This study was conducted in the following steps: (1) data were collected from electronically available aggregated reports; (2) WT was estimated according to age and sex from the collected data using the previously developed prediction equation, and (3) pre-formed water calculated by subtracting metabolic, respiratory, transcutaneous derived water from predicted WT was compared with the value estimated from DRs.

We used data from the 2016 National Health and Nutrition Survey, Japan (NHNS-J) [16,17,18]. This survey commenced in 1946, with the purpose of obtaining basic data necessary to receive food aid after World War II from each country under the General Headquarters of the Allied Forces. It is a cross-sectional household examination survey conducted in November of each year with the exception of 2016, when it was conducted from 1 October to 30 November because of the exceptionally large sample. Participants were selected using stratified random sampling from the 2010 census enumeration area of all 47 prefectures of Japan, with 10 districts per prefecture (only Tokyo, which has a large population, has 15 districts). In these areas, household members aged one year or older were included, except for the 13 districts affected by natural disasters, such as earthquakes and typhoons, in 2016. The number of households that gave valid responses to the dietary section of this survey was 10,745 out of 24,187 households (response rate = 44.4%). The present analyses included individuals aged 15–80 years who completed the dietary survey (10,546 men and 12,355 women).

Dietary intake was assessed from single-day semi-weighed household DRs, excluding trip or festivity days [19]. Before the dietary survey, participants were instructed on how to complete the DR by well-trained workers (mainly registered dietitians). A household member, usually responsible for preparing meals, was entrusted with weighing all food and beverages consumed by the household members and assigning approximate proportions of each dietary item to individual household members. When data were missing or illogical, workers visited the household and verified the portion sizes of food and beverages on the DR forms. Energy and nutrient intake were calculated from the weight of food and beverages consumed, based on the 2010 Standard Tables of Food Composition in Japan [20]. After the participants had completed the dietary survey, a physical examination was conducted in a facility within walking distance of their residence. The height and body weight were evaluated to the nearest 0.1 cm and 0.1 kg, respectively, using a stadiometer and weighing scale, with the participants barefoot and wearing light clothing. If participants were unavailable to measure these variables or could not travel to the facility, values were obtained from self-reports or measured at their homes. All data were available electronically in the form of aggregated reports in the official website of the Ministry of Health, Labour, and Welfare [21].

The WT was calculated using a previously developed equation derived from select variables using a multiple regression model with the WT measured by DLW methods as a dependent variable [4]. Data were collected from 5604 people including Japanese data that we provided for the ages of eight days to 96 years from across 23 countries and stored in the international DLW database, based on which a model predictive equation for WT in adults aged 18 years and older was developed. The coefficient of determination (R2) for this model was 0.471. The model used the following equation [4]:

$$\beginC & = + \;PA + \;body\; weigh\\&\quad + \;se (1\;if\;men,\;0\;if\;women) \\ &\quad + \;humidit\\&\quad + \;athlete\; statu (1\;if\;yes,0\;if\;no) \\ & \quad + \;HD(2\;if\;low\;HDI,1\;if\;middle\;HDI,0\;if\;high\;HDI) \\&\quad + \;altitud + \;ag_8 + \;ag\\&\quad + }\;temperatur_ + }\;temperatur} \end$$

(1)

where C represents WT. The intercept (β0) of the equation was − 713.1 ml. The coefficients of the binary variables of sex (β3), athlete status (β5), and human development index (HDI; β6), were 374.9 ml, 1070 ml, and 104.6 ml, respectively. The coefficients of the continuous variables of physical activity level (PAL; β1), body weight (β2), humidity (β4), altitude (β7), age2 (β8), age (β9), temperature2 (β10), and temperature (β11), were 1076 ml, 14.34 ml (kg), 5.823 ml (%), 0.4726 ml (m), − 0.3529 ml (years), 24.78 ml (years), 1.865 ml (℃), and − 19.66 ml (℃), respectively. The product of the above coefficients and all characteristic variables of the participants, such as PAL (continuous), body weight (continuous), sex (1 for men, 0 for women), humidity (continuous), athlete status (1 for yes, 0 for no), HDI (2 for low HDI countries, 1 for middle HDI countries, 0 for high-HDI countries), altitude (continuous), age2 (continuous), age (continuous), temperature2 (continuous), and temperature (continuous) were calculated. WT was calculated as the sum of the above products and intercepts.

Calibrated EI was calculated by multiplying the EI estimated from the DR by 1.09, because it was previously reported that the values estimated from DRs were underestimated by approximately 9% compared with total energy expenditure (TEE), as measured using the DLW method in Japanese older adults [15]. The predictive basal metabolic rate (pBMR) was estimated using the equation by Ganpule et al. for Japanese individuals [22], given that this equation provided the best results in a comparison of several different equations for calculating pBMR [23]. We assumed that EI and TEE had similar values [24], and PAL was substituted with calibrated EI/pBMR to compensate for the absence of PAL data in NHNS-J. As water intake from food was not reported in NHNS-J, and the mean ratio of water from foods in the DRs of previous studies was 69% [25], water intake from food was estimated at 69% of the food weight from the DR. Based on the sum of water intake from food and beverages, pre-formed water was estimated. Japan was considered a high-HDI country in accordance with a previous study [4]. We were unable to evaluate athletic status in this survey, therefore, we assumed that there were no athletes across all age groups. For altitude, a value of 189.2 m was used for all participants, which is the average value for the inhabited area in Japan [26]. The temperature and relative humidity during the survey period adopted the mean values as on November 2016 in all surveyed areas determined from the database of the Japan Meteorological Agency (temperature: 10.9℃ and relative humidity: 74.7%) [27].

The carbon dioxide production rate (rCO2), metabolic, respiratory, transcutaneous, and pre-formed water were calculated using Eqs. 2–6. We assumed that EI and TEE showed similar values, and rCO2 (mg/day) was calculated using the calibrated EI (kcal/day), food quotient (FQ), and Eq. (2) referenced in a previous study [28]:

$$rC = calibrated\,EI/(1.106 + (3.94/FQ))$$

(2)

We assumed that the respiratory quotient was equal to the FQ, which was calculated by multiplying the coefficients (protein: 0.8, fat: 0.7, carbohydrates: 1.0) and dietary protein, fat, and carbohydrate intake. Metabolic water (Wmet; ml/day) was calculated using Eq. (3) [9]:

$$\eqalign} = & Calibrated\;EI \times (1/100,000) \cr & \left[ _} + _} + _} + _}} \right] \cr}$$

(3)

The intake of fat (%fat), protein (%pro), carbohydrates (%carb), and alcohol (%alc) per calibrated EI, as estimated from the single-day DR, were multiplied by their coefficients and totalled. Metabolic water was estimated by multiplying the total value by the calibrated EI (kcal/day). Respiratory water (Wres; ml/day) was calculated from the concentration of water in the atmosphere, estimated from the average air temperature and relative humidity during the period when the DR was made, using Eq. (4) [9]:

$$} = \left[ \right] \times 0.035rC$$

(4)

The mean temperature, relative humidity, and absolute humidity during the study were 10.9 °C, 74.7%, and 7.45 g/m3 in November 2016, respectively [27]. For respiratory air volume, 3.5% of the inhaled air was assumed to be CO2 and was calculated from the rCO2 obtained using above equation. Transcutaneous water (Wtrans; ml/day) was calculated using Eq. (5) [9]:

$$} = \left[ _}/21.7} \right] \times 0.5 \times BSA \times 1.44$$

(5)

The transdermal absorption rate per m2 of body surface area (BSA) in an atmosphere saturated with water vapor (21.7 mg/L) was 0.18 g/m2. The BSA (m2) was estimated using the Dubois equation [29]. As clothing reduces the rate of evaporation of moisture from the skin, the clothing coefficient was assumed to be 50%. Pre-formed water (Wpre; L/day) was calculated by subtracting the metabolic, respiratory, and transcutaneous water from the WT using Eq. (6) [9]:

$$_= WT-\left[_+_+_\right]$$

(6)

Pre-formed water includes the fluids consumed from food and drinks.

All analyses were performed after stratifying by age (15–19, 20–29, 30–39, 40–49, 50–59, 60–69, and ≥ 70 years) and sex (male or female) according to the summary tables reported by the NHNS-J. For descriptive statistics, continuous and categorical variables of participant characteristics were expressed as mean and standard deviations or 95% confidence intervals (CI), and as numbers and percentages, respectively.

We used a restricted cubic spline model with three knots based on age distribution (5th (18 years), 50th (48 years), and 95th (77 years) percentiles) to evaluate the curvilinearity of the relationship between water consumption and age [30, 31]. The statistical significance of non-linearity was assessed using the Wald test, comparing the likelihood ratio of the spline model with the linear model, with p values of < 0.05 indicating a statistically significant non-linear relationship between the WT and age [32]. For the sensitivity analysis, we performed the same procedure using the TEE evaluated by DLW methods reported in previous Japanese studies [15, 33,34,35] because EI from DRs may not be uniformly underestimated in age groups [13, 14].

We compared the distribution of pre-formed water estimated by the prediction equation and DRs according to sex- and age-stratified models. The analysis results are presented as mean differences and 95% CI. To assess the relationship between underestimation of pre-formed water estimated from the DR and age, the p-value of the linear trend was calculated using a regression model and the continuous variable of age.

A two-tailed significance level of 5% was adopted and STATA MP, version 15.0 (StataCorp LP, College Station, TX, USA) was used for all analyses.