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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Association of Selective Serotonin Reuptake Inhibitor Exposure During Pregnancy With Speech, Scholastic, and Motor Disorders in Offspring

IMPORTANCE

Speech/language, scholastic, and motor disorders are common in children. It is unknown whether exposure to selective serotonin reuptake inhibitors (SSRIs) during pregnancy influences susceptibility to these disorders.

OBJECTIVE

To examine whether SSRI exposure during pregnancy is associated with speech/language, scholastic, and motor disorders in offspring up to early adolescence.

DESIGN, SETTING, AND PARTICIPANTS

This prospective birth cohort study examined national population-based register data in Finland from 1996 to 2010. The sampling frame includes 845 345 pregnant women and their singleton offspring with data on maternal use of antidepressants and depression-related psychiatric disorders during pregnancy.

EXPOSURES

There were 3 groups of offspring: 15 596 were in the SSRI-exposed group, ie, had mothers diagnosed as having depression-related psychiatric disorders with a history of purchasing SSRIs during pregnancy; 9537 were in the unmedicated group, ie, had mothers diagnosed as having depression-related psychiatric disorders without a history of purchasing SSRIs during pregnancy; and 31 207 were in the unexposed group, ie, had mothers without a psychiatric diagnosis or a history of purchasing SSRIs.

MAIN OUTCOMES AND MEASURES

Cumulative incidence of speech/language, scholastic, or motor disorders (829, 187, and 285 instances, respectively) from birth to 14 years. All hypotheses tested were formulated before data collection.

RESULTS

Of the 56 340 infants included in the final cohort, 28 684 (50.9%) were male and 48 782 (86.6%) were 9 years or younger. The mean (SD) ages of children at diagnosis were 4.43 (1.67), 3.55 (2.67), and 7.73 (2.38) for speech/language, scholastic, and motor disorders, respectively. Offspring of mothers who purchased SSRIs at least twice during pregnancy had a significant 37% increased risk of speech/language disorders compared with offspring in the unmedicated group. The cumulative hazard of speech/language disorders was 0.0087 in the SSRI-exposed group vs 0.0061 in the unmedicated group (hazard ratio, 1.37; 95% CI, 1.11-1.70; P = .004). There was a significantly increased risk of these disorders in offspring in the SSRI-exposed and unmedicated groups compared with offspring in the unexposed group. For scholastic and motor disorders, there were no differences between offspring in the SSRI-exposed group and in the unmedicated group.

CONCLUSIONS AND RELEVANCE

Exposure to SSRIs during pregnancy was associated with an increased risk of speech/language disorders. This finding may have implications for understanding associations between SSRIs and child development.

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.

Prenatal Nicotine Exposure and Risk of Schizophrenia Among Offspring in a National Birth Cohort

OBJECTIVE

Cigarette smoking during pregnancy is a major public health problem leading to adverse health outcomes and neurodevelopmental abnormalities among offspring. Its prevalence in the United States and Europe is 12%-25%. This study examined the relationship between prenatal nicotine exposure (cotinine level) in archived maternal sera and schizophrenia in offspring from a national birth cohort.

METHOD

The authors conducted a population-based nested case-control study of all live births in Finland from 1983 to 1998. Cases of schizophrenia in offspring (N=977) were identified from a national registry and matched 1:1 to controls on date of birth, sex, and residence. Maternal serum cotinine levels were prospectively measured, using quantitative immunoassay, from early- to mid-gestation serum specimens archived in a national biobank.

RESULTS

A higher maternal cotinine level, measured as a continuous variable, was associated with an increased odds of schizophrenia (odds ratio=3.41, 95% confidence interval, 1.86-6.24). Categorically defined heavy maternal nicotine exposure was related to a 38% increased odds of schizophrenia. These findings were not accounted for by maternal age, maternal or parental psychiatric disorders, socioeconomic status, and other covariates. There was no clear evidence that weight for gestational age mediated the associations.

CONCLUSIONS

To the authors' knowledge, this is the first study of the relationship between a maternal smoking biomarker and schizophrenia. It provides the most definitive evidence to date that smoking during pregnancy is associated with schizophrenia. If replicated, these findings suggest that preventing smoking during pregnancy may decrease the incidence of schizophrenia.

Estimation for diffusion processes under misspecified models

The asymptotic behavior of the maximum likelihood estimator of a parameter in the drift term of a stationary ergodic diffusion process is studied under conditions in which the true drift function and true noise function do not coincide with those specified by the parametric model.

The Development of the Sexual Self-Concept Inventory for Early Adolescent Girls

The Sexual Self-Concept Inventory (SSCI) was developed to assess sexual self-concept in an ethnically diverse sample of urban early adolescent girls. Three scales (Sexual Arousability, Sexual Agency, and Negative Sexual Affect) were shown to be distinct and reliable dimensions of girls' sexual self-concepts. Validity was established through comparisons with established instruments. Sexual Arousability and Sexual Agency were associated with positive sexual self-esteem, positive future orientation toward sex, intentions to engage in intercourse, and lower levels of sexual experience. Negative Sexual Affect was associated with stronger abstinence attitudes and lack of intentions or orientation toward sex in the near future. The results indicate that the SSCI constitutes a valid means of assessing early adolescent girls' views of their sexuality and sexual behavior and may be of use in studies of health and risk-related decision making.

Hypothyroxinemia During Gestation and Offspring Schizophrenia in a National Birth Cohort

BACKGROUND

Evidence from animal and human studies indicates that thyroid hormone deficiency during early gestation alters brain development. As schizophrenia is associated with prenatal brain insults and premorbid cognitive deficits, we tested the a priori hypothesis that serologically defined maternal thyroid deficiency during early gestation to mid-gestation is associated with schizophrenia in offspring.

METHODS

The investigation is based on the Finnish Prenatal Study of Schizophrenia, a nested case-control study that included archived maternal sera from virtually all pregnancies since 1983 (N = >1 million). We identified all offspring in the cohort with a diagnosis of schizophrenia based on the national inpatient and outpatient register and matched them on sex, date of birth, and residence in Finland at time of onset of the case to comparison subjects (1:1) from the cohort. Maternal sera of 1010 case-control pairs were assessed for free thyroxine, and sera of 948 case-control pairs were assessed for thyroid-stimulating hormone.

RESULTS

Maternal hypothyroxinemia (free thyroxine ≤10th percentile, normal thyroid-stimulating hormone) was associated with an increased odds of schizophrenia (odds ratio = 1.75, 95% confidence interval = 1.22-2.50, p = .002). When adjusted for maternal psychiatric history, province of birth, and maternal smoking during pregnancy, the association remained significant (odds ratio = 1.70, 95% confidence interval = 1.13-2.55, p = .010).

CONCLUSIONS

In a large, national birth cohort, prospectively documented hypothyroxinemia during early gestation to mid-gestation was associated with increased odds of schizophrenia in offspring. This information can inform translational studies of maternal hypothyroxinemia examining molecular and cellular deviations relevant to schizophrenia.

Gestational Exposure to Selective Serotonin Reuptake Inhibitors and Offspring Psychiatric Disorders: A National Register-Based Study

OBJECTIVE

To investigate the impact of gestational exposure to selective serotonin reuptake inhibitors (SSRIs) on offspring neurodevelopment.

METHOD

This is a cohort study using national register data in Finland between the years 1996 and 2010. Pregnant women and their offspring were categorized into 4 groups: SSRI exposed (n = 15,729); exposed to psychiatric disorder, no antidepressants (n = 9,651); exposed to SSRIs only before pregnancy (n = 7,980); and unexposed to antidepressants and psychiatric disorders (n = 31,394). We investigated the cumulative incidence of offspring diagnoses of depression, anxiety, autism spectrum disorder (ASD), and attention-deficit/hyperactivity disorder (ADHD) for the 4 groups from birth to 14 years, adjusting for confounders.

RESULTS

The cumulative incidence of depression among offspring exposed prenatally to SSRIs was 8.2% (95% CI = 3.1-13.3%) by age 14.9 years, compared with 1.9% (95% CI = 0.9-2.9%) in the psychiatric disorder, no medication group (adjusted hazard ratio [HR] = 1.78; 95% CI = 1.12-2.82; p = .02) and to 2.8% (95% CI = 1.4-4.3%) in the SSRI discontinued group (HR = 1.84; 95% CI = 1.14-2.97; p = .01). Rates of anxiety, ASD, and ADHD diagnoses were comparable to rates in offspring of mothers with a psychiatric disorder but no medication during pregnancy. Comparing SSRI exposed to unexposed individuals, the HRs were significantly elevated for each outcome.

CONCLUSION

Prenatal SSRI exposure was associated with increased rates of depression diagnoses in early adolescence but not with ASD or ADHD. Until confirmed, these findings must be balanced against the substantial adverse consequences of untreated maternal depression.

An adaptive resampling test for detecting the presence of significant predictors

This paper investigates marginal screening for detecting the presence of significant predictors in high-dimensional regression. Screening large numbers of predictors is a challenging problem due to the non-standard limiting behavior of post-model-selected estimators. There is a common misconception that the oracle property for such estimators is a panacea, but the oracle property only holds away from the null hypothesis of interest in marginal screening. To address this difficulty, we propose an adaptive resampling test (ART). Our approach provides an alternative to the popular (yet conservative) Bonferroni method of controlling familywise error rates. ART is adaptive in the sense that thresholding is used to decide whether the centered percentile bootstrap applies, and otherwise adapts to the non-standard asymptotics in the tightest way possible. The performance of the approach is evaluated using a simulation study and applied to gene expression data and HIV drug resistance data.

Empirical likelihood based tests for stochastic ordering under right censorship

This paper develops an empirical likelihood approach to testing for stochastic ordering between two univariate distributions under right censorship. The proposed test is based on a maximally selected local empirical likelihood statistic. The asymptotic null distribution is expressed in terms of a Brownian bridge. The new procedure is shown via a simulation study to have superior power to the log-rank and weighted Kaplan-Meier tests under crossing hazard alternatives. The approach is illustrated using data from a randomized clinical trial involving the treatment of severe alcoholic hepatitis.

Pregnancy Complications Following Prenatal Exposure to SSRIs or Maternal Psychiatric Disorders: Results From Population-Based National Register Data

OBJECTIVE

Using national register data, the authors examined the relationship between prenatal selective serotonin reuptake inhibitor (SSRI) treatment and pregnancy complications, accounting for psychiatric diagnoses related to SSRI use.

METHOD

This was a population-based prospective birth cohort study using national register data. The sampling frame included 845,345 offspring, representing all singleton live births in Finland between 1996 and 2010. Pregnancies were classified as exposed to SSRIs (N=15,729), unexposed to SSRIs but with psychiatric diagnoses (N=9,652), and unexposed to medications and psychiatric diagnoses (N=31,394). Pregnancy outcomes in SSRI users were compared with those in the unexposed groups.

RESULTS

Offspring of mothers who received SSRI prescriptions during pregnancy had a lower risk for late preterm birth (odds ratio=0.84, 95% CI=0.74-0.96), for very preterm birth (odds ratio=0.52, 95% CI=0.37-0.74), and for cesarean section (odds ratio=0.70, 95% CI=0.66-0.75) compared with offspring of mothers unexposed to medications but with psychiatric disorders. In contrast, in SSRI-treated mothers, the risk was higher for offspring neonatal complications, including low Apgar score (odds ratio=1.68, 95% CI=1.34-2.12) and monitoring in a neonatal care unit (odds ratio=1.24, 95% CI=1.14-1.35). Compared with offspring of unexposed mothers, offspring of SSRI-treated mothers and mothers unexposed to medications but with psychiatric disorders were both at increased risk of many adverse pregnancy outcomes, including cesarean section and need for monitoring in a neonatal care unit.

CONCLUSIONS

In a large national birth cohort, treatment of maternal psychiatric disorders with SSRIs during pregnancy was related to a lower risk of preterm birth and cesarean section but a higher risk of neonatal maladaptation. The findings provide novel evidence for a protective role of SSRIs on some deleterious reproductive outcomes, possibly by reducing maternal depressive symptoms. The divergent findings suggest that clinical decisions on SSRI use during pregnancy should be individualized, taking into account the mother's psychiatric and reproductive history.

Optimal design strategies for sibling studies with binary exposures

Sibling studies have become increasingly popular because they provide better control over confounding by unmeasured family-level risk factors than can be obtained in standard cohort studies. However, little attention has been devoted to the development of efficient design strategies for sibling studies in terms of optimizing power. We here address this issue in commonly encountered types of sibling studies, allowing for continuous and binary outcomes and varying numbers of exposed and unexposed siblings. For continuous outcomes, we show that in families with sibling pairs, optimal study power is obtained by recruiting discordant (exposed-control) pairs of siblings. More generally, balancing the exposure status within each family as evenly as possible is shown to be optimal. For binary outcomes, we elucidate how the optimal strategy depends on the variation of the binary response; as the within-family correlation increases, the optimal strategy tends toward only recruiting discordant sibling pairs (as in the case of continuous outcomes). R code for obtaining the optimal strategies is included.

Autism with intellectual disability related to dynamics of head circumference growth during early infancy

BACKGROUND

It is not yet definitively known whether dynamic features of head circumference growth are associated with autism. To address this issue, we carried out a nested matched case-control study using data from national well baby clinics in Finland; autism cases were identified from the Finnish Hospital and Outpatient Discharge Registry.

METHODS

A nonparametric Bayesian method was used to construct growth velocity trajectories between birth and 2 years of age in autism cases and matched control subjects (n = 468 in main analyses, 1:1 matched control subjects). Estimates of odds ratios for autism risk in relation to the growth velocities were obtained using conditional logistic regression.

RESULTS

Growth velocity of head circumference at 3 months of age, adjusting for gestational age at birth and maternal age, is significantly associated with autism (p = .014); the finding was observed in subjects with comorbid intellectual disability (ID) (p = .025) but not in those without ID (p = .15). Height growth velocity among subjects with autism and without ID is significantly associated with autism at 6 months (p = .007), and weight growth velocity at 18 months without ID (p = .02) and 24 months without ID (p = .042) and with ID (p = .037).

CONCLUSIONS

Acceleration in head circumference growth is associated with autism with comorbid ID at 3 months but not subsequently. This association is unrelated to acceleration in height and weight, which are not strongly associated with autism until after 6 months.

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.

Reduction in incidence of hospitalizations for psychotic episodes through early identification and intervention

OBJECTIVE

This study examined whether the incidence of hospitalization for psychosis was reduced by a communitywide system of early identification and intervention to prevent onset of psychosis.

METHODS

The Portland Identification and Early Referral program (PIER) was initiated in 2001. Youths and young adults ages 12-35 were identified by professionals in a wide variety of educational, health, and mental health settings. PIER program staff assessed, confirmed risk of psychosis, and provided treatment for 24 months to eligible and consenting young people (N=148). The monthly rate of first hospital admission for psychosis was the outcome measure for efficacy of identification and intervention. Admission rates before and after the program began accepting referrals were compared, both in the experimental area (Greater Portland) and in aggregated urban areas of Maine (control areas). Autoregressive integrated moving-average (ARIMA) models were used to assess the effect.

RESULTS

On the basis of ARIMA models, the rate of first hospital admission for psychosis decreased significantly by 26% (95% confidence interval [CI]=-64% to -11%) in the Greater Portland area. The rate increased by 8% (CI=-5% to 36%) in the control areas. Taking into account the increase in the control areas, the actual percentage reduction in Greater Portland during the intervention period was 34% (26% plus 8%). The reduction in admissions was largest for individuals with nonaffective nonschizophrenic psychosis.

CONCLUSIONS

PIER has demonstrated that populationwide early identification is feasible. Preventive intervention can reduce rates of initial hospitalizations for psychosis in a midsized city.

Elevated maternal C-reactive protein and increased risk of schizophrenia in a national birth cohort

OBJECTIVE

The objective of the present study was to investigate an association between early gestational C-reactive protein, an established inflammatory biomarker, prospectively assayed in maternal sera, and schizophrenia in a large, national birth cohort with an extensive serum biobank.

METHOD

A nested case-control design from the Finnish Prenatal Study of Schizophrenia cohort was utilized. A total of 777 schizophrenia cases (schizophrenia, N=630; schizoaffective disorder, N=147) with maternal sera available for C-reactive protein testing were identified and matched to 777 control subjects in the analysis. Maternal C-reactive protein levels were assessed using a latex immunoassay from archived maternal serum specimens.

RESULTS

Increasing maternal C-reactive protein levels, classified as a continuous variable, were significantly associated with schizophrenia in offspring (adjusted odds ratio=1.31, 95% confidence interval=1.10-1.56). This finding remained significant after adjusting for potential confounders, including maternal and parental history of psychiatric disorders, twin/singleton birth, urbanicity, province of birth, and maternal socioeconomic status.

CONCLUSIONS

This finding provides the most robust evidence to date that maternal inflammation may play a significant role in schizophrenia, with possible implications for identifying preventive strategies and pathogenic mechanisms in schizophrenia and other neurodevelopmental disorders.

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.

Circulating pro-surfactant protein B as a risk biomarker for lung cancer

BACKGROUND

Our prior studies of lung cancer suggested that a novel biomarker (pro-surfactant protein B or pro-SFTPB) might serve as a predictive marker for this disease. We aimed to determine the potential use of pro-SFTPB for distinguishing lung cancer cases from matched controls as a risk marker.

METHODS

Study subjects were drawn from the longitudinal Physicians' Health Study (PHS). Cases (n = 188) included individuals who were cancer-free at study enrollment but developed lung cancer during follow-up. Controls (n = 337) were subjects who did not develop lung cancer. Cases and controls were matched on date of study enrollment, age at enrollment, and smoking status and amount. Baseline plasma samples drawn at enrollment were analyzed for pro-SFTPB using ELISA to detect differences in protein expression levels for cases and controls.

RESULTS

Pro-SFTPB nondetectable status was significantly associated with lung cancer risk [OR = 5.88; 95% confidence interval (CI) 1.24-27.48]. Among subjects with detectable levels of the protein, increasing plasma concentration of pro-SFTPB was associated with higher lung cancer risk (OR = 1.41 per unit increase in log pro-SFTPB; 95% CI 1.08-1.84).

CONCLUSION

These results suggest a nonlinear, J-shaped association between plasma pro-SFTPB levels and lung cancer risk, with both nondetectable and higher levels of the marker being associated with lung cancer.

IMPACT

These results show promise of a risk marker that could contribute to predicting risk for lung cancer development and to narrowing the high-risk population for low-dose computed tomography screening.

Maternal serum persistent organic pollutants in the Finnish Prenatal Study of Autism: A pilot study

Recent research emphasizes the contribution of environmental as well as genetic factors to the etiology of autism but studies testing associations between chemical exposures and autism have been limited. Prenatal exposure to persistent organic pollutants (POPs) has previously been associated with decrements in cognitive and developmental performance. We conducted a pilot study in the Finnish Prenatal Study of Autism (FiPS-A). Seventy-five cases with autism and 75 controls matched on sex, birth year, urbanization and maternal age were sampled from first-born children in the Finnish Maternity Cohort, which includes over 1million births. The study sample included births occurring from 1991 to 2000. Subjects were followed up for autism through 2007. DDT, DDE, PCB-118, PCB-138, PCB-153, PCB-156, PCB-170, PCB-180, hexachlorobenzene, and BDE-47 were measured in archived maternal serum samples taken during pregnancy using gas chromatography-high resolution mass spectrometry. Correlations between pollutant measures were assessed and mechanistically-related weighting schemes for summarizing PCB levels were compared. Case and control differences were assessed using graphical and statistical methods. All analytes, with the exception of DDT and BDE-47, were detected above the limit of quantification in all samples. The correlation between levels of individual PCB congeners and weighted summary measures was high (0.71-1.00). Paired t-tests revealed no significant differences between cases and controls for log-transformed mean values of any analyte; however, in an adjusted model the odds ratios for autism were 1.91 (p=0.29) and 1.79 (p=0.36) respectively, for subjects with total PCBs and DDE above the 90th percentile of control values. Levels of prenatal PCB exposure in FIPS-A were similar to the levels which previously correlated with poorer neurodevelopmental measures in other populations. Further study in a larger sample will be required to fully determine whether exposure to high POP levels is associated with autism diagnosis in the population.

Severity and persistence of asthma and mental health: a birth cohort study

BACKGROUND

The goal of the current study was to investigate asthma and mental health among youth in the community, and to consider the role of asthma severity and persistence in this link. Method Data were drawn from the Raine Study, a population-based birth cohort study in Western Australia. Logistic regression models and generalized estimating equations were used to examine the relationship between asthma at age 5 years and the range of internalizing and externalizing mental health problems at ages 5-17 years. Analyses were stratified by asthma severity and persistence, and adjusted for a range of potential confounders.

RESULTS

More severe and persistent asthma at age 5 was associated with significantly increased odds of affective, anxiety, somatic, oppositional defiant and conduct problems at ages 5-17. Mild asthma and remitted asthma were not associated with heightened vulnerability to mental disorders.

CONCLUSIONS

Our results suggest that youth with symptomatic asthma are more likely to suffer from a wide range of mental health problems, and that the likelihood of mental health problems appears to increase as a function of asthma severity. Youth with poorly controlled and/or more severe and persistent asthma may be considered a vulnerable group who might benefit from mental health screening in clinical, school and community settings.

Birth weight and neurocognition in schizophrenia spectrum disorders

Low birth weight is associated with both schizophrenia and neurocognitive impairment. Yet, to our knowledge, no previous study has examined the relationship between lower birth weight and neurocognitive deficits in schizophrenia spectrum disorders (SSD). In this preliminary study, we investigated the relationship using a broad neuropsychological battery in cases with SSD and matched control subjects. The sample consisted of all subjects in the Developmental Insult and Brain Anomaly in Schizophrenia study, a nested case-control investigation developed from a large birth cohort, which followed subjects longitudinally. Case ascertainment was based on computerized record linkages between the birth cohort members and the Kaiser Permanente Medical Care Plan, and all diagnoses were confirmed by consensus diagnosis following the Diagnostic Interview for Genetic Studies. Lower birth weight was associated with impairment in executive function, working memory, generalized intellectual function, and neuromotor function in cases with SSD but not in control subjects. No deficits were observed in verbal memory for either group. These results support the hypothesis that lower birth weight plays a role in neuropsychological disruptions in SSD and that the antecedents of lower birth weight may have a greater impact on these disruptions in SSD than in controls. These data may facilitate a better understanding of the etiopathogenesis of the cognitive underpinnings of SSD.

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.

Power and Sample Size Calculations for Generalized Estimating Equations via Local Asymptotics

We consider the problem of calculating power and sample size for tests based on generalized estimating equations (GEE), that arise in studies involving clustered or correlated data (e.g., longitudinal studies and sibling studies). Previous approaches approximate the power of such tests using the asymptotic behavior of the test statistics under fixed alternatives. We develop a more accurate approach in which the asymptotic behavior is studied under a sequence of local alternatives that converge to the null hypothesis at root-m rate, where m is the number of clusters. Based on this approach, explicit sample size formulae are derived for Wald and quasi-score test statistics in a variety of GEE settings. Simulation results show that in the important special case of logistic regression with exchangeable correlation structure, previous approaches can inflate the projected sample size (to obtain nominal 90% power using the Wald statistic) by over 10%, whereas the proposed approach provides an accuracy of around 2%.