The application of logistic regression to pedestrian-walkway safety

Review of Business, Spring, 2009 by Marcus Besser, Mark Marpet, Howard Medoff

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]

Exhibit 1. A classification of Falls as to Type, from the Bureau of
Labor Statistics

1.0 Falls
    1.0 Falls, unspecified
    1.1. Falls to a lower level
         1.1.0 Falls to a lower level, unspecified
         1.1.1 Falls down stairs of steps
         1.1.2 Falls from floor, dock, or ground level
               1.1.2.0 Falls from floor, dock, or ground level,
                unspecified
...
         1.2.0 Jump from a scaffold, platform, loading dock
         1.2.1 Jump from structure, structural element, n.e.c.
         1.2.2 Jump from nonmoving vehicle
         1.2.9 Jump to lower level, n.e.c.
         1.3 Falls on same level
         1.3.0 Fall on same level, unspecified
         1.3.1 Fall to floor, walkway, or other surface
         1.3.2 Fall onto or against objects
         1.3.9 Fall on same level, n.e.c.
...
1.9 Fall, n.e.c.

n.e.c. means "not elsewhere classified"

U.S. Dept of Labor, Bureau of Labor Statistics, 2007, pp. DE-4-DE5

This is just a small portion of the full list, which classifies
thousands of items.