Table 2.

Association of ICU Admission with Hospital Length of Stay among Patients with Sepsis and Acute Respiratory Failure, Using Variable Modeling Approaches to Assess Length of Stay in the Setting of In-Hospital Mortality

Model	Test Statistic	Sepsis	ARF	Interpretation
Analyses Coding Deaths as Long LOS
IVQR with deaths set as 99th percentile LOS (primary analysis)	β-Coefficient (95% CI, P value)	1.32 (1.01 to 1.63, <0.001)*	–0.82 (–1.17 to –0.46, <0.001)*	Sepsis: primary result is due to ICU admission associated with increased mortality and increased LOS. ARF: primary result is due to ICU admission associated with decreased mortality and decreased LOS.
2SLS with deaths set as 99th percentile LOS†‡	β-Coefficient (95% CI, P value)	1.59 (0.13 to 3.06, 0.03)*	–2.04 (–3.53 to –0.57, 0.006)*
2SLS with deaths set as 99th percentile LOS and outcome log(LOS)†‡	Log β-coefficient (95% CI, P value, % change in hospital LOS)	0.25 (0.12 to 0.38, <0.001, +28.8%)*ǁ	–0.13 (–0.26 to –0.01, 0.04, −12.3%)*
Anazlyses That Exclude, Ignore, or Censor Deaths
Survival average causal effect IV 2SLS†	β-Coefficient (95% CI, P value)	0.51 (0.46 to 0.56)* + α	0.45 (0.39 to 0.50) + α	Sepsis: primary result is due to ICU admission associated with increased mortality and increased LOS. ARF: primary result due to ICU admission associated with decreased mortality but no change in LOS or accompanied by increased LOS.
Cox proportional hazard censoring on death§	Hazard ratio of discharge (95% CI, P value)	0.71 (0.70 to 0.73, <0.001)*	0.72 (0.70 to 0.74, <0.001)*
2SLS with deaths ignored‡	β-Coefficient (95% CI, P value)	0.75 (–0.23 to 1.74, 0.13)	0.16 (–0.90 to 1.22, 0.76)
2SLS with deaths excluded‡	β-Coefficient (95% CI, P value)	1.34 (0.28 to 2.40, 0.01)*	0.26 (–0.79 to 1.30, 0.63)
IVQR with deaths excluded	β-Coefficient (95% CI, P value)	0.89 (0.68 to 1.11, <0.001)*	0.06 (–0.18 to 0.31, 0.61)
2SLS with deaths ignored and outcome log(LOS)‡	Log β-coefficient (95% CI, P value, % change in hospital LOS)	0.14 (0.04 to 0.25, 0.009, +14.5%)*ǁ	0.09 (–0.02 to 0.20, 0.10, +9.5%)
2SLS with deaths excluded and outcome log(LOS)‡	Log β-coefficient (95% CI, P value, % change in hospital LOS)	0.26 (0.15 to 0.37, <0.001, +29.1%)*ǁ	0.04 (–0.06 to 0.15, 0.41, +4.5%)
Linear regression with deaths ignored and outcome log(LOS)†	Log β-coefficient (95% CI, P value, % change in hospital LOS)	0.31 (0.29 to 0.32, <0.001, 36.3%)*ǁ	0.35 (0.33 to 0.37, <0.001, 41.9%)*

Definition of abbreviations: 2SLS = two-stage least squares linear instrumental variable regression; ARF = acute respiratory failure; CI = confidence interval; IV = instrumental variable; IVQR = instrumental variable quantile regression; LAPS2 = laboratory-based acute physiology score v2; LOS = length of stay.

^*P < 0.05. Inclusion criteria restricted patients to those without mechanical ventilation or vasopressors and with LAPS2 ⩾ 100 in the emergency department. All models were adjusted for patient-level covariates: age, gender, ethnicity, race, insurance, LAPS2, COPS2, and hospital. Log(LOS) was calculated as log(LOS + 0.01) to account for any LOS = 0.

^† Normality assumption is violated.

^‡ Anderson-Rubin test for P value and 95% CI.

^§ Proportionality assumption is violated.

^ǁ Percent changes are included for the log(LOS) outcomes to allow for comparison with non-log β-coefficients.