Poor agreement between methods used in population studies to estimate the volume of human milk consumed: a Bland-Altman analysis

Abstract

Background

Measuring the volume of human milk consumed by infants is essential for understanding infant feeding patterns, and their impact on long-term nutrition and health. The study aimed to evaluate the agreement and quantify biases among three methods used to quantify the volume of human milk among children on partial breastfeeding up to 33 months of age.

Methods

A cross-sectional, observational study was conducted between November and December 2022, with socially vulnerable children in the Federal District, Brazil. Dietary intake was assessed using two non-consecutive 24-hour recalls. Human milk volume was estimated using three methods: age/dose-to-mother (DTM), age/partial feeding, and age/feeding. Pearson’s correlation coefficient was used to assess associations between methods. Bland-Altman analysis was applied to evaluate agreement between estimates by each method. Statistical significance was set at 5%.

Results

Eighty children were evaluated (mean age of 19 months; SD = 6.12), including 15 aged 7–12 months, and 65 aged 13–33 months. Among children aged 7–12 months, moderate and statistically significant correlations were observed between age/DTM × age/partial feeding (r = 0.544, p = 0.02) and between age/partial feeding × age/feeding (r = 0.649, p = < 0.001). The correlation between age/DTM and age/feeding was weak and not statistically significant (r = 0.309, p = 0.097). Most individual estimates fell within the limits of agreement. However, the age/DTM method yielded higher estimated of human milk volume - mean of 321 g/day (95% CI 273, 368) and 333 g/day (95% CI 273, 393) more than the age/feeding and age/partial feeding, respectively. The agreement between methods decreased as estimated milk volume increased.

Conclusions

Although moderate positive correlations were observed among the methods, the age/partial feeding and age/feeding approaches demonstrated the highest level of agreement. No consistent agreement was found between the age/DTM method and the other two approaches.

Supplementary information

The online version contains supplementary material available at 10.1186/s13006-025-00786-6.

Background

Breastfeeding is considered an important practice for promoting the health of the mother-child dyad and a key component for adequate nutrient intake in infants and young children. The World Health Organization (WHO) recommends that infants be exclusively breastfed for the first 6 months of life. After this period, breastfeeding should be continued with other safe and nutritionally adequate foods until two years of age or beyond [1].

Measuring the volume of human milk consumed by infants is essential for understanding infant feeding patterns, as well as its influence on long-term nutrition and health. Different methods have been used to measure human milk intake, varying in accuracy and applicability. Indirect methods, such as dietary surveys and breastfeeding diaries, are often used due to their simplicity and low cost, but are prone to recall errors and reporting biases [2]. Direct methods, such as the weighing method (weighing the child before and after breastfeeding), can provide more accurate estimates, but can be inconvenient, compromise the normal breastfeeding pattern, and be logistically challenging in large studies [3].

Another direct, noninvasive, and accurate method is using stable isotopes, such as deuterium (²H₂O or D₂O), to measure the volume of human milk. The method is known as the dose-to-mother (DTM) method, in which a dose of labeled water is given to the mother, and the transfer of the isotope through the human milk to the child can be monitored. Although the DTM method provides more accurate data and is less prone to observation and reporting errors, difficulties remain in using it in population studies. These difficulties are associated with the high cost and demands of inputs and analyses [4].

The need to estimate the volume of human milk consumed in population studies, in which the application of direct methods is prohibitive, encouraged the development of studies to obtain prediction equations for this purpose. One of the first of these studies was described by Drewett et al. (1989), who estimated the volume of human milk considering the child’s age and the number of feedings per day, based on the weighing method [5]. The method by Briefel et al. (2010), also based on the weighing method, provides an estimate by considering the number of feedings per day for different ages and adjusting the amount of human milk by the total daily volume of liquids received [6]. On the other hand, the method by da Costa et al. (2010) is based on the DTM method [7]. The meta-analysis carried out compiled studies that used the DTM in several countries around the world, allowing the quantification of human milk production by the age of the child and the estimation of the reduction in human milk volume from the ingestion of other liquids (non-milk water intake) [7].

Estimating human milk consumption in population studies is challenging because it is linked to data that can be obtained through interviews/questionnaires, which generally record the child’s age, the number of feedings, and the child’s complementary food intake [8, 9]. Recently, Haszard et al. (2024) [10] published predictive equations to estimate human milk volume in children in New Zealand between 7 and 10 months of age. The estimation of human milk consumption should more accurately produce data on infant food consumption to inform policies and programs aimed at infant nutrition, providing support for identifying nutritional needs, monitoring child growth and development, and evaluating the effectiveness of nutritional interventions [10, 11]. Thus, the present study aimed to evaluate the agreement and quantify the biases between three methods used to estimate the volume of human milk among partially breastfed children up to 33 months of age.

Methods

Study design, setting, and eligibility criteria

An observational, cross-sectional study was conducted using data collected during the second follow-up period of the prospective cohort study called “Project to Evaluate the Implementation of the Happy Child Program in Brasilia (PIPA-DF)”. The data collection occurred in November and December 2022.

For this study, socially vulnerable children from the Federal District (DF) who participated in the Happy Child Program were selected [12]. All families served by the Happy Child Program with children up to 24 months of age were considered eligible for the evaluations. The age criterion was necessary to allow for 12 full months of membership in the Happy Child Program and, therefore, in the study. The youngest child was selected in families with more than one child between 0 and 24 months. The inclusion criteria were (1) being enrolled in the Happy Child Program for at least 6 months; and (2) being eligible for the program throughout the follow-up period in the cohort study. Families whose child’s caregiver was unable to respond to the questionnaires due to the existence of any cognitive deficit, or who were beneficiaries of another government social program, were not included.

Study variables

For descriptive analysis, sociodemographic variables (age, sex, race, family income) were considered, as well as variables regarding food consumption (frequency of breastfeeding throughout the day, type of breastfeeding, consumption of human milk and other liquids).

Consumption of human milk and other liquids

A team of eight interviewers, previously trained by nutritionists to collect data on food consumption, administered two 24-hour recalls to the caregiver, on non-consecutive days, about the child’s diet on the previous day, using the Multiple-Pass Method: 1. Quick List; 2. Forgotten Foods; 3. Timing and Meal Definition; 4. Detail and Review; 5. Final Review [13]. To assist in standardizing the measurements, a graphic support material (pamphlet) was prepared containing volumes and weights of cups, plates, bowls and utensils commonly used for children for the interviewers to take into the field.

Three methods were applied to estimate the volume of human milk consumed by children: estimation by age/feeding [5], estimation by age/partial feeding [6], and estimation by age/DTM [7]. Information on the child’s age in months and total fluid intake (water, teas, juices, soft drinks, nectars, coffee, soda, infant formulas, vitamins, dairy products, yogurts, chocolate-flavored milk drinks or other milk drinks) in addition to human milk throughout the day were used [5–7]. Soups and porridges were not considered for calculating the amount of fluid consumed, as they are considered semi-solid foods. Similarly, the water and milk ingredients in preparations (purees, etc.) or present in foods (water in the composition of fruits and vegetables) were not considered for calculating the amount of fluid consumed.

Estimation for age/DTM, consists of the method proposed by da Costa et al. (2010) [7]: The estimate is made based on the DTM and considers information about the child’s age in months and the total consumption of liquids other than human milk (water, juices, infant formulas, etc.) throughout the day. This method proposes an estimate based on the volume of human milk estimated for the age groups in months: 0–1 (0.6 kg/d), 1–2 (0.7 kg/d), 2–3 (0.75 kg/d), 3–4 (0.82 kg/d), 4–5 (0.80 kg/d), 5–6 (0.82 kg/d), 6–7 (0.79 kg/d), 7–8 (0.74 kg/d), 8–9 (0.77 kg/d), 9–10 (0.92 kg/d), 10–11 (0.86 kg/d), 11–12 (0.80 kg/d), and 12–24 (0.64 kg/d). After identifying the age group, the following equation was used:

Estimated human milk = amount of human milk (kg/d) according to age group × 1000 - [Amount of liquids (g) × 0.45]

The value of 45% is the reduction in human milk production for each 100 g of non-milk water intake in the adjusted model in the meta-analysis of DTM data from a study conducted by da Costa et al., 2010 [7].

When the estimated value of human milk volume provided a negative value, that is, when the amount of non-milk water intake was greater than the human milk volume for the age group, and to avoid truncating several estimated human milk values into a single value, the minimum value of 70 g/day of human milk was assigned. The value of 70 g/day of human milk was obtained from personal communication of preliminary data from the International Atomic Energy Agency table on human milk volume by the DTM method. The following strategy was used to organize the human milk estimates by DTM: the child with the highest volume of liquid consumed was assigned a value of 70 g/day of human milk, and the others were given an increasing value of 1 g/day starting at 70 g/day. In this way, the child with the estimated liquid consumption value just below this was assigned 71 g/day of human milk consumption. Thus, we had an increasing estimate of 71 to 88 g/day of human milk consumption for children with estimated intake of liquids other than human milk.

Estimation of age/feeding, consists of the method proposed by Drewett et al. (1989) [5]: This estimate considers only the child’s age in days and the number of feedings for the calculation using the equation below:

Estimated human milk = 489 – (0.63 × age) + (13.45 × number of feedings)

For the child’s age in days, the age in months was multiplied by 30, considering the average duration of one month.

Estimation of age/partial feeding, consists of the method proposed by Briefel et al. (2010) [6]: This method considers the age group and whether the child is exclusively or partially breastfed. According to the authors, children who were receiving any combination of human milk and infant formula, cow’s milk, flavored milk, soy milk, or rice milk as a beverage were considered to be partially breastfed. The estimate is obtained according to Table 1.

Table 1.

Coding rules for attributing human milk in 24-hour recalls for partial-fed infants

Age in months	Partial breastfeeding
6–11.9 months	608.64 g*
	Volume per feeding (g)
12–17.9 months	90
18–41.9 months	60

Source: Adapted from Briefel et al. (2010) [6].

Coding rule: * If the total daily volume of other milks exceeds the daily value listed for infants, the 3 fluid ounces per feeding (30 g) rule is recommended. The volume of human milk is divided equally among the number of feedings

For children between 6 and 11.9 months old, the daily volume from Table 1 was considered and subtracted from the amount of other liquids ingested to obtain the volume of human milk ingested per day. In cases where the volume of other liquids exceeded the daily volume described by Briefel et al. (2010) [6], the estimate was made considering the rule of 3 liquid ounces per feeding. To convert values, 1 liquid ounce was considered to correspond to 30 g. Data from zero feedings (n = 9) were excluded, that is, when the child was not breastfed.

Statistical analysis

The data were processed using JASP software, version 0.18.3.0. [14]. The sample was characterized by descriptive statistics with the respective error and variation measures. Subsequently, Pearson’s correlation coefficient was determined between the estimates of human milk volume. Finally, Bland-Altman analysis was applied to verify the agreement between the results obtained by each method.

Bland-Altman analysis was performed considering the three methods in pairs for the estimates of human milk volume of children up to 12 months of age. Then, Bland-Altman analysis was performed between the age/DTM [7] and age/partial feeding [6] methods for children up to 33 months of age.

The age/feeding [5] method was not used for children over 12 months of age, since it was designed for estimates of children up to this age. Therefore, the methods of age/DTM [7] and age/partial feeding [6] were selected for estimates for children over 12 months of age.

The Bland-Altman analysis is based on the graphical contrast of dispersion between the difference between the variables and the mean of two measurements obtained for the same individuals. Graphs are generated comparing the pairs with the points of the estimates containing the bias and the limits of agreement. The bias assumes the null value when the methods fully agree. The limits of agreement are defined as two standard deviations, downward and upward, and provide the acceptable error around the mean for the values (mean difference ±1.96 standard deviation). The Bland-Altman plot also allows outliers and trends to be obtained [15]. The statistical significance value was set at 5%.

Ethical considerations

Since this study involved human participants, PIPA-DF was submitted for review by the Research Ethics Committee of the Faculty of Health Sciences at the University of Brasília (CAAE: 32390620.0.0000.0030). Prior to data collection, the children’s legal guardians provided consent by signing the free and informed consent form (FICF). The study was conducted in accordance with the ethical principles outlined in the Declaration of Helsinki, with careful attention to minimizing risks, maximizing potential benefits, and safeguarding the privacy and confidentiality of participant data.

Results

Eighty children with a mean age of 19 months (SD = 6.12) were evaluated. Fifteen of the children were between 7 and 12 months, and 65 children were between 13 and 33 months. Of these, 53% were female and 67% were black or mixed race. Regarding family income, 64% of the children lived in households with up to R$1,000.00 per month (or US$178.00 per month and US$2,136 per year). All children were receiving complementary feeding at the time of the first recall, and nine children were not breastfed at the time of the second application of the 24-h recall.

The first evaluation analyzed two 24-h recalls of 15 children between 7 and 12 months of age. The estimates of the volume of ingested human milk varied between 90 and 990 grams per day. The second assessment, which considered the two recalls of children between 7 and 33 months old, totaling 151 recalls, showed estimates of 60 to 990 grams per day. These data are provided in Table 2.

Table 2.

Descriptive statistic by age range for three methods of human milk volume estimate

Age 7–12 months
	Age (months)	Age/DTM	Age/feeding	Age/partial feeding
Days of intake (n)	30
Mean	11	643	322	310
Std. Deviation	1.7	134.7	36.7	187.6
Median	11	676	318	353
IQR	3.0	141.1	36.2	256.9
Minimum	7	311	277	90
Maximum	12	862	419	990

Age 7–33 months
	Age (months)	Age/DTM	Age/feeding	Age/partial feeding
Days of intake (n)	151
Mean	19	370	-	195
Std. Deviation	6.2	209.0	-	139.8
Median	19	374	-	180
IQR	8.0	330.6	-	180.0
Minimum	7	70	-	60
Maximum	33	862	-	990

Note: Age/DTM calculated as per da Costa et al. (2010) [7], age/feeding calculated as Drewett et al. (1989) [5], age/partial feeding calculated as Briefel et al. (2010) [6], IQR, interquartile range

In the correlation analysis between the methods for estimating human milk volume (g/day) for the age range between 7 and 12 months (Fig. 1 and Supplementary table 1), a moderate positive and significant correlation was observed in the Pearson coefficient between age/DTM [7] x age/partial feeding [6] (r = 0.544, p = 0.02), age/partial feeding [6] x age/feeding [5] (r = 0.649, p= < 0.001), and age/DTM [7] x age/feeding [5] (r = 0.309, p = 0.097), with a weak positive correlation.

Fig. 1.

Correlation among estimation methods for human milk volume (aged 7–12 months). Note: Age/DTM calculated as per da Costa et al. (2010) [7], age/feeding calculated as Drewett et al. (1989) [5], age/partial feeding calculated as Briefel et al. (2010) [6]

In Figure 2 and Supplementary table 2, the Bland-Altman plots show the limits of agreement, the bias between the methods, and the outliers. In the interval between the limits of agreement, the values are expected to be concentrated, and values outside the limits are considered outliers.

Fig. 2.

Bland-Altman plots for pairs of human milk volume estimates (7–12 months; age/DTM, age/feeding, age/partial feeding). Note: Age/DTM calculated as per da Costa et al. (2010) [7], age/feeding calculated as Drewett et al. (1989) [5], age/partial feeding calculated as Briefel et al. (2010) [6]

The results showed that most of the individual values are within the limits of agreement, except for one estimate. This high estimated value of human milk consumption is due to the case of a child in whom a frequency of eleven feedings/day was reported in one of the recalls, with no consumption of other liquids in the 24 hours. The methods do not show agreement, and as the estimated volume of human milk increases, the difference between the methods increases.

The volume of human milk estimated by the age/DTM [7] method is on mean 321 g/day (95% CI 273, 368) and 333 g/day (273, 393) greater than the estimate by age/feeding [5] and age/partial feeding [6], respectively. (Fig. 2). The average difference between age/partial feeding [6] and age/feeding [5] estimates is −12 g/day (−74, 50), which indicates that the age/feeding [5] method estimates 12 g more human milk volume than age/partial feeding [6] estimated human milk volume. Thus, the estimates human milk volume of these two methods agree, especially for estimated consumption values between 300 and 400 g/day. However, the difference between their estimates increases as the human milk volume increases.

The Bland-Altman plots for the estimates of human milk volume (g/day) for children 7 to 33 months of age are presented in Figure 3 and supplementary table 3. Four estimates are outside the lower (−1.96 SD) limit of agreement (outliers). On average, the age/DTM [7] method estimates human milk volume by 175 g/day (142, 209), and as human milk volume increases, the difference in estimates between age/DTM [7] and age/partial feeding [6] also increases (trend).

Fig. 3.

Bland-Altman plots comparing age/DTM and age/partial feeding volume estimates in children aged 7–33 months. Note: Age/DTM calculated as per da Costa et al. (2010) [7] and age/partial feeding calculated as Briefel et al. (2010) [6]

Discussion

In this study, three methods used to estimate the volume of human milk consumed by 7 to 33-month-old children were compared: estimates by the methods of age/DTM [7], age/partial feeding [6], and age/feeding [5]. We found significant variations between the estimated volume of human milk provided, resulting from the variables used in each method. Thus, both the methods of age/feeding [5] and age/partial feeding [6] consider age and number of feedings, leading to greater agreement between the methods, as the methodology used in the estimate is similar. The method by age/DTM [7] is derived from a direct and robust measurement method, which is expected, as verified in the estimates, to present higher values than the other two methods.

As an example, we can verify these aspects, considering an 8-month-old child. With a quantity of liquid reported in the recall of 274 g and 6 feedings per day, the following estimates were obtained: 647 g/day by age/DTM [7], 335 g/day by age/partial feeding [6], and 411 g/day by age/feeding [5]. Thus, the estimate by age/DTM [7] presents a value approximately 40 to 50% higher than those obtained in the other methods. Thus, the age/DTM [7] yields higher daily human milk estimate compared to the other two methods with implications for nutrition assessments of infants’ dietary intake.

Estimates are indirect methods of assessing consumption. However, the proposed method by age/DTM [7] is based on a measurement method that does not interfere with breastfeeding on demand, which makes its estimates higher than weighing methods, which have limitations in measuring all feedings in 24 hours. Additionally, the study by da Costa et al. (2010) [7] estimates the contribution of other liquids in addition to the estimated amount of breast milk by age, considering that there is a reduction in human milk volume for every 100 g of non-milk water intake. Given the benefits of breastfeeding for children, estimates for the volume of human milk ingested and the repercussions for the assessment of children’s consumption and their recommendations are important [16]. The estimates obtained with the method of age/DTM [7], with data on the volume of human milk by the DTM method, are applicable and useful for estimating the volume of human milk consumed in population studies.

Human milk intake estimates have been obtained by frequency of feedings/day, duration, and frequency of feedings/day indirectly or directly by the DTM method and have commonly been used in association and concordance studies. An example of this application was the study by Olga et al. (2023), who assessed the associations between human milk volume, macronutrient intake, and child growth using the DTM method [17].

In addition, according to a study by Whyte, Mclean-Smith, and Reid (2022), conducted in Jamaica, to assess the agreement of the DTM method with 24-h recall in measuring exclusive breastfeeding (frequency and duration), moderate agreement was found between the two measures [18]. The present study highlights the possible underestimation of the contribution of human milk, both in breastfeeding practice and in nutrient intake, in population studies. Thus, it reinforces the importance of broad and representative human milk volume data from various populations to facilitate estimates closer to the real contribution of human milk in child nutrition.

The method by age/DTM [7], when considering the consumption of other liquids, may be useful for studies in contexts where there is greater dietary diversity, such as in populations of developing countries, where early introduction of other liquids is common [19]. The age/partial feeding [6] and age/feeding [5] methods, which have agreement with one another, may be more suitable in research contexts where human milk consumption pattern is more uniform, such as in studies carried out in populations with high adherence to predominant breastfeeding practices [20].

Furthermore, studies have demonstrated the importance of collecting more than one recall in the assessment of breastfeeding, especially exclusive breastfeeding, since they tend to overestimate this practice. However, the estimate based on the method of age/DTM [7] provides more robust information because it is derived from the DTM and considers other liquids other than breast milk at the time of the estimate. This information becomes even more accurate when two or more recalls are applied [21, 22].

This study highlights the importance of an accurate estimate of human milk consumption as a supplement to the diet, especially for situations of social vulnerability more susceptible to nutritional risk. Therefore, more studies with methodological rigor should investigate human milk consumption, and catch the attention of health policy makers to the continuity of actions to encourage breastfeeding. Such an initiative was carried out by Haszard et al. (2024) for children between 7 and 10 months old in New Zealand [10]. They developed predictive equations compared with DTM data, incorporating data on maternal and infant characteristics, as well as children’s food intake. The mean volume of human milk estimated by Haszard et al. (2024) was 762 ml/day or 785 g/day. These values are comparable to the values estimated in the present study for children age 7 to 12 months of 643 g/day by age/DTM [7] and higher than the values estimated by age/feeding [5] and age/partial feeding [6], 322 g/day and 310 g/day, respectively.

This study has important strengths to highlight. This is the first study on the subject with children 7 to 33 months of age. The application of the comparison between the methods in a population with a wider age range allowed a more detailed view of the variations in human milk consumption. In addition, the presented results can help in choosing the most appropriate method for each context to ensure accurate quantification of human milk consumption in future studies.

Some limitations are also worth noting. First, the absence of a reference method that would allow the validation of the human milk volume estimates is noteworthy. However, the use of three methods widely accepted in the scientific community, combined with the agreement analysis using the Bland-Altman plot, provides robustness to the comparison and allows a critical evaluation of the observed differences [23]. Second, the consumption estimates were made from data collected by 24-h dietary recalls, which depend on the memory and accuracy of caregivers. However, to reduce measurement bias, the Multiple-Pass Method was applied [13], and two recalls were collected on non-consecutive days. Lastly, breastfeeding is recognized as extending beyond nutrition, constituting a holistic process that strengthens emotional bonds, promotes comprehensive health, and exerts a positive impact on the entire family system. It fosters shared responsibility, enhances the valuation of motherhood, and increases awareness of caregiving practices, thereby reinforcing social support networks and establishing a foundation of affection, health, and cohesion that transcends childhood and contributes to the family’s overall well-being. This encompasses physical, emotional, and behavioral dimensions that were not included in this analysis.

Our study points to the need for further studies that contribute to a better estimate of the volume of human milk based on more robust data obtained with the DTM method. The initiative of the International Atomic Energy Agency to launch a new and expanded database on human milk intake in 2022 puts this possibility into perspective [24].

Conclusion

The present study showed that, although comparisons between the methods presented a moderate positive correlation in the estimates of human milk volume, the methods that provided the best agreement between them were age/partial feeding [6] and age/feeding [5]. There is no agreement between the methods of age/DTM, age/feeding, and age/partial feeding [5–7]. In addition, the daily volume of human milk estimated by the age/DTM [7] method was superior to the methods of age/feeding [5] and age/partial feeding [6]. The estimates tended to proportionately increase their difference as the volume of human milk increases. Therefore, when evaluating human milk intake in population studies, the choice of method should consider contextual factors that may influence this intake in different age groups.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Author contributions

The submission lists only a corresponding author: Amanda de Araujo Lima Cavalcanti (amandanutri06@gmail.com) Author contributions: A.A.L.C. and E.S.O.P. wrote the main manuscript text and prepared figures and tables. E.S.O.P., B.A.G. and I.M.C. participated in data collection. A.A.L.C. and T.H.M.C. performed the statistical analysis. The manuscript text was supervised by T.H.M.C., N. P. and V.S.S.G. All authors reviewed the manuscript.

Funding

The project was approved by public call no. 01/2021 of the Federal District Research Support Foundation (FAP-DF) and linked to Notice no. 04/2020 – DF Challenge Program. This study was financed in part by the Coordination of Superior Level Staff Improvement – Brasil (CAPES) – Finance Code 001.

Data availability

The data that support the findings of this study are not openly available due to reasons of sensitivity and are available from the corresponding author upon reasonable request. The data were collected with the approval of the ethics committee of the Faculty of Health Sciences of the University of Brasilia.

Declarations

Ethical approval

The project was approved by the Ethics and Research Committee of the Faculty of Health Sciences of the University of Brasilia (UnB) (CAAE: 32390620.0.0000.0030), and the children’s guardians signed the Free and Informed Consent Form (FICF) before the start of data collection.

Competing interests

The authors declare no competing interests.