2. A model for the cost of blindness
Page 10
2. A model for the cost of blindness
A model is required to estimate the total true cost of blindness. It should also help to understand the limitations of the data collected thus far. As is well-known and also shown by the data collected for this project, the costs of blindness differ from individual to individual and between different groups of individuals. If a model for the cost of blindness for the various demographic categories of blind and vision New Zealanders is to be found, two values need to be identified for each of the demographic groups.
1. The proportion of individuals within each group that have a cost must be identified. We assume that not all blind people experience a given cost of blindness and that this may differ from group to group and from cost to cost.
2. For those people who do have a cost of blindness there will be an average cost that those people expend whether it be in dollars, hours expended or some other less quantifiable amount.
The true cost of blindness could be defined as the total amount of extra time, money and other resources that a blind or vision impaired person must expend or have expended on their behalf to attain the same quality of life as their sighted peers. As stated within the Gravitas report, the data collected does not consider the opportunity costs of blindness. Placing a value on the inability to obtain or retain a driver's licence is difficult to quantify. The myriad qualitative costs of blindness many of which are mentioned in the Gravitas report would require some imaginative approaches to evaluating the quality of life if any attempt to quantify them is to be considered. For example, the total distance travelled per annum in pursuit of recreational activities could be thought of as an indicator of a person's quality of life. To measure this would be difficult, but would need
Page 11
to be measured for the sighted and blind populations if the difference is to be found.
If we assume that all costs of blindness could be measured in dollar terms, the theoretical total cost of blindness for a person of a particular demographic group would be found as the sum, over all potential costs, of the probability that each cost is incurred times the average cost for those who do incur a cost. In mathematical terms this can be expressed
The notation in this expression allows a different total cost for each group Tg to be based on the probability pgj that people in group g incur cost j and the average value cgj spent by people in group g who do actually incur that cost j. Costs can be based on extra time expended (converted to dollar terms), and on opportunity costs such as lost income or loss of independence. Perceived costs of blindness could also be included in this model, such as the value of losing a driver's licence after an accident leading to blindness. A cost that is thought to be a cost of blindness by some blind or vision impaired people may not be a cost of blindness for others.
This model can then be used to find an expected cost of blindness for any person chosen at random from the blind or vision impaired population given that we have knowledge of their demographic make-up. Of course, this expected value should be an accurate estimate of the cost that the "average" person from that group would incur.
Page 12
Estimates are just that and some understanding of the variability that could be expected from all people in the same group should help individuals identify the magnitude of their personal cost of blindness in relation to the average person. An easy way to identify the way an individual's cost of blindness fits in with the group's cost of blindness is to use quartiles. The lower quartile, median, and upper quartile are a set of three summary statistics that divide the cost of blindness for the group into four quarters. If a person's costs of blindness is between the lower quartile and the median, they would then know that they have a cost that is below that of most other people with similar demographic characteristics and above that same cost for at least a quarter of their peers.
From the data collected thus far, there are few costs of blindness that had sufficient respondents to allow us to determine these quartiles. The two cost categories that are given greater analysis in this report are for personal use of taxis, and daily living costs.
This model is limited in two ways if used in conjunction with the information provided in the Gravitas report. First, the Gravitas report does not allow for the censoring of responses, which affect both the propensity to incur an expense and the resulting expenditure. Secondly, this model does not allow for competition between different costs of blindness that may exist. Decisions over the need for this competition to be included in a model for the total true costs of blindness are left to other researchers.