Identification of Confounders in the Assessment of the Relationship between Lead Exposure and Child Development

Identification of Confounders in the Assessment of the Relationship between Lead Exposure and Child Development SHILU TONG, MBBS, PhD AND YING LU, MBBS

PURPOSE: To explore the best approach to identify and adjust for confounders in epidemiologic practice. METHODS: In the Port Pirie cohort study, the selection of covariates was based on both a priori and an empirical consideration. In an assessment of the relationship between exposure to environmental lead and child development, change-in-estimate (CE) and significance testing (ST) criteria were compared in identifying potential confounders. The Pearson correlation coefficients were used to evaluate the potential for collinearity between pairs of major quantitative covariates. In multivariate analyses, the effects of confounding factors were assessed with multiple linear regression models. RESULTS: The nature and number of covariates selected varied with different confounder selection criteria and different cutoffs. Four covariates (i.e., quality of home environment, socioeconomic status (SES), maternal intelligence, and parental smoking behaviour) met the conventional CE criterion (⭓10%), whereas 14 variables met the ST criterion (p ⭐ 0.25). However, the magnitude of the relationship between blood lead concentration and children’s IQ differed slightly after adjustment for confounding, using either the CE (partial regression coefficient: ⫺4.4; 95% confidence interval (CI): ⫺0.5 to ⫺8.3) or ST criterion (⫺4.3; 95% CI: ⫺0.2 to ⫺8.4). CONCLUSIONS: Identification and selection of confounding factors need to be viewed cautiously in epidemiologic studies. Either the CE (e.g., ⭓ 10%) or ST (e.g., p ⭐ 0.25) criterion may be implemented in identification of a potential confounder if a study sample is sufficiently large, and both the methods are subject to arbitrariness of selecting a cut-off point. In this study, the CE criterion (i.e., ⭓ 10%) appears to be more stringent than the ST method (i.e., p ⭐ 0.25) in the identification of confounders. However, the ST rule cannot be used to determine the trueness of confounding because it cannot reflect the causal relationship between the confounder and outcome. This study shows the complexities one can expect to encounter in the identification of and adjustment for confounders. Ann Epidemiol 2001;11:38–45.  2000 Elsevier Science Inc. All rights reserved. Bias (Epidemiology), Confounding Factors (Epidemiology), Selection Criteria, Epidemiologic Research.

KEY WORDS:

INTRODUCTION The association between an exposure and outcome is usually assessed in analytical epidemiologic research. If an association is found, it is required to determine whether the association is valid — viz. the potential roles of chance, bias, and confounding need to be taken into account. If a valid association can be established, then the use of the Bradford Hill criteria can assist us in making causal inferences (1, 2). In such a structured epidemiologic process, one of the most important and difficult issues is how to identify confounding and how to deal with confounders.

From the Centre for Public Health Research, Queensland University of Technology, Kelvin Grove, Australia. Address reprint requests to: Dr. Shilu Tong, Centre for Public Health Research, Queensland University of Technology, Locked Bag No. 2, Kelvin Grove, Qld. 4059, Australia. Received November 19, 1999; revised June 2, 2000; accepted June 28, 2000.  2000 Elsevier Science Inc. All rights reserved. 655 Avenue of the Americas, New York, NY 10010

It is well known that an assessment of the relationship between exposure and outcome can be distorted in an epidemiologic study whenever an extraneous factor, which is associated with exposure status and also causally connects to the outcome, is not considered. This phenomenon is referred to as confounding and the extraneous factor as a confounder (1–4). Epidemiologists are also aware that any factor which is intermediate on the causal pathway or is affected in part by exposure or outcome should not be regarded as a confounder and therefore should not be adjusted for (1, 2, 5). However, in reality, there is no clear-cut criterion for deciding which variable should be regarded as a potential confounder and which should not. Controversy exists over how to identify confounding variables and how to assess them in both qualitative and quantitative terms (1–10). Mickey and Greenland suggest that, in situations in which the best decision (of whether or not to adjust) is not always obvious, the change-in-estimate 1047-2797/01/$–see front matter PII S1047-2797(00)00176-9

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Selected Abbreviations and Acronyms ST ⫽ significance testing CE ⫽ change-in-estimate WISC-R ⫽ Wechsler Intelligence Scale for Children — Revised HOME ⫽ Home Observation for Measurement of the Environment inventory SES ⫽ Socioeconomic status GHQ ⫽ General Health Questionnaire

(CE) criterion tends to be superior, though significance testing (ST) methods can perform acceptably if their significance levels are set much higher than conventional levels (to values of 0.20 or more) (6). However, the impact of various confounder selection criteria on effect estimation has not been thoroughly investigated although some simulation studies have been conducted (6, 7). Recently, causal graphs were proposed to be applied in the qualitative analysis of potential confounders (10). At present, two commonly used confounder selection criteria are CE and ST. These two methods were compared in statistical analyses of the Port Pirie cohort data. Some conceptual and statistical issues regarding identification and selection of confounding factors are illustrated with practical examples in this paper.

METHODS Data Collection In the Port Pirie cohort study, the primary objective was to examine the relationship between exposure to environmental lead and child development. A total of 375 children living in and around the lead smelting town — Port Pirie, South Australia, were followed from birth to age 11–13 years. A series of blood samples was collected from these children. Details of the research design were reported elsewhere (11–14). In order to calculate lifetime average blood lead concentration, a plot of blood lead against age was constructed for each child. The lifetime average blood lead concentration up to a particular age was estimated by dividing the area under the curve by the specific age. This method of averaging copes readily with the unequal time periods between successive samples. Children’s IQ at age 11–13 years was assessed with the Wechsler Intelligence Scale for Children — Revised (WISC-R) (15) by a single trained examiner who was unaware of any aspects of a child’s lead-exposure and developmental histories. Information on the covariates which might confound the association between lead exposure and children’s IQ was collected as follows: Demographic Variables. The specific demographic vari-

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ables considered as potential confounders were gender, child’s age, and child’s school age. It is well known that some demographic variables are related to both lead exposure and developmental status (e.g., child’s age). Children of the same age may be in different “grades” at school, which may affect developmental measures (16). Moreover, it has been suggested that gender may act as an effect modifier in some studies of low-level lead exposure (17, 18). Psycho-social and environmental factors: Several psycho-social and environmental factors (e.g., socioeconomic status (SES), the care-giving environment, parent’s marital status, and family size) also have appeared to be potential confounders in most studies of lead exposure and child development (19–21). It has been argued that parental smoking may influence childhood development (22, 23), and indeed, was found to be associated with blood lead level in the Port Pirie children (24). Moreover, since family functioning and parental psychiatric status may also affect child development, standardised measurements of these covariates were correspondingly considered (25, 26). The specific psycho-social and environmental factors measured in this study are discussed below. Socioeconomic Status (SES). The Daniel Scale (27), which is based on the prestige of the parents’ occupations, was employed as a surrogate measure for social status. The Daniel score is inversely related to prestige, i.e., the higher the Daniel score, the lower the prestige. The SES of each family was evaluated when the child was born and again at ages 2, 4, 7 and 11–13 years. The average Daniel score was used as an indicator of SES. Care-Giving Environment in Early Childhood. The Home Observation for Measurement of the Environment inventory (28) or “HOME” inventory was used to assess each child’s care-giving environment. The HOME scores, which were measured at ages 3 and 5 years, were averaged to form an aggregate HOME score. The HOME inventory evaluates the quality of the care-giving environment. Family Functioning. The child’s family function was assessed using the General Function Scale (GFS) of the Family Assessment Device (25). Parents’ Psychiatric Status. The parents’ mental health status was measured with the 12-item General Health Questionnaire (GHQ) (26). Other factors thought to potentially confound the association studied were parent’s marital status, parental smoking habit(s), family size (number of siblings), life events (e.g., separation of parents, death of relatives, accidents, or serious illnesses), period of family’s dwelling in Port Pirie, and assessment site (school or others). Familial Variables. These variables are important predictors of children’s intelligence. Since they may also be associated with the quality of home environment and therefore associated with exposure status, they were considered as potential confounders (29, 30). These variables included

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maternal intelligence and paternal education. Maternal intelligence was evaluated with the Wechsler Adult Intelligence Scale-Revised (31), and paternal education was assessed in terms of the number of years of secondary school education. Biomedical Factors. These included maternal age, birthweight, birth order, feeding style during infancy (breast, bottle, and mixed), duration of breastfeeding, whether any medication had been used in the last two weeks before testing, and whether the child had ever been absent from school for two weeks or longer in any single school term during the last five years. Statistical Analysis A covariate selection process was carried out separately for each age of blood sampling, since the importance of covariates in an assessment of a lead-IQ relationship may change over time (the full data set will be available on request). However, the major purpose of this paper is to evaluate the impact of the covariate selection process on the assessment of the relationship between lifetime average blood lead concentration and child development, because lifetime average blood lead concentration was consistently associated with neurobehavioural function in this cohort of children (11–14). The selection of covariates was based on both a priori and empirical considerations. First, the important antecedents or correlates of children’s IQ (e.g., child’s age, birth weight, and birth order), judged by knowledge and literature, were considered in the stages of data collection and included in the analyses. Second, the variables which were associated with both blood lead concentration and children’s IQ (p ⭐ 0.25) were considered as potential confounders. Finally, the CE criterion was used as a guide to evaluate the individual effect of each potential confounder. A covariate was considered to be a confounder if the partial regression coefficient of the lead term varied by more than ten percent when the covariate was added to (or deleted from) the model. The combined effect of potential confounders was assessed by the same rule, and was identified by the CE of the regression coefficients after adjustment for all the potential confounding factors. Potential multicollinearity of major quantitative covariates was evaluated using the Pearson correlation analytical method. The possible effect modifications between blood lead and other covariates were also explored through stratified analyses (it will be reported separately). The effect of potential confounders on the nature and magnitude of the lead-IQ relationship was evaluated using multiple linear regression modelling. In addition, covariates selected by different confounder selection criteria were compared and its impact on the point-estimate of the exposure-outcome relationship was also assessed. To simplify the procedure, we displayed the results for the CE and ST criteria separately.

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RESULTS Identification of Confounders Mean IQ scores and blood lead concentrations over categories of covariates that may confound the relationship under study are shown in Table 1. Many of the sociodemographic and biomedical factors were associated with both blood lead concentration and children’s IQ (p ⭐ 0.25), which suggests that these factors would be potential confounders in the assessment of the relationship between lead exposure and IQ. In simple regression analyses, SES, quality of home environment, and maternal intelligence were the variables found to be most strongly associated with both blood lead and IQ and accounted for 18.3%, 23.6%, and 11.0% of variance of the lifetime average blood lead concentration, and 15.5%, 20.8%, and 16.9% of variance of IQ, respectively. Evaluation of Multicollinearity The Pearson correlation coefficients between all pairs of major quantitative covariates were estimated (Table 2). Overall, these covariates were not highly correlated. Only eight out of 55 coefficients had absolute values greater than 0.3. The inter-correlations of maternal intelligence, Daniel scores and HOME scores were moderately strong, and their estimated correlation coefficients were close or equal to |0.50|. The Use of CE Criterion Additional regression analyses were carried out to assess the generic impact of the confounder selection strategy on estimation of the main effect of lead. Table 3 shows that the estimated regression coefficients of blood lead were influenced to differing extents when each of these variables was added to the simple regressions on children’s IQ. For instance, the magnitude of the estimated simple regression coefficients of lifetime average blood lead was decreased by 11.8–39.9% when the HOME scores, Daniel scores and maternal intelligence and parents’ smoking behaviour were individually included in the model, indicating that these variables may be important confounders in this study. The effect estimates were changed by less than 10 percent, however, when other covariates were separately added into the regression models. Comparison of the CE and ST Analyses Table 4 provides the results of a range of CE and ST analyses. Various number of covariates was selected according to different cut-off points. In general, CE criterion is stricter than ST criterion. For example, three to seven variables were selected as potential confounders using CE% ⫽ 5, 10, 15, 20, or 25, whereas nine to fourteen covariates were picked

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TABLE 1. Children’s IQ and lifetime average blood lead concentration (PbB) by covariatea Covariates Sex Boys Girls Age (years) 11 12 13 Years resident in Port Pirie ⭐ 15 ⬎ 15 Daniel scores ⬍ 45 45–55 ⬎ 55 HOME scores ⬍ 40 40–45 ⬎ 45 Life event Yes No Maternal IQ ⭐ 85 86–100 ⬎ 100

IQ

PbB

101.0 99.1 (0.15)

14.4 13.8 (0.23)

99.6 100.3 102.7 (0.61)

14.5 13.8 11.9 (0.11)

100.6 99.9 (0.56)

12.7 14.5 (⬍ 0.001)

105.0 102.5 96.2 (⬍ 0.001)

11.2 13.2 15.8 (⬍ 0.001)

94.1 100.8 106.1 (⬍ 0.001)

17.3 13.6 11.5 (⬍ 0.001)

98.4 101.1 (0.04)

14.8 13.7 (0.04)

94.1 101.5 107.8 (⬍ 0.001) Paternal secondary education (years) ⭐3 99.8 ⬎3 103.3 (0.001) Maternal age (years) ⭐ 25 98.9 ⬎ 25 101.0 (0.10) Birthweight (g) ⭐ 2500 98.5 2501–3500 99.8 ⬎ 3500 100.6 (0.60) Sibling number in the household None 97.8 One 101.2 ⭓ Two 100.2 (0.07) a

17.0 14.1 11.7 (⬍ 0.001) 14.1 13.2 (0.10) 15.0 13.3 (⬍ 0.001) 15.8 14.0 13.9 (0.36) 14.9 14.2 13.7 (0.28)

Covariates Grade 5–6 7–8 Family functioning Lower Middle Higher Parents’ marital status Married Non-married Parents’ general health Lower Middle Higher Parental smoking behaviour None One Both Testing site Schools Others Birth rank First Second ⭓ Third Medication in the last 2 weeks Yes No

IQ

PbB

98.2 102.1 (0.007)

14.9 13.3 (0.01)

101.3 101.1 99.0 (0.12)

13.9 13.1 14.6 (0.21)

100.6 97.6 (0.09)

13.6 16.9 (⬍ 0.001)

98.7 100.8 100.9 (0.07)

13.8 13.9 14.4 (0.31)

102.7 97.7 96.4 (0.01)

13.3 14.5 16.4 (⬍ 0.001)

100.0 100.3 (0.87)

13.5 17.5 (⬍ 0.001)

100.2 99.6 100.5 (0.59)

14.3 14.0 13.9 (0.53)

99.9 100.2 (0.83)

13.7 14.3 (0.39)

Absence from school (⭓ 2 weeks) Yes 97.7 No 100.8 (0.04) Feeding style of infants Breast 102.1 Mixed 101.3 Bottle 98.3 (0.007) Duration of breast-feeding (months) 0 97.0 1–6 99.7 ⬎6 101.9 (0.05)

15.9 13.6 (⬍ 0.001) 13.0 12.4 15.3 (⬍ 0.001) 15.3 14.7 12.6 (0.004)

P-values are shown in parentheses (Student t test for two categories and ANOVA for others).

up by the ST criterion with the same cutoffs. Only three key covariates were always selected regardless of which criterion was used. The covariate-adjusted relationships between lifetime average blood lead concentration and children’s IQ at age 11–13 years, using the commonly used CE (i.e., ⭓ 10%) or ST (i.e., ⭐ 0.25) criterion, were compared. The

partial regression coefficient of lifetime average blood lead concentration with use of the CE and ST criterion was ⫺4.4 [95% confidence interval (CI): ⫺0.5 to ⫺8.3] and ⫺4.3 (95% CI: ⫺0.2 to ⫺8.4), respectively, whereas the unadjusted regression coefficient was ⫺11.6 (95% CI: ⫺7.8 to ⫺15.4).

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TABLE 2. Pearson correlation between each pair of covariates Age 1 2 3 4 5 6 7 8 9 10 11

Maternal age 2

Dwelling length 3

Daniel scores 4

HOME scores 5

FAD 6

GHQ 7

Sibling no. 8

Maternal IQ 9

Birth weight 10

Duration of breast-feeding 11

⫺0.14 ⫺0.21 ⫺0.12 0.06 0.06 0.03 0.08 0.01 ⫺0.15 0.10 1

0.01 ⫺0.26 0.36 ⫺0.08 ⫺0.01 ⫺0.05 0.36 0.21 0.16 2

0.16 ⫺0.07 ⫺0.01 0.01 ⫺0.11 ⫺0.14 0.08 ⫺0.19 3

⫺0.50 0.12 0.06 ⫺0.12 ⫺0.52 0.05 ⫺0.38 4

⫺0.20 ⫺0.07 0.15 0.50 0.07 0.34 5

0.29 ⫺0.05 ⫺0.11 0.05 ⫺0.02 6

0.00 ⫺0.08 0.05 ⫺0.02 7

0.09 ⫺0.02 0.22 8

0.04 0.35 9

⫺0.02 10

DISCUSSION The results of this study indicate that there is an apparent difference in identification of confounders using the CE or ST criterion. The implementation of the former is likely to select important confounders only, whereas the implementation of the latter is more liberal. However, surprisingly, the point-estimate of the exposure-outcome relationship is quite similar after adjustment for confounding using either the CE or ST rule in this study. CE or ST Criterion How to select and adjust for a confounder is an important issue in epidemiologic data analysis. However, there has been little discussion or debate over the confounder selec-

tion criterion in epidemiologic research since Mickey and Greenland put forward their ideas in 1989 (6). The usual approach (1)—viz, to start with a complex model and then to reduce it by using either the CE and ST—may not be practicable for large studies like the Port Pirie cohort study because it may be counterproductive if too many covariates are included in the same model. Our view is that the best model is one with the smallest number of variables which can explain the greatest amount of variance. In this study, it was found that both number and nature of variables selected differ with different confounder selection criteria and different cutoffs. For example, only four variables (HOME scores, Daniel scores, maternal IQ, and parents’ smoking behaviour) met the conventional CE criterion (⭓ 10%) for confounding, whereas 14 variables met the ST

TABLE 3. Change-in-estimate of the main effect of lead by covariate Variable HOME scores (HOME) Daniel scores (SES) Maternal IQ (MIQ) Parental smoking behav. (PSB) Duration of breastfeeding (DBF) Feeding style of infants (FSI) Years resident in Pt Pirie (YRPP) Age Grade (GRD) Sibling number Maternal age (MA) Family functioning (FF) Sex Parents’ marital status (PMS) Birthweight Paternal 2nd education (PSE) Life event (LE) Birth rank Absence from school (AFS) Medication Testing site

CE (%)

R2(%)

F

⫺39.9 ⫺35.0 ⫺26.5 ⫺11.8 ⫺8.9 ⫺8.2 6.9 ⫺4.5 ⫺4.3 ⫺3.6 ⫺2.8 ⫺2.4 1.8 ⫺0.9 ⫺0.6 ⫺0.2 0.2 0.0 0.0 0.0 0.0

8.1 5.3 8.4 3.4 1.8 0.4 0.1 ⫺0.3 0.7 0.7 ⫺0.1 ⫺0.2 0.3 ⫺0.1 ⫺0.4 ⫺0.3 ⫺0.3 ⫺0.5 ⫺0.3 ⫺0.3 ⫺0.2

11.45 7.56 11.81 13.50 4.28 1.78 1.35 0.08 2.37 2.34 0.63 0.69 2.00 0.77 0.35 0.01 0.14 0.10 0.03 0.08 0.03

p-value ⬍ ⬍ ⬍ ⬍

0.001 0.001 0.001 0.001 0.02 0.22 0.34 0.89 0.06 0.08 0.52 0.48 0.15 0.39 0.72 0.98 0.81 0.87 0.96 0.90 0.96

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TABLE 4. Comparison of the change-in-estimate (CE) and significance test (ST) analysesa 5% CE HOME SES MIQ PSB DBF FSI YRPP

a

10%

15%

20%

25%

ST

CE

ST

CE

ST

CE

ST

CE

ST

HOME SES MIQ PSB DBF FSI GRD LE AFS

HOME SES MIQ PSB

HOME SES MIQ PSB DBF FSI GRD LE AFS PMS PSE MA

HOME SES MIQ

HOME SES MIQ PSB DBF FSI GRD LE AFS PMS PSE MA

HOME SES MIQ

HOME SES MIQ PSB DBF FSI GRD LE AFS PMS PSE MA

HOME SES MIQ

HOME SES MIQ PSB DBF FSI GRD LE AFS PMS PSE MA SEX FF

The percentages at the head of each column represent the cut-offs used in both CE and ST criterion. Abbreviations of variables are explained in Table 3.

criterion (p ⭐ 0.25). This suggests that the CE criterion (i.e., ⭓ 10%) may be more stringent than the ST method (i.e., p ⭐ 0.25) in the identification of confounders. However, it should be pointed out that the outcome of identifying confounders using the ST criterion is largely determined by a sample size. Therefore, it is unlikely that we can find a universal rule for all studies. Furthermore, different sets of variables were selected by the different confounder selection criterion with different cutoffs (Table 4). Another finding from this study is that, regardless of utilising which criterion, either the CE rule or ST, for adjustment for confounding, there was only a slight difference in the estimate of the lead-IQ relationship. The data from this study appear to provide supportive evidence for the recommendations made by Mickey and Greenland (6) that both the confounder selection criteria (i.e., CE and ST) should be acceptable if they are appropriately implemented. It also indicates that the impact of each covariate varies markedly on the assessment of the relationship between exposure to environmental lead and cognitive development. Four major confounders in this study are the quality of home environment, SES, maternal intelligence, and parents’ smoking behaviour. Other covariates seemed to have minimal impacts on the assessment. Our data suggest that it is important to take major confounders into account in making a valid assessment of the lead-effect relationship. Over-Adjustment or Under-Adjustment An association between blood lead concentration and children’s IQ remained evident after controlling for a wide range of putative confounders. However, some pitfalls may arise when adjusting for confounders. Quality of the home environment was found to be a determinant of children’s intelligence and was also a correlate of lead exposure. Therefore,

it was treated as a confounder in this study. However, there may be three hypothetical models that can describe the role of the quality of home environment in the assessment of the adverse effects of lead exposure. The first model (Model I) satisfies the classical criteria for “confounding” given in standard epidemiology texts: a mechanistic association between HOME scores and children’s IQ and a statistical association between HOME scores and blood lead concentration. If this represents the true situation, HOME scores should be taken into account in an assessment of the lead-IQ relation. The second model (Model II) depicts the hypothetical situation in which the observed impact on children’s IQ of HOME scores is mediated entirely by the amount of lead in the home environment which was ingested or inhaled. It is plausible that, in homes in which parents are less well educated and in which less attention is given to providing the child with a stimulating environment, less attention is also paid to other aspects of child and family care, such as domestic cleaning and maintenance. If this were the predominant mechanism, then it would theoretically be inappropriate to include HOME score in the analytic model. It is entirely plausible, however, that HOME scores may be partly artificial/stochastic, and partly causal in its association with lead exposure (Model III), i.e., the associations of HOME scores with IQ actually consist of two components, one of which is artefactually associated with exposure, the other being causally associated with exposure. Thus, HOME score could play a dual role, serving in part as a classical confounder and also as a mediator of exposure. The estimated Pearson correlation coefficient between HOME scores and lifetime average blood lead concentration was 0.55, which indicates that such consideration may be important. It is impossible, however, to distinguish the relative

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contributions of each component, and the treatment of this variable as a pure confounder may therefore underestimate the effect of lead on child development. In the analyses of the Port Pirie cohort data, HOME scores and other variables (e.g., maternal IQ and parental smoking behaviour) were included in the analyses as pure confounders (Model I). The strength of association between blood lead concentrations and children’s IQ was remarkably attenuated, but the association remained significant after adjustment. This analytical strategy is conservative in that it assumes that all these ‘non-lead’ variables are associated with children’s IQ via independent mechanisms that do not involve lead exposure, i.e., they are acting as pure confounders. In fact, it is plausible, however—even likely—that part of the effect of these variables was mediated via altered exposure to lead (Model III). Although this analytical procedure may have partitioned some variation which was truly attributable to the lead exposure, this may still be the prudent way to proceed until a better understanding of these mechanisms has been reached. Adequate or Inadequate Information on Confounding Residual confounding may arise when the data are classified into categories that are too broad. Some confounding factors (e.g., HOME scores and maternal IQ) that may be regarded as continuous variables were analysed in a categorical fashion, in order to avoid making assumptions about the form of their associations with the outcome of interest (e.g., linear, curvilinear, etc.) and to ensure the best use of the data (e.g., by creating a “missing” category, other data on the child can still be used in the regression analysis even if his/her value for that variable was recorded as “missing”). The aggregation of these variables might have resulted in some residual confounding. However, associations of blood lead with children’s IQ remained evident when these covariates were adjusted for, either in narrower categories (e.g., dividing the HOME scores and maternal IQ from 5 to 2 and from 10 to 5 point groups, respectively), or as continuous variables. A poor proxy for, or misclassification of, the underlying confounder(s) of interest may also result in residual confounding. For example, SES per se may not affect a child’s IQ, but it may convey information about many other factors that are causally associated with children’s IQ (e.g., educational stimulation, medical care, etc.). Therefore, SES is probably acting as a proxy for one or more fundamental underlying variables which are difficult to assess directly and precisely. In this study, the parents’ occupational prestige scale (i.e., Daniel score)—which is widely used in Australia—was employed as an index of SES. Several other measurements, e.g., parental education and quality of home environment, would also have reflected aspects of SES. However, it is unclear how well these proxies may have

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represented the underlying determinants of IQ. The validity of measuring confounders also needs to be emphasised. For example, the HOME scale was developed in Arkansas, USA, and may not be an appropriate measure of a child’s stimulation at home in an Australian community.

CONCLUDING REMARKS How to identify, measure and adjust for a confounding factor is an important methodological issue in epidemiologic research. It is a common practice to select and adjust for confounding factors through stratified analyses and/or modelling. However, it is important to consider them in both the stages of study design and data analysis since an adequate measurement and a valid assessment of confounders are essential for adjustment later. In epidemiologic research, prior knowledge and information about the investigated associations are important. It is desirable to use both a priori and empirical methods in identification of and adjustment for confounders, although statistical procedures may assist in identifying ‘yet unknown’ confounders. This study shows the complexities one can expect to encounter in the identification of and adjustment for confounders. As epidemiologists are aware, confounding can never be ruled out as an alternative explanation of the findings unless confounders are appropriately considered, measured, and adjusted. The authors would like to thank Profs. Tony McMichael and Jorn Olsen, as well as Drs. Peter Baghurst and David Purdie for their helpful comments on the manuscript.

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