Fig 1.
Left-truncation and right-censoring in KM and Cox fits.
For a fixed study period (start to end), an individual’s observation window (intake to outcome) falls into one of four cases. Only the portion of the stay that overlaps with the study period is used in the KM regression. However, the elapsed LOS is properly counted from intake.
Table 1.
HistLOS statistics for October and November 2023.
Fig 2.
HistLOS KM curves for October and November 2023.
KM curves with 95% CI bands show longer stays for November than October, an artifact of many long residents exiting in November. Klein tests (shown when P < 0.05) aid in identifying the region of separation between curves; an overall Cox score test is presented later. HistLOS includes the full stay of any dogs with in-period outcomes, with no truncation or censoring.
Table 2.
Descriptive ExitLOS stay statistics for October and November 2023.
Fig 3.
ExitLOS KM curves for October and November 2023.
KM curves with censoring marks and 95% CI bands show LOS shrunk from October to November, because of a spike in transfer outcomes in November. Truncation marks are (color coded) at the top and bottom. Klein tests (shown when P < 0.05) aid in identifying the region of separation between curves. (An overall Cox score test will be presented in Table 3) ExitLOS uses data on dogs in the shelter for any part of the study period but (left-)truncates and (right-)censors at the boundaries of the period (Fig 1).
Table 3.
Statistical comparisons of the KM curves of two monthly periods, for each type of LOS computation.
Table 4.
Descriptive statistics of quarterly ExitLOS observations, July 1, 2018 – June 30, 2024.
Fig 4.
Cox scores of ExitLOS for consecutive quarterly periods.
These are computed from quarterly ExitLOS periods. A test is labelled by the starting month of the second period in the pair, e.g., 20−10 for the comparison of October-December 2020 to July-September 2020. The Cox z statistic is in the top subplot and the P value in the bottom. Positive z corresponds to faster outcomes for the chronologically later period. Dashed lines mark the 0.05 significance level. Eight of 23 changes are statistically significant (P < 0.05), which suggests that the quarter-to-quarter variation is not just noise.
Fig 5.
Means and 90th stay percentiles of ExitLOS by quarterly period.
These are computed, with 95% CI bands, from quarterly ExitLOS KM fits from July 1, 2018, to June 30, 2024, with periods labelled by their starting month (e.g., 20−07 for July- September 2020). For the 90th stay percentile, the CI band is computed by inverting the 95% CI bands of the KM curves. Dashed lines show the mean (17.1) and 90th stay percentile (36) for a KM aggregate curve covering the entire six-year period. (These are not the arithmetic means of the quarterly values.) The changes in LOS are operationally consequential as mean LOS has a proportional impact on housing and staffing needs.
Table 5.
Descriptive statistics of ExitLOS observations for pre- COVID-19 and post-COVID-19 periods.
Table 6.
KM results for the pre-COVID-19 and post-COVID-19 periods.
Fig 6.
KM curves for the pre-COVID-19 and post-COVID-19 periods.
The pre-COVID-19 period is July 1, 2018 – February 29, 2020. The post-COVID-19 period is January 1, 2022 – October 31, 2023. KM curves are for ExitLOS, with (left-)truncation and (right-)censoring at the boundaries of the period (Fig 1). Censoring marks on the KM curves and 95% CI bands are shown. Truncation marks are (color coded) at the top and bottom. The P values of Klein time-point tests are shown when P < 0.05. There is clear separation between the two periods for all time points up to 205.
Table 7.
Cox proportional hazards regressions comparing the post-COVID-19 to the pre-COVID-19 period.
Fig 7.
Log cumulative hazard plot for the pre-COVID-19 and post-COVID-19 periods.
The pre-COVID-19 period is July 1, 2018 – February 29, 2020; the post-COVID-19 period is January 1, 2022 – October 31, 2023.