Adjustment for time-invariant and time-varying confounders in 'unexplained residuals' models for longitudinal data within a causal framework and associated challenges.

'Unexplained residuals' models have been used within lifecourse epidemiology to model an exposure measured longitudinally at several time points in relation to a distal outcome. It has been claimed that these models have several advantages, including: the ability to estimate multiple total causal effects in a single model, and additional insight into the effect on the outcome of greater-than-expected increases in the exposure compared to traditional regression methods. We evaluate these properties and prove mathematically how adjustment for confounding variables must be made within this modelling framework. Importantly, we explicitly place unexplained residual models in a causal framework using directed acyclic graphs. This allows for theoretical justification of appropriate confounder adjustment and provides a framework for extending our results to more complex scenarios than those examined in this paper. We also discuss several interpretational issues relating to unexplained residual models within a causal framework. We argue that unexplained residual models offer no additional insights compared to traditional regression methods, and, in fact, are more challenging to implement; moreover, they artificially reduce estimated standard errors. Consequently, we conclude that unexplained residual models, if used, must be implemented with great care.

Joint modelling compared with two stage methods for analysing longitudinal data and prospective outcomes: A simulation study of childhood growth and BP.

There is a growing debate with regards to the appropriate methods of analysis of growth trajectories and their association with prospective dependent outcomes. Using the example of childhood growth and adult BP, we conducted an extensive simulation study to explore four two-stage and two joint modelling methods, and compared their bias and coverage in estimation of the (unconditional) association between birth length and later BP, and the association between growth rate and later BP (conditional on birth length). We show that the two-stage method of using multilevel models to estimate growth parameters and relating these to outcome gives unbiased estimates of the conditional associations between growth and outcome. Using simulations, we demonstrate that the simple methods resulted in bias in the presence of measurement error, as did the two-stage multilevel method when looking at the total (unconditional) association of birth length with outcome. The two joint modelling methods gave unbiased results, but using the re-inflated residuals led to undercoverage of the confidence intervals. We conclude that either joint modelling or the simpler two-stage multilevel approach can be used to estimate conditional associations between growth and later outcomes, but that only joint modelling is unbiased with nominal coverage for unconditional associations.

Challenges in modelling the random structure correctly in growth mixture models and the impact this has on model mixtures.

Lifecourse trajectories of clinical or anthropological attributes are useful for identifying how our early-life experiences influence later-life morbidity and mortality. Researchers often use growth mixture models (GMMs) to estimate such phenomena. It is common to place constrains on the random part of the GMM to improve parsimony or to aid convergence, but this can lead to an autoregressive structure that distorts the nature of the mixtures and subsequent model interpretation. This is especially true if changes in the outcome within individuals are gradual compared with the magnitude of differences between individuals. This is not widely appreciated, nor is its impact well understood. Using repeat measures of body mass index (BMI) for 1528 US adolescents, we estimated GMMs that required variance-covariance constraints to attain convergence. We contrasted constrained models with and without an autocorrelation structure to assess the impact this had on the ideal number of latent classes, their size and composition. We also contrasted model options using simulations. When the GMM variance-covariance structure was constrained, a within-class autocorrelation structure emerged. When not modelled explicitly, this led to poorer model fit and models that differed substantially in the ideal number of latent classes, as well as class size and composition. Failure to carefully consider the random structure of data within a GMM framework may lead to erroneous model inferences, especially for outcomes with greater within-person than between-person homogeneity, such as BMI. It is crucial to reflect on the underlying data generation processes when building such models.

Prospective development and validation of a model to predict heart failure hospitalisation.

OBJECTIVE: Acute heart failure syndrome (AHFS) is a major cause of hospitalisation and imparts a substantial burden on patients and healthcare systems. Tools to define risk of AHFS hospitalisation are lacking. METHODS: A prospective cohort study (n=628) of patients with stable chronic heart failure (CHF) secondary to left ventricular systolic dysfunction was used to derive an AHFS prediction model which was then assessed in a prospectively recruited validation cohort (n=462). RESULTS: Within the derivation cohort, 44 (7%) patients were hospitalised as a result of AHFS during 1 year of follow-up. Predictors of AHFS hospitalisation included furosemide equivalent dose, the presence of type 2 diabetes mellitus, AHFS hospitalisation within the previous year and pulmonary congestion on chest radiograph, all assessed at baseline. A multivariable model containing these four variables exhibited good calibration (Hosmer-Lemeshow p=0.38) and discrimination (C-statistic 0.77; 95% CI 0.71 to 0.84). Using a 2.5% risk cut-off for predicted AHFS, the model defined 38.5% of patients as low risk, with negative predictive value of 99.1%; this low risk cohort exhibited <1% excess all-cause mortality per annum when compared with contemporaneous actuarial data. Within the validation cohort, an identically applied model derived comparable performance parameters (C-statistic 0.81 (95% CI 0.74 to 0.87), Hosmer-Lemeshow p=0.15, negative predictive value 100%). CONCLUSIONS: A prospectively derived and validated model using simply obtained clinical data can identify patients with CHF at low risk of hospitalisation due to AHFS in the year following assessment. This may guide the design of future strategies allocating resources to the management of CHF.

Statistical profiling of hospital performance using acute coronary syndrome mortality.

BACKGROUND: In order to improve the quality of care delivered to patients and to enable patient choice, public reports comparing hospital performances are routinely published. Robust systems of hospital 'report cards' on performance monitoring and evaluation are therefore crucial in medical decision-making processes. In particular, such systems should effectively account for and minimise systematic differences with regard to definitions and data quality, care and treatment quality, and 'case mix'. METHODS: Four methods for assessing hospital performance on mortality outcome measures were considered. The methods included combinations of Bayesian fixed- and random-effects models, and risk-adjusted mortality rate, and rank-based profiling techniques. The methods were empirically compared using 30-day mortality in patients admitted with acute coronary syndrome. Agreement was firstly assessed using median estimates between risk-adjusted mortality rates for a hospital and between ranks associated with a hospital's risk-adjusted mortality rates. Secondly, assessment of agreement was based on a classification of hospitals into low, normal or high performing using risk-adjusted mortality rates and ranks. RESULTS: There was poor agreement between the point estimates of risk-adjusted mortality rates, but better agreement between ranks. However, for categorised performance, the observed agreement between the methods' classification of the hospital performance ranged from 90 to 98%. In only two of the six possible pair-wise comparisons was agreement reasonable, as reflected by a Kappa statistic; it was 0.71 between the methods of identifying outliers with the fixed-effect model and 0.77 with the hierarchical model. In the remaining four pair-wise comparisons, the agreement was, at best, moderate. CONCLUSIONS: Even though the inconsistencies among the studied methods raise questions about which hospitals performed better or worse than others, it seems that the choice of the definition of outlying performance is less critical than that of the statistical approach. Therefore there is a need to find robust systems of 'regulation' or 'performance monitoring' that are meaningful to health service practitioners and providers.

Waiting times for radiotherapy after breast-conserving surgery and the association with survival: a path analysis.

AIMS: To investigate the association between radiotherapy waiting times and survival in women who have undergone breast-conserving surgery using data from two English cancer registry regions. The data were analysed using path analysis to account for the complex variable interrelationships within the data. MATERIALS AND METHODS: Cases of female invasive breast cancer diagnosed during the period 1 January 1998 to 31 December 2005 were identified and linked to an extract of Hospital Episode Statistics data. A subset of these linked records where women underwent breast-conserving surgery was extracted (n=18,158). Patient, tumour and treatment information were extracted. A path model was developed with three outcome variables: survival, time to receive radiotherapy and receipt of chemotherapy before radiotherapy. RESULTS: During the study period, the median radiotherapy waiting time in region 1 increased from 70 days to 128.5 days. In region 2, the median wait increased from 44 days in 1998 to 68 days in 2001, then decreased to 42 days by 2005. In the path model, radiotherapy waiting time was not associated with survival (hazard ratio=1.00, 95% confidence interval 0.99-1.01 per week increase in both regions). Patients receiving chemotherapy before radiotherapy waited 12.3 weeks (region 1) and 6.3 weeks (region 2) longer for their radiotherapy than those not receiving chemotherapy. Patients with stage II/III disease waited longer than patients with stage I disease. Younger age, diagnosis of stage II/III disease and presence of co-morbidities were associated with increased odds of receiving chemotherapy before radiotherapy. CONCLUSIONS: This study found no association between waiting times for radiotherapy and survival in two regions of England, despite increases in waiting times over the study period. Such an association, if real, may only become apparent after a longer period of follow-up.

Trends in the association between blood pressure and obesity in a Taiwanese population between 1996 and 2006.

In the last decades, the prevalence of obesity has increased in the Taiwanese population. This has the potential to impact on the risks of cardiovascular diseases and diabetes. This study investigated trends in the changes in several indices of obesity in the last decade, and the relationship between blood pressure (BP) and these obesity indices available in Mei-Jaw Corporation health-screening data from 1996/1998 to 2006. Three cross-sectional surveys among healthy individuals ages 20-59 years, in which 14,362 subjects examined in year 1996, 17,368 in 1998, and 28,524 in 2006, were included in the analysis. Body weight and height data were available from 1996, whereas %body fat, waist circumference and waist-hip ratio (Whratio) were only available from 1998 onwards. We found that the association between systolic BP and body weight, body mass index, %body fat, Whratio and waist became stronger for both men and women in 2006 than 1996 after adjustment for age, education level, alcohol intake, smoking and betel nut chewing. In contrast, non-obese people seemed to have lower diastolic BP in 2006 than in 1996. This trend is consistent irrespective of the index of obesity used. Among healthy individuals, the average values for the obesity indices increased in men but remained similar in women. However, in both men and women, the relationship between obesity and BP has changed. Further research is required to investigate the impact of these intriguing changes in the associations on the risk of cardiovascular diseases in the Taiwanese population.

The impact of the Calman-Hine report on the processes and outcomes of care for Yorkshire's breast cancer patients.

BACKGROUND: The 1995 Calman-Hine plan outlined radical reform of the UK's cancer services with the aim of improving outcomes and reducing inequalities in National Health Service cancer care. Its main recommendation was to concentrate care into the hands of site-specialist multidisciplinary teams. This study aimed to determine whether these teams improved processes and outcomes of care for breast cancer patients. PATIENTS AND METHODS: All patients diagnosed and treated with breast cancer in the Yorkshire region of the UK from 1995 to 2000 were identified within the Northern and Yorkshire Cancer Registry and Information Service database. Changes in the use of breast-conserving surgery, adjuvant radiotherapy following breast-conserving surgery and 5-year survival were assessed among these patients in relation to their managing breast cancer team's degree of adherence to the manual of cancer service standards (which outlines the specification of the 'ideal' breast cancer team) and the extent of site specialisation of each team's surgeons. RESULTS: Variation was observed in the extent to which the breast cancer teams in Yorkshire had conformed to the Calman-Hine recommendations. Increases in adherence to the recommendations in the manual of cancer service standards were associated with a reduction in the use of breast-conserving surgery [odds ratio (OR) = 0.83, 95% confidence interval (CI) = 0.70-0.98, P < 0.01]. Increases in both surgical specialisation (OR = 1.23, 95% CI = 1.00-1.55, P = 0.06) and adherence to the manual of cancer service standards (OR = 1.22, 95% CI = 0.97-1.52, P = 0.05) were associated with the increased use of radiotherapy following breast-conserving surgery. There was a trend towards improved 5-year survival (hazard ratio = 0.93, 95% CI = 0.86-1.01, P = 0.10) in relation to increasing surgical site specialisation. All these effects were present after adjustment for the casemix factors of age, stage of disease, socio-economic background and year of diagnosis. CONCLUSIONS: The extent of implementation of the Calman-Hine report has been variable and, on the basis of limited clinical and organisational information available, its recommendations appear to be associated with improvements in processes and outcomes of care for breast cancer patients.

Socioeconomic background in relation to stage at diagnosis, treatment and survival in women with breast cancer.

In a large population-based series of invasive breast cancer patients, we investigated socioeconomic background (SEB) in relation to (a) stage at diagnosis; (b) treatment pattern; and (c) 5-year survival. Women diagnosed during 1998-2000 and resident in the Northern and Yorkshire regions of England were identified from the cancer registry database (N=12,768). Logistic regression and Cox proportional hazards analyses were used to estimate associations between SEB (defined using the Townsend Index for area of residence) and tumour stage, treatment pattern, and survival. Living in a more deprived area was associated with increased likelihood of being diagnosed with stage III or IV disease (age-adjusted odds ratio (OR) 1.13; 95% confidence interval (CI) 1.08-1.18 per quartile increase in Townsend score), and, after adjustment for age and stage, reduced odds of having surgery (OR 0.85; 95% CI 0.80-0.91), and receiving radiotherapy (OR 0.91; 95% CI 0.88-0.94). Amongst patients receiving surgery, those living in more deprived areas had decreased odds of having breast conserving surgery (age plus stage-adjusted OR 0.92; 95% CI 0.89-0.95). Living in a more deprived area was also associated with increased mortality (age- plus stage-adjusted hazard ratio 1.08; 95% CI 1.05-1.11). These effects may operate through several pathways, such as later presentation leading to advanced disease.

Haplotype uncertainty in association studies.

Inferring haplotypes from genotype data is commonly undertaken in population genetic association studies. Within such studies the importance of accounting for uncertainty in the inference of haplotypes is well recognised. We investigate the effectiveness of correcting for uncertainty using simple methods based on the output provided by the PHASE haplotype inference methodology. In case-control analyses investigating non-Hodgkin lymphoma and haplotypes associated with immune regulation we find little effect of making adjustment for uncertainty in inferred haplotypes. Using simulation we introduce a higher degree of haplotype uncertainty than was present in our study data. The simulation represents two genetic loci, physically close on a chromosome, forming haplotypes. Considering a range of allele frequencies, degrees of linkage between the loci, and frequency of missing genotype data, we detail the characteristics of genetic regions which may be susceptible to the influence of haplotype uncertainty. Within our evaluation we find that bias is avoided by considering haplotype probabilities or using multiple imputation, provided that for each of these methods haplotypes are inferred separately for case and control populations; furthermore using multiple imputation provides the facility to incorporate haplotype uncertainty in the estimation of confidence intervals. We discuss the implications of our findings within the context of the complexity of haplotype inference for larger marker rich regions as would typically be encountered in genetic analyses.

The impact of the Calman-Hine report on the processes and outcomes of care for Yorkshire's colorectal cancer patients.

The 1995 Calman-Hine plan outlined radical reform of the UK's cancer services with the aim of improving outcomes and reducing inequalities in NHS cancer care. Its main recommendation was to concentrate care into the hands of site-specialist, multi-disciplinary teams. This study aimed to determine if the implementation of Calman-Hine cancer teams was associated with improved processes and outcomes of care for colorectal cancer patients. The design included longitudinal survey of 13 colorectal cancer teams in Yorkshire and retrospective study of population-based data collected by the Northern and Yorkshire Cancer Registry and Information Service. The population was all colorectal cancer patients diagnosed and treated in Yorkshire between 1995 and 2000. The main outcome measures were: variations in the use of anterior resection and preoperative radiotherapy in rectal cancer, chemotherapy in Dukes stage C and D patients, and five-year survival. Using multilevel models, these outcomes were assessed in relation to measures of the extent of Calman-Hine implementation throughout the study period, namely: (i) each team's degree of adherence to the Manual of Cancer Service Standards (which outlines the specification of the 'ideal' colorectal cancer team) and (ii) the extent of site specialisation of each team's surgeons. Variation was observed in the extent to which the colorectal cancer teams in Yorkshire had conformed to the Calman-Hine recommendations. An increase in surgical site specialisation was associated with increased use of preoperative radiotherapy (OR=1.43, 95% CI=1.04-1.98, P<0.04) and anterior resection (OR=1.43, 95% CI=1.16-1.76, P<0.01) in rectal cancer patients. Increases in adherence to the Manual of Cancer Service Standards was associated with improved five-year survival after adjustment for the casemix factors of age, stage of disease, socioeconomic status and year of diagnosis, especially for colon cancer (HR=0.97, 95% CI=0.94-0.99 P<0.01). There was a similar trend of improved survival in relation to increased surgical site specialisation for rectal cancer, although the effect was not statistically significant (HR=0.93, 95% CI=0.84-1.03, P=0.15). In conclusion, the extent of implementation of the Calman-Hine report has been variable and its recommendations are associated with improvements in processes and outcomes of care for colorectal cancer patients.

Use of itemized Till receipts to adjust for correlated dietary measurement error.

Recent studies suggest that measurement error in food frequency questionnaires includes a person-specific component correlated with that of other self-reported dietary assessments. Use of biomarkers has been recommended to adequately calibrate dietary assessment tools for unbiased estimation of associations between diet and disease. Data on biomarkers of intake are often collected only in small subsamples, because collection of biomarker data can be expensive and inconvenient for participants. In this paper, the authors propose a novel approach using itemized household grocery till receipts to calibrate dietary assessment. Till receipts are not self-recorded and the data obtained from them are not subject to person-specific bias, but the data need to be supported by self-completed diaries for foods eaten away from home. Till receipts may also prove cheaper to collect in larger samples. The authors discuss the many methodological challenges of using household-level data and discuss how till receipts might be used in practice, with or without the use of biomarkers.

What is the effect of adjusting for more than one measure of current body size on the relation between birthweight and blood pressure?

The statistical validity of the negative associations observed between birthweight and disease in later life has recently been questioned, because these associations might be due, in part, to inappropriate adjustment for current body size, creating a statistical artefact known as the 'reversal paradox'. The aim of this study was to explore the effect of adjusting for more than one measure of current body size on the association between birthweight and disease in later life using simulations and meta-analyses of empirical studies. The simulations examined the relation between birthweight and adult systolic blood pressure before and after adjusting for one, two or three measures of current body size by including current weight and subsequently adding body mass index and height in successive analytical models. Meta-analyses were then performed to compare the effect sizes observed among empirical studies reporting associations between birthweight and blood pressure before and after adjusting for one or two measures of current body size. The meta-analyses confirmed the results of the simulations - both showed that associations between birthweight and blood pressure tend to become increasingly negative following adjustment for current body size, and that this effect is enhanced after adjusting for additional measures of current body size.

Problems of correlations between explanatory variables in multiple regression analyses in the dental literature.

Multivariable analysis is a widely used statistical methodology for investigating associations amongst clinical variables. However, the problems of collinearity and multicollinearity, which can give rise to spurious results, have in the past frequently been disregarded in dental research. This article illustrates and explains the problems which may be encountered, in the hope of increasing awareness and understanding of these issues, thereby improving the quality of the statistical analyses undertaken in dental research. Three examples from different clinical dental specialties are used to demonstrate how to diagnose the problem of collinearity/multicollinearity in multiple regression analyses and to illustrate how collinearity/multicollinearity can seriously distort the model development process. Lack of awareness of these problems can give rise to misleading results and erroneous interpretations. Multivariable analysis is a useful tool for dental research, though only if its users thoroughly understand the assumptions and limitations of these methods. It would benefit evidence-based dentistry enormously if researchers were more aware of both the complexities involved in multiple regression when using these methods and of the need for expert statistical consultation in developing study design and selecting appropriate statistical methodologies.

In vitro quantification of changes in human dentine tubule parameters using SEM and digital analysis.

Dentine hypersensitivity is recognized as a pain arising from fluid movement within dentine tubules that are open to the oral environment. Blocking the tubules is considered to be the principal aim of treatment, and the accurate assessment of tubule occlusion is the primary goal of many in vitro studies. This assessment usually comprises either measuring tubule permeability or scanning electron microscope examination of the dentine surface. Several scanning microscopy studies have claimed to quantify tubule occlusion, but are descriptive, qualitative or semi-quantitative evaluations. The present study was undertaken to assess the use of digital image analysis in quantifying the effectiveness of a selected desensitizing agent from micrographs of control and treated dentine surfaces. Using a dentine disc model, an accurate methodology was sought to investigate the occluding potential of Butler Protect (J.O. Butler, Chicago, IL, USA). Subjective examination of the images indicated there was little difference after a single application, but considerable effect after 20 applications. Quantitative digital analysis of a test image, demonstrated reproducibility between two examiners when used in fully- and semi-automated mode. After a single application of Butler Protect, multilevel statistical modelling demonstrated decreases in tubule area and maximum, minimum and mean diameter measurements (P < 0.001), whereas single level analysis showed increases in area and maximum and mean diameters. Multiple application of Butler Protect demonstrated even greater decreases in all parameters (P < 0.001). This quantitative methodology was reproducible between examiners and, when combined with good controls and multilevel statistical modelling, was able to discriminate a single application of desensitizing agent.

Statistical power for analyses of changes in randomized controlled trials.

Randomized controlled trials (RCTs) are widely recommended as the most useful study design to generate reliable evidence and guidance to daily practices in medicine and dentistry. However, it is not well-known in dental research that different statistical methods of data analysis can yield substantial differences in study power. In this study, computer simulations are used to explore how using different univariate and multivariate statistical methods of analyzing change in continuous outcome variables affects study power, and the sample size required for RCTs. Results show that, in general, analysis of covariance (ANCOVA) yields greater power than other statistical methods in testing the superiority of one treatment over another, or in testing the equivalence between two treatments. Therefore, ANCOVA should be used in preference to change score or percentage change score to reduce type II error rates.

Morbidity following dental treatment of children under intubation general anaesthesia in a day-stay unit.

OBJECTIVES: To determine which variables were best related to the overall morbidity of a child undergoing dental general anaesthetic (GA) and then to use these variables to determine those factors that might influence the extent and severity of morbidity experienced by healthy children following dental GA. SAMPLE AND METHODS: Data were collected on anxiety, pain and morbidity, GA procedure and dental procedure from 121 children attending a day stay GA unit for dental treatment. Patients were interviewed preoperatively, postoperatively before discharge then four further times over the next 148 h. Data were analysed using multivariate regression. RESULTS: Thirty-one per cent of subjects had restorative work, 60% had at least one tooth extracted, 54% had a surgical procedure. Use of local analgesia reduced postoperative pain whilst an increase in the number of surgical procedures increased it. Increase in anaesthetic time was related to increased odds of feeling sleepy and nauseous, females were more likely to complain of sleepiness or weakness. Feelings of dizziness were increased if the patient was given local analgesia during the procedure. CONCLUSIONS: Pain following dental GA was the most prevalent and long lasting symptom of postoperative morbidity in this study. Reductions in operating time and improvement in pain control have the potential to reduce reported morbidity following dental GA.

Unification of the "burst" and "linear" theories of periodontal disease progression: a multilevel manifestation of the same phenomenon.

Previously, burst and linear theories for periodontal disease progression were proposed based on different but limited statistical methods of analysis. Multilevel modeling provides a new approach, yielding a more comprehensive model. Random coefficient models were used to analyze longitudinal periodontal data consisting of repeated measures (level 1), sites (level 2), teeth (level 3), and subjects (level 4). Large negative and highly significant correlations between random linear and quadratic time coefficients indicated that subjects and teeth with greater-than-average linear change experienced decelerated variation. Conversely, subjects and teeth with less-than-average linear change experienced accelerated variation. Change therefore exhibited a dynamic regression to the mean at the tooth and subject levels. Since no equilibrium was attained throughout the study, changes were cyclical. When considered as a multilevel system, the "linear" and "burst" theories of periodontal disease progression are a manifestation of the same phenomenon: Some sites improve while others progress, in a cyclical manner.