Missing observations are common in cluster randomised trials. The problem is exacerbated when modelling bivariate outcomes jointly, as the proportion of complete cases is often considerably smaller than the proportion having either of the outcomes fully observed. Approaches taken to handling such missing data include the following: complete case analysis, single-level multiple imputation that ignores the clustering, multiple imputation with a fixed effect for each cluster and multilevel multiple imputation. We contrasted the alternative approaches to handling missing data in a cost-effectiveness analysis that uses data from a cluster randomised trial to evaluate an exercise intervention for care home residents. We then conducted a simulation study to assess the performance of these approaches on bivariate continuous outcomes, in terms of confidence interval coverage and empirical bias in the estimated treatment effects. Missing-at-random clustered data scenarios were simulated following a full-factorial design. Across all the missing data mechanisms considered, the multiple imputation methods provided estimators with negligible bias, while complete case analysis resulted in biased treatment effect estimates in scenarios where the randomised treatment arm was associated with missingness. Confidence interval coverage was generally in excess of nominal levels (up to 99.8%) following fixed-effects multiple imputation and too low following single-level multiple imputation. Multilevel multiple imputation led to coverage levels of approximately 95% throughout. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Diet during pregnancy and lactation may have a role in the development of allergic diseases. There are few human studies on the topic, especially focusing on food allergies. We sought to study the associations between maternal diet during pregnancy and lactation and cow’s milk allergy (CMA) in offspring. A population-based birth cohort with human leukocyte antigen-conferred susceptibility to type 1 diabetes was recruited in Finland between 1997 and 2004 (n=6288). Maternal diet during pregnancy and lactation was assessed by a validated, 181-item semi-quantitative food frequency questionnaire. Register-based information on diagnosed CMA was obtained from the Social Insurance Institution and completed with parental reports. The associations between maternal food consumption and CMA were assessed using logistic regression, comparing the highest and the lowest quarters to the middle half of consumption. Consumption of milk products in the highest quarter during pregnancy was associated with a lower risk of CMA in offspring (odds ratio (OR) 0.56, 95% confidence interval (CI) 0.37–0.86; P<0.01). When stratified by maternal allergic rhinitis and asthma, there was evidence of an inverse association between high use of milk products and CMA in offspring of non-allergic mothers (OR 0.30, 95% CI 0.13–0.69, P<0.001). Cord blood IgA correlated positively with the consumption of milk products during pregnancy, indicating exposure to CMA and activation of antigen-specific immunity in the infant during pregnancy. High maternal consumption of milk products during pregnancy may protect children from developing CMA, especially in offspring of non-allergic mothers.

Convergence problems often arise when complex linear mixed-effects models are fitted. Previous simulation studies (see, e.g. [Buyse M, Molenberghs G, Burzykowski T, Renard D, Geys H. The validation of surrogate endpoints in meta-analyses of randomized experiments. Biostatistics. 2000;1:49-67, Renard D, Geys H, Molenberghs G, Burzykowski T, Buyse M. Validation of surrogate endpoints in multiple randomized clinical trials with discrete outcomes. Biom J. 2002;44:921-935]) have shown that model convergence rates were higher (i) when the number of available clusters in the data increased, and (ii) when the size of the between-cluster variability increased (relative to the size of the residual variability). The aim of the present simulation study is to further extend these findings by examining the effect of an additional factor that is hypothesized to affect model convergence, i.e. imbalance in cluster size. The results showed that divergence rates were substantially higher for data sets with unbalanced cluster sizes - in particular when the model at hand had a complex hierarchical structure. Furthermore, the use of multiple imputation to restore balance' in unbalanced data sets reduces model convergence problems.

We examined maternal dietary intake of fatty acids and foods which are sources of fatty acids during lactation and whether they are associated with the risk of preclinical and clinical type 1 diabetes in the offspring.

We have composed a sample of 68 massive stars in our galaxy whose projected rotational velocity, effective temperature, and gravity are available from high-precision spectroscopic measurements. The additional seven observed variables considered here are their surface nitrogen abundance, rotational frequency, magnetic field strength, and the amplitude and frequency of their dominant acoustic and gravity modes of oscillation. A multiple linear regression to estimate the nitrogen abundance combined with principal component analysis, after addressing the incomplete and truncated nature of the data, reveals that the effective temperature and the frequency of the dominant acoustic oscillation mode are the only two significant predictors for the nitrogen abundance, while the projected rotational velocity and the rotational frequency have no predictive power. The dominant gravity mode and the magnetic field strength are correlated with the effective temperature but have no predictive power for the nitrogen abundance. Our findings are completely based on observations and their proper statistical treatment and call for a new strategy in evaluating the outcome of stellar evolution computations.

The aim of the present study was to examine the associations between the maternal intake of fatty acids during pregnancy and the risk of preclinical and clinical type 1 diabetes in the offspring. The study included 4887 children with human leucocyte antigen (HLA)-conferred type 1 diabetes susceptibility born during the years 1997–2004 from the Finnish Type 1 Diabetes Prediction and Prevention Study. Maternal diet was assessed with a validated FFQ. The offspring were observed at 3- to 12-month intervals for the appearance of type 1 diabetes-associated autoantibodies and development of clinical type 1 diabetes (average follow-up period: 4·6 years (range 0·5–11·5 years)). Altogether, 240 children developed preclinical type 1 diabetes and 112 children developed clinical type 1 diabetes. Piecewise linear log-hazard survival model and Cox proportional-hazards regression were used for statistical analyses. The maternal intake of palmitic acid (hazard ratio (HR) 0·82, 95 % CI 0·67, 0·99) and high consumption of cheese during pregnancy (highest quarter v. intermediate half HR 0·52, 95 % CI 0·31, 0·87) were associated with a decreased risk of clinical type 1 diabetes. The consumption of sour milk products (HR 1·14, 95 % CI 1·02, 1·28), intake of protein from sour milk (HR 1·15, 95 % CI 1·02, 1·29) and intake of fat from fresh milk (HR 1·43, 95 % CI 1·04, 1·96) were associated with an increased risk of preclinical type 1 diabetes, and the intake of low-fat margarines (HR 0·67, 95 % CI 0·49, 0·92) was associated with a decreased risk. No conclusive associations between maternal fatty acid intake or food consumption during pregnancy and the development of type 1 diabetes in the offspring were detected.

Abstract Ante‐dependence models are flexible nonstationary covariance structures for repeated measurements that generalize stationary autoregressive models. The structures can only be used for data in which the times of measurement are common across units. They can be defined in the Gaussian setting by conditional independence relationships: an r th order structure holds if and only if two repeated measurements are conditionally independent given r intermediate measurements. Equivalently, an r th order ante‐dependence covariance matrix has a inverse of band form of order r + 1, with no other constraints on the matrix, other than that it is positive definite. It provides a compromise between the unrealistic stationary structures, such as the autoregressive, and the potentially inefficient unstructured form. In certain repeated measurements settings, it allows test statistics to be constructed with known small sample distributions, that can be regarded as generalizations of Wilks' lambda statistic.

Transition Models for Longitudinal Data† M. G. Kenward, M. G. Kenward London School of Hygiene & Tropical Medicine, London, UKSearch for more papers by this author M. G. Kenward, M. G. Kenward London School of Hygiene & Tropical Medicine, London, UKSearch for more papers by this author First published: 29 September 2014 https://doi.org/10.1002/9781118445112.stat05544 †This article was originally published online in 2005 in Encyclopedia of Biostatistics, © John Wiley & Sons, Ltd and republished in Wiley StatsRef: Statistics Reference Online, 2014. Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat No abstract is available for this article. References 1Diggle, P. D., Liang, K. -Y. & Zeger, S. L. (1994). Analysis of Longitudinal Data. Clarendon Press, Oxford. 10.2307/2986113 CASWeb of Science®Google Scholar 2Korn, E. L. & Whittmore, A. S. (1979). Methods for analyzing panel studies of acute health effects of air pollution, Biometrics 35, 795–802. 10.2307/2530111 CASPubMedWeb of Science®Google Scholar 3Zeger, S. L., Liang, K. -Y. & Self, S. G. (1985). The analysis of binary longitudinal data with time-independent covariates, Biometrika 72, 31–38. Web of Science®Google Scholar Wiley StatsRef: Statistics Reference OnlineBrowse other articles of this reference work:BROWSE BY TOPICBROWSE A-Z ReferencesRelatedInformation

Longitudinal studies, where data are repeatedly collected on subjects over a period, are common in medical research. When estimating the effect of a time‐varying treatment or exposure on an outcome of interest measured at a later time, standard methods fail to give consistent estimators in the presence of time‐varying confounders if those confounders are themselves affected by the treatment. Robins and colleagues have proposed several alternative methods that, provided certain assumptions hold, avoid the problems associated with standard approaches. They include the g‐computation formula, inverse probability weighted estimation of marginal structural models and g‐estimation of structural nested models. In this tutorial, we give a description of each of these methods, exploring the links and differences between them and the reasons for choosing one over the others in different settings. Copyright © 2012 John Wiley & Sons, Ltd.

Methods We begin by illustrating the MI approaches with an example, a cost-effectiveness analysis of a CRT evaluating an intervention for postnatal depression (2659 participants, 100 clusters ICC for cost 0.17, ICC for QALYs 0.04). We conducted a simulation study to assess the performance of the alternative methods. Missing data scenarios were simulated according to factors hypothesized to influence performance, amongst them ICCs, number and size of clusters and the proportion of missing data.

OBJECTIVE:To study the associations between timing and diversity of introduction of complementary foods during infancy and atopic sensitization in 5-year-old children.METHODS:In the Finnish DIPP (type 1 diabetes prediction and prevention) birth cohort (n = 3781), data on the timing of infant feeding were collected up to the age of 2 years and serum IgE antibodies toward four food and four inhalant allergens measured at the age of 5 years. Logistic regression was used for the analyses.RESULTS:Median duration of exclusive and total breastfeeding was 1.4 (interquartile range: 0.2-3.5) and 7.0 (4.0-11.0) months, respectively. When all the foods were studied together and adjusted for confounders, short duration of breastfeeding decreased the risk of sensitization to birch allergen; introduction of oats <5.1 months and barley <5.5 months decreased the risk of sensitization to wheat and egg allergens, and oats additionally associated with milk, timothy grass, and birch allergens. Introduction of rye <7.0 months decreased the risk of sensitization to birch allergen. Introduction of fish <6 months and egg ≤11 months decreased the risk of sensitization to all the specific allergens studied. The introduction of <3 food items at 3 months was associated with sensitization to wheat, timothy grass, and birch allergens; the introduction of 1-2 food items at 4 months and ≤4 food items at 6 months was associated with all endpoints, but house dust mite. These results were particularly evident among high-risk children when the results were stratified by atopic history, indicating the potential for reverse causality.CONCLUSIONS:The introduction of complementary foods was consecutively done, and with respect to the timing of each food, early introduction of complementary foods may protect against atopic sensitization in childhood, particularly among high-risk children. Less food diversity as already at 3 months of age may increase the risk of atopic sensitization.

In this paper, we formalize the application of multivariate meta‐analysis and meta‐regression to synthesize estimates of multi‐parameter associations obtained from different studies. This modelling approach extends the standard two‐stage analysis used to combine results across different sub‐groups or populations. The most straightforward application is for the meta‐analysis of non‐linear relationships, described for example by regression coefficients of splines or other functions, but the methodology easily generalizes to any setting where complex associations are described by multiple correlated parameters. The modelling framework of multivariate meta‐analysis is implemented in the package mvmeta within the statistical environment R. As an illustrative example, we propose a two‐stage analysis for investigating the non‐linear exposure–response relationship between temperature and non‐accidental mortality using time‐series data from multiple cities. Multivariate meta‐analysis represents a useful analytical tool for studying complex associations through a two‐stage procedure. Copyright © 2012 John Wiley & Sons, Ltd.

Background In Russia male drinking patterns have serious negative health effects; however the impact of alcohol on divorce is relatively unexplored. In other settings heavy drinking and discrepant drinking within couples increases the probability of marital breakdown. Longitudinal data, rather than cross-sectional, is preferable to establish the direction of any causal link. Methods The association between married couple drinking patterns and subsequent divorce was investigated in a national population-based panel study in Russia. Follow-up data on 4,266 married couples was extracted from 14 consecutive annual rounds (1994–2009) of the Russian Longitudinal Monitoring Survey. The overall follow-up rate of couples was 90%, and loss to follow-up was unrelated to drinking behaviour. At interview couples provided information about family relationships, drinking habits in the last 30 days and socio-demographic variables. Discrete time hazard models were fitted using pooled logistic regression to estimate the probability of divorce among married couples as a function of the previous round’s drinking patterns and other covariates. Results Increased odds of divorce were associated with greater frequency of husband drinking (P<0.001) and greater frequency of wife drinking (P<0.001), and remained significant after mutual adjustment. Wife’s hazardous drinking was also associated with a higher risk of divorce (OR 1.45, 95% CI 1.06–1.92) after adjustment for husband’s drinking. Husbands who were abstainers also had raised odds of divorce compared to moderate drinkers (OR 1.36, CI 1.01–1.84). There was a significant positive relationship between husband’s maximum daily volume of ethanol from vodka and divorce, after adjustment for frequency. After testing for interaction between husband’s and wife’s drinking, there was no evidence that couples with discrepant drinking frequencies had increased risk of divorce. Conclusion This study adds to the very sparse literature investigating the association of drinking with divorce using longitudinal data. The results suggest that in Russia heavy and frequent drinking of both husbands and wives put couples at greater risk of future divorce. The thresholds where frequency and volume adversely affect marital stability are higher in husbands, than in wives. Male abstainers have a higher degree of marital dysfunction, lending support to the idea that many Russian male abstainers are ex-drinkers. More research is needed to understand the causal pathways from drinking to marital breakdown in Russia, and the overall population-level impact of drinking on partnerships.

Aims Early introduction of supplementary foods has been implicated to play a role in the development of beta-cell autoimmunity. We set out to study the effects of breastfeeding and age at introduction of supplementary foods on the development of beta-cell autoimmunity.Methods A prospective birth cohort of 6069 infants with HLA-DQB-conferred susceptibility to Type 1 diabetes was recruited between 1996 and 2004. Antibodies against islet cells, insulin, glutamate dehydroxylase and islet antigen 2 were measured at 3- to 12-month intervals. The families recorded at home the age at introduction of new foods and, for each visit, completed a structured dietary questionnaire. The endpoint was repeated positivity for islet cell antibodies plus at least one other antibody and/or clinical Type 1 diabetes (n = 265).Results Early introduction of root vegetables (by the age of 4 months) was related to increased risk of developing positivity for the endpoint [hazard ratio (95% CI) for the earliest third 1.75 (1.11-2.75) and for the middle third 1.79 (1.22-2.62) compared with the last third (> 4 months), likelihood ratio test P = 0.006], independently of the introduction of other foods and of several putative socio-demographic and perinatal confounding factors. Introducing wheat, rye, oats and/or barley cereals (P = 0.013) and egg (P = 0.031) early was related to an increased risk of the endpoint, but only during the first 3 years of life.Conclusions Early introduction of root vegetables during infancy is independently associated with increased risk of beta-cell autoimmunity among Finnish children with increased genetic susceptibility to Type 1 diabetes.

We evaluated the intake of vitamin D by pregnant Finnish women and examined associations between maternal intake of vitamin D and the development of advanced beta cell autoimmunity and type 1 diabetes in their offspring.

Environmental stressors often show effects that are delayed in time, requiring the use of statistical models that are flexible enough to describe the additional time dimension of the exposure–response relationship. Here we develop the family of distributed lag non‐linear models (DLNM), a modelling framework that can simultaneously represent non‐linear exposure–response dependencies and delayed effects. This methodology is based on the definition of a ‘cross‐basis’, a bi‐dimensional space of functions that describes simultaneously the shape of the relationship along both the space of the predictor and the lag dimension of its occurrence. In this way the approach provides a unified framework for a range of models that have previously been used in this setting, and new more flexible variants. This family of models is implemented in the package dlnm within the statistical environment R. To illustrate the methodology we use examples of DLNMs to represent the relationship between temperature and mortality, using data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) for New York during the period 1987–2000. Copyright © 2010 John Wiley & Sons, Ltd.

Aim. - Reactive oxygen intermediates have been implicated in mediating the destruction of insulin-producing beta cells and antioxidant nutrients thought to protect against such a process. This study aimed to assess the associations between serum alpha- and beta-carotene concentrations, and the risk of advanced beta-cell autoimmunity, in children with HLA-conferred susceptibility to type 1 diabetes.Methods. - This case-control study, comprising 108 case children with advanced beta-cell autoimmunity and 216 matched control children, was nested within the nutrition study of the Type 1 Diabetes Prediction and Prevention (DIPP) birth cohort. Serum alpha- and beta-carotene samples were collected each year from the age of 1 to 6 years. For each case-control group, serum samples were analyzed up to the time of seroconversion in the case children. Associations were studied using a conditional logistic-regression model.Results. - Neither serum alpha- nor beta-carotene concentration was significantly associated with the risk of advanced beta-cell autoimmunity. There was marginal evidence (P = 0.049) of an inverse association between serum beta-carotene concentration and the risk of developing advanced beta-cell autoimmunity at a time closest to seroconversion after adjusting for parental education, maternal age, duration of gestation, diabetes in first-degree relatives, number of earlier deliveries and maternal smoking during pregnancy.Conclusion. - The present study data provided no clear evidence to support an association between serum alpha- or beta-carotene concentration and advanced beta-cell autoimmunity. (C) 2010 Elsevier Masson SAS. All rights reserved.

BACKGROUND:Evidence for a putative role of maternal diet during pregnancy in the development of β-cell autoimmunity in the child is scarce. The authors study the association of food consumption during pregnancy and the development of β-cell autoimmunity in the offspring. SUBJECTS AND METHODS:A prospective Finnish birth cohort of 4297 infants with human leukocyte antigen (HLA)-DQB1-conferred susceptibility to type 1 diabetes and their mothers. Blood samples were collected from the children at 3-12 months intervals to measure type 1 diabetes-associated antibodies: antibodies against islet cells (ICA), insulin, glutamate dehydroxylase, and islet antigen 2. The mothers completed a validated food frequency questionnaire. The end-point was repeated positivity for ICA together with at least one of the other three antibodies. Piecewise-exponential survival models were used. The effective sample size was 3723, with 138 end-points. The median follow-up time was 4.4 years. RESULTS:Maternal consumption of butter, low-fat margarines, berries, and coffee were inversely associated with the development of advanced β-cell autoimmunity in the offspring, adjusted for genetic risk group and familial diabetes. These associations for low-fat margarines (use vs. non-use HR 0.60, 95% CI: 0.38-0.93, p = 0.02), berries (continuous variable HR 0.90, 95% CI: 0.83-0.98, p = 0.02) and coffee (highest quarter vs. lowest HR 0.62, 95% CI: 0.40-0.97, p = 0.04), remained significant when adjusting for potential confounding sociodemographic, perinatal, and other dietary factors. CONCLUSIONS:In this study assessing total food consumption of the mother during pregnancy, only few among the 27 food groups tested were weakly related to the development of advanced β-cell autoimmunity in Finnish children.