OR] = 1.2), their mother (adjusted OR = 1.1), or their sibling (adjusted OR = 1.2) were diagnosed with an AD. With regard to specific ADs, we found a statistically significant increase in odds of ASD in probands diagnosed with autoimmune thyroiditis (adjusted OR = 2.7). Further analyses considering ADs by body system yielded a statistically significant increase in odds of ASD in probands with ADs associated with the central/peripheral nervous (adjusted OR = 4.8) and skin/mucous membrane (adjusted OR = 1.3) systems. Probands of mothers diagnosed with ear/eye (adjusted OR = 1.6) or respiratory (adjusted OR = 1.4) ADs, or siblings diagnosed with skin/mucous membrane ADs (adjusted OR = 1.3) also had increased odds of ASD. CONCLUSION: The findings suggest that there may be common pathogenic, developmental mechanisms related to autoimmunity that are associated with the etiology of ASD.

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.

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.

Association of Maternal Insecticide Levels With Autism in Offspring From a National Birth Cohort.

OBJECTIVE: Autism is a complex neurodevelopmental disorder with a largely unknown etiology. To date, few studies have investigated prenatal exposure to toxins and risk of autism by using maternal biomarkers of exposure. Persistent organic pollutants are lipophilic halogenated organic compounds and include the insecticide dichlorodiphenyltrichloroethane (DDT), as well as its metabolite p,p'-dichlorodiphenyl dichloroethylene (p,p'-DDE), and polychlorinated biphenyls (PCBs). The objective of this study was to test whether elevated maternal levels of persistent organic pollutants are associated with autism among offspring. METHOD: The investigation was derived from the Finnish Prenatal Study of Autism, a national birth cohort study based on a nested case-control design. Cases of autism among children born between 1987 and 2005 were ascertained by national registry linkages. In cases of childhood autism and matched control subjects (778 matched case-control pairs), maternal serum specimens from early pregnancy were assayed for levels of p,p'-DDE and total levels of PCBs. RESULTS: The odds of autism among offspring were significantly increased with maternal p,p'-DDE levels that were in the highest 75th percentile, with adjustment for maternal age, parity, and history of psychiatric disorders (odds ratio=1.32, 95% CI=1.02, 1.71). The odds of autism with intellectual disability were increased by greater than twofold with maternal p,p'-DDE levels above this threshold (odds ratio=2.21, 95% CI=1.32, 3.69). There was no association between total levels of maternal PCBs and autism. CONCLUSIONS: These findings provide the first biomarker-based evidence that maternal exposure to insecticides is associated with autism among offspring. Although further research is necessary to replicate this finding, this study has implications for the prevention of autism and may provide a better understanding of its pathogenesis.

Testing for Marginal Linear Effects in Quantile Regression.

This paper develops a new marginal testing procedure to detect the presence of significant predictors associated with the conditional quantiles of a scalar response. The idea is to fit the marginal quantile regression on each predictor one at a time, and then base the test on the t-statistics associated with the most predictive predictors. A resampling method is devised to calibrate this test statistic, which has non-regular limiting behavior due to the selection of the most predictive variables. Asymptotic validity of the procedure is established in a general quantile regression setting in which the marginal quantile regression models can be misspecified. Even though a fixed dimension is assumed to derive the asymptotic results, the proposed test is applicable and computationally feasible for large-dimensional predictors. The method is more flexible than existing marginal screening test methods based on mean regression, and has the added advantage of being robust against outliers in the response. The approach is illustrated using an application to an HIV drug resistance dataset.

Computer-Assisted Motivational Interviewing Intervention to Facilitate Teen Pregnancy Prevention and Fitness Behavior Changes: A Randomized Trial for Young Men.

PURPOSE: Despite recent declines, teen unintended pregnancy and sexually transmitted infections in the United States remain at levels higher than comparable nations. Initiatives to prevent teen pregnancy have focused primarily on female adolescents; how to effectively engage young men to reduce their risk of fathering a teen pregnancy has not been well studied. We proposed to adapt an innovative computer-assisted motivational interviewing (CAMI) intervention, originally designed and tested with young women, for use with young men, aged 15-24 years, to reduce their risk of fathering a teen pregnancy. This manuscript describes the design of a CAMI intervention for young men aimed at preventing teen pregnancy and improving fitness. METHODS: This randomized controlled trial will recruit 945 sexually active young men between the ages of 15 and 24 years from three health centers in New York City. Participants will be assigned by permuted block randomization to two study arms: one aimed at reducing involvement in unintended teen pregnancy (CAMI-teen pregnancy prevention) and the other at improving overall fitness (CAMI-Fitness). Except for topic, both intervention arms will provide four sessions of Motivational Interviewing coaching and use a mobile app to track behavior and set goals. We will assess young men's sexual and reproductive health behaviors and fitness at baseline, 12, 24, 36, and 64 weeks using a mobile device app created for the study. RESULTS: Pending ongoing study. CONCLUSIONS: Results from the study are expected to enhance our understanding of the efficacy of CAMI to enhance young men's reproductive health and fitness behaviors.

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.