Question

If an independent survey found that 20% of all boxes of chocolates in hospitals were of the Cadbury brand, would you be able to calculate the population risk difference for consumption for the first 60 minutes after a box is opened? Assume that the Cadbury chocolates are the exposed group? If possible, calculate this quantity.

The number of chocolates consumed by healthcare providers (all types) over the course of the first 60 minutes and the second 60 minutes after the box was opened.

Type of Chocolate	First 60 Minutes of Observation		Second 60 Minutes of Observation
	Number of Chocolates                                    Followed	Number Consumed	Number of Chocolates               Followed	Number Consumed
Nestle	135	45	90	23
Cadbury	123	55	68	21

¹ If a chocolate was missing by the end of an hour of observation, it was assumed to have been consumed by a healthcare provider during that hour.

Table E1.2. The number of chocolates that were observed to be consumed during the 6- hours of observation.

Healthcare   Provider Position		Nestle   Chocolates		Cadbury Chocolates	Provider Total
Doctor		17		12	29
Nurse		21		33	54
Other		61		47	108
Brand Total		99		92	191

Answer 1

Here we want to calculate the population risk difference for consumption for the first 60 minutes after a box is opened.

The sample consumption data for the first 60 minutes are given as follows:

Type of Chocolates	consumed	Not consumed	Total	Cumulative Incidence / Risk
Nestle(Unexposed group)	45	90	135	45/135 = 0.33333333
Cadbury(Exposed group)	55	68	123	55/123 = 0.44715447154

Risk difference = cumulative incidence in the group with the exposure - cumulative incidence in the unexposed group

= 0.44715447154 -  0.33333333333 = 0.11382113821

So, there are 11.38% more consumption in Cadbury than in Nestle in first 60 mins after the box is opened.