Paul R. Burton

EXTENDING THE SIMPLE LINEAR REGRESSION MODEL TO ACCOUNT FOR CORRELATED RESPONSES: AN INTRODUCTION TO GENERALIZED ESTIMATING EQUATIONS AND MULTI-LEVEL MIXED MODELLING

Much of the research in epidemiology and clinical science is based upon longitudinal designs which involve repeated measurements of a variable of interest in each of a series of individuals. Such designs can be very powerful, both statistically and scientifically, because they enable one to study changes within individual subjects over time or under varied conditions. However, this power arises because the repeated measurements tend to be correlated with one another, and this must be taken into proper account at the time of analysis or misleading conclusions may result. Recent advances in statistical theory and in software development mean that studies based upon such designs can now be analysed more easily, in a valid yet flexible manner, using a variety of approaches which include the use of generalized estimating equations, and mixed models which incorporate random effects. This paper provides a particularly simple illustration of the use of these two approaches, taking as a practical example the analysis of a study which examined the response of portable peak expiratory flow meters to changes in true peak expiratory flow in 12 children with asthma. The paper takes the reader through the relevant practicalities of model fitting, interpretation and criticism and demonstrates that, in a simple case such as this, analyses based upon these model-based approaches produce reassuringly similar inferences to standard analyses based upon more conventional methods.

Association of polymorphisms within the tumour necrosis factor (TNF) genes and childhood asthma

Tumour necrosis factor alpha (TNFα) is a potent modulator of immune and inflammatory responses, and has been implicated in a variety of autoimmune diseases, including asthma. Increased levels of TNFα have been detected in both sputa and bronchoalveolar lavage fluid of asthmatic subjects during acute attacks. Interindividual variation in TNFα levels may be genetically determined and polymorphisms within the TNF genes and nearby HLA Class II region have been associated with differences in TNFα production. Objective To investigate the association of differences in asthma‐related phenotypes with two biallelic polymorphisms: a G to A substitution at position −308 of the TNFα gene promoter (TNF1 and TNF2 alleles) and an NcoI polymorphism in the first intron of the lymphotoxin alpha gene (LT‐α*1 and LT‐α*2 alleles).

Inhalant allergen‐specific T‐cell reactivity is detectable in close to 100% of atopic and normal individuals: covert responses are unmasked by serum‐free medium

Background It is widely held that in vitro T cell responses to allergens are more prominent in atopic than in normal individuals, though this conclusion is based upon culture techniques which fail to detect proliferative responses in a significant minority of atopies and many normals.

A POLYMORPHISM OF THE CC16 GENE IS ASSOCIATED WITH AN INCREASED RISK OF ASTHMA

Several quantitative traits associated with the asthma phenotype have been linked to markers on chromosome 11q13, although the gene responsible has yet to be well established. The gene for Clara cell secretory protein (CC16) is an ideal candidate for involvement in an inherited predisposition to asthma because of its chromosomal location, the role of the CC16 protein in controlling airway inflammation, and differences in levels of the protein between asthmatics and healthy controls. All three CC16 exons were screened in an unselected population of 266 subjects from 76 families and a cohort of 52 severely asthmatic children. A combination of single strand conformational polymorphism (SSCP) analysis, heteroduplex analysis, DNA sequencing, and restriction digestion was used. Mutation detection methods identified an adenine to guanine substitution in the CC16 gene at position 38 (A38G) downstream from the transcription initiation site within the non-coding region of exon 1. In the unselected population, 43.6% were homozygous for the polymorphic sequence (38GG) and 46.2% were heterozygous (38AG). All the asthmatic and unaffected children from both populations were selected for an unmatched case control analysis consisting of 67 asthmatic and 46 unaffected subjects. Those homozygous for the published sequence (38AA) had a 6.9-fold increased risk of developing asthma (p=0.049) and heterozygotes (38AG) a 4.2-fold increased risk (p=0.028). Modelling of genotype as a continuous covariate indicated evidence of a significant linear trend across the three genotypes (odds ratio=2.84 per unit increase in genotype code, p=0.018). These associations were independent of age, gender, and tobacco smoke exposure. These data and the known anti-inflammatory role of CC16 in the respiratory tract suggest that alteration to the gene at position 38 may contribute to asthma.

Genetic variance components analysis for binary phenotypes using generalized linear mixed models (GLMMs) and Gibbs sampling

The common complex diseases such as asthma are an important focus of genetic research, and studies based on large numbers of simple pedigrees ascertained from population‐based sampling frames are becoming commonplace. Many of the genetic and environmental factors causing these diseases are unknown and there is often a strong residual covariance between relatives even after all known determinants are taken into account. This must be modelled correctly whether scientific interest is focused on fixed effects, as in an association analysis, or on the covariances themselves. Analysis is straightforward for multivariate Normal phenotypes, but difficulties arise with other types of trait. Generalized linear mixed models (GLMMs) offer a potentially unifying approach to analysis for many classes of phenotype including multivariate Normal traits, binary traits, and censored survival times. Markov Chain Monte Carlo methods, including Gibbs sampling, provide a convenient framework within which such models may be fitted. In this paper, Bayesian inference Using Gibbs Sampling (a generic Gibbs sampler; BUGS) is used to fit GLMMs for multivariate Normal and binary phenotypes in nuclear families. BUGS is easy to use and readily available. We motivate a suitable model structure for Normal phenotypes and show how the model extends to binary traits. We discuss parameter interpretation and statistical inference and show how to circumvent a number of important theoretical and practical problems that we encountered. Using simulated data we show that model parameters seem consistent and appear unbiased in smaller data sets. We illustrate our methods using data from an ongoing cohort study. Genet. Epidemiol. 17:118–140, 1999.

Clinical significance not statistical significance: a simple Bayesian alternative to p values.

OBJECTIVES: To take the common Bayesian interpretation of conventional confidence intervals to its logical conclusion, and hence to derive a simple, intuitive way to interpret the results of public health and clinical studies. DESIGN AND SETTING: The theoretical basis and practicalities of the approach advocated is at first explained and then its use is illustrated by referring to the interpretation of a real historical cohort study. The study considered compared survival on haemodialysis (HD) with that on continuous ambulatory peritoneal dialysis (CAPD) in 389 patients dialysed for end stage renal disease in Leicestershire between 1974 and 1985. Careful interpretation of the study was essential. This was because although it had relatively low statistical power, it represented all of the data that were available at the time and it had to inform a critical clinical policy decision: whether or not to continue putting the majority of new patients onto CAPD. MEASUREMENTS AND ANALYSIS: Conventional confidence intervals are often interpreted using subjective probability. For example, 95% confidence intervals are commonly understood to represent a range of values within which one may be 95% certain that the true value of whatever one is estimating really lies. Such an interpretation is fundamentally incorrect within the framework of conventional, frequency-based, statistics. However, it is valid as a statement of Bayesian posterior probability, provided that the prior distribution that represents pre-existing beliefs is uniform, which means flat, on the scale of the main outcome variable. This means that there is a limited equivalence between conventional and Bayesian statistics, which can be used to draw simple Bayesian style statistical inferences from a standard analysis. The advantage of such an approach is that it permits intuitive inferential statements to be made that cannot be made within a conventional framework and this can help to ensure that logical decisions are taken on the basis of study results. In the particular practical example described, this approach is applied in the context of an analysis based upon proportional hazards (Cox) regression. MAIN RESULTS AND CONCLUSIONS: The approach proposed expresses conclusions in a manner that is believed to be a helpful adjunct to more conventional inferential statements. It is of greatest value in those situations in which statistical significance may bear little relation to clinical significance and a conventional analysis using p values is liable to be misleading. Perhaps most importantly, this includes circumstances in which an important public health or clinical decision must be based upon a study that has unavoidably low statistical power. However, it is also useful in situations in which a decision must be based upon a large study that indicates that an effect that is highly statistically significant seems too small to be of practical relevance. In the illustrative example described, the approach helped in making a decision regarding the use of CAPD in Leicestershire during the latter half of the 1980s.

Mental health disorders in children and young people: scope, cause and prevention

Objective: To review the scope and characteristics of mental health disorders in children and young people in Australia; detail some emerging concepts of the causal pathways of mental health disorders in children and young people; and discuss aspects of the prevention of mental health disorders and the promotion of mental health in children and young people. Method: An integrated review of selected literature. Results: (i) While as many as one in five Australian children aged from four to 17 have significant mental health problems there remains a need for prevalence estimates in subsections of the population, notably children and young people of Aboriginal and Torres Strait Islander descent; (ii) appropriate studies of gene-environment interaction will require better measurement and developmental exposition of those risk exposures that are known to be on the causal pathway to mental health disorder; and (iii) universal, selective and indicated prevention trials and evaluations directed at anxiety, depression and conduct disorder are needed. Conclusion: Preventive intervention and promotion in mental health must entail effective collaboration at national, state and local levels between health, welfare and education sectors. These sectors must be informed by high quality epidemiology and a knowledge of the causal pathways of mental health disorders. Such intervention must also improve the movement of scientific knowledge to political policy on one hand and to praxis on the other. This will require a clear and persistent vision of the urgency, costs and consequences of mental health disorders in children and young people coupled with effective leadership and political resolve.

The intrapartum CTG prior to neonatal encephalopathy at term: a case‐control study

Objective To compare cardiotocograph (CTG) records during labour in cases of neonatal encephalopathy and matched controls.

Measuring the impact of conjugate vaccines on invasive Haemophilus influenzae type b infection in Western Australia

Abstract: Haemophilus influenzae type b (Hib) causes serious infections in 26–59 per 100 000 non–Aboriginal Australian children under five years of age. Aboriginal children suffer much higher rates of infection (≥ 150 per 100 000), and at an earlier age, and have a greater risk of death and disability due to Hib infection. In 1992 and 1993, four conjugate Hib vaccines were introduced in Australia, and a nationally funded program of infant vaccination was begun in July 1993. This study aimed at evaluating the effectiveness of Hib vaccination in Aboriginal and non–Aboriginal children in Western Australia using a population–based active surveillance system for non–Aboriginal children and a case control study for Aboriginal children. The incidence of invasive Hib disease in non–Aboriginal children fell from 30.9 per 100 000 before vaccination was available to 6.3 per 100 000 in the second year after its introduction. The vaccine efficacy was estimated to be 80 per cent for Aboriginal children (odds ratio 0.20, 95 per cent CI 0.01–2.76) and, after adjustment for confounders, 75 per cent (odds ratio 0.25, CI 0.02–3.66). Based on the adjusted value (75 per cent), and using a Bayesian approach, we estimate that the posterior probability was 0.55 that the true vaccine efficacy is greater than 70 per cent, and 0.69 that the efficacy is greater than 50 per cent. We conclude that Hib vaccination is effective in preventing invasive Hib disease in Aboriginal and non–Aboriginal children in Australia. Aust N Z J Public Health 1998; 22: 67–72)

An analysis of sudden infant death syndrome in Aboriginal infants

The purpose of this case-control study was to identify antenatal and perinatal risk factors for sudden infant death syndrome (SIDS) in Aboriginal infants in Western Australia (WA). Cases were all Aboriginal infants born in WA from 1980 to 1990 inclusive and classified as dying from SIDS in WA. Controls consisted of a matched group and a random group both selected from liveborn Aboriginal infants born from 1980 to 1990. Multivariate modelling showed that SIDS in Aboriginal infants was strongly related to young maternal age (< 20 years, odds ratio (OR) = 2.89), high parity (parity > 3, OR = 4.40) and being small-for-gestational age (OR = 3.36) but was not associated with single marital status (OR = 0.95) or male sex (OR = 0.97). Although the study was based on routinely collected data, results do highlight some important groups for SIDS prevention. To gain further knowledge in terms of SIDS in Aboriginal infants, there is an urgent need to collect information concerning infant care practices in the Aboriginal community.