Study population and measures

We refer to Pereyra-Elìas et al. [15,16] for more comprehensive information on the study population, used measurements, descriptive statistics, etc. In short, the UK Millennium Cohort Study [33–39] is a nationally representative study that recruited 18,552 families with children born at the turn of the new century. Data has been collected at sweeps at ages 9 months and 3, 5, 7, 11, 14, and 17 years [40]. Mothers were asked how long the child had been breastfed at the sweeps at ages 9 months, 3 years, and 5 years. At sweep 6, when the children were approximately 14 years old, mothers completed a test of word comprehension. Following Pereyra-Elìas et al. [15,16], we used this test score as a measure of the mother’s cognitive ability. In the present study, the analytic sample size varied between 5797 (grades in English) and 9409 (verbal ability at age 5) with a mean value of 8482. These analytic sample sizes could probably be labeled as large, which is advantageous in that it contributes to high statistical power in the analyses.

The children’s verbal ability was assessed with the British Ability Scales (BAS) subtests Naming Vocabulary (age 5), Word Reading (age 7), and Verbal Similarities (age 11). At age 14, the children completed a test of word comprehension (similar to the test completed by their mothers at the same sweep). The children’s spatial ability was assessed with the BAS subtest Pattern Construction (ages 5 and 7). At age 11, the children completed the Cambridge Neuropsychological Test Automated Battery (CANTAB). Following Pereyra-Elìas et al. [15], we analyzed the Strategy (assessment of how systematically the tests were executed) and Number or Errors aspects of the CANTAB. The latter two scores were reversed so high scores would indicate high ability. Grades in mathematics and in English were measured at age 16 (sweep 7). For increased comparability, all ability scores and grades were standardized (M = 0, SD = 1). Breastfeeding was coded as years of breastfeeding duration.

Ethics statement

All sweeps of the UK Millennium Cohort Study have been approved by the National Health Services (NHS) Research Ethics Committee (MREC). Written informed consent has been obtained from parents, as well as from the children themselves as they have grown up [40]. For the present study, we accessed anonymized data on 26/6/2023 from the UK Data Service platform (data are available at http://doi.org/10.5255/UKDA-SN-8172-4). No ethical approval was required for this secondary analysis.

Statistical analyses and predictions

Effects of breastfeeding on the eight (four verbal and four spatial) measures of children’s cognitive ability and two grades when adjusting for maternal cognitive ability were estimated with ordinary least squares regression. Here, both a hypothesis of a genuine increasing effect and a hypothesis of a spurious effect due to residual confounding predicted positive adjusted effects. Effects of breastfeeding on maternal ability when adjusting for the child’s ability and educational outcomes were also estimated with ordinary least squares regression. Here, a hypothesis of a genuine increasing effect predicted negative adjusted effects. This would mean that among equally able children, those who had been breastfed more had less able mothers but had still been able to “catch up” with their less breastfed peers with more able mothers. As an example, if among children with average ability (standardized score = 0), those who had been breastfed more had less able mothers (e.g. average maternal score = -0.5) than those who had been breastfed less (e.g. average maternal score = 0.5), this would mean that the intergenerational change in ability had been more positive for the children who had been breastfed more (0 –(-0.5) = 0.5) compared with those who had been breastfed less (0–0.5 = -0.5). A negative effect of breastfeeding on maternal cognitive ability when adjusting for the child’s ability would indicate that breastfeeding had compensated for having a less able mother. Contrarily, due to the positive associations between breastfeeding and maternal and the child’s ability and educational outcomes, a hypothesis of spuriousness due to residual confounding predicted a positive effect of breastfeeding on maternal ability when adjusting for the child’s ability and educational outcomes. It should be noted that we do not claim a causal effect of children’s cognitive ability on maternal cognitive ability. The reason for estimating the effect of breastfeeding on maternal cognitive ability while adjusting for the child’s ability, in addition to estimating the effect of breastfeeding on the child’s ability while adjusting for maternal ability, was to assess if the latter effect was truly increasing or spurious due to residual confounding.

In addition to ordinary least squares regression, we used latent change score modeling [41–43] to estimate effects of breastfeeding on intergenerational change in cognitive ability from mothers to their children (Fig 1). In these structural equation models, the child’s ability and educational outcomes were regressed on maternal ability and a latent intergenerational change score, with both regression effects set to unity. This means that the child’s ability and educational outcomes were defined as maternal ability + change and, consequently, that change was defined as the child’s ability–maternal ability. The latent change score was, in turn, regressed on breastfeeding. According to a hypothesis of a genuine increasing effect, this latter effect should be positive. Fitting the three models described above on the same data allowed us to evaluate if breastfeeding appears to have a truly increasing effect on children’s cognitive ability or whether the effect is spurious due to residual confounding and regression to the mean.

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Fig 1. Latent change score modeling.

Latent change score modeling where the child’s cognitive ability (CCA) was regressed on maternal cognitive ability (MCA) and intergenerational change in cognitive ability (ΔCA). Intergenerational change in ability was, in turn, regressed on breastfeeding (BF).

https://doi.org/10.1371/journal.pone.0297216.g001

Three differences between the present analyses and the analyses conducted by Pereyra-Elìas et al. [15,16] can be noted: (1) Pereyra-Elìas et al. used breastfeeding as a categorical predictor and compared the effect of categorized breastfeeding durations (< 2 months, 2 to < 4 months, 4 to < 6 months, 6 to < 12 months, and ≥ 12 months, respectively) with “never breastfed” as the reference category. We, on the other hand, used breastfeeding as a continuous predictor with values coded as years of breastfeeding; (2) Pereyra-Elìas et al. [16] predicted”failure” and “high pass” as dichotomous educational outcomes in mathematics and in English, respectively. We, on the other hand, used grades on a scale from 1 to 9 (then standardized) as continuous outcomes; (3) We did not adjust for possible confounders in addition to maternal cognitive ability while Pereyra-Elìas et al. adjusted for a large number of potential confounders, including socioeconomic position, maternal age and use of alcohol and tobacco, etc. This difference reflects the difference in the objectives of the studies. Pereyra-Elìas et al. wanted to evaluate if the effect of breastfeeding on the child’s cognitive ability and educational outcomes persisted when adjusting for a large number of potential confounders. Our objective, on the other hand, was to assess if findings from different models, but all with the same variables (breastfeeding, maternal cognitive ability, and the child’s cognitive ability and educational outcomes), would converge. As the models were fitted to the same data, characteristics of the sample were constant across the analyzed models and could, consequently, not explain possible differences in what the models indicate. For example, as the analyzed data were the same, the mothers’ socioeconomic position would not be able to explain if, for example, one model would indicate an increasing effect of breastfeeding on the child’s cognitive ability while another model would indicate a decreasing effect. If we find that effects of breastfeeding on the child’s cognitive ability appear to be due to residual confounding due to measurement error in the confounder, adding additional potential confounders to the model would correspond to assessing if residual confounding is confounded by other confounders. We believe that this would complicate interpretations of findings with little or no added value.

It is important to note that the present study was not meant as an exact replication of Pereyra-Elìas et al. [15,16]. Instead, we set out to evaluate if effects of breastfeeding on the child’s cognitive ability and educational outcomes when adjusting for maternal cognitive ability appear to be genuine (i.e. non-spurious) or spurious due to residual confounding due to measurement error. The evaluation was conducted by assessing the convergence of findings from different models. However, as Pereyra-Elìas et al. analyzed effects between breastfeeding and cognitive ability and educational outcomes in the same dataset, it makes sense to compare our findings to theirs. Analyses were conducted with R 4.1.3 statistical software [44] employing the lavaan package [45]. The analytic script is available at the Open Science Framework at https://osf.io/c93ha/.

Limitations

The present study, as well as the original studies by Pereyra-Elìas et al. [15,16], was based on data from a modern Western society (the UK). We concluded that estimated effects of breastfeeding on the child’s cognitive ability and educational outcomes when adjusting for maternal cognitive ability may have been spurious due to residual confounding and regression to the mean rather than genuine. However, it is possible that this conclusion does not apply to other circumstances and societies, e.g. with nutritional deficiency.

As described in the Method section, we did not adjust for potential confounders in addition to maternal cognitive ability, e.g. socioeconomic position. We made this choice in order not to distract from the main point, i.e. that analyses can suggest very different conditions depending on which model is fitted to data. It is important to bear in mind that potential confounders were constant across the analyzed models and could not, consequently, account for the inconsistent findings. For example, as data came from the same mothers and children, the mothers’ socioeconomic position could not explain why some models suggested an increasing effect of breastfeeding on the child’s cognitive ability and educational outcomes while other models indicated a decreasing effect.

Maternal cognitive ability was measured after all but the last of the measurements of their child’s cognitive ability, at age 14. Hence, it is possible, at least theoretically, that the child’s cognitive ability may have affected maternal cognitive ability rather than, as assumed, the other way around. However, this should not affect our main conclusion that estimated effects of breastfeeding of the child’s cognitive ability when adjusting for maternal cognitive ability could be due to residual confounding due to error in the measurement of maternal ability. If anything, this suboptimal timing of measurements should make us even more cautious not to assume a genuine increasing effect of breastfeeding.

We have, in a manner of speaking, retained the null hypothesis of no genuine increasing effect of breastfeeding on the child’s cognitive ability and educational outcomes, and retention of a null hypothesis could be due to lack of statistical power. However, lack of power is usually seen as a potential problem when findings are not statistically significant. In the present case, with a single exception, all estimated effects were highly statistically significant (see Table 2). However, the effects had the wrong sign compared with what they would be expected to have with a genuine increasing effect. If power were increased, for example by increasing the sample size, the estimated effects would be expected to become even more statistically significant but not to change sign. Consequently, it is hard to see how lack of agreement between the present findings and a hypothesis of a genuine increasing effect could be explained by lack of power.

The objective of the current study was not to present a comprehensive review of research on cognitive ability and its determinants. Instead, and more specifically, the objective was to reanalyze the data used by Pereyra-Elìas et al. [15,16] and to evaluate their conclusion that a positive effect of breastfeeding on the child’s cognitive ability and educational outcomes persisted when adjusting for possible confounders, including maternal cognitive ability. Readers interested in comprehensive reviews are recommended to read, for example, works by Deary [e.g. 47,48] or Sternberg [e.g. 49].