Mark S. Gilthorpe

Simpson's Paradox, Lord's Paradox, and Suppression Effects are the same phenomenon--the reversal paradox.

This article discusses three statistical paradoxes that pervade epidemiological research: Simpsons paradox, Lords paradox, and suppression. These paradoxes have important implications for the interpretation of evidence from observational studies. This article uses hypothetical scenarios to illustrate how the three paradoxes are different manifestations of one phenomenon – the reversal paradox – depending on whether the outcome and explanatory variables are categorical, continuous or a combination of both; this renders the issues and remedies for any one to be similar for all three. Although the three statistical paradoxes occur in different types of variables, they share the same characteristic: the association between two variables can be reversed, diminished, or enhanced when another variable is statistically controlled for. Understanding the concepts and theory behind these paradoxes provides insights into some controversial or contradictory research findings. These paradoxes show that prior knowledge and underlying causal theory play an important role in the statistical modelling of epidemiological data, where incorrect use of statistical models might produce consistent, replicable, yet erroneous results.

Risk factors for oral epithelial dysplasia—the role of smoking and alcohol

The present study provides an assessment of the importance of tobacco and alcohol consumption upon the development of oral epithelial dysplasia (OED) in a large group of European patients. Data were collected in a case-control study based upon 630 patients with OED and 643 control subjects selected from UK dental hospital patients with oral disease not caused by tobacco or alcohol. Logistic regression was used to determine the association of several independent factors on the risk of OED. No relationship emerged between patients gender, age or ethnicity and risk of OED. The regression model demonstrated a combined effect of tobacco smoking and alcohol drinking upon the risk of OED. Non-filter cigarette smoking was a significant predictor of OED, as was alcohol consumption, and the two habits compounded one another in the overall risk of disease. When both factors combined were included in the model through interaction terms, their individual impact was only moderately reduced, illustrating the importance of both factors in their own right. However, more detailed analysis of tobacco smoking habits revealed that the increased risk of OED from smoking was largely attributable to heavy smoking (20 cigarettes per day, OR = 4.38, 95% C.I. = 2.6, 7.2) especially non-filter cigarettes (OR = 1.95, 95% C.I. = 0.9, 4.0) relative to non-smoking. Both heavy smoking and non-filtered tobacco were higher risks for OED than alcohol consumption alone. Tobacco cessation was associated with a significant decline in risk of OED, the reduction being rapid and marked. For alcohol consumption the association with OED was considerably stronger for drinkers of fortified wines and spirits (OR = 3.75, 95% C.I. = 1.40, 10.05 and OR = 1.36, 95% C.I. = 0.76, 2.45, respectively). It is concluded that, while tobacco and alcohol synergistically influence the development of OED, exclusive tobacco consumption is more likely than exclusive alcohol consumption to give rise to OED. The risk of OED may thus be significantly reduced by behavioural changes such as moderation of tobacco and alcohol use.

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 specialities 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.

Associations between tooth loss and mortality patterns in the Glasgow Alumni Cohort

Objective: To use data from the Glasgow Alumni Cohort to investigate whether oral health in young adulthood is independently associated with later life cardiovascular disease (CVD) and cancer mortality. Methods and results: Of the original cohort (n = 15 322), 12 631 subjects were traced through the National Health Service Central Register. Of these, 9569 men and 2654 women were 30 years or younger at baseline. During up to 57 years of follow-up, 1432 deaths occurred among subjects with complete data, including 509 deaths from CVD and 549 from cancer. After adjusting for potential confounders, no substantial association was found between the number of missing teeth (as a continuous variable) and all-cause mortality (hazard ratio (HR) for each extra missing tooth  = 1.01; 95% confidence interval (CI) 1.00 to 1.02), CVD mortality (HR = 1.01; 95% CI 0.99 to 1.03) or cancer mortality (HR = 1.00; 95% CI 0.98 to 1.02). When the number of missing teeth was treated as a categorical variable, there was evidence that students with nine or more missing teeth at baseline had an increased risk of CVD (HR = 1.35; 95% CI 1.03 to 1.77) compared with those with fewer than five missing teeth. When the number of missing teeth was transformed using fractional polynomials, there seemed to be a non-linear relation between missing teeth and CVD mortality. Conclusions: Although some evidence was found to support the relation between tooth loss and CVD mortality, causal mechanisms underlying this association remain uncertain.

Mortality of copper cadmium alloy workers with special reference to lung cancer and non-malignant diseases of the respiratory system, 1946-92.

OBJECTIVES--To identify and quantify any relations between occupational exposure to cadmium oxide fume and mortalities from lung cancer and from chronic non-malignant diseases of the respiratory system. METHODS--The mortality experience of 347 copper cadmium alloy workers, 624 workers employed in the vicinity of copper cadmium alloy work (vicinity workers), and 521 iron and brass foundry workers (all men) was investigated for the period 1946-92. All subjects were first employed in these types of work in the period 1922-78 and for a minimum period of one year at one of two participating factories. Two analytical approaches were used, indirect standardisation and Poisson regression. RESULTS--Compared with the general population of England and Wales, mortality from lung cancer among copper cadmium alloy workers was close to expectation (observed deaths 18, expected deaths 17.8, standardised mortality ratio (SMR) 101, 95% confidence interval (95% CI) 60 to 159). A significant excess was shown for lung cancer among vicinity workers but not among iron and brass foundry workers (vicinity workers: observed 55, expected 34.3, SMR 160, 95% CI 121 to 209, P < 0.01; iron and brass foundry workers: observed 19, expected 17.8, SMR 107, 95% CI 64 to 167). Increased SMRs for non-malignant diseases of the respiratory system were shown for each of the three groups (alloy workers: observed 54, expected 23.5, SMR 230, 95% CI 172 to 300, P < 0.001; vicinity workers: observed 71, expected 43.0, SMR 165, 95% CI 129 to 208, P < 0.001; iron and brass foundry workers: observed 34, expected 17.1, SMR 199, 95% CI 137 to 278, P < 0.01). Work histories of the copper cadmium alloy workers were combined with independent assessments of cadmium exposures over time to develop individual estimates of cumulative exposure to cadmium; this being a time dependent variable. Poisson regression was used to investigate risks of lung cancer and risks of chronic non-malignant diseases of the respiratory system in relation to three levels of cumulative cadmium exposure (< 1600, 1600-4799, > or = 4800 micrograms.m-3.y). After adjustment for age, year of starting alloy work, factory, and time from starting alloy work, there was a significant positive trend (P < 0.01) between cumulative exposure to cadmium and risks of mortality from chronic non-malignant diseases of the respiratory system. Relative to a risk of unity for the lowest exposure category, risks were 4.54 (95% CI 1.96 to 10.51) for the middle exposure category and 4.74 (95% CI 1.81 to 12.43) for the highest exposure category. There was a non-significant negative trend between cumulative cadmium exposure and risks of mortality from lung cancer. Relative to a risk of unity for the lowest exposure category, risks were 0.85 (95% CI 0.27 to 2.68) for the middle exposure category and 0.81 (95% CI 0.18 to 3.73) for the highest exposure category. Similar findings were obtained when adjustment was made for age only. CONCLUSIONS--The findings are consistent with the hypothesis that exposure to cadmium oxide fume increases risks of mortality from chronic non-malignant diseases of the respiratory system. The findings do not support the hypothesis that exposure to cadmium oxide fume increases risks of mortality for lung cancer.

Epidemiology of Functional Dyspepsia and Subgroups in the Italian General Population: An Endoscopic Study

BACKGROUND & AIMS Population-based endoscopic studies are needed to assess the epidemiology of functional dyspepsia (FD) and the newly suggested subgroups of meal-related symptoms and epigastric pain. We evaluated the prevalence of, and risk factors for, FD in the Italian general population. METHODS A total of 1533 inhabitants of 2 villages were invited to undergo symptom evaluation using a validated questionnaire, esophagogastroduodenoscopy, and (13)C-urea breath test; 1033 subjects (67.4%) took part. RESULTS Of the 1033 subjects, 156 (15.1%; 95% confidence interval [CI], 12.9-17.3) had dyspepsia, and of these 114 (11%; 95% CI, 9.2-12.9) had FD. Of the 114 subjects with FD, 77 (67.5%) had meal-related symptoms (postprandial fullness and/or early satiation) and 55 (48.2%) had epigastric pain. Only 18 subjects (15.8%) had both meal-related symptoms and epigastric pain; this was fewer than expected by chance alone (P < .001). Unemployment (odds ratio [OR], 5.80; 95% CI, 1.56-21.60), divorce (OR, 2.76; 95% CI, 1.10-6.91), smoking (OR, 1.74; 95% CI, 1.11-2.70), and irritable bowel syndrome (OR, 3.38; 95% CI, 1.85-6.19) were significantly associated with FD. Unemployment, divorce, and irritable bowel syndrome were associated with both meal-related symptoms and epigastric pain, while smoking was associated only with meal-related symptoms. CONCLUSIONS FD is present in 11% of the Italian general population. Unemployment and divorce seem to increase the risk of FD, and smoking seems to be associated with meal-related symptoms. Two distinct subgroups of FD, as suggested by Rome III, seem to exist in the general population.

A critical evaluation of statistical approaches to examining the role of growth trajectories in the developmental origins of health and disease

The developmental origins of health and disease hypothesis suggests that small birth size in conjunction with rapid compensatory childhood growth might yield a greater risk of developing chronic diseases in later life. For example, there is evidence that people who developed coronary heart disease and diabetes experienced different growth trajectories from those who did not develop these diseases. However, some of the methods used in these articles may have been flawed. We critically evaluate proposed approaches for identifying the growth trajectories distinctive to those developing later disease and identifying critical phases of growth during the early lifecourse. Among the approaches we examined (tracing the z-scores, lifecourse plots and models, lifecourse path analysis, conditional body size analysis, multilevel analysis, latent growth curve models and growth mixture models) conditional body size analysis, multilevel analysis, latent growth curve models and growth mixture models are least prone to collinearity problems caused by repeated measures. Multilevel analysis is more flexible when body size is not measured at the same age for all cohort members. Strengths and weaknesses of each approach are illustrated using real data. Demonstrating the influence of growth trajectories on later disease is complex and challenging; therefore, it is likely that a combination of approaches will be required to unravel the complexity in lifecourse research.

Rural/urban differences in the association between deprivation and healthcare utilisation

Whilst associations between inequalities in healthcare utilisation and socio-economic deprivation are well established in the UK it is argued that deprivation indices, such as the Townsend index, remain insensitive to rural/urban differences. This study examines how Townsend and its components differ in their association with healthcare utilisation across the rural/urban spectrum of a large health region. Our research was carried out in the West Midlands National Health Service region (population 5.3 million), comprising of a similar geographical population diversity to that of the United Kingdom (UK) using Hospital Episode Statistics (1994/5-1998/9) and 1991 census socio-demographic data. Retrospective multilevel multivariate models compare three ward-level healthcare utilisation measures (standardised episode-, admission-, and bed-rates) in relation to the Townsend index of material deprivation, its components, and four rural/urban characteristics (population density, population potential, electoral ward area and perimeter size). The associations between outcomes and Townsend were generally not attenuated by the rural/urban characteristics. The constituent component of car-ownership was similarly unperturbed, whereas population potential significantly perturbed the home-ownership model and overcrowding was significantly perturbed by all four rural/urban characteristics considered. A deprivation index may encapsulate different meanings to that of its components when used to assess variations in healthcare utilisation. Constituent components may yield considerable perturbation in relation to healthcare utilisation across the rural/urban spectrum, whilst the composite measure does not. In particular, and contrary to anecdotal opinion, car-ownership and unemployment (as recorded in the 1991 UK census) exhibited a stable relationship across different rural/urban areas with respect to healthcare utilisation.

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.

Joint disease mapping using six cancers in the Yorkshire region of England

ObjectivesThe aims of this study were to model jointly the incidence rates of six smoking related cancers in the Yorkshire region of England, to explore the patterns of spatial correlation amongst them, and to estimate the relative weight of smoking and other shared risk factors for the relevant disease sites, both before and after adjustment for socioeconomic background (SEB).MethodsData on the incidence of oesophagus, stomach, pancreas, lung, kidney, and bladder cancers between 1983 and 2003 were extracted from the Northern & Yorkshire Cancer Registry database for the 532 electoral wards in the Yorkshire region. Using postcode of residence, each case was assigned an area-based measure of SEB using the Townsend index. Standardised incidence ratios (SIRs) were calculated for each cancer site and their correlations investigated. The joint analysis of the spatial variation in incidence used a Bayesian shared-component model. Three components were included to represent differences in smoking (for all six sites), bodyweight/obesity (for oesophagus, pancreas and kidney cancers) and diet/alcohol consumption (for oesophagus and stomach cancers).ResultsThe incidence of cancers of the oesophagus, pancreas, kidney, and bladder was relatively evenly distributed across the region. The incidence of stomach and lung cancers was more clustered around the urban areas in the south of the region, and these two cancers were significantly associated with higher levels of area deprivation. The incidence of lung cancer was most impacted by adjustment for SEB, with the rural/urban split becoming less apparent. The component representing smoking had a larger effect on cancer incidence in the eastern part of the region. The effects of the other two components were small and disappeared after adjustment for SEB.ConclusionThis study demonstrates the feasibility of joint disease modelling using data from six cancer sites. Incidence estimates are more precise than those obtained without smoothing. This methodology may be an important tool to help authorities evaluate healthcare system performance and the impact of policies.