Rapid weight gain during infancy is one of the strongest risk factors for obesity later in childhood [1–3] and has also been associated with increased blood pressure [4] and increased risk of diabetes [5]. Monitoring patterns of growth during infancy may be important for predicting the risk of both childhood and adult obesity [6–8]. It is well established that birthweight is associated with weight gain during infancy. Other factors which influence growth in infancy in addition to genetic factors include nutrition in infancy, maternal pre-pregnancy BMI and gestational weight gain and smoking during and after pregnancy [1, 2, 9].

Weight gain in infancy is closely linked with feeding practices. Formula-fed infants reach a higher weight-for-age and length-for-age Z-score by 6 months relative to breastfed infants, and this difference continues until one year of age [10, 11]. A large cohort study of over 17,000 infants nested within a randomised controlled trial conducted in Belarus, was able to show a clear dose response relationship between formula feeding and increased length and weight gain,where the relationship was strongest when infants were aged from 3 to 6 months [12]. There is also evidence that shorter duration of breastfeeding is associated with higher childhood BMI [13–16], however in some studies this has not been the case [17]. In studies where a positive association was not found there was usually no effect rather than an inverse effect and this may because the studies lacked statistical power to detect an association [17]. The differences in patterns of growth may be due to the actual content of breastmilk and formula which may relate to metabolic programming and/or other factors such as self regulation of energy intake [18].

It is plausible that differences in feeding behaviours and mother-child interactions between breastfed and formula-fed infants may also be important factors influencing weight gain. Formula-fed infants have, on average, a different feeding pattern from breastfed infants, with a higher volume (total daily volume and per feed), lower frequency of feeds, and longer time interval between feeds [19, 20]. In a prospective study of healthy infants, formula-fed infants had a 20-30% higher feeding volume (measured using ingested volumes) at 6 weeks than did breastfed infants, and they had fewer overall feeds at 4 months of age [19]. In another prospective study, infants who were bottlefed from birth were twice as likely to empty the bottle or cup in late infancy, according to maternal report, than infants fed breastmilk exclusively from the breast in early infancy [21]. These findings may reflect the fact that mothers who are formula feeding tend to monitor their infants' intake and are more likely to feed to schedule rather than on demand [22]. These differences in feeding behaviours suggest that mothers who formula feed may be less responsive to infant cues of hunger and satiety; hence, infants who are bottlefed may be less able to self regulate their intake compared with breastfed infants. Once established, these behaviours may be difficult to modify. This in turn may have implications for the development of healthy eating patterns in later childhood and the prevention of childhood and adult obesity [23, 24].

Developing a standard definition of overweight and obesity in children in order to determine prevalence and establish trends has always been problematic [25]. In 2006 the World Health Organisation revised its growth standards for children [26, 27] and defined cut off points for defining overweight and obesity in children. The WHO Child Growth Standards are widely recognised as the optimal growth charts for use regardless of ethnicity, socioeconomic status and type of feeding. Using the WHO standard curves, overweight and obesity are defined as weight-for-height >2 and >3 SDs respectively, above the World Health Organization growth standard median. Being 'at risk of overweight' was defined as a value >1 SD and ≤2 SDs above the median weight-for-height Z-score. A systematic review of rapid weight gain in infancy and subsequent obesity defined clinically relevant rapid weight gain as a difference of >0.67 SD in weight-for-age Z-score between birth and follow up [3].

Given the suggestion that interventions aimed at modifying early weight gain could prevent adult obesity [1], our aim was to determine which modifiable risk factors, especially those related to feeding practices or behaviours, are associated with rapid weight gain in early infancy. To do this we used birth data and baseline assessment information from the NOURISH early feeding trial [28].

In this analysis the two main modifiable factors associated with rapid weight gain in early infancy were formula feeding and feeding on schedule. Formula feeding has been well established as a likely risk factor for excessive early weight gain [35–37] however our finding that feeding style may also be related to weight gain is novel and suggests that both the content of formula milk as well as feeding dynamics, may be important for preventing rapid weight gain in infancy.

It is well known that rapid weight gain in early life is associated with later obesity and that weight gain is modified by feeding types and practices. Duration of any breastfeeding has been associated with a modest but consistent protective effect against later obesity in numerous observational studies and in three meta-analyses [16, 38, 39], but the mechanisms for this are still not defined clearly. The actual content of breastmilk including its high fat and low protein content, together with numerous immune related components and biologically active compounds are thought to play a major role in the protective effect [40]. It is also possible that one of the mechanisms behind the relationship between breastfeeding and obesity may be behavioural. A number of studies have shown that breastfed infants seem to self regulate their intake better than formula fed infants [21, 41] and in one study in exclusively breastfed infants, their intake was inversely associated with the energy density and fat content of the breastmilk [42]. A recent review of evidence suggests that although most infants have some ability to self regulate intake in early life, not all infants are able to readjust their intake back to baseline levels after caregiver interventions [43]. This suggests that behavioural factors such as patterns of maternal control over feeding and feeding to schedule may be important mechanisms behind the relationship between breastfeeding and childhood obesity. Our findings support this hypothesis.

A recent analysis of the KOALA birth cohort study [33], which included 2834 infants in the Netherlands, showed that breastfeeding duration was inversely associated with weight gain in the first year of life and children gained on average 37.6 g less in their first year for each additional month of breastfeeding, P < 0.001. Consistent with this they found that with each additional month of breastfeeding a significantly decreased odds of being overweight at one year [OR = 0.96 (95% CI 0.93-1.00), P < 0.05)]. These findings are comparable with the results of our study. However, they also found that although breastfeeding mothers more often fed on demand, patterns of feeding (ie. feeding on demand/to schedule or mixed feeding) were unrelated to weight gain, BMI or overweight after adjustment for breastfeeding, which differs from our findings. One possible explanation for the difference is the methods used in the study in the Netherlands where they used linear regression and absolute weight gain as the outcome, whereas our study used logistic regression and looked at rapid weight gain defined by a difference in weight-for-age Z-scores of above 0.67 as has been suggested in a systematic review [3].

A prospective study of 73 infants conducted in Canada aimed to interpret growth of infants in early life comparing the WHO and CDC growth curves. They showed a difference in Z-score of 0.5 in weight-for-age by 6 months of age between infants who were breastfed only (no formula) to 6 months of age (n = 25) and those who were formula fed only at 6 months (n = 28) [35]. Interestingly, the increased rate of weight gain occurred concurrently with changes in infant feeding, suggesting that a change from breastfeeding to formula was associated with an upward shift in the rate of weight gain. This was similar to our finding which showed that formula fed infants had a greater weight-for-age Z-score and a greater difference in Z-score between birth and assessment. The authors hypothesized that overfeeding and differences in nutrient intake and responses to hunger and satiation are responsible for their findings.

Our finding that formula fed infants were twice as likely to have introduced solid foods by the time of the assessment (in some cases earlier than 4 months) is similar to the finding of other studies [44]. We also found that lower maternal education may also be linked to early introduction of solids and formula feeding only which has also been shown in other studies [45, 46].

Strengths of our study include prospective design and objective measures of outcomes by trained staff which reduced the likelihood of measurement bias. However, because our data on key exposures (feeding style and type) were collected at the same time as weight, this analysis is not strictly longitudinal. Other limitations were that important potential confounders such as gestational weight gain, mode of breastfeeding (ie. via a bottle, as in expressed breastmilk or via breast) and infant sleep duration [47] (which may be a confounder or an intermediary) were not measured in our study. Because of the large variation in age for the baseline assessment we adjusted for age of the infant in our analyses. With regard to measurement of rapid weight gain, some studies have suggested that change in weight-for-length Z-score between assessment and birth may give a better reflection of rapid weight change but because we did not collect birth length we could not perform these analyses. With regard to generalisability of the sample, mothers in our sample were well educated with a low rate of maternal smoking, and the majority of families had incomes greater than A$70,000 per year, indicating that our sample was from a middle class background and therefore reflecting the population characteristics of the cities of Brisbane and Adelaide [48]. Almost half of mothers in our sample were overweight/obese (48.6%); however, this may have been due to the fact that many of them had not returned to their pre-pregnancy weight status by 4-7 months after birth of their child.

Although there have been many studies looking at the effect of breastfeeding on weight gain and later obesity, to date there have been few studies examining the effects of feeding styles as a risk factor for rapid weight gain and growth. Ours is one of the only studies to show that feeding on schedule is a risk factor for clinically significant excess weight gain in infancy. Our study is also one of the few to use breastfeeding as the 'norm' and referent group and formula feeding as the comparator group and thereby as a risk factor for rapid weight gain [49]. Because formula fed infants were more than twice as likely to be fed on schedule relative to breastfed infants, it is plausible that improving breastfeeding rates in early infancy may be effective in reducing rapid weight gain and thereby the burden of obesity at a population level. Because NOURISH is a prospective study, in future reports we can examine the predictive value of rapid weight gain in infancy on obesity risk in this Australian sample. Our future plans are to follow the cohort to two years of age when predictors of overweight and obesity can be determined. This study contributes to the already established literature that rapid weight gain is associated with formula feeding, however our finding that feeding to schedule is also associated with weight gain is novel. An application of our results could be that if mothers choose to start on formula they should receive anticipatory guidance to promote feeding on demand, thus allowing the infant to better regulate their own intake.