Multiple imputation methods for bivariate outcomes in cluster randomised trials.

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.

Maternal diet during pregnancy and lactation and cow's milk allergy in offspring.

BACKGROUND/OBJECTIVES: 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. SUBJECTS/METHODS: 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. RESULTS: 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. CONCLUSIONS: High maternal consumption of milk products during pregnancy may protect children from developing CMA, especially in offspring of non-allergic mothers.

Maternal intake of fatty acids and their food sources during lactation and the risk of preclinical and clinical type 1 diabetes in the offspring.

AIMS: 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. METHODS: The subjects comprised a cohort of 2,939 mother-child pairs from the prospective Type 1 Diabetes Prediction and Prevention Study. Composition of maternal diet during the third month of lactation was assessed by a validated food frequency questionnaire. Among the children with HLA-conferred susceptibility to type 1 diabetes, 172 developed preclinical and 81 clinical diabetes. Average follow-up for preclinical type 1 diabetes was 7.5 years (range 0.2-14.0 years) and for clinical type 1 diabetes 7.7 years (0.2-14.0 years). RESULTS: Maternal intake of fatty acids during lactation was not associated with the risk of type 1 diabetes in the offspring. After adjusting for putative confounders, maternal total consumption of red meat and meat products during lactation was associated both with increased risk for preclinical [hazard ratio (HR) 1.19, 95 % CI 1.02-1.40, p = 0.038] and clinical type 1 diabetes (HR 1.27, 95 % CI 1.06-1.52, p = 0.025). In particular, consumption of processed meat products showed an association with increased risk for type 1 diabetes (HR 1.23, 95 % CI 1.02-1.48, p = 0.045). Maternal use of vegetable oils was associated with increased risk for preclinical type 1 diabetes (HR 1.21, 95 % CI 1.03-1.41, p = 0.023). CONCLUSIONS: Maternal consumption of red meat, especially processed meat, during lactation may increase the risk of type 1 diabetes.

Introduction of complementary foods in infancy and atopic sensitization at the age of 5 years: timing and food diversity in a Finnish birth cohort.

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.

Methods for dealing with time-dependent confounding.

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.

Multivariate meta-analysis for non-linear and other multi-parameter associations.

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.

Maternal dietary fat and fatty acid intake during lactation and the risk of asthma in the offspring.

AIM: To explore the association between maternal dietary fat and fatty acid (FA) intake during lactation, and the risk of asthma in the offspring by the age of 5 years. METHODS: The subjects comprised 1798 mother-child pairs from the Type 1 Diabetes Prediction and Prevention (DIPP) Nutrition Study. Dietary intake was assessed by a validated 181-item food frequency questionnaire, which covered the third month of lactation. The cumulative incidence of asthma was assessed at the age of 5 years with a questionnaire modified from the International Study of Asthma and Allergies in Childhood (ISAAC). Cox proportional hazards regression was used for statistical analysis. RESULTS: The maternal use of margarines during lactation was associated with a marginally increased risk of asthma [hazard ratio (HR) for user vs. nonuser 1.96, 95% confidence interval (CI) 1.01-3.82, p = 0.047] after adjusting for putative confounders. The maternal intakes of n-3 polyunsaturated FA (PUFA) and fish during lactation were not associated with the risk of asthma. CONCLUSION: Maternal use of margarines during lactation was weakly associated with an increased risk of asthma in the offspring at the age of 5 years. Other fats or FAs during lactation were not associated with the risk of asthma. However, the nonadherence to dietary recommendations regarding especially fats of our study population may restrict the generalizability of our results.

Maternal food consumption during pregnancy and risk of advanced ß-cell autoimmunity in the offspring.

BACKGROUND: Evidence for a putative role of maternal diet during pregnancy in the development of ß-cell autoimmunity in the child is scarce. The authors study the association of food consumption during pregnancy and the development of ß-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 ß-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 ß-cell autoimmunity in Finnish children.

Early introduction of root vegetables in infancy associated with advanced ß-cell autoimmunity in young children with human leukocyte antigen-conferred susceptibility to Type 1 diabetes.

AIMS: Early introduction of supplementary foods has been implicated to play a role in the development of ß-cell autoimmunity. We set out to study the effects of breastfeeding and age at introduction of supplementary foods on the development of ß-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 ß-cell autoimmunity among Finnish children with increased genetic susceptibility to Type 1 diabetes.

Are serum α- and ß-carotene concentrations associated with the development of advanced beta-cell autoimmunity in children with increased genetic susceptibility to type 1 diabetes?

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 α- and ß-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 α- and ß-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 α- nor ß-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 ß-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 α- or ß-carotene concentration and advanced beta-cell autoimmunity.

Distributed lag non-linear models.

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.

Serum fatty acids and risk of advanced beta-cell autoimmunity: a nested case-control study among children with HLA-conferred susceptibility to type I diabetes.

BACKGROUND/OBJECTIVES: N-3 (omega-3) fatty acids have been reported to decrease the risk for development of beta-cell autoimmunity and clinical type I diabetes. We set out to examine whether different serum fatty acids are associated with the development of advanced beta-cell autoimmunity in children carrying human leukocyte antigen DQ beta-1 (HLA-DQB1)-conferred susceptibility to type I diabetes. SUBJECTS/METHODS: Within a cohort, serum total fatty acid composition of 108 children with advanced beta-cell autoimmunity and of 216 matched persistently autoantibody-negative controls was analyzed using gas chromatography. Non-fasting serum samples were obtained annually at the ages of 1-6 years. Conditional logistic regression was applied to analyze the associations between advanced beta-cell autoimmunity and serum fatty acids. RESULTS: The serum fatty acid profile of myristic acid (odds ratio (OR) 1.48, 95% confidence interval (CI) 1.09-2.00, P=0.011), pentadecanoic acid (OR 1.65, 95% CI 1.19-2.28, P=0.003), palmitoleic acid isomers 16:1 n-7 (omega-7) (OR 1.41, 95% CI 1.03-1.92, P=0.030) and 16:1 n-9 (omega-9) (OR 1.45, 95% CI 1.05-2.01, P=0.026) and conjugated linoleic acid (OR 1.67, 95% CI 1.16-2.41, P=0.006) closest to the time of the appearance of multiple autoantibodies were positively associated with the risk of advanced beta-cell autoimmunity after adjustment for potential confounding factors. Serum linoleic acid showed inverse, marginal association with the end point. CONCLUSIONS: Serum biomarkers of milk and ruminant meat fat consumption are directly associated and linoleic acid is inversely associated with advanced beta-cell autoimmunity in children with HLA-conferred susceptibility to type I diabetes.

Maternal intake of vitamin D during pregnancy and risk of advanced beta cell autoimmunity and type 1 diabetes in offspring.

AIMS/HYPOTHESIS: 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. METHODS: The research was carried out within the Diabetes Prediction and Prevention study (DIPP), which is a population-based birth cohort of infants at genetic risk of type 1 diabetes. Mothers of 3,723 infants born between 1997 and 2002 completed a validated 181-item food frequency questionnaire, which included questions on dietary supplements. The offspring were observed at 3 to 12 month intervals for the appearance of autoantibodies associated with type 1 diabetes and for the development of clinical type 1 diabetes. RESULTS: Maternal mean daily intake of vitamin D was 5.1 microg from food and 1.3 microg from supplements. The maternal intake of vitamin D, either from food or from supplements, was not associated with the risk of advanced beta cell autoimmunity/type 1 diabetes in offspring (HR [95% CI] for intake of vitamin D from food 1.25 [0.80-1.95], for vitamin D intake from supplements 1.05 [0.95-1.16]), or with the risk of type 1 diabetes alone (HR [95% CI] for intake of vitamin D from food 0.84 [0.41-1.72], for vitamin D intake from supplements 1.09 [0.99-1.20]). CONCLUSIONS/INTERPRETATION: Maternal intake of vitamin D either from food or supplements during pregnancy is not associated with advanced beta cell autoimmunity/type 1 diabetes or with type 1 diabetes alone in Finnish offspring carrying increased genetic susceptibility to type 1 diabetes.

Childhood leukaemia: long-term excess mortality and the proportion 'cured'.

Survival from childhood leukaemia has increased, but the proportion of children cured is unknown. The proportion 'cured' is defined as the proportion of survivors for whom, as a group, there is no longer excess mortality compared to the general population. Average time to cure is defined as the time since diagnosis at which the excess mortality rate has declined to or below a predetermined small value. Data on children diagnosed with leukaemia during 1971-2000 in Great Britain were used to estimate trends in survival, the proportion cured and the average time to cure. Five-year survival for all types of leukaemia combined rose from 33 to 79% by 2000. The percentage cured rose from 25 to 68% by 1995; it is predicted to increase to 73% for those diagnosed more recently. Average time to cure increased from 12 years (95% confidence interval (CI): 11-14) to 19 years (95% CI: 14-26) for lymphoid leukaemia (average annual increase of 0.3 years; P<0.001), but remained at about 5 years for acute nonlymphoblastic leukaemia. The proportion of children cured of leukaemia has risen dramatically, but the period of excess mortality associated with lymphoid leukaemia has also increased, possibly because of late relapse, secondary malignancy and toxicity from treatment.

Serum alpha- and gamma-tocopherol concentrations and risk of advanced beta cell autoimmunity in children with HLA-conferred susceptibility to type 1 diabetes mellitus.

AIMS/HYPOTHESIS: The aim of our study was to assess the associations of serum alpha- and gamma-tocopherol concentrations with the risk of advanced beta cell autoimmunity in children with HLA-conferred genetic susceptibility to type 1 diabetes mellitus. METHODS: A case-control study with 108 cases with advanced beta cell autoimmunity and 216 matched control participants nested within the birth cohort of the Type 1 Diabetes Prediction and Prevention Project. A serum sample for vitamin E analyses was collected from all the children in the cohort at the age of 1 year and thereafter at 12 month intervals. For each case-control group, all the repeated serum samples up to the age of seroconversion to autoantibody positivity in the case were analysed. A conditional logistic regression model was used to determine potential associations between seroconversion and serum tocopherol concentrations. RESULTS: Serum alpha- or gamma-tocopherol concentrations were not significantly associated with the risk of advanced beta cell autoimmunity. The odds ratio (95% CI) for micromol/l increase in serum concentration of the first-year sample was 0.97 (0.92-1.03) for alpha-tocopherol and 1.10 (0.70-1.74) for gamma-tocopherol. However, there was an interaction between high values of gamma-tocopherol at the age of 1 year and the time of seroconversion (p = 0.024). CONCLUSIONS/INTERPRETATION: It seems unlikely that high concentrations of alpha- or gamma-tocopherol protect against advanced beta cell autoimmunity in young children.

Age at introduction of new foods and advanced beta cell autoimmunity in young children with HLA-conferred susceptibility to type 1 diabetes.

AIMS/HYPOTHESIS: Evidence for the role of infant feeding in the development of beta cell autoimmunity is inconsistent. We set out to study the effects of breastfeeding and of age at introduction of supplementary foods on the development of beta cell autoimmunity. SUBJECTS AND METHODS: A prospective birth cohort of 3,565 infants with HLA-DQB1-conferred susceptibility to type 1 diabetes was recruited between 1996 and 2001 from two university hospital areas in Finland. Blood samples were collected at 3- to 12-month intervals to measure antibodies against islet cells, insulin, glutamate dehydroxylase and islet antigen 2. The families kept a record on 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 together with at least one of the other three antibodies. RESULTS: The overall or exclusive duration of breastfeeding was not associated with the risk of developing the endpoint. An early age at introduction of fruits and berries (< or =4 months) was related to increased risk of developing positivity for the endpoint (hazard ratio [95% CI] for earliest tertile 2.02 [1.03-3.95] and for midtertile 1.97 [1.06-3.64] compared with latest tertile >4 months). Also, introducing roots between 3 and 3.9 months (midtertile) was related to increased risk of the endpoint (hazard ratio [95% CI] for the earliest tertile 1.04 [0.57-1.90] and for midtertile 1.82 [1.19-2.79] compared with latest tertile). These associations were independent of several putative socio-demographic and perinatal confounding factors. CONCLUSIONS/INTERPRETATION: Our findings suggest that an early age at introduction of fruits and berries and roots associates independently with beta cell autoimmunity, contradicting earlier findings from smaller birth cohort studies.

Use of antimicrobials and risk of type 1 diabetes in a population-based mother-child cohort.

AIMS/HYPOTHESIS: The aim of this study was to investigate whether the use of antimicrobials is associated with the risk of childhood type 1 diabetes. MATERIALS AND METHODS: The study population included all children born in Finland between 1996 and 2000 who were diagnosed with type 1 diabetes by the end of 2002. For each case (n=437), four matched controls were selected. Data on diabetes and the maternal use of antimicrobials was derived from nationwide registries. RESULTS: Maternal use of phenoxymethyl penicillins (odds ratio [OR]=1.70, 95% CI 1.08-2.68, p=0.022) or quinolone antimicrobials (OR=2.43, 95% CI 1.16-5.10, p=0.019) before pregnancy was associated with an increased risk of type 1 diabetes in the child, whereas the use of other specific antimicrobials was not related to the risk. The risk was also higher among mother-child pairs where macrolides were used both by the mother before pregnancy and by the child, compared with pairs where neither used macrolides (OR=1.76, 95% CI 1.05-2.94, p=0.032). Maternal use of antimicrobials during pregnancy was not associated with an increased risk. The high use of antimicrobials by the child (more than seven vs seven or less purchases) was related to greater risk (OR=1.66, 95% CI 1.24-2.24, p=0.001). CONCLUSIONS/INTERPRETATION: Overall, the use of antimicrobials before pregnancy, during pregnancy or during childhood was not related to the risk of childhood type 1 diabetes. However, the use of some specific antimicrobials by the mother before pregnancy and by the child may be associated with an increased risk. Further studies are needed to confirm these associations and to elucidate the underlying mechanisms of action.

A comparison of two methods for the estimation of precision with incomplete longitudinal data, jointly modelled with a time-to-event outcome.

Several methods for the estimation and comparison of rates of change in longitudinal studies with staggered entry and informative drop-outs have been recently proposed. For multivariate normal linear models, REML estimation is used. There are various approaches to maximizing the corresponding log-likelihood; in this paper we use a restricted iterative generalized least squares method (RIGLS) combined with a nested EM algorithm. An important statistical problem in such approaches is the estimation of the standard errors adjusted for the missing data (observed data information matrix). Louis has provided a general technique for computing the observed data information in terms of completed data quantities within the EM framework. The multiple imputation (MI) method for obtaining variances can be regarded as an alternative to this. The aim of this paper is to develop, apply and compare the Louis and a modified MI method in the setting of longitudinal studies where the source of missing data is either death or disease progression (informative) or end of the study (assumed non-informative). Longitudinal data are simultaneously modelled with the missingness process. The methods are illustrated by modelling CD4 count data from an HIV-1 clinical trial and evaluated through simulation studies. Both methods, Louis and MI, are used with Monte Carlo simulations of the missing data using the appropriate conditional distributions, the former with 100 simulations, the latter with 5 and 10. It is seen that naive SEs based on the completed data likelihood can be seriously biased. This bias was largely corrected by Louis and modified MI methods, which gave broadly similar estimates. Given the relative simplicity of the modified MI method, it may be preferable.