The application of logistic regression to pedestrian-walkway safety.

Executive Summary

The cost of walkway accidents--pedestrian slips and falls--is substantial. To reduce the incidence of slips, and subsequent falls, companies install and maintain 'slip-resistant' floor surfaces. Monitoring floor slipperiness using an instrument called a tribometer allows businesses to record quantitative information that allows them to apply quality-control protocols to maintenance procedures, in order to minimize fall-accident rates.

In regression analysis, you are given data that has (hypothetically) been generated by a mathematical function whose parameters are not known, and you must estimate those underlying parameters. Ordinary regression is used to predict a continuous outcome. Logistic Regression is used when the outcome is dichotomous: yes/no. Because slipping--or not slipping--is a dichotomous event, and because Logistic Regression is a mathematical model that can explicitly model dichotomous events, it has recently been utilized in walkway-safety analysis. For example, Logistic Regression has been used to describe the likelihood of falling, and to associate walkway and gait characteristics to the probability of falling. Researchers have used the characteristics of the flooring surface materials, contaminants, and shoe sole materials and textures as factors that might help to predict increased risk of falls or the ability to recover from a slip; they have also considered aspects of normal gait to see if these might be associated with falling. Logistic Regression has been used by the authors to characterize tribometric instruments used to evaluate walkway safety, as well as to evaluate a novel method for barefoot-friction metrology.

In summary. Logistic Regression provides a powerful tool for improved understanding of how the tribometer can be used accurately to assess walkway slip-resistance.

The Objective of this Paper

This paper will explore how Logistic Regression has recently been applied to walkway-safety prediction and tribometer characterization.

Introduction: The Magnitude of the Problem

The cost of walkway accidents (pedestrian slip-, trip-, fall-, and misstep-precipitated injuries) is huge, both to society and to business. Rice and MacKenzie reported that, for 1985, the economic cost of slip and fall injuries to society--direct, morbidity, and mortality costs taken together--was estimated to exceed 37 billion dollars (Rice, et al., 1989). They found that fall accidents were the second largest generator of unintentional, accidental-injury costs, and the largest generator of accidental mortality in the elderly. Englander, Hodson and Terragrossa (Hodson, et al., 1996, 733-746) projected these costs to the year 2020, taking into account demographic trends, i.e., the aging of the population. They estimated that the cost to the United States would be over 64 billion dollars in 1995, and over 85 billion in the year 2020. Leamon and Murphy investigated the cost of walkway accidents to business; their 1995 research paper was entitled, rather understatedly, "More than a Trivial Problem," with an estimated per-worker cost of falls ranging from $44 to $550, depending upon the industrial sector. Leamon (Leamon, et al., 1995). Buck and Coleman (Buck, et al., 1985, pp. 949-958), Proctor and Coleman (Proctor, et al., 1988, pp. 269-285), and Proctor (Proctor, 1993, 367-377), studied walkway accidents in workplaces in the United Kingdom. The cost to the U.K. was thought to exceed 150 million pounds annually (1982 data).

The collection and analysis of fall-related injury statistics within the United States is accomplished by a number of governmental and private organizations, viz., the Bureau of Labor Statistics, the National Electronic Injury Surveillance System (NEISS), and the National Safety Council. The Bureau of Labor Statistics (BLS) classifies falls in a hierarchal manner. Exhibit 1 provides only a portion of their extensive list. For example: the percentage of total injuries for 'falls on the same level' (item 1.3.0) averaged 64% from 1999 to 2001. The average number of injuries (1999-2001) for falls resulting in days away from work was approximately 300,000 (Yuon et. al, 2006, pp. 83-93). Slips precipitate the plurality, if not the majority (a), of walkway accidents (Manning, D.P. et al., 1988, pp. 121-130, and Bentley et al. 1998, pp. 1859-1872).

[ILLUSTRATION OMITTED]

The National Safety Council (2002) reported that the slips and falls are the leading cause of death in the workplace and the cause of more than 20% of disabling injuries. The National Safety Council has also estimated that costs associated with employee slip-and-fall accidents (compensation and medical) are approximately $70 billion/year (National Safety Council, 2002). Liberty Mutual Workplace Safety Index reported that costs associated with falls on the same level were $5.7 billion/year (Liberty Mutual Research Institute, 2002). Regardless of the source, it is clear that the number of slip accidents and the resulting direct costs to business are significant and, due to the aging of the population, shows no signs of abating.

To reduce the incidence of slips and falls, a number of Risk-management-based loss prevention techniques have been discussed in industry periodicals. For example banking industry literature suggests that banks can reduce the walkway-accident-related claims of their customers and employees by developing slip-and-fall prevention policy and by analyzing losses to gauge the effectiveness of implemented policies and programs. Among the measures suggested are the design (or re-design) and maintenance of the bank's property to reduce the potential for slips and falls, good housekeeping, periodic inspections, and employee education and training (Erikson, 2004).

Food-service companies, viz., supermarkets and convenience stores, hotels, motels, and restaurants, are subject to slip-precipitated accidents and injuries both from customers and from their employees (Kohr, 1991, and DiPilla, 2006). These companies, the industry literature suggests, can mandate (and supply) the footwear used by their employees, design and install 'slip-resistant' kitchen floor surfaces, and implement an integrated program that includes facility design, inspection and maintenance. Use of checklists that require employees to monitor flooring conditions periodically (sweep logs), both in the store and the parking lot, are common measures, as is the installation of slip-resistant floor surfaces in areas that are likely to become contaminated.

Monitoring floor slipperiness, by using a portable tribometer, (b) allows business owners to collect quantitative information that allows them to determine the flooring condition with respect to pedestrian safety. The use of decision-science tools--both to characterize the chance of a fall and to analyze tribometers' results--is a relatively recent development in walkway safety. Because slipping--or not slipping--is a dichotomous pair of events, a mathematical model that reflects that dichotomous situation is especially useful for analyzing walkway-safety situations. Similarly, a tribometer that has a slip/no-slip result can be effectively characterized by a mathematical model that can model a dichotomous-event set. Logistic regression is just such a technique, where a dichotomous dependent variable is predicted employing a continuous variable (or variables) and/or, using dummy-variable sets, (c) to employ dichotomous, trichotomous, etc., events as independent variables. In other words, we can use a set of continuous inputs (like friction) and/or discrete inputs (like wet/dry) to predict either the chance, i.e., the probability of, a fall, or the chance (the probability) that a tribometer will indicate a slip at a given setting.

Introduction: Regression

Regression is a term used to describe the process of fitting a line or curve to a dataset. Logistic regression is the term used to describe the process of fitting a logistic curve to a dataset. Let's gently look at each of these ideas in some detail.

Regression analysis is the statistical equivalent of the TV game show, Jeopardy. In that game show, an answer is given, and the contestant must respond with the question that would have generated that answer. In regression analysis, one is given data that could have been generated by some hypothetical but unknown mathematical function, and one must estimate the underlying parameters of the function that would best generate that set of data. In some situations, regression analysis is more complex than Jeopardy: in the TV game, the contestant gets to choose from a number of categories; in regression analysis the categories themselves may or may not be known.

Ordinary Regression

For example, take the following data, which represents the emergency response time for an ambulance as a function of the straight-line distance between the emergency vehicle to the destination.

It is easier to visualize such data if it is plotted in a graphical format. It is conventional to plot the variable that determines the relationship (called the independent variable, which here is the distance-as-the-crow-flies that the ambulance must travel) on the horizontal axis, and the determined variable (the dependent variable; here, the response time) on the vertical axis.

[GRAPHIC OMITTED]

The relationship between the variables can be determined by, first, hypothesizing what the underlying relationship should look like and, secondly, estimating the parameters of that relationship. In this example, we can hypothesize that there is a certain amount of time that it takes to receive the call from the dispatcher, followed by the time that it takes to travel to the destination site. The former time is approximately constant. The latter time is roughly proportional to the distance that the ambulance must travel; it is not exactly proportional because of the interplay between traffic, one-way streets, and the like. Based upon this information, we can hypothesize that the underlying form of the relationship looks like a straight line:

Print Get the Mag Weekly Updates