# Use of Kaplan-Meier and Cox regressions in the distribution of length of stay in animal shelters for pre-specified calendar periods: Definition, computation, and examples of dog length of stay in orange county California

## TL;DR

This paper introduces a new statistical method to accurately calculate the length of stay for animals in shelters, avoiding misleading results from traditional approaches.

## Contribution

The paper proposes using Kaplan-Meier and Cox regression with left-truncation and right-censoring for accurate length-of-stay analysis in animal shelters.

## Key findings

- The proposed method corrects misleading interpretations of length of stay in animal shelters.
- Significant changes in length of stay were observed in 8 out of 23 quarterly periods.
- Post-pandemic changes in length of stay may be linked to operational policies, not just demographic factors.

## Abstract

Computations of length of stay in animal shelters rely on fixed animal cohorts. This is appropriate for research studies that pre-select cohorts, but it is problematic for operational assessments of animal shelters in fixed calendar periods or for comparisons among periods or shelters. Considering only the length of stay of animals whose stay ended within the study period leads to misinterpretation. The use of the Kaplan-Meier and Cox proportional hazards methods with left-truncation and right-censoring is proposed to correctly account for all animals present in the shelter for any fraction of a study period, including those that were present at the beginning and those that remain in care at the end of the period. Examples of dog length of stay in Orange County Animal Care in California show that this computation method corrects the misleading view of historically used calculations of length of stay. Statistically significant changes in length of stay are observed in 8 out of 23 quarterly periods. In a comparison of length of stay before and after the COVID-19 pandemic, the observed significant change in length of stay cannot be explained by variations in sizes and ages of incoming dogs and may be connected to operational policies that restricted visitor access. The proposed approach enables timely tracking of length of stay, accurate comparisons, and assessment of shelter practices and resource needs.