Diagnosing and Handling Common Violations of Missing at Random.

Ignorable likelihood (IL) approaches are often used to handle missing data when estimating a multivariate model, such as a structural equation model. In this case, the likelihood is based on all available data, and no model is specified for the missing data mechanism. Inference proceeds via maximum likelihood or Bayesian methods, including multiple imputation without auxiliary variables. Such IL approaches are valid under a missing at random (MAR) assumption. Rabe-Hesketh and Skrondal (Ignoring non-ignorable missingness. Presidential Address at the International Meeting of the Psychometric Society, Beijing, China, 2015; Psychometrika, 2023) consider a violation of MAR where a variable A can affect missingness of another variable B also when A is not observed. They show that this case can be handled by discarding more data before proceeding with IL approaches. This data-deletion approach is similar to the sequential estimation of Mohan et al. (in: Advances in neural information processing systems, 2013) based on their ordered factorization theorem but is preferable for parametric models. Which kind of data-deletion or ordered factorization to employ depends on the nature of the MAR violation. In this article, we therefore propose two diagnostic tests, a likelihood-ratio test for a heteroscedastic regression model and a kernel conditional independence test. We also develop a test-based estimator that first uses diagnostic tests to determine which MAR violation appears to be present and then proceeds with the corresponding data-deletion estimator. Simulations show that the test-based estimator outperforms IL when the missing data problem is severe and performs similarly otherwise.

Ignoring Non-ignorable Missingness.

The classical missing at random (MAR) assumption, as defined by Rubin (Biometrika 63:581-592, 1976), is often not required for valid inference ignoring the missingness process. Neither are other assumptions sometimes believed to be necessary that result from misunderstandings of MAR. We discuss three strategies that allow us to use standard estimators (i.e., ignore missingness) in cases where missingness is usually considered to be non-ignorable: (1) conditioning on variables, (2) discarding more data, and (3) being protective of parameters.

The Role of Conditional Likelihoods in Latent Variable Modeling.

In psychometrics, the canonical use of conditional likelihoods is for the Rasch model in measurement. Whilst not disputing the utility of conditional likelihoods in measurement, we examine a broader class of problems in psychometrics that can be addressed via conditional likelihoods. Specifically, we consider cluster-level endogeneity where the standard assumption that observed explanatory variables are independent from latent variables is violated. Here, "cluster" refers to the entity characterized by latent variables or random effects, such as individuals in measurement models or schools in multilevel models and "unit" refers to the elementary entity such as an item in measurement. Cluster-level endogeneity problems can arise in a number of settings, including unobserved confounding of causal effects, measurement error, retrospective sampling, informative cluster sizes, missing data, and heteroskedasticity. Severely inconsistent estimation can result if these challenges are ignored.

Parental income and mental disorders in children and adolescents: prospective register-based study.

BACKGROUND: Children with low-income parents have a higher risk of mental disorders, although it is unclear whether other parental characteristics or genetic confounding explain these associations and whether it is true for all mental disorders. METHODS: In this registry-based study of all children in Norway (n = 1 354 393) aged 5-17 years from 2008 to 2016, we examined whether parental income was associated with childhood diagnoses of mental disorders identified through national registries from primary healthcare, hospitalizations and specialist outpatient services. RESULTS: There were substantial differences in mental disorders by parental income, except for eating disorders in girls. In the bottom 1% of parental income, 16.9% [95% confidence interval (CI): 15.6, 18.3] of boys had a mental disorder compared with 4.1% (95% CI: 3.3, 4.8) in the top 1%. Among girls, there were 14.2% (95% CI: 12.9, 15.5) in the lowest, compared with 3.2% (95% CI: 2.5, 3.9) in the highest parental-income percentile. Differences were mainly attributable to attention-deficit hyperactivity disorder in boys and anxiety and depression in girls. There were more mental disorders in children whose parents had mental disorders or low education, or lived in separate households. Still, parental income remained associated with children's mental disorders after accounting for parents' mental disorders and other factors, and associations were also present among adopted children. CONCLUSIONS: Mental disorders were 3- to 4-fold more prevalent in children with parents in the lowest compared with the highest income percentiles. Parents' own mental disorders, other socio-demographic factors and genetic confounding did not fully explain these associations.

A Dyadic IRT Model.

We propose a dyadic Item Response Theory (dIRT) model for measuring interactions of pairs of individuals when the responses to items represent the actions (or behaviors, perceptions, etc.) of each individual (actor) made within the context of a dyad formed with another individual (partner). Examples of its use include the assessment of collaborative problem solving or the evaluation of intra-team dynamics. The dIRT model generalizes both Item Response Theory models for measurement and the Social Relations Model for dyadic data. The responses of an actor when paired with a partner are modeled as a function of not only the actor's inclination to act and the partner's tendency to elicit that action, but also the unique relationship of the pair, represented by two directional, possibly correlated, interaction latent variables. Generalizations are discussed, such as accommodating triads or larger groups. Estimation is performed using Markov-chain Monte Carlo implemented in Stan, making it straightforward to extend the dIRT model in various ways. Specifically, we show how the basic dIRT model can be extended to accommodate latent regressions, multilevel settings with cluster-level random effects, as well as joint modeling of dyadic data and a distal outcome. A simulation study demonstrates that estimation performs well. We apply our proposed approach to speed-dating data and find new evidence of pairwise interactions between participants, describing a mutual attraction that is inadequately characterized by individual properties alone.

A Constrained Metropolis-Hastings Robbins-Monro Algorithm for Q Matrix Estimation in DINA Models.

In diagnostic classification models (DCMs), the Q matrix encodes in which attributes are required for each item. The Q matrix is usually predetermined by the researcher but may in practice be misspecified which yields incorrect statistical inference. Instead of using a predetermined Q matrix, it is possible to estimate it simultaneously with the item and structural parameters of the DCM. Unfortunately, current methods are computationally intensive when there are many attributes and items. In addition, the identification constraints necessary for DCMs are not always enforced in the estimation algorithms which can lead to non-identified models being considered. We address these problems by simultaneously estimating the item, structural and Q matrix parameters of the Deterministic Input Noisy "And" gate model using a constrained Metropolis-Hastings Robbins-Monro algorithm. Simulations show that the new method is computationally efficient and can outperform previously proposed Bayesian Markov chain Monte-Carlo algorithms in terms of Q matrix recovery, and item and structural parameter estimation. We also illustrate our approach using Tatsuoka's fraction-subtraction data and Certificate of Proficiency in English data.

Seasonal and pandemic influenza during pregnancy and risk of fetal death: A Norwegian registry-based cohort study.

Previous studies of fetal death with maternal influenza have been inconsistent. We explored the effect of maternal influenza-like illness (ILI) in pregnancy on the risk of fetal death, distinguishing between diagnoses during regular influenza seasons and the 2009/2010 pandemic and between trimesters of ILI. We used birth records from the Medical Birth Registry of Norway to identify fetal deaths after the first trimester in singleton pregnancies (2006-2013). The Norwegian Directorate of Health provided dates of clinical influenza diagnoses by primary-health-care providers, whereas dates of laboratory-confirmed influenza A (H1N1) diagnoses were provided by the Norwegian Surveillance System for Communicable Diseases. We obtained dates and types of influenza vaccinations from the Norwegian Immunisation Registry. Cox proportional-hazards regression models were fitted to estimate hazard ratios (HRs) of fetal death, with associated 95% confidence intervals (CIs), comparing women with and without an ILI diagnosis in pregnancy. There were 2510 fetal deaths among 417,406 eligible pregnancies. ILI during regular seasons was not associated with increased risk of fetal death: adjusted HR = 0.90 (95% CI 0.64-1.27). In contrast, ILI during the pandemic was associated with substantially increased risk of fetal death, with an adjusted HR of 1.75 (95% CI 1.21-2.54). The risk was highest following first-trimester ILI (adjusted HR = 2.28 [95% CI 1.45-3.59]). ILI during the pandemic-but not during regular seasons-was associated with increased risk of fetal death in the second and third trimester. The estimated effect was strongest with ILI in first trimester.

Pairwise residuals and diagnostic tests for misspecified dependence structures in models for binary longitudinal data.

Maximum likelihood estimation of models for binary longitudinal data is typically inconsistent if the dependence structure is misspecified. Unfortunately, diagnostics specifically designed for detecting such misspecifications are scant. We develop residuals and diagnostic tests based on comparing observed and expected frequencies of response patterns over time in the presence of arbitrary time-varying and time-invariant covariates. To overcome the sparseness problem, we use lower-order marginal tables, such as two-way tables for pairs of time-points, aggregated over covariate patterns. Our proposed pairwise concordance residuals are valuable for exploratory diagnostics and for constructing both generic tests for misspecified dependence structure as well as targeted adjacent pair concordance tests for excess serial dependence. The proposed methods are straightforward to implement and work well for general situations, regardless of the number of time-points and the number and types of covariates.

The transition model test for serial dependence in mixed-effects models for binary data.

Generalized linear mixed models for longitudinal data assume that responses at different occasions are conditionally independent, given the random effects and covariates. Although this assumption is pivotal for consistent estimation, violation due to serial dependence is hard to assess by model elaboration. We therefore propose a targeted diagnostic test for serial dependence, called the transition model test (TMT), that is straightforward and computationally efficient to implement in standard software. The TMT is shown to have larger power than general misspecification tests. We also propose the targeted root mean squared error of approximation (TRSMEA) as a measure of the population misfit due to serial dependence.

A competing risks approach to "biologic" interaction.

In epidemiology, the concepts of "biologic" and "statistical" interactions have been the subject of extensive debate. We present a new approach to biologic interaction based on Rothman's original (Am J Epidemiol, 104:587-592, 1976) discussion of sufficient causes. We do this in a probabilistic framework using competing risks and argue that sufficient cause interaction between two factors can be evaluated via the parameters in a particular statistical model, the additive hazard rate model. We present empirical conditions for presence of sufficient cause interaction and an example based on data from a liver cirrhosis trial illustrates the ideas.

Risk of fetal death after pandemic influenza virus infection or vaccination.

BACKGROUND: During the 2009 influenza A (H1N1) pandemic, pregnant women were at risk for severe influenza illness. This concern was complicated by questions about vaccine safety in pregnant women that were raised by anecdotal reports of fetal deaths after vaccination. METHODS: We explored the safety of influenza vaccination of pregnant women by linking Norwegian national registries and medical consultation data to determine influenza diagnosis, vaccination status, birth outcomes, and background information for pregnant women before, during, and after the pandemic. We used Cox regression models to estimate hazard ratios for fetal death, with the gestational day as the time metric and vaccination and pandemic exposure as time-dependent exposure variables. RESULTS: There were 117,347 eligible pregnancies in Norway from 2009 through 2010. Fetal mortality was 4.9 deaths per 1000 births. During the pandemic, 54% of pregnant women in their second or third trimester were vaccinated. Vaccination during pregnancy substantially reduced the risk of an influenza diagnosis (adjusted hazard ratio, 0.30; 95% confidence interval [CI], 0.25 to 0.34). Among pregnant women with a clinical diagnosis of influenza, the risk of fetal death was increased (adjusted hazard ratio, 1.91; 95% CI, 1.07 to 3.41). The risk of fetal death was reduced with vaccination during pregnancy, although this reduction was not significant (adjusted hazard ratio, 0.88; 95% CI, 0.66 to 1.17). CONCLUSIONS: Pandemic influenza virus infection in pregnancy was associated with an increased risk of fetal death. Vaccination during pregnancy reduced the risk of an influenza diagnosis. Vaccination itself was not associated with increased fetal mortality and may have reduced the risk of influenza-related fetal death during the pandemic. (Funded by the Norwegian Institute of Public Health.).

Musculoskeletal pain and overuse syndromes in adult acquired major upper-limb amputees.

OBJECTIVES: (1) To compare the prevalence of self-reported musculoskeletal pain in upper-limb amputees (ULAs) in Norway with that of a control group drawn from the Norwegian general population; (2) to describe musculoskeletal pain bothersomeness in ULAs; (3) to estimate the association between prosthesis wear and self-reported musculoskeletal pain in ULAs; and (4) to describe the occurrence of musculoskeletal overuse syndromes in a sample of ULAs. DESIGN: Cross-sectional study: postal questionnaires and clinical examinations. SETTING: Norwegian ULA population. Clinical examinations performed at 3 clinics. PARTICIPANTS: Questionnaires: population-based amputee sample (n=224; 57.4% response rate). Random control sample (n=318; 33.1% response rate). Clinical examinations: combined referred sample and convenience sample (n=70; 83.3% of those invited). Survey inclusion criteria: adult, resident in Norway and mastering Norwegian (amputees and controls), acquired major upper-limb amputation (amputees only). INTERVENTIONS: Not applicable. MAIN OUTCOME MEASURES: Self-reported musculoskeletal pain and pain bothersomeness. Self-reported pain in prosthesis wearers and nonwearers. Clinically assessed diagnoses of musculoskeletal overuse syndromes. RESULTS: Self-reported musculoskeletal pain was more frequent in ULAs than in the control group except for lower back pain. In ULAs, 57.0% reported neck/upper back pain (odds ratio [OR]=2.56; 95% confidence interval [CI], 1.64-3.98), and 58.9% reported shoulder pain (OR=4.00; 95% CI, 2.51-6.36). The percentage difference for arm pain was 24.8% (P<.001). All pain was reported as bothersome. We found no difference in pain prevalence between prosthesis wearers and nonwearers. Musculoskeletal overuse syndromes were found in 6.1% to 24.2% of ULAs, depending on diagnosis and case-definition criteria. CONCLUSIONS: Upper-limb loss increases the risk of self-reported musculoskeletal pain in the neck/upper back, shoulders, and in the remaining arm. Prosthesis wear does not prevent musculoskeletal pain. Further studies should be conducted to investigate the effects of prosthesis wear and possible preventive measures, and to ascertain our preliminary prevalence estimates of overuse syndromes.

Assessing physical function in adult acquired major upper-limb amputees by combining the Disabilities of the Arm, Shoulder and Hand (DASH) Outcome Questionnaire and clinical examination.

OBJECTIVES: To describe physical function in adult acquired major upper-limb amputees (ULAs) by combining self-assessed arm function and physical measures obtained by clinical examinations; to estimate associations between background factors and self-assessed arm function in ULAs; and to assess whether clinical examination findings may be used to detect reduced arm function in unilateral ULAs. SURVEY: postal questionnaires and clinical examinations. SETTING: Norwegian ULA population. Clinical examinations performed at 3 clinics. PARTICIPANTS: Questionnaires: population-based sample (n=224; 57.4% response rate). Clinical examinations: combined referred sample and convenience sample of questionnaire responders (n=70; 83.3% of those invited). SURVEY inclusion criteria: adult acquired major upper-limb amputation, resident in Norway, mastering of spoken and written Norwegian. INTERVENTIONS: Not applicable. MAIN OUTCOME MEASURES: The Disabilities of the Arm, Shoulder and Hand (DASH) Outcome Questionnaire, and clinical examination of joint motion and muscle strength with and without prostheses. RESULTS: Mean DASH score was 22.7 (95% confidence interval [CI], 20.3-25.0); in bilateral amputees, 35.7 (95% CI, 23.0-48.4); and in unilateral amputees, 22.1 (95% CI, 19.8-24.5). A lower unilateral DASH score (better function) was associated with paid employment (vs not in paid employment: adjusted regression coefficient [aB]=-5.40, P=.033; vs students: aB=-13.88, P=.022), increasing postamputation time (aB=-.27, P=.001), and Norwegian ethnicity (aB=-14.45, P<.001). At clinical examination, we found a high frequency of impaired neck mobility and varying frequencies of impaired joint motion and strength at the shoulder, elbow, and forearm level. Prosthesis wear was associated with impaired joint motion in all upper-limb joints (P<.006) and with reduced shoulder abduction strength (P=.002). Impaired without-prosthesis joint motion in shoulder flexion (ipsilateral: aB=12.19, P=.001) and shoulder abduction (ipsilateral: aB=12.01, P=.005; contralateral: aB=28.82, P=.004) was associated with increased DASH scores. CONCLUSIONS: Upper-limb loss clearly affects physical function. DASH score limitation profiles may be useful in individual clinical assessments. Targeted clinical examination may indicate patients with extra rehabilitational needs. Such examinations may be of special importance in relation to prosthesis function.

Classical latent variable models for medical research.

Latent variable models are commonly used in medical statistics, although often not referred to under this name. In this paper we describe classical latent variable models such as factor analysis, item response theory, latent class models and structural equation models. Their usefulness in medical research is demonstrated using real data. Examples include measurement of forced expiratory flow, measurement of physical disability, diagnosis of myocardial infarction and modelling the determinants of clients' satisfaction with counsellors' interviews.

A simulation study of three methods for detecting disease clusters.

BACKGROUND: Cluster detection is an important part of spatial epidemiology because it can help identifying environmental factors associated with disease and thus guide investigation of the aetiology of diseases. In this article we study three methods suitable for detecting local spatial clusters: (1) a spatial scan statistic (SaTScan), (2) generalized additive models (GAM) and (3) Bayesian disease mapping (BYM). We conducted a simulation study to compare the methods. Seven geographic clusters with different shapes were initially chosen as high-risk areas. Different scenarios for the magnitude of the relative risk of these areas as compared to the normal risk areas were considered. For each scenario the performance of the methods were assessed in terms of the sensitivity, specificity, and percentage correctly classified for each cluster. RESULTS: The performance depends on the relative risk, but all methods are in general suitable for identifying clusters with a relative risk larger than 1.5. However, it is difficult to detect clusters with lower relative risks. The GAM approach had the highest sensitivity, but relatively low specificity leading to an overestimation of the cluster area. Both the BYM and the SaTScan methods work well. Clusters with irregular shapes are more difficult to detect than more circular clusters. CONCLUSION: Based on our simulations we conclude that the methods differ in their ability to detect spatial clusters. Different aspects should be considered for appropriate choice of method such as size and shape of the assumed spatial clusters and the relative importance of sensitivity and specificity. In general, the BYM method seems preferable for local cluster detection with relatively high relative risks whereas the SaTScan method appears preferable for lower relative risks. The GAM method needs to be tuned (using cross-validation) to get satisfactory results.

Likelihood ratio tests in behavioral genetics: problems and solutions.

The likelihood ratio test of nested models for family data plays an important role in the assessment of genetic and environmental influences on the variation in traits. The test is routinely based on the assumption that the test statistic follows a chi-square distribution under the null, with the number of restricted parameters as degrees of freedom. However, tests of variance components constrained to be non-negative correspond to tests of parameters on the boundary of the parameter space. In this situation the standard test procedure provides too large p-values and the use of the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) for model selection is problematic. Focusing on the classical ACE twin model for univariate traits, we adapt existing theory to show that the asymptotic distribution for the likelihood ratio statistic is a mixture of chi-square distributions, and we derive the mixing probabilities. We conclude that when testing the AE or the CE model against the ACE model, the p-values obtained from using the chi(2)(1 df) as the reference distribution should be halved. When the E model is tested against the ACE model, a mixture of chi(2)(0 df), chi(2)(1 df) and chi(2)(2 df) should be used as the reference distribution, and we provide a simple formula to compute the mixing probabilities. Similar results for tests of the AE, DE and E models against the ADE model are also derived. Failing to use the appropriate reference distribution can lead to invalid conclusions.

Early respiratory infections, asthma, and allergy: 10-year follow-up of the Oslo Birth Cohort.

OBJECTIVE: It has been hypothesized that early infections protect against the development of atopic disease, but there have been few long-term follow-up studies. We estimated the associations between early respiratory infections and doctor-diagnosed asthma, allergic rhinitis, and skin-prick sensitization in children at 10 years of age in the Oslo Birth Cohort, established in 1992-1993. We also considered birth order and attendance at a child care center as proxy measures of increased exposure to infections early in life. METHODS: A total of 2540 children were followed from birth to the age of 10 years. Experiences of respiratory infections were recorded in follow-up surveys at 6 and 12 months. At age 10, questions were asked about current symptoms of asthma and allergic rhinitis and about having ever received a doctor diagnosis for these diseases. A subsample (n = 1740) of the cohort was tested for skin-prick test reactivity. RESULTS: Current asthma was related to lower respiratory tract infection (adjusted odds ratio [OR]: 2.1; 95% confidence interval: 1.3-3.0) and croup (adjusted OR: 2.3; 95% confidence interval: 1.3-4.2) in the first year. ORs for allergic rhinitis and skin-prick sensitization were smaller but mainly positive. Birth order and child care attendance at age 1 year were not significantly associated with any of the studied outcomes. CONCLUSIONS: Early respiratory infections did not protect against the development of asthma, allergic rhinitis, or sensitization to common allergens during the first 10 years of life but increased the risk for asthma symptoms at age 10 in this population.