Pairwise fitting of piecewise mixed models for the joint modeling of multivariate longitudinal outcomes, in a randomized crossover trial.

Many statistical models have been proposed in the literature for the analysis of longitudinal data. One may propose to model two or more correlated longitudinal processes simultaneously, with a goal of understanding their association over time. Joint modeling is then required to carefully study the association structure among the outcomes as well as drawing joint inferences about the different outcomes. In this study, we sought to model the associations among six nutrition outcomes while circumventing the computational challenge posed by their clustered and high-dimensional nature. We analyzed data from a 2 × $\times$ 2 randomized crossover trial conducted in Kenya, to compare the effect of high-dose and low-dose iodine in household salt on systolic blood pressure (SBP) and diastolic blood pressure (DBP) in women of reproductive age and their household matching pair of school-aged children. Two additional outcomes, namely, urinary iodine concentration (UIC) in women and children were measured repeatedly to monitor the amount of iodine excreted through urine. We extended the model proposed by Mwangi et al. (2021, Communications in Statistics: Case Studies, Data Analysis and Applications, 7(3), 413-431) allowing flexible piecewise joint models for six outcomes to depend on separate random effects, which are themselves correlated. This entailed fitting 15 bivariate general linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We analyzed the outcomes separately and jointly using piecewise linear mixed-effects (PLME) model and further validated the results using current state-of-the-art Jones and Kenward methodology (JKME model) used for analyzing randomized crossover trials. The results indicate that high-dose iodine in salt significantly reduced blood pressure (BP) compared to low-dose iodine in salt. Estimates for the random effects and residual error components showed that SBP and DBP had strong positive correlation, with effect of the random slope indicating that significantly related outcomes are strongly associated in their evolution. There was a moderately strong inverse relationship between evolutions of UIC and BP both in women and children. These findings confirmed the original hypothesis that high-dose iodine salt has significant lowering effect on BP. We further sought to evaluate the performance of our proposed PLME model against the widely used JKME model, within the multivariate joint modeling framework through a simulation study mimicking a 2 × 2 $2\times 2$ crossover design. From our findings, the multivariate joint PLME model performed exceptionally well both in estimation of random-effects matrix (G) and Hessian matrix (H), allowing satisfactory model convergence during estimation. It allowed a more complex fit to the data with both random intercepts and slopes effects compared to the multivariate joint JKME model that allowed for random intercepts only. When a hierarchical viewpoint is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive definite. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters. The key highlight in this evaluation shows that multivariate joint JKME model is a powerful tool especially while fitting mixed models with random intercepts only, in crossover design settings. Addition of random slopes may lead to model complexities in most cases, resulting in unsatisfactory model convergence during estimation. To circumvent convergence pitfalls, extention of JKME model to PLME model allows a more flexible fit to the data (generated from crossover design settings), especially in the multivariate joint modeling framework.

Evaluation of a flexible piecewise linear mixed-effects model in the analysis of randomized cross-over trials.

Cross-over designs are commonly used in randomized clinical trials to estimate efficacy of a new treatment. They have received a lot of attention, particularly in connection with regulatory requirements for new drugs. The main advantage of using cross-over designs over conventional parallel designs is increased precision, thanks to within-subject comparisons. In the statistical literature, more recent developments are discussed in the analysis of cross-over trials, in particular regarding repeated measures. A piecewise linear model within the framework of mixed effects has been proposed in the analysis of cross-over trials. In this article, we report on a simulation study comparing performance of a piecewise linear mixed-effects (PLME) model against two commonly cited models-Grizzle's mixed-effects (GME) and Jones & Kenward's mixed-effects (JKME) models-used in the analysis of cross-over trials. Our simulation study tried to mirror real-life situation by deriving true underlying parameters from empirical data. The findings from real-life data confirmed the original hypothesis that high-dose iodine salt have significantly lowering effect on diastolic blood pressure (DBP). We further sought to evaluate the performance of PLME model against GME and JKME models, within univariate modeling framework through a simulation study mimicking a 2 × 2 cross-over design. The fixed-effects, random-effects and residual error parameters used in the simulation process were estimated from DBP data, using a PLME model. The initial results with full specification of random intercept and slope(s), showed that the univariate PLME model performed better than the GME and JKME models in estimation of variance-covariance matrix (G) governing the random effects, allowing satisfactory model convergence during estimation. When a hierarchical view-point is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive-definite. The PLME model is preferred especially in modeling an increased number of random effects, compared to the GME and JKME models that work equally well with random intercepts only. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters.

Handling missing data in a composite outcome with partially observed components: simulation study based on clustered paediatric routine data.

Composite scores are useful in providing insights and trends about complex and multidimensional quality of care processes. However, missing data in subcomponents may hinder the overall reliability of a composite measure. In this study, strategies for handling missing data in Paediatric Admission Quality of Care (PAQC) score, an ordinal composite outcome, were explored through a simulation study. Specifically, the implications of the conventional method employed in addressing missing PAQC score subcomponents, consisting of scoring missing PAQC score components with a zero, and a multiple imputation (MI)-based strategy, were assessed. The latent normal joint modelling MI approach was used for the latter. Across simulation scenarios, MI of missing PAQC score elements at item level produced minimally biased estimates compared to the conventional method. Moreover, regression coefficients were more prone to bias compared to standards errors. Magnitude of bias was dependent on the proportion of missingness and the missing data generating mechanism. Therefore, incomplete composite outcome subcomponents should be handled carefully to alleviate potential for biased estimates and misleading inferences. Further research on other strategies of imputing at the component and composite outcome level and imputing compatibly with the substantive model in this setting, is needed.

Pairwise joint modeling of clustered and high-dimensional outcomes with covariate missingness in pediatric pneumonia care.

Multiple outcomes reflecting different aspects of routine care are a common phenomenon in health care research. A common approach of handling such outcomes is multiple univariate analyses, an approach which does not allow for answering research questions pertaining to joint inference. In this study, we sought to study associations among nine pediatric pneumonia care outcomes spanning assessment, diagnosis and treatment domains of care, while circumventing the computational challenge posed by their clustered and high-dimensional nature and incompletely recorded covariates. We analyzed data from a cluster randomized trial conducted in 12 Kenyan hospitals. There were varying degrees of missingness in the covariates of interest, and these were multiply imputed using latent normal joint modeling. We used the pairwise joint modeling strategy to fit a correlated random effects joint model for the nine outcomes. This entailed fitting 36 bivariate generalized linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We also analyzed the nine outcomes separately before and after multiple imputation. We observed joint effects of patient-, clinician- and hospital-level factors on pneumonia care indicators before and after multiple imputation of missing covariates. In both pairwise joint modeling and separate univariate analysis methods, enhanced audit and feedback improved documentation and adherence to recommended clinical guidelines over time in six and five pneumonia care indicators, respectively. Additionally, multiple imputation improved precision of parameter estimates compared to complete case analysis. The strength and direction of association among pneumonia outcomes varied within and across the three domains of pneumonia care.

Association between multimorbidity and socioeconomic deprivation on short-term mortality among patients with diffuse large B-cell or follicular lymphoma in England: a nationwide cohort study.

OBJECTIVES: We aimed to assess the association between multimorbidity and deprivation on short-term mortality among patients with diffuse large B-cell (DLBCL) and follicular lymphoma (FL) in England. SETTING: The association of multimorbidity and socioeconomic deprivation on survival among patients diagnosed with DLBCL and FL in England between 2005 and 2013. We linked the English population-based cancer registry with electronic health records databases and estimated adjusted mortality rate ratios by multimorbidity and deprivation status. Using flexible hazard-based regression models, we computed DLBCL and FL standardised mortality risk by deprivation and multimorbidity at 1 year. RESULTS: Overall, 41 422 patients aged 45-99 years were diagnosed with DLBCL or FL in England during 2005-2015. Most deprived patients with FL with multimorbidities had three times higher hazard of 1-year mortality (HR: 3.3, CI 2.48 to 4.28, p<0.001) than least deprived patients without comorbidity; among DLBCL, there was approximately twice the hazard (HR: 1.9, CI 1.70 to 2.07, p<0.001). CONCLUSIONS: Multimorbidity, deprivation and their combination are strong and independent predictors of an increased short-term mortality risk among patients with DLBCL and FL in England. Public health measures targeting the reduction of multimorbidity among most deprived patients with DLBCL and FL are needed to reduce the short-term mortality gap.

Excess Mortality by Multimorbidity, Socioeconomic, and Healthcare Factors, amongst Patients Diagnosed with Diffuse Large B-Cell or Follicular Lymphoma in England.

(1) Background: Socioeconomic inequalities of survival in patients with lymphoma persist, which may be explained by patients' comorbidities. We aimed to assess the association between comorbidities and the survival of patients diagnosed with diffuse large B-cell (DLBCL) or follicular lymphoma (FL) in England accounting for other socio-demographic characteristics. (2) Methods: Population-based cancer registry data were linked to Hospital Episode Statistics. We used a flexible multilevel excess hazard model to estimate excess mortality and net survival by patient's comorbidity status, adjusted for sociodemographic, economic, and healthcare factors, and accounting for the patient's area of residence. We used the latent normal joint modelling multiple imputation approach for missing data. (3) Results: Overall, 15,516 and 29,898 patients were diagnosed with FL and DLBCL in England between 2005 and 2013, respectively. Amongst DLBCL and FL patients, respectively, those in the most deprived areas showed 1.22 (95% confidence interval (CI): 1.18-1.27) and 1.45 (95% CI: 1.30-1.62) times higher excess mortality hazard compared to those in the least deprived areas, adjusted for comorbidity status, age at diagnosis, sex, ethnicity, and route to diagnosis. (4) Conclusions: Deprivation is consistently associated with poorer survival among patients diagnosed with DLBCL or FL, after adjusting for co/multimorbidities. Comorbidities and multimorbidities need to be considered when planning public health interventions targeting haematological malignancies in England.

Dealing with missing information on covariates for excess mortality hazard regression models - Making the imputation model compatible with the substantive model.

Missing data is a common issue in epidemiological databases. Among the different ways of dealing with missing data, multiple imputation has become more available in common statistical software packages. However, the incompatibility between the imputation and substantive model, which can arise when the associations between variables in the substantive model are not taken into account in the imputation models or when the substantive model is itself nonlinear, can lead to invalid inference. Aiming at analysing population-based cancer survival data, we extended the multiple imputation substantive model compatible-fully conditional specification (SMC-FCS) approach, proposed by Bartlett et al. in 2015 to accommodate excess hazard regression models. The proposed approach was compared with the standard fully conditional specification multiple imputation procedure and with the complete-case analysis using a simulation study. The SMC-FCS approach produced unbiased estimates in both scenarios tested, while the fully conditional specification produced biased estimates and poor empirical coverages probabilities. The SMC-FCS algorithm was then used for handling missing data in the evaluation of socioeconomic inequalities in survival from colorectal cancer patients diagnosed in the North Region of Portugal. The analysis using SMC-FCS showed a clearer trend in higher excess hazards for patients coming from more deprived areas. The proposed algorithm was implemented in R software and is presented as Supplementary Material.

Investigating the inequalities in route to diagnosis amongst patients with diffuse large B-cell or follicular lymphoma in England.

INTRODUCTION: Diagnostic delay is associated with lower chances of cancer survival. Underlying comorbidities are known to affect the timely diagnosis of cancer. Diffuse large B-cell (DLBCL) and follicular lymphomas (FL) are primarily diagnosed amongst older patients, who are more likely to have comorbidities. Characteristics of clinical commissioning groups (CCG) are also known to impact diagnostic delay. We assess the association between comorbidities and diagnostic delay amongst patients with DLBCL or FL in England during 2005-2013. METHODS: Multivariable generalised linear mixed-effect models were used to assess the main association. Empirical Bayes estimates of the random effects were used to explore between-cluster variation. The latent normal joint modelling multiple imputation approach was used to account for partially observed variables. RESULTS: We included 30,078 and 15,551 patients diagnosed with DLBCL or FL, respectively. Amongst patients from the same CCG, having multimorbidity was strongly associated with the emergency route to diagnosis (DLBCL: odds ratio 1.56, CI 1.40-1.73; FL: odds ratio 1.80, CI 1.45-2.23). Amongst DLBCL patients, the diagnostic delay was possibly correlated with CCGs that had higher population densities. CONCLUSIONS: Underlying comorbidity is associated with diagnostic delay amongst patients with DLBCL or FL. Results suggest a possible correlation between CCGs with higher population densities and diagnostic delay of aggressive lymphomas.

Handling missing data in modelling quality of clinician-prescribed routine care: Sensitivity analysis of departure from missing at random assumption.

Missing information is a major drawback in analyzing data collected in many routine health care settings. Multiple imputation assuming a missing at random mechanism is a popular method to handle missing data. The missing at random assumption cannot be confirmed from the observed data alone, hence the need for sensitivity analysis to assess robustness of inference. However, sensitivity analysis is rarely conducted and reported in practice. We analyzed routine paediatric data collected during a cluster randomized trial conducted in Kenyan hospitals. We imputed missing patient and clinician-level variables assuming the missing at random mechanism. We also imputed missing clinician-level variables assuming a missing not at random mechanism. We incorporated opinions from 15 clinical experts in the form of prior distributions and shift parameters in the delta adjustment method. An interaction between trial intervention arm and follow-up time, hospital, clinician and patient-level factors were included in a proportional odds random-effects analysis model. We performed these analyses using R functions derived from the jomo package. Parameter estimates from multiple imputation under the missing at random mechanism were similar to multiple imputation estimates assuming the missing not at random mechanism. Our inferences were insensitive to departures from the missing at random assumption using either the prior distributions or shift parameters sensitivity analysis approach.

Longitudinal associations between neighbourhood trust, social support and physical activity in adolescents: evidence from the Olympic Regeneration in East London (ORiEL) study.

BACKGROUND: Most UK adolescents do not achieve recommended levels of physical activity (PA). Previous studies suggest that the social environment could contribute to inequalities in PA behaviours, but longitudinal evidence is limited. We examined whether neighbourhood trust and social support were longitudinally associated with four common forms of PA: walking to school, walking for leisure, outdoor PA and pay and play PA. We further assessed whether gender moderated these associations. METHODS: We used longitudinal data from the Olympic Regeneration in East London (ORiEL) study. In 2012, 3106 adolescents aged 11-12 were enrolled from 25 schools in four deprived boroughs of East London, UK. Adolescents were followed-up in 2013 and 2014. The final sample includes 2664 participants interviewed at waves 2 and 3. We estimated logistic regression models using generalised estimating equations (GEEs) (pooled models) and proportional odds models (models of change) to assess associations between the social environment exposures and the PA outcomes, adjusting for potential confounders. Item non-response was handled using multilevel multiple imputation. RESULTS: We found that different aspects of the social environment predict different types of PA. Neighbourhood trust was positively associated with leisure-type PA. Social support from friends and family was positively associated with walking for leisure. There was some evidence that changes in exposures led to changes in the PA outcomes. Associations did not systematically differ by gender. CONCLUSION: These results confirm the importance of the social environment to predict PA and its change over time in a deprived and ethnically diverse adolescent population.

Comorbidity prevalence among cancer patients: a population-based cohort study of four cancers.

BACKGROUND: The presence of comorbidity affects the care of cancer patients, many of whom are living with multiple comorbidities. The prevalence of cancer comorbidity, beyond summary metrics, is not well known. This study aims to estimate the prevalence of comorbid conditions among cancer patients in England, and describe the association between cancer comorbidity and socio-economic position, using population-based electronic health records. METHODS: We linked England cancer registry records of patients diagnosed with cancer of the colon, rectum, lung or Hodgkin lymphoma between 2009 and 2013, with hospital admissions records. A comorbidity was any one of fourteen specific conditions, diagnosed during hospital admission up to 6 years prior to cancer diagnosis. We calculated the crude and age-sex adjusted prevalence of each condition, the frequency of multiple comorbidity combinations, and used logistic regression and multinomial logistic regression to estimate the adjusted odds of having each condition and the probability of having each condition as a single or one of multiple comorbidities, respectively, by cancer type. RESULTS: Comorbidity was most prevalent in patients with lung cancer and least prevalent in Hodgkin lymphoma patients. Up to two-thirds of patients within each of the four cancer patient cohorts we studied had at least one comorbidity, and around half of the comorbid patients had multiple comorbidities. Our study highlighted common comorbid conditions among the cancer patient cohorts. In all four cohorts, the odds of having a comorbidity and the probability of multiple comorbidity were consistently highest in the most deprived cancer patients. CONCLUSIONS: Cancer healthcare guidelines may need to consider prominent comorbid conditions, particularly to benefit the prognosis of the most deprived patients who carry the greater burden of comorbidity. Insight into patterns of cancer comorbidity may inform further research into the influence of specific comorbidities on socio-economic inequalities in receipt of cancer treatment and in short-term mortality.

Associations between school and neighbourhood ethnic density and physical activity in adolescents: Evidence from the Olympic Regeneration in East London (ORiEL) study.

While most adolescents do not achieve the recommended level of physical activity in the UK, the risk of physical inactivity varies across ethnic groups. We investigated whether own-group school and neighbourhood ethnic density can explain ethnic differences in adolescent physical activity. We used longitudinal data from the Olympic Regeneration in East London (ORiEL) study. In 2012, 3106 adolescents aged 11-12 were recruited from 25 schools in East London, UK. Adolescents were followed-up in 2013 and 2014. Own-group ethnic density was measured in 2012-2014 at school-level and in 2011 at neighbourhood-level, and calculated as the percentage of pupils/residents who were of the same ethnic group. Analyses were restricted to White British (n = 382), White Mixed (n = 190), Bangladeshi (n = 337), and Black African groups (n = 251). We estimated adjusted logistic regression models with generalised estimating equations for self-reported walking to school, walking for leisure, and outdoor physical activity. At school-level, there was consistent evidence that own-group ethnic density amplifies ethnic differences in walking to school. For each 10 percentage point increase in own-group ethnic density, there was evidence of increased probability of walking to school in Bangladeshi adolescents (OR = 1.20; 95% CI 1.09-1.31) and decreased probability of walking to school in Black African (OR = 0.58; 95% CI 0.45-0.75) and White Mixed adolescents (OR = 0.51; 95% CI 0.35-0.76). Associations with walking for leisure and outdoor physical activity were in expected directions but not consistently observed in all ethnic groups. At neighbourhood-level, evidence was more restricted. Amplification of ethnic differences was found for walking to school in Bangladeshi adolescents (OR = 1.31; 95% CI 1.14-1.51) and for outdoor physical activity in White British adolescents (OR = 0.85; 95% CI 0.76-0.94). Our results suggest that own-group ethnic density contributes to explaining differences in physical activity by amplifying ethnic differences in some forms of physical activity.

Analysis of Hierarchical Routine Data With Covariate Missingness: Effects of Audit & Feedback on Clinicians' Prescribed Pediatric Pneumonia Care in Kenyan Hospitals.

Background: Routine clinical data are widely used in many countries to monitor quality of care. A limitation of routine data is missing information which occurs due to lack of documentation of care processes by health care providers, poor record keeping, or limited health care technology at facility level. Our objective was to address missing covariates while properly accounting for hierarchical structure in routine pediatric pneumonia care. Methods: We analyzed routine data collected during a cluster randomized trial to investigating the effect of audit and feedback (A&F) over time on inpatient pneumonia care among children admitted in 12 Kenyan hospitals between March and November 2016. Six hospitals in the intervention arm received enhance A&F on classification and treatment of pneumonia cases in addition to a standard A&F report on general inpatient pediatric care. The remaining six in control arm received standard A&F alone. We derived and analyzed a composite outcome known as Pediatric Admission Quality of Care (PAQC) score. In our analysis, we adjusted for patients, clinician and hospital level factors. Missing data occurred in patient and clinician level variables. We did multiple imputation of missing covariates within the joint model imputation framework. We fitted proportion odds random effects model and generalized estimating equation (GEE) models to the data before and after multilevel multiple imputation. Results: Overall, 2,299 children aged 2 to 59 months were admitted with childhood pneumonia in 12 hospitals during the trial period. 2,127 (92%) of the children (level 1) were admitted by 378 clinicians across the 12 hospitals. Enhanced A&F led to improved inpatient pediatric pneumonia care over time compared to standard A&F. Female clinicians and hospitals with low admission workload were associated with higher uptake of the new pneumonia guidelines during the trial period. In both random effects and marginal model, parameter estimates were biased and inefficient under complete case analysis. Conclusions: Enhanced A&F improved the uptake of WHO recommended pediatric pneumonia guidelines over time compared to standard audit and feedback. When imputing missing data, it is important to account for the hierarchical structure to ensure compatibility with analysis models of interest to alleviate bias.

Random effects models for estimation of the probability and time to progression of a continuous biomarker.

Biomarkers play a key role in the monitoring of disease progression. The time taken for an individual to reach a biomarker exceeding or lower than a meaningful threshold is often of interest. Due to the inherent variability of biomarkers, persistence criteria are sometimes included in the definitions of progression, such that only two consecutive measurements above or below the relevant threshold signal that "true" progression has occurred. In previous work, a novel approach was developed, which allowed estimation of the time to threshold using the parameters from a linear mixed model where the residual variance was assumed to be pure measurement error. In this paper, we extend this methodology so that serial correlation can be accommodated. Assuming that the Markov property holds and applying the chain rule of probabilities, we found that the probability of progression at each timepoint can be expressed simply as the product of conditional probabilities. The methodology is applied to a cohort of HIV positive individuals, where the time to reach a CD4 count threshold is estimated. The second application we present is based on a study on abdominal aortic aneurysms, where the time taken for an individual to reach a diameter exceeding 55 mm is studied. We observed that erroneously ignoring the residual correlation when it is strong may result in substantial overestimation of the time to threshold. The estimated probability of the biomarker reaching a threshold of interest, expected time to threshold, and confidence intervals are presented for selected patients in both applications.

Association between age, deprivation and specific comorbid conditions and the receipt of major surgery in patients with non-small cell lung cancer in England: A population-based study.

INTRODUCTION: We investigated socioeconomic disparities and the role of the main prognostic factors in receiving major surgical treatment in patients with lung cancer in England. METHODS: Our study comprised 31 351 patients diagnosed with non-small cell lung cancer in England in 2012. Data from the national population-based cancer registry were linked to Hospital Episode Statistics and National Lung Cancer Audit data to obtain information on stage, performance status and comorbidities, and to identify patients receiving major surgical treatment. To describe the association between prognostic factors and surgery, we performed two different analyses: one using multivariable logistic regression and one estimating cause-specific hazards for death and surgery. In both analyses, we used multiple imputation to deal with missing data. RESULTS: We showed strong evidence that the comorbidities 'congestive heart failure', 'cerebrovascular disease' and 'chronic obstructive pulmonary disease' reduced the receipt of surgery in early stage patients. We also observed gender differences and substantial age differences in the receipt of surgery. Despite accounting for sex, age at diagnosis, comorbidities, stage at diagnosis, performance status and indication of having had a PET-CT scan, the socioeconomic differences persisted in both analyses: more deprived people had lower odds and lower rates of receiving surgery in early stage lung cancer. DISCUSSION: Comorbidities play an important role in whether patients undergo surgery, but do not completely explain the socioeconomic difference observed in early stage patients. Future work investigating access to and distance from specialist hospitals, as well as patient perceptions and patient choice in receiving surgery, could help disentangle these persistent socioeconomic inequalities.

Longitudinal associations between perceptions of the neighbourhood environment and physical activity in adolescents: evidence from the Olympic Regeneration in East London (ORiEL) study.

BACKGROUND: Most UK adolescents do not achieve recommended levels of physical activity. Previous studies suggested that perceptions of the neighbourhood environment could contribute to explain differences in physical activity behaviours. We aimed to examine whether five measures of perceptions - perceived bus stop proximity, traffic safety, street connectivity, enjoyment of the neighbourhood for walking/cycling, and personal safety - were longitudinally associated with common forms of physical activity, namely walking to school, walking for leisure, and a composite measure of outdoor physical activity. We further aimed to investigate the moderating role of gender. METHODS: We used longitudinal data from the Olympic Regeneration in East London (ORiEL) study, a prospective cohort study. In 2012, 3106 adolescents aged 11 to 12 were recruited from 25 schools in 4 deprived boroughs of East London. Adolescents were followed-up in 2013 and 2014. The final sample includes 2260 adolescents surveyed at three occasions. We estimated logistic regression models using Generalised Estimating Equations to test the plausibility of hypotheses on the nature of the longitudinal associations (general association, cumulative effect, co-varying trajectories), adjusting for potential confounders. Item non-response was handled using multiple imputation. RESULTS: Longitudinal analyses indicate little evidence that perceptions of the neighbourhood are important predictors of younger adolescent physical activity. There was weak evidence that greater perceived proximity to bus stops is associated with a small decrease in the probability of walking for leisure. Results also indicate that poorer perception of personal safety decreases the probability of walking for leisure. There was some indication that better perception of street connectivity is associated with more outdoor physical activity. Finally, we found very little evidence that the associations between perceptions of the neighbourhood and physical activity differed by gender. CONCLUSIONS: This study suggests that younger adolescents' perceptions of their neighbourhood environment, and changes in these perceptions, did not consistently predict physical activity in a deprived and ethnically diverse urban population. Future studies should use situation-specific measures of the neighbourhood environment and physical activity to better capture the hypothesised processes and explore the relative roles of the objective environment, parental and adolescents' perceptions in examining differences in types of physical activity.

Characteristics of patients with missing information on stage: a population-based study of patients diagnosed with colon, lung or breast cancer in England in 2013.

BACKGROUND: Stage is a key predictor of cancer survival. Complete cancer staging is vital for understanding outcomes at population level and monitoring the efficacy of early diagnosis initiatives. Cancer registries usually collect details of the disease extent but staging information may be missing because a stage was never assigned to a patient or because it was not included in cancer registration records. Missing stage information introduce methodological difficulties for analysis and interpretation of results. We describe the associations between missing stage and socio-demographic and clinical characteristics of patients diagnosed with colon, lung or breast cancer in England in 2013. We assess how these associations change when completeness is high, and administrative issues are assumed to be minimal. We estimate the amount of avoidable missing stage data if high levels of completeness reached by some Clinical Commissioning Groups (CCGs), were achieved nationally. METHODS: Individual cancer records were retrieved from the National Cancer Registration and linked to the Routes to Diagnosis and Hospital Episode Statistics datasets to obtain additional clinical information. We used multivariable beta binomial regression models to estimate the strength of the association between socio-demographic and clinical characteristics of patients and missing stage and to derive the amount of avoidable missing stage. RESULTS: Multivariable modelling showed that old age was associated with missing stage irrespective of the cancer site and independent of comorbidity score, short-term mortality and patient characteristics. This remained true for patients in the CCGs with high completeness. Applying the results from these CCGs to the whole cohort showed that approximately 70% of missing stage information was potentially avoidable. CONCLUSIONS: Missing stage was more frequent in older patients, including those residing in CCGs with high completeness. This disadvantage for older patients was not explained fully by the presence of comorbidity. A substantial gain in completeness could have been achieved if administrative practices were improved to the level of the highest performing areas. Reasons for missing stage information should be carefully assessed before any study, and potential distortions introduced by how missing stage is handled should be considered in order to draw the most correct inference from available statistics.

Microbial Performance of Food Safety Control and Assurance Activities in a Fresh Produce Processing Sector Measured Using a Microbial Assessment Scheme and Statistical Modeling.

Current approaches such as inspections, audits, and end product testing cannot detect the distribution and dynamics of microbial contamination. Despite the implementation of current food safety management systems, foodborne outbreaks linked to fresh produce continue to be reported. A microbial assessment scheme and statistical modeling were used to systematically assess the microbial performance of core control and assurance activities in five Kenyan fresh produce processing and export companies. Generalized linear mixed models and correlated random-effects joint models for multivariate clustered data followed by empirical Bayes estimates enabled the analysis of the probability of contamination across critical sampling locations (CSLs) and factories as a random effect. Salmonella spp. and Listeria monocytogenes were not detected in the final products. However, none of the processors attained the maximum safety level for environmental samples. Escherichia coli was detected in five of the six CSLs, including the final product. Among the processing-environment samples, the hand or glove swabs of personnel revealed a higher level of predicted contamination with E. coli , and 80% of the factories were E. coli positive at this CSL. End products showed higher predicted probabilities of having the lowest level of food safety compared with raw materials. The final products were E. coli positive despite the raw materials being E. coli negative for 60% of the processors. There was a higher probability of contamination with coliforms in water at the inlet than in the final rinse water. Four (80%) of the five assessed processors had poor to unacceptable counts of Enterobacteriaceae on processing surfaces. Personnel-, equipment-, and product-related hygiene measures to improve the performance of preventive and intervention measures are recommended.

A novel approach to estimation of the time to biomarker threshold: applications to HIV.

In longitudinal studies of biomarkers, an outcome of interest is the time at which a biomarker reaches a particular threshold. The CD4 count is a widely used marker of human immunodeficiency virus progression. Because of the inherent variability of this marker, a single CD4 count below a relevant threshold should be interpreted with caution. Several studies have applied persistence criteria, designating the outcome as the time to the occurrence of two consecutive measurements less than the threshold. In this paper, we propose a method to estimate the time to attainment of two consecutive CD4 counts less than a meaningful threshold, which takes into account the patient-specific trajectory and measurement error. An expression for the expected time to threshold is presented, which is a function of the fixed effects, random effects and residual variance. We present an application to human immunodeficiency virus-positive individuals from a seroprevalent cohort in Durban, South Africa. Two thresholds are examined, and 95% bootstrap confidence intervals are presented for the estimated time to threshold. Sensitivity analysis revealed that results are robust to truncation of the series and variation in the number of visits considered for most patients. Caution should be exercised when interpreting the estimated times for patients who exhibit very slow rates of decline and patients who have less than three measurements. We also discuss the relevance of the methodology to the study of other diseases and present such applications. We demonstrate that the method proposed is computationally efficient and offers more flexibility than existing frameworks. Copyright © 2016 John Wiley & Sons, Ltd.

A characterization of missingness at random in a generalized shared-parameter joint modeling framework for longitudinal and time-to-event data, and sensitivity analysis.

We consider a conceptual correspondence between the missing data setting, and joint modeling of longitudinal and time-to-event outcomes. Based on this, we formulate an extended shared random effects joint model. Based on this, we provide a characterization of missing at random, which is in line with that in the missing data setting. The ideas are illustrated using data from a study on liver cirrhosis, contrasting the new framework with conventional joint models.