Method The Bwamanda study We did a secondary analysis of the historical data from the Bwamanda study, conducted from 1989 to 1991 in a rural area of the northwest part of the Democratic Republic of Congo, (DRC), located at 19.2 degrees east and 3.2 degrees north. The people of Bwamanda are, up till today, predominantly subsistence farmers and the basic diet consists of mainly of maize, cassava supplemented with fish, vegetables and fruits. Health care in the area is provided by a central hospital and 10 minor health centres with a few of these providing some limited nutritional rehabilitation services. With virtually unchanged living conditions in the study area, the secondary analysis was viewed to be contemporary and relevant. Study design The Bwamanda study was a dynamic population study with follow-up including thrice-monthly survey rounds, making up 15 months of follow-up and 6 contacts. At the first round 4 235 preschool children were enrolled and at the last round a total of 5 657 were enrolled. A full description of the study population can be found in Van den Broeck, Eeckels & Vuylsteke (1993). Trained interviewers conducted interviews according to an interviewer’s manual. They determined the children’s age on the basis of birth date noted on children’s road to health chart or on parents’ identity paper or on the basis of an interview using a local events calendar. Children were examined for kwashiorkor by using the presence of pitting oedema of the feet or ankles as a criterion. All children were examined for marasmus through inspection of abnormal visibility of skeletal structures and by absence or near-absence of palpable gluteus muscle. A locally constructed measuring board was used for measuring the length of children below 24 months, while a microtoise was used for measuring children older than 24 months. In both cases length was measured to the nearest 0.1 cm. A spring scale (CMS weighting equipment) was used to weigh the children to the nearest 100 g. We applied the WHO Child Growth Standard for anthropometric scoring (World Health Organization, 2006). Z-scores were calculated for weight for length/height (WHZ) and for length/height for age (HAZ). At each contact interviewers undertook face-to-face interviews with the most proximal caregiver of the child, usually the biological mother. The questionnaire included a single non-quantitative 24-h recall with the 41 locally most consumed food items listed and interviewees providing “yes or no” answers to the questions if children had consumed the listed food items during the previous day. The food items had been identified through a pilot study. The interviewees were also asked about number of meals prepared for the families, special meals prepared for the child and breastfeeding. Statistical method In an initial descriptive analysis, we tabulated the percentage (95% confidence interval) of individuals eating the different items, grouped by those who developed kwashiorkor, those who did not and those who developed marasmus. We used a two-sample test for equality of proportions to test if the fractions were different. Here, we were interested in estimation of risks of developing kwashiorkor specific to age, diet, frequency of food consumption, and infectious diseases. We were also interested in the duration of a particular diet; did a child eat a food item at each visit occurring every three months over the last 15 months, or only at, for example, one of the interview rounds prior to developing kwashiorkor. Smooth-in-time hazard functions as proposed by Hanley and Miettinen allow this type of analysis (Hanley & Miettinen, 2009). We specified Hanley–Miettinen smooth-in-time risk models containing all potential causal factors, including food items, special meals prepared for the child, breastfeeding, disease status, nutritional status, birth rank, age, season and number of meals. To select a representative sample from the study population we used the method proposed by Miettinen, and used the whole study population as reference series (Miettinen, 2010). In the analysis we include all new cases of kwashiorkor, but use a representative sample of the non-cases. With a relatively small number of cases, there is little to be gained by letting the number of non-cases become arbitrarily large, having in mind the computational cost of running the model. Results are reported as log-odds ratios (LOR) and risk reductions. In line with this method we took the dataset to consist of 35 person moments (c) where kwashiorkor was observed as the case series, and a representative sample (b) of the infinite number of person moments that constitute the 46 397 person-months in the study base. We use a (b)/(c)-ratio of 150 assuring variances and covariance have minimal errors (less than 1 percentage) compared to using the entire series. Age function and age as a risk factor Given that risk is not changing linearly with age, as seen in Fig. 1, we developed an age variable that accounted for nonlinear change in risk. Such transformations are required when risk does not change linearly with age. Accordingly age was included as an independent variable in the model. Based on visual inspection of how kwashiorkor was distributed according to age, a transformation of the age variable was done: (1) f age = a exp − b Age ∗ exp − a exp − b Age . To find the parameters a and b, we optimized Eq. (2) with binomial errors using logistic regression. (2) y = a + b ∗ f age . The AIC (Akaike Information criteria Information criteria) was used to compare models. To find the parameters which minimized AIC we used an algorithm combining the golden section search and successive parabolic interpolation, an efficient and automated method to find the best model. Here we used the optimize function in R to find the parameters which minimized AIC, resulting in a = 11.55, and b = 0.90 (Brent, 1973). Figure 1: Three months prevalence of kwashiorkor according to age in months in intervals of six months. Prevalence of kwashiorkor (y-axis) against age in months (x-axis). Prevalence aggregated by age group. Short vertical blue lines indicate age groups. Black dots indicate age of those children who developed kwashiorkor. Age at first time a child was observed with kwashiorkor was used. Other risk factors The risk factors associated with kwashiorkor were defined in two steps; first we specified a log-linear hazard model with binomial errors where the independent variables were all food types, presence or absence of diarrhoea, and stunting and wasting at last visit. We defined time as the natural logarithm of number of months a person had, or had not, consumed a specific food item. We assumed that the food items reported at a given point in time were consumed up until the next contact, with the interview during the current visit providing data on any alterations in the consumption patterns since the previous contact. Each variable was multiplied with the natural logarithm of time the item had been consumed or not. Next, we used the BIC (Bayesian Information Criteria) implemented in R’s MASS package (stepAIC) to find the most plausible model based on our data; the posteriori most probable candidate model. The fitted candidate model corresponding to the lowest value of BIC is the candidate model corresponding to the highest Bayesian posterior probability. Based on the selected model we address the risk of developing kwashiorkor given a prior personal profile. We report risk reduction estimates on the basis of profiles. To test if the model could also explain the difference between subjects who developed marasmus from those who developed kwashiorkor we applied the final selected model, with the same 35 person moments (c2) where kwashiorkor was observed as the case series, but this time with the references constituted by a sample of the infinite number of person moments including 1 173 person-months observed in 372 new cases of marasmus.

Results Table 1 reports the distribution of age, the HAZ score and the WHZ score for children with different nutritional status. It shows that children with kwashiorkor were younger than children with no kwashiorkor and marasmus. HAZ and WHZ scores were lower in children with kwashiorkor than in children with no kwashiorkor, but HAZ and WHZ scores were lower in children with marasmus than in children with kwashiorkor. Table 2 shows that the proportion of children with diarrhoea and anaemia was significantly higher in children with kwashiorkor and marasmus than in normal children. The percentage of children that were dehydrated was also highest in children with kwashiorkor and marasmus. In addition the table shows that there were significantly more boys than girls with marasmus. Age in month HAZ WHZ Q10 Q50 Q90 Q10 Q50 Q90 Q10 Q50 Q90 Kwashiorkor 15.9 26.5 38.4 −4.3 −2.3 −0.8 −2.5 −1.0 0.1 Reference population 7.4 35.9 66.5 −2.9 −1.4 −0.1 −1.4 −0.1 1.2 Marasmus 10.8 28.8 64.0 −4.5 −2.7 −1.2 −2.8 −1.3 0.1 DOI: 10.7717/peerj.350/table-1 Normal Kwashiorkor Marasmus n = 20 114 n = 41 n = 451 Coughing (%) 35.5 (34.8, 36.1) 34.1 (20.5, 50.7) 43.0 (39.7, 48.5) Diarrhoea (%) 5.1 (4.8, 5.4) 14.6 (6.1, 29.9) 12.1 (9.4, 15.4) Anaemia (%) 17.4 (16.9, 18.0) 39.0 (24.6, 55.5) 23.9 (20.3, 27.9) Fever (%) 10.8 (10.3, 11.2) 15.4 (6.4, 31.2) 16.9 (13.8, 20.5) Dehydrated (%) 0.4 (0.3, 0.5) 7.3 (1.9, 21.0) 4.9 (3.2, 7.3) Sex (% male) 51.2 (49.9, 52.5) 47.7 (32.7, 63.1) 60.7 (55.9, 65.3) Age in months. First round

(Q10, Q50, Q90) 6.9, 32.5, 61.1 8.8, 18.1, 29.4 5.3, 24.8, 60.1 DOI: 10.7717/peerj.350/table-2 Table 3 reports the consumption of different food items by the children in the survey round prior to the incidence of kwashiorkor. A high proportion of the children had consumed cassava roots, maize and cassava leaves. The proportion who had consumed cassava roots and maize was non-significantly higher for those who developed kwashiorkor, but for cassava leaves the consumption was lowest for the children with kwashiorkor. The proportion of children who had consumed yam, pineapple, citrus, snails, and eggs was non-significantly higher for the children who developed kwashiorkor than for the others. On the other hand the proportion of children with kwashiorkor who had consumed okra, ground nuts, banana, squash, meat, chili, fish and other vegetables was non-significantly lower than for the rest. There were no significant differences in proportion of children who had consumed palm oil between children who developed kwashiorkor and the other children. The diet of children who developed kwashiorkor was characterized by low consumption of sweet potatoes, papaya and “other vegetables” [0.0%, 2.3% (95% CI [0.4, 12.1]) and 2.3% (95% CI [0.4, 12.1])]. In comparison the children who did not develop kwashiorkor had higher consumption of sweet potatoes, papaya and “other vegetables” [6.8% (95% CI [6.4, 7.2]), 15.5% (95% CI [15, 16.1]) and 15.1% (95% CI [14.6, 15.7])]. The children who developed marasmus also had higher consumption of these food items than the children who developed kwashiorkor [4.5% (95% CI [2.6, 7.5]) 11.8% (95% CI [8.5, 16.0]) and 17.6% (95% CI [13.7, 22.5])]. Food items Children with kwashiorkor Children without kwashiorkor Children with marasmus Food items Children with kwashiorkor Children without kwashiorkor Children with marasmus % (95% CI) % (95% CI) % (95% CI) % (95% CI) % (95% CI) % (95% CI) African pear 0.0 (0.0, 8.2) 0.0 (0.0, 0.1) 0.0 (0.0, 1.3) Okra 2.3 (0.4, 12.1) 4.5 (4.2, 4.8) 5.2 (3.2, 8.4) Amaranth 7.0 (2.4, 18.6) 1.8 (1.7, 2.1) 3.1 (1.6, 5.8) Palm oil 86.0 (72.0, 93.4) 88.8 (88.3, 89.3) 80.3 (75.4, 84.5) Aubergine 0.0 (0.0, 8.2) 0.8 (0.7, 0.9) 0.0 (0.0, 1.3) Papaya 2.3 (0.4, 12.1) 15.5 (15.0, 16.1)* 11.8 (8.5, 16.0)* Avocado 0.0 (0.0, 8.2) 0.2 (0.1, 0.2) 0.0 (0.0, 1.3) Pineapple 4.7 (1.3, 15.5) 1.4 (1.2, 1.6) 1.7 (0.7, 4.0) Banana 9.3 (3.7, 21.6) 19.1 (18.5, 19.7) 16.3 (12.5, 21.0) Powder milk 0.0 (0.0, 8.2) 0.0 (0.0, 0.1) 0.0 (0.0, 1.3) Beans 31.1 (30.4, 31.8) 0.4 (0.3, 0.5) 0.0 (0.0, 1.3) Rice 2.3 (0.4, 12.1) 0.6 (0.5, 0.8) 0.0 (0.0, 1.3) Breadfruit 0.0 (0.0, 8.2) 1.1 (0.9, 1.2) 1.7 (0.7, 4.0) Sesame 0.0 (0.0, 8.2) 0.1 (0.1, 0.2) 0.3 (0.1, 1.9) Cassava leaves 76.7 (62.3, 86.8) 79.2 (78.6, 79.9) 70.7 (65.2, 75.6) Shrimp 0.0 (0.0, 8.2) 0.1 (0.1, 0.2) 0.0 (0.0, 1.3) Caterpillars 2.0 (1.8, 2.2) 2.0 (1.8, 2.2) 1.0 (0.4, 3.0) Snails 2.3 (0.4, 12.1) 1.4 (1.3, 1.6) 1.4 (0.5, 3.5) Cassava roots 76.7 (62.3, 86.8) 72.6 (71.9, 73.3) 72.3 (66.9, 77.2) Soya 4.7 (1.3, 15.5) 5.2 (4.9, 5.5) 5.9 (3.7, 9.2) Chili pepper 4.7 (1.3, 15.5) 8.9 (8.4, 9.3) 4.5 (2.6, 7.5) Spinach 2.3 (0.4, 12.1) 2.8 (2.6, 3.1) 2.1 (1.0, 4.5) Egg 4.7 (1.3, 15.5) 0.7 (0.5, 0.8)** 1.0 (0.4, 3.0) Squash 0.0 (0.0, 8.2) 4.9 (4.6, 5.2) 5.2 (3.2, 8.4) Fish 18.6 (9.7, 32.6) 31.1 (30.4, 31.8) 25.3 (20.6, 30.6) Sugar cane 0.0 (0.0, 8.2) 0.7 (0.6, 0.9) 0.3 (0.1, 1.9) Fruit (others) 0.0 (0.0, 8.2) 1.8 (1.6, 2.0) 1.0 (0.4, 3.0) Sweet potato 0.0 (0.0, 8.2) 6.8 (6.4, 7.2) 4.5 (2.6, 7.5) Ground nuts 18.6 (9.7, 32.6) 28.6 (27.9, 29.3) 23.9 (19.3, 29.1) Termites 0.0 (0.0, 8.2) 0.3 (0.3, 0.4) 0.0 (0.0, 1.3) Maize 97.7 (87.9, 99.6) 93.5 (93.1, 93.8) 91.7 (88.0, 94.4) Tomatoes 0.0 (0.0, 8.2) 1.3 (1.1, 1.5) 0.0 (0.0, 1.3) Mango 0.0 (0.0, 8.2) 0.9 (0.7, 1.0) 0.7 (0.2, 2.5) Wheat 0.0 (0.0, 8.2) 0.6 (0.5, 0.7) 0.3 (0.1, 1.9) Meat 0 .0 (0.0, 8.2) 4.7 (4.4, 5.0) 5.5 (3.4, 8.8) Other vegetables 2.3 (0.4, 12.1) 15.1 (14.6, 15.7)* 17.6 (13.7, 22.5)** Milk 0.0 (0.0, 8.2) 0.1 (0.1, 0.1) 0.0 (0.0, 1.3) Yam 2.3 (0.4, 12.1) 1.3 (1.1, 1.4) 0.7 (0.2, 2.5) Mushroom 0.0 (0.0, 8.2) 2.3 (2.1, 2.5) 1.7 (0.7, 4.0) DOI: 10.7717/peerj.350/table-3 Given that the β-carotene could be the main acting agent in sweet potatoes, papaya and “other vegetables” we constructed a variable, PaSV (papaya, sweet potato and “other vegetables”), which combined all these items, weighted by the β-carotene content of 100 g of each item. The weighting of sweet potatoes equalled 1 and papaya 1/3. The variable “other vegetables” includes taro, taro leaves and wild vegetables. Taro leaves are rich in β-carotene and a study from DRC shows that wild vegetables are also rich in β-carotene (Termote et al., 2012). The PaSV variable did not encompass cassava leaves and amaranth. Since we have not been able to determine the more precise content of the other vegetables in our study, we have weighted the “other vegetables” low, with the weighing equal to 1/10. For the construction of smooth-in-time risk models we defined time for this combined variable as for the single food items. The most probable model based on BIC included age, time, PaSV, and HAZ. The two variables were correlated (R2 = 0.50). As seen in Fig. 1 the risk of developing kwashiorkor was highest in the age interval between 16 and 38 months. Table 4 shows the coefficients for the non-proportional hazard model with person moments sampled from the entire population. The log-odds for the continuous variable HAZ; LOR −0.8 (CI 95% [−1.1, −0.5]), length/height for age Z-score, describes an increased risk of developing kwashiorkor with lower height for age. Chronic malnourished children on average have a negative HAZ score, hence the negative log-odds. We found the log-odds for the time variable to be LOR 4.7 (CI 95% [3.4, 6.1]), for the combined variable for food items containing β-carotene it was LOR −9.2 (CI 95% [−21.0, −3.1]), for PaSV, and their interaction it was LOR 8.1 (CI 95% [−11.1, −2.1]). These findings must be understood together. A child not consuming the PaSV food items will have PaSV = 0, and thus the interaction term is also zero. The risk of developing kwashiorkor therefore increases the longer the child does not consume the PaSV food items. On the other hand, as illustrated in Fig. 2 a child consuming PaSV food items, PaSV >0, will reduce the risk over time. The overall model fit was good with an AIC of 251.3 and a Nagelkerke R2 index of 0.44. Term Log odds—estimate Confidence interval, 95% Intercept −15.5 −18.1, −13.4 Age function of age (months) 10.1 6.1, 14.8 T months 4.7 3.4 , 6.1 PaSV −9.2 −21.0, −3.1 HAZ −0.8 −1.1, −0.5 T ∗ PaSV −8.1 −11.1, −2.1 DOI: 10.7717/peerj.350/table-4 Figure 2: Risk reduction for developing kwashiorkor showing reduction of consuming β-carotene rich products according to age in months. The dotted line is risk reduction after two months, dashed line after four months, and solid line after six months. (A) shows risk reduction for a child with a height-for-age Z-score (HAZ) of minus five, (B) for a child with HAZ of minus three, and (C) a child with HAZ of zero. HAZ-scores are based on the WHO-2006 Child Growth Standards [17]. Table 5 shows the findings from sampling control-moments only from children who developed marasmus. The table shows that the HAZ score for those who developed marasmus is the same as the HAZ score for the children who developed kwashiorkor (LOR = 0.0, CI 95% [−0.1, 0.2]). Then again it shows that there is a difference with regards to consumption of products containing β-carotene with the LOR for PaSV being −6.8 (CI 95% [−17.8, −1.7]) and for PaSV combined with the time variable T the LOR was −6.3 (CI 95% [−9.0, −0.8]). The age of children who developed kwashiorkor was also different from children who developed marasmus with LOR being 7.9 (CI 95% [4.3, 12.1]). The age of children with marasmus was distributed within the age of 11–64 months, while the age of children with kwashiorkor mainly fell between 16 and 38 months, reaching a top around 26 months. Term Log odds—estimate Confidence interval, 95% Intercept −9.7 −12.1, −7.7 Age function of age (months) 7.9 4.3, 12.1 T months 4.2 3.2, 5.4 PaSV −6.8 −17.8, −1.7 HAZ 0.0 −0.3, 0.2 T ∗ PaSV −6.3 −9.0, −0.8 DOI: 10.7717/peerj.350/table-5 Ethical approval for the Bwamanda study was granted by the University of Leuven’s Tropical Childcare Health Working Group. Community consent was obtained verbally from community leaders, whereas individual verbal consent was obtained from children’s caretakers.