[Case-cohort surveys]. / Les enquêtes cas-cohorte.

In this paper, we present the main tools for conception, implementation and analysis of case-cohort surveys. In particular, we describe the classical weighted estimators, the weighted approach recently suggested by Breslow et al. and the multiple imputation approach, an alternative to weighted analysis of case-cohort data. Variance estimators are also described. We show how to obtain the subcohort size. Finally, we mention the functions and procedures available in R, SAS and Stata software and we illustrate their implementation using simulated subcohorts from the PRIME cohort.

[The case series method]. / La méthode de la série de cas.

The case series method was developed by Farrington (1995) to investigate the strength of association between a time-varying exposure and an acute rare potentially recurrent event, using cases only. It can be used when the exposure can only be causally related to the event during a limited period of time. It has been widely used in pharmaco-epidemiology, particularly in the study of vaccine safety. The method is derived from a Poisson model by conditioning on the individual total number of events and its exposure history. As a consequence of this conditioning, the effects of fixed covariates cancel out, so that the method has a particular advantage as compared with cohort and case-control studies.

Relative-risk ratio was a useful measure of differential association in cohort and case-series studies.

OBJECTIVE: The framework consists of cohort or case-series studies with intermittent exposure and two types of events. The aim is to define and estimate an association measure between the exposure and the occurrence of one type of event rather than the other. STUDY DESIGN AND SETTING: The model and the estimation method are obtained by extending Farrington's approach for one type of recurrent event. The proposed association measure "RR(c)" is the ratio of the relative risks pertaining to each type of event. The estimated RR(c) and its confidence interval are derived under the independence assumption between the counts of the two types of events. The data that are analyzed are part of the data of a study on antimicrobial resistance in children. RESULTS: An interpretation of the RR(c) is proposed in terms of an odds ratio, which parallels a similar association measure defined in cross-sectional studies ("OR(c)"). The estimated value of the RR(c) agrees with the OR(c) reported in previous studies. CONCLUSION: The RR(c) appears as a useful tool for evaluating the risk of colonization (or infection) with resistant rather than susceptible bacteria following a previous intake of a given antibiotic conditional on colonization (or infection) with any bacteria.

Misspecification of the covariance structure in generalized linear mixed models.

When fitting marginal models to correlated outcomes, the so-called sandwich variance is commonly used. However, this is not the case when fitting mixed models. Using two data sets, we illustrate the problems that can be encountered. We show that the differences or the ratios between the naive and sandwich standard deviations of the fixed effects estimators provide convenient means of assessing the fit of the model, as both are consistent when the covariance structure is correctly specified, but only the latter is when that structure is misspecified. When the number of statistical units is not too small, the sandwich formula correctly estimates the variance of the fixed effects estimator even if the random effects are misspecified, and it can be used in a diagnostic tool for assessing the misspecification of the random effects. A simple comparison with the naive variance is sufficient and we propose considering a ratio of the naive and sandwich standard deviation out of the [3/4; 4/3] interval as signaling a risk of erroneous inference due to a model misspecification. We strongly advocate broader use of the sandwich variance for statistical inference about the fixed effects in mixed models.

Sensitivity analysis of incomplete longitudinal data departing from the missing at random assumption: Methodology and application in a clinical trial with drop-outs.

Statistical analyses of longitudinal data with drop-outs based on direct likelihood, and using all the available data, provide unbiased and fully efficient estimates under some assumptions about the drop-out mechanism. Unfortunately, these assumptions can never be tested from the data. Thus, sensitivity analyses should be routinely performed to assess the robustness of inferences to departures from these assumptions. However, each specific scientific context requires different considerations when setting up such an analysis, no standard method exists and this is still an active area of research. We propose a flexible procedure to perform sensitivity analyses when dealing with continuous outcomes, which are described by a linear mixed model in an initial likelihood analysis. The methodology relies on the pattern-mixture model factorisation of the full data likelihood and was validated in a simulation study. The approach was prompted by a randomised clinical trial for sleep-maintenance insomnia treatment. This case study illustrated the practical value of our approach and underlined the need for sensitivity analyses when analysing data with drop-outs: some of the conclusions from the initial analysis were shown to be reliable, while others were found to be fragile and strongly dependent on modelling assumptions. R code for implementation is provided.

An epidemiological reconsideration of the Geschwind-Galaburda theory of cerebral lateralization.

To contribute to the Geschwind-Galaburda theory of cerebral lateralization, we examined the relationship of left-handedness to allergic disorders and stuttering, using epidemiological data of two French samples, one of which (N = 9591) is representative of the French male population between 17 and 24 years of age. Results showed a higher frequency of stuttering but not of allergic disorders in left-handers. Extreme right-handedness was observed to be significantly associated with a lower frequency of allergic disorders; response bias might explain such a relationship. Findings were confirmed after allowing for potential confounding factors, such as age and education. In both samples, stuttering and allergic disorders were significantly related.

Handedness, immune disorders and information bias.

In order to investigate the relations between handedness and migraine or immune disorders, we performed a case control study comparing the handedness of patients suffering from systemic lupus erythematosus (SLE), type I diabetes, Graves' disease, or migraine to that of a random sample of controls from the general population. A handedness index was measured from a 10-item questionnaire. No significant difference was observed. But when the controls who denied having ever suffered from migraine or any allergic disease were set apart from those who gave at least one positive answer to the same questions, the former were found more right-handed, i.e. with a lower handedness index than the latter (P less than 0.05) and than the SLE patients (P less than 0.05). More generally, the mean observed handedness index of controls giving a positive answer to any question about their health was found repeatedly higher than that of controls giving a negative answer: this was observed for 27 of the 32 questions. These results are highly suggestive of an information bias, the subjects saying they use the right hand for each of the 10 activities considered in the questionnaire being more likely to deny having suffered from a given disease or used, more or less recently, some drug or medical service. Our conviction is that previous observations dealing with the same topic are also more easily explained by the presence of an information bias than by Geschwind's theory. The implications for the design of further epidemiologic studies are discussed.

Correlated nondifferential misclassifications of disease and exposure: application to a cross-sectional study of the relation between handedness and immune disorders.

In cross-sectional studies, misclassifications of exposure and of health status may be related. For instance some subjects may tend to overreport both exposure and disease. A misclassification is said to be nondifferential if the sensitivity and the specificity which characterize it do not depend on the true status of the subjects for the other variables. Nondifferential misclassifications of two dichotomic variables may be correlated if the probability of being misclassified for one of them depends on the presence of an error of classification for the second one. Models are presented to estimate the bias induced by correlated nondifferential misclassifications on an odds ratio whose true value is unity. For most usual situations, when the great majority of the subjects are healthy and nonexposed, the influence of overreporting is shown to be larger than that of underreporting. It appears to be relatively easy to find a spurious, but significant, relationship. Real data are analysed to show that the potential consequences of correlated nondifferential misclassifications are not purely theoretical. In a sample of 1676 subjects from the general population we observed significant relations between left-hand shift and various aspects of health status: reporting a history of eczema, experience of a serious health problem in the past, experience of a serious health problem presently, use during the last month of analgesics or of drugs for circulatory problems, or digestion, consultation with a physiotherapist or hospitalization during the last year. These results, as with many similar ones previously reported, are highly suggestive of an information bias. They are less easily explained by biological hypotheses, e.g. Geschwind's theory of cerebral lateralization, than by correlated misclassifications resulting from overreporting of both the use of the left hand and the existence of some health problems by healthy right-handers. The modelling used in this report supports this hypothesis.

Personal factors related to the perception of occupational exposure: an application of a job exposure matrix.

Whether certain personal characteristics influence the perception of exposure to dusts, gases or fumes was assessed in 6803 men and 6765 women drawn from nonmanual worker households in seven French cities. Factors modifying the strength of the association between two estimates of exposure (here a job exposure matrix estimate and exposure reported by the subjects) are potential recall determinants of exposure. This association was significantly stronger in men than in women, suggesting a better perception of exposure in men. The strength of the association between both estimates of exposure increased significantly among men according to educational level. Smoking habits had no effect on the perception of exposure. The perception of exposure did not vary significantly according to respiratory symptoms in women. In men, subjects without chronic cough or chronic bronchitis had a significantly higher perception of exposure than the others, but no difference was shown for wheezing, dyspnoea or asthma.

Predictive value of viral load and other markers for progression to clinical AIDS after CD4+ cell count falls below 200/microL. SEROCO & HEMOCO Study Group.

BACKGROUND: To assess the predictive value of biological and clinical events for progression to AIDS (1993 European classification) when the CD4+ cell count falls below 200/microL (CD4 threshold) in different exposure groups. To investigate whether such markers remain predictive independently of the serum HIV-1 RNA level at the CD4 threshold. METHODS: The predictive value of biological and clinical events occurring during the 24 months prior to the occurrence of CD4 threshold (n = 333) was quantified in a Cox model. Another Cox model was carried out in a subset of 77 patients in whom viral load from stored sera was available. Furthermore, changes in viral load during the 24 months preceding the CD4 threshold were assessed in a mixed model according to subsequent development of AIDS. RESULTS: Among the 333 patients, the slope of the CD4+ cell counts, the emergence of p24 antigen, persistent thrush, and age at the CD4 threshold were independent predictors of progression to clinical AIDS (44.7%). Among the subset of 77 patients, the HIV-1 RNA level at the CD4 threshold, persistent thrush and age remained independent predictors of progression to AIDS (45.5%). The increase of the HIV-1 RNA level was moderate, both in non-progressors (24.0% per year) and in those who subsequently developed AIDS (27.1% per year), (P = 0.93). Viral load was consistently higher in the latter group (P = 0.002). CONCLUSION: At a late stage of infection, age and persistent thrush remain predictive of progression to AIDS, independently of viral load.

Dietary intake and other determinants of blood vitamins in an elderly population.

The relationships of diet, plasma lipids, age, gender, ponderal index, cigarette and alcohol consumption, drug use and infections to blood concentrations of retinol, beta-carotene, alpha-tocopherol, ascorbic acid and vitamins B1, B2, B6 status were studied among 291 men and women aged 60-82 years. Statistically significant correlations between dietary intake and blood indicator levels were found respectively for beta-carotene, alpha-tocopherol, ascorbic acid, vitamins B2 and B6, but not for retinol and thiamin, when the effects of other parameters were controlled. The main other determinants were cigarette consumption which had a negative effect on status for retinol, beta-carotene, alpha-tocopherol, ascorbic acid and vitamin B2; alcohol consumption for retinol, vitamin B6 (positive effect on status) and beta-carotene (decrease of plasma level); plasma lipids and use of hypolipaemic drugs for fat-soluble vitamins; ponderal index for beta-carotene and vitamin B6; gender and use of antibiotics for ascorbic acid. The apparent relation between gender and level of retinol, beta-carotene, alpha-tocopherol and vitamin B6 status was not any more significant after adjustment for alcohol or cigarette consumption. Tobacco and alcohol appear to be associated factors which should be controlled for in studies investigating relations between these vitamins and diseases influenced by smoking and drinking habits.

Vitamin status, immunity and infections in an elderly population.

The relations between vitamin status and immunological parameters or number of infections have been investigated in self-sufficient healthy individuals aged 60 and over. A total of 411 subjects agreed to participate, but 202 were discarded from the main statistical analysis since they could have had their immune or nutritional status modified by a recent infection, vaccination or drug consumption. Plasma concentrations of retinol, alpha-tocopherol, ascorbic acid and vitamin B6 were determined. Three indices of cellular immunity were measured: percentages of T-cell subsets, lymphoproliferative response to phytohaemaglutinin and delayed-type hypersensitivity to 7 ubiquitous antigens. A questionnaire about past infections was presented. Two results, supported by previous experimental observations, should be underlined. Vitamin B6 status was positively related to percentages of T-cell subsets: the lowest percentages of CD5 and CD4 cells were observed in the low B6 status group (50.6 and 32.6 per cent) and the highest percentages in the high B6 status group (62.0 and 41.0 per cent), with intermediate values in the medium group (57.6 and 39.5 per cent). Vitamin E status was negatively related to the number of past infections: subjects with a high alpha-tocopherol plasma concentration had fewer infections during the last 3 years (1.0) than those with a medium (2.2) or a low (2.3) concentration. In spite of these two observations, cellular immunity did not seem to be strongly related to vitamin status in the supposedly healthy population studied.

Does multivitamin supplementation prevent infections in healthy elderly subjects? A controlled trial.

We performed a double blind randomized study in order to assess the efficacy of a multivitamin supplement for the prevention of common infections in healthy elderly subjects. Non-institutionalized, independent subjects over 60 years of age, living in the Nevers area (central France) were recruited by announcements and randomly assigned to a treatment or a placebo group. The treatment or placebo tablets were to be taken daily for 4 months. The principal criterion of response was the incidence of infections, as recorded from a detailed questionnaire presented at entrance, in the middle (2 months) and at the end (4 months) of the study. Blood samples were taken at the entrance in the study and after two and four months in order to monitor vitamin status. No significant difference was found between the two groups for the incidence of infections. In fact the observed incidences during the two two-month periods were higher in the treatment (0.38 and 0.21) than in the placebo group (0.29 and 0.13). After two months and after four months of supplementation, blood vitamin indicators of the subjects were significantly higher in the treatment than in the placebo group for vitamins B1, B2, B6, E and folates (p < 0.001). The improvement of the vitamin C status was slightly higher in the treatment than in the placebo group. For vitamin A status, the evolution was similar in the two groups. In conclusion, short-term supplementation of healthy elderly subjects with the investigated supplement is not likely to afford a meaningful protection against common infections.

[Jackknife and bootstrap]. / Le canif et les bretelles.

The jackknife and the bootstrap are two non parametric methods which provide estimates- of the bias and the variance of an estimator, without any assumption about its statistical distribution. The jackknife is based on the observation of the estimator for subsamples, generally of size n-1, obtained from the original sample. The bootstrap is based on the observation of the estimator on size n samples drawn from the original sample. The two methods are presented, their principle is illustrated through their application to simple examples and to more complex epidemiological problems.

[Modeling correlated data in epidemiology: mixed or marginal model?]. / Modélisation de données corrélées en épidémiologie: modèle mixte ou marginal?

Correlated observations (within centers, families, subjects,.) are common in epidemiology. Even when one is only interested in the modeling of means according to risk factors, it is also necessary to model the variance-covariance matrix of the observations in order to make correct inferences on the parameters of interest. All the more so when the aim of the survey is the measurement of these correlations or of the variance of the random effects from which they are assumed to originate. We discuss, within the framework of the linear and of the logistic models, the implications of two choices for the modeling of covariances. The mixed model shows the unobserved elements responsible for the similarity between certain observations. In a longitudinal survey, for instance, one can use a random effect, specific to each subject, expressing how much a subject's trajectory is translated as compared to what is expected according to its characteristics (age, sex,.). The marginal approach leads to modeling separately the means and the covariance matrix of the observations. The distinction between these two approaches is important for non linear models, in particular the logistic one. We insist on the interconnection between a mixed model formulation and a marginal one, as well as on the implication of the choice in terms of the parameters' interpretation.

[Modeling incomplete observations]. / Modélisation d'observations incomplètes.

Incomplete observations, common in epidemiology as in many other fields, lead to problems of bias, precision and power. Using a simple example with 3 binary variables, we discuss situations where the observed odds ratio is biased. We present and compare the main strategies of analysis: complete observations modeling, missing data indicator, weighted analysis, simple imputation, multiple imputation, selection models, shared variable models.

[Analysis of repeated binary data: sensitivity to missing data]. / Analyse de données binaires répétées: sensibilité aux données manquantes.

BACKGROUND: In longitudinal studies, it is extremely rare that all the planned measurements are actually performed. Missing data are often consecutive to drop-outs, but may also be intermittent. In both cases, the analysis of incomplete data necessarily requires assumptions that are generally unverifiable, and the need for sensitivity analyses has been advocated over the past few years. In this article, the attention will be given to longitudinal binary data. METHODS: A method is proposed, which is based on a log-linear model. A sensitivity parameter is introduced that represents the relationship between the response mechanism and the missing data mechanism. It is recommended not to estimate this parameter, but to consider a range of plausible values, and to estimate the parameters of interest conditionally on these plausible values. This allows to assess the sensitivity of the conclusion of a study to various assumptions regarding the missing data mechanism. RESULTS: This method was applied to a randomized clinical trial comparing the efficacy of two treatment regimens in patients with persistent asthma. The sensitivity analysis showed that the conclusion of this study was robust to missing data.

[The center effect in multicenter studies: fixed or random?]. / L'effet centre dans les études multicentriques: fixe ou aléatoire?

The multiplication of multicentric clinical studies leads to a generalization of the use of a center effect in statistical analyses. In the simple situation where the dependent variable is quantitative and there is only a simple factor of interest, the formalisation of such a protocol corresponds to a two way ANOVA (with the factor of interest and the center factor) with generally a term of interaction. Even such a simple situation leads to interrogations, one of them being to determine whether the centre effect is fixed or random. In the first situation, the conclusion of the study will concern only the centres evaluated in the study, while in the second, the conclusion will concern the whole population from which the centers have been randomly selected. Such a generalizability has a cost: a loss of power in determining the effect of the factor of interest (the loss being as important as the interaction factor of interest x centre factor is large) and the necessity of sophisticated statistical software. This paper will focus on successively: the notion of ANOVA, of fixed or random effect (with the conceptual, formal and numerical differences that distinguish these two approaches). A numerical example is proposed.

[Use of GEE for modeling censored correlated data: application to the study of risk factors for withdrawal of totally implantable vascular access devices in cystic fibrosis]. / Utilisation des GEE pour la modélisation de données censurées corrélées: application à l'étude des facteurs de risque de retrait des chambres implantables chez le mucoviscidosique.

BACKGROUND: The proportional hazards model proposed by Cox for modeling censored data is not suited for correlated delays, for instance when several events can be observed on each subject. METHODS: To analyze correlated delays, we propose to use a log-linear marginal model equivalent to Cox model. Correlations are taken into account through the use of Liang and Zeger's Generalized Estimating Equations (GEE) and of their robust variance estimator. An advantage of this method is that it can be implemented through the SAS GENMOD procedure. When ties are observed, we propose to use multiple imputations, creating M data sets without ties from the original one. RESULTS: This method is applied to a retrospective survey on the risk of withdrawing totally implantable vascular access devices (TIVAD) because of complication in cystic fibrosis patients: 265 TIVAD implanted in 200 patients were observed. Risk factors were characteristics of the device or of the patient. Results obtained with the robust variance estimator and ten imputations show that the use of the device for taking blood (vs exclusive perfusion of antibiotics), polyurethane catheter (vs. silicon), use of counterpressure for upkeeping and pulmonary colonization by Pseudomonas Aeruginosa are significantly associated to withdrawal. Under the Cox model which does not account for the correlations, some conclusions differ because the robust variance of the estimators is smaller than the variance obtained under the working assumption of independent delays. CONCLUSION: This approach allows the modeling of correlated survival data with SAS software. Our results illustrate the necessity of accounting for existing correlations.