Re: The survival time of chocolates on hospital wards: covert observational study
A Comment on "The survival time of chocolates on hospital wards: covert observational study"
David A. Pink, Research Professor, Physics Department, St.Francis Xavier University, Antigonish, NS, Canada Erzsebet, Papp-Szabo, Senior Research Associate, Physics Department, University of Guelph, Guelph, ON, Canada, Andras T. Papp, Junior Medical Officer, Joondalup Health Campus, Hollywood Private Hospital, Perth, WA, Australia
Recently Gajendragadkar et al.1 published a seminal study of the consumption of chocolates on hospital wards. Statistical analyses showed that (a) taken as a group, healthcare assistants and nurses were the largest consumers of chocolate, (b) overall, ward chocolate consumers preferred Roses chocolates compared with Quality Street chocolates and (c) an exponential decay model best explained the time course ofa box of chocolates being consumed in a ward environment. While observations (a) and (b) raise important questions, we would like to address observation (c) in light of the comment "The behavioural or anthropological basis of this model remains unclear and is in need of further investigation, although similar patterns are seen in a variety of biological processes."
It is worth noting that the exponential decay model was fitted to the total data and no analyses of the different categories of consumers were carried out. In this case, we can consider the observed exponential decay to be a quantity averaged over a range of consumers, and treat the case in which we have a large number of chocolates accessible to a large number of consumers. With this proviso we can consider the number of chocolates to be a continuous differentiable function of time. Accordingly, at the risk of stressing the obvious, we bring the following to the attention of readers.
Let us assume that the dynamics of consumption is dominated by parameters describing, for example, becoming satiated. To analyze the result of such a simple model, let us denote by C the number of chocolates initially accessible to consumers. We take this initial time, t, to be t=0. We denote by N(t) the total number of chocolates consumed in the time interval [0,t]. Let us suppose that the average effect of satiation at time t is proportional, on the average, to the number of chocolates consumed up to that time, C-N(t), and that its magnitude is defined by a coefficient of satiation, which we denote by S. A positive value of S means that the consumation rate of chocolates is, on the average, a decreasing quantity as time increases. Accordingly, we can write,
dN(t)⁄dt= S[C-N(t) ] (1)
The solution to this differential equation, with the initial condition that, when t=0, N(0)=0, is
N(t)= C[1-exp(-St) ] (2)
where exp(x) is the exponential function. The number of chocolates remaining at time t is
C-N(t)= Cexp(-St) (3)
This simple model accounts for the observed exponential decay of the data averaged over all chocolate consumers in the study and identifies a single parameter governing the dynamics, the coefficient of satiation, S. It is perhaps noteworthy that the value of S is strongly product-dependent: for Roses, S=0.0083 per min, whereas for Quality Street S=0.0050 per min. The success of this model does raise some possibly-interesting questions: is the value of S consumer occupation-dependent, and which external parameters might it depend upon, e.g. time of day, proximity to coffee-breaks and stress levels.
This work was unsupported by any granting agency or commercial interest. None of the authors have any connection to the chocolate industry. EP-S is a discerning chocolate consumer.
1 Gajendragadkar, P.R., Moualed, D.J., Nicolson, P.L.R., Adjei, F.D., Cakebread, H.E., Duehmke, R.M., Martin, C.A. The survival time of chocolates on hospital wards: covert observational study. BMJ 2013;347:f7198
Competing interests: No competing interests