MemoA03
ClientDr. ABC
Client OrganizationABC Department
Version2.0
StatusDraft
ClassificationInternal use only
Note: The primary exposure is pre-disposition stay. Total emergency stay is reported in the appendix.

1 Overview

1.1 Introduction

The purpose of this memo is to estimate whether pre-disposition stay and CTAS are associated with hospitalization. Pre-disposition stay is the primary stay measure. It ends when the disposition decision is made. Total emergency stay is reported in the appendix, because it also includes time after that decision, and that later time can be a consequence of deciding to hospitalize. Other available covariates, and a model that includes them together, are also in the appendix.

Data preparation is completed in Memo A00. This memo reads analytic_nacrs.rds and does not rebuild derived fields. ambulance_flag is omitted because it is a recode of arrival_mode. Consult service is not modeled. Every hospitalized visit has a consult, and no visit coded None is hospitalized, so a logistic odds ratio for that variable is not estimable.

The outcome is hospitalization. A visit is coded hospitalized when disposition is Admitted inpatient. Memo A00 stores that indicator as admitted_flag.

A result is treated as statistically significant when its Wald p value is below 0.05. Significant odds-ratio rows and their interpretations are shown on a yellow background. These are associations in synthetic records, not causal effects.

1.2 Data

Training data notice: The visits are randomly generated synthetic records. Preprocessing is completed in Memo A00.
Analytic NACRS file used for the logistic models
File Visits Hospitalized Not hospitalized Covariates
analytic_nacrs.rds 30000 5810 24190 11

2 Primary model

The primary model enters pre-disposition stay and CTAS together. CTAS uses level 1, the most urgent level, as the reference. Duration terms are fitted per minute. The table also shows the coefficient rescaled to 60 minutes; the p value is unchanged because it comes from the same test.

Let \(Y_i = 1\) if visit \(i\) is hospitalized and \(Y_i = 0\) otherwise. Then

\[\operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) = \log\left(\frac{\Pr(Y_i = 1)}{1 - \Pr(Y_i = 1)}\right).\]

\(\mathbf{1}(\cdot)\) is an indicator function. A category that does not appear in an equation is the reference level.

2.1 Pre-disposition stay

\[ \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) = \beta_0 + \beta_{\mathrm{PreLOS}}\,\mathrm{PreLOS}_i \]

Pre-disposition stay alone
Term Odds ratio 95% CI P value
Pre-disposition stay 1.003 1.003 to 1.004 <0.001
Pre-disposition stay, per 60 minutes 1.226 1.204 to 1.249 <0.001

In this single-covariate model, each additional minute before the disposition decision is associated with higher odds of hospitalization (OR 1.003, 95% CI 1.003 to 1.004, p <0.001). Rescaled to 60 minutes, the OR is 1.226 (95% CI 1.204 to 1.249). This association is statistically significant.

2.2 CTAS level

\[ \begin{aligned} \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) &= \beta_0 + \beta_{2}\,\mathbf{1}(\mathrm{CTAS}_i = 2) + \beta_{3}\,\mathbf{1}(\mathrm{CTAS}_i = 3) \\ &\quad {}+ \beta_{4}\,\mathbf{1}(\mathrm{CTAS}_i = 4) + \beta_{5}\,\mathbf{1}(\mathrm{CTAS}_i = 5) \end{aligned} \]

CTAS level alone
Term Odds ratio 95% CI P value
CTAS level: 2 vs 1 0.435 0.401 to 0.473 <0.001
CTAS level: 3 vs 1 0.226 0.207 to 0.246 <0.001
CTAS level: 4 vs 1 0.106 0.095 to 0.118 <0.001
CTAS level: 5 vs 1 0.054 0.046 to 0.064 <0.001

In this single-covariate model, compared with CTAS 1, CTAS 2 is associated with lower odds of hospitalization (OR 0.435, 95% CI 0.401 to 0.473, p <0.001). This association is statistically significant.

In this single-covariate model, compared with CTAS 1, CTAS 3 is associated with lower odds of hospitalization (OR 0.226, 95% CI 0.207 to 0.246, p <0.001). This association is statistically significant.

In this single-covariate model, compared with CTAS 1, CTAS 4 is associated with lower odds of hospitalization (OR 0.106, 95% CI 0.095 to 0.118, p <0.001). This association is statistically significant.

In this single-covariate model, compared with CTAS 1, CTAS 5 is associated with lower odds of hospitalization (OR 0.054, 95% CI 0.046 to 0.064, p <0.001). This association is statistically significant.

This is the primary model. It enters pre-disposition stay and CTAS together. CTAS level 1 remains the reference. Each odds ratio is adjusted for the other covariate.

\[ \begin{aligned} \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) &= \beta_0 + \beta_{2}\,\mathbf{1}(\mathrm{CTAS}_i = 2) + \beta_{3}\,\mathbf{1}(\mathrm{CTAS}_i = 3) \\ &\quad {}+ \beta_{4}\,\mathbf{1}(\mathrm{CTAS}_i = 4) + \beta_{5}\,\mathbf{1}(\mathrm{CTAS}_i = 5) \\ &\quad {}+ \beta_{\mathrm{PreLOS}}\,\mathrm{PreLOS}_i \end{aligned} \]

Hospitalization on pre-disposition stay and CTAS
Term Odds ratio 95% CI P value
Pre-disposition stay 1.000 1.000 to 1.001 0.027
Pre-disposition stay, per 60 minutes 1.024 1.003 to 1.045 0.027
CTAS level: 2 vs 1 0.441 0.406 to 0.480 <0.001
CTAS level: 3 vs 1 0.231 0.212 to 0.252 <0.001
CTAS level: 4 vs 1 0.109 0.098 to 0.122 <0.001
CTAS level: 5 vs 1 0.056 0.048 to 0.067 <0.001

Interpretation

After adjustment for the other covariates in this model, each additional minute before the disposition decision is associated with higher odds of hospitalization (OR 1.000, 95% CI 1.000 to 1.001, p 0.027). Rescaled to 60 minutes, the OR is 1.024 (95% CI 1.003 to 1.045). This association is statistically significant.

After adjustment for the other covariates in this model, compared with CTAS 1, CTAS 2 is associated with lower odds of hospitalization (OR 0.441, 95% CI 0.406 to 0.480, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with CTAS 1, CTAS 3 is associated with lower odds of hospitalization (OR 0.231, 95% CI 0.212 to 0.252, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with CTAS 1, CTAS 4 is associated with lower odds of hospitalization (OR 0.109, 95% CI 0.098 to 0.122, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with CTAS 1, CTAS 5 is associated with lower odds of hospitalization (OR 0.056, 95% CI 0.048 to 0.067, p <0.001). This association is statistically significant.

3 Appendix

The appendix is not the primary analysis. Total emergency stay includes time after the disposition decision. The other covariates, and the model that includes them alongside pre-disposition stay and CTAS, are exploratory. Reference levels elsewhere are sex F, health zone Edmonton, and arrival mode Walk-in.

3.1 Emergency department length of stay

Total emergency stay includes minutes after the disposition decision. Those minutes can be a consequence of deciding to hospitalize, so this is not the primary model.

\[ \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) = \beta_0 + \beta_{\mathrm{LOS}}\,\mathrm{LOS}_i \]

Emergency department length of stay alone
Term Odds ratio 95% CI P value
Emergency department length of stay 1.006 1.006 to 1.006 <0.001
Emergency department length of stay, per 60 minutes 1.430 1.404 to 1.457 <0.001

In this single-covariate model, each additional minute of emergency department length of stay is associated with higher odds of hospitalization (OR 1.006, 95% CI 1.006 to 1.006, p <0.001). Rescaled to 60 minutes, the OR is 1.430 (95% CI 1.404 to 1.457). This association is statistically significant.

3.2 Age

\[ \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) = \beta_0 + \beta_{\mathrm{Age}}\,\mathrm{Age}_i \]

Age alone
Term Odds ratio 95% CI P value
Age 1.044 1.042 to 1.046 <0.001

In this single-covariate model, each additional year of age is associated with higher odds of hospitalization (OR 1.044, 95% CI 1.042 to 1.046, p <0.001). This association is statistically significant.

3.3 Sex

\[ \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) = \beta_0 + \beta_{\text{M}}\,\mathbf{1}(\mathrm{Sex}_i = \text{M}) \]

Sex alone
Term Odds ratio 95% CI P value
Sex: M vs F 1.125 1.062 to 1.191 <0.001

In this single-covariate model, compared with F, M is associated with higher odds of hospitalization (OR 1.125, 95% CI 1.062 to 1.191, p <0.001). This association is statistically significant.

3.4 Health zone

\[ \begin{aligned} \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) &= \beta_0 + \beta_{\text{Calgary}}\,\mathbf{1}(\mathrm{Zone}_i = \text{Calgary}) + \beta_{\text{Central}}\,\mathbf{1}(\mathrm{Zone}_i = \text{Central}) \\ &\quad {}+ \beta_{\text{North}}\,\mathbf{1}(\mathrm{Zone}_i = \text{North}) + \beta_{\text{South}}\,\mathbf{1}(\mathrm{Zone}_i = \text{South}) \end{aligned} \]

Health zone alone
Term Odds ratio 95% CI P value
Health zone: Calgary vs Edmonton 0.822 0.767 to 0.881 <0.001
Health zone: Central vs Edmonton 0.866 0.787 to 0.953 0.003
Health zone: North vs Edmonton 0.889 0.797 to 0.991 0.034
Health zone: South vs Edmonton 1.322 1.199 to 1.459 <0.001

In this single-covariate model, compared with Edmonton, Calgary is associated with lower odds of hospitalization (OR 0.822, 95% CI 0.767 to 0.881, p <0.001). This association is statistically significant.

In this single-covariate model, compared with Edmonton, Central is associated with lower odds of hospitalization (OR 0.866, 95% CI 0.787 to 0.953, p 0.003). This association is statistically significant.

In this single-covariate model, compared with Edmonton, North is associated with lower odds of hospitalization (OR 0.889, 95% CI 0.797 to 0.991, p 0.034). This association is statistically significant.

In this single-covariate model, compared with Edmonton, South is associated with higher odds of hospitalization (OR 1.322, 95% CI 1.199 to 1.459, p <0.001). This association is statistically significant.

3.5 Arrival mode

\[ \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) = \beta_0 + \beta_{\text{Ground ambulance}}\,\mathbf{1}(\mathrm{Arrival}_i = \text{Ground ambulance}) \]

Arrival mode alone
Term Odds ratio 95% CI P value
Arrival mode: Ground ambulance vs Walk-in 1.352 1.251 to 1.462 <0.001

In this single-covariate model, compared with Walk-in, Ground ambulance is associated with higher odds of hospitalization (OR 1.352, 95% CI 1.251 to 1.462, p <0.001). This association is statistically significant.

3.6 Injury indicator

\[ \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) = \beta_0 + \beta_{\mathrm{Injury}}\,\mathrm{Injury}_i \]

Injury indicator alone
Term Odds ratio 95% CI P value
Injury indicator 0.709 0.637 to 0.789 <0.001

In this single-covariate model, a value of 1 on the injury indicator, compared with 0, is associated with lower odds of hospitalization (OR 0.709, 95% CI 0.637 to 0.789, p <0.001). This association is statistically significant.

3.7 Mental health indicator

\[ \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) = \beta_0 + \beta_{\mathrm{MH}}\,\mathrm{MH}_i \]

Mental health indicator alone
Term Odds ratio 95% CI P value
Mental health indicator 0.603 0.515 to 0.707 <0.001

In this single-covariate model, a value of 1 on the mental health indicator, compared with 0, is associated with lower odds of hospitalization (OR 0.603, 95% CI 0.515 to 0.707, p <0.001). This association is statistically significant.

3.8 Pain score

\[ \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) = \beta_0 + \beta_{\mathrm{Pain}}\,\mathrm{Pain}_i \]

Pain score alone
Term Odds ratio 95% CI P value
Pain score 1.003 0.994 to 1.012 0.577

In this single-covariate model, each additional point on the pain score is associated with higher odds of hospitalization (OR 1.003, 95% CI 0.994 to 1.012, p 0.577). This association is not statistically significant.

3.9 Triage wait

\[ \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) = \beta_0 + \beta_{\mathrm{TriageWait}}\,\mathrm{TriageWait}_i \]

Triage wait alone
Term Odds ratio 95% CI P value
Triage wait 0.878 0.871 to 0.885 <0.001
Triage wait, per 60 minutes 0.000 0.000 to 0.001 <0.001

In this single-covariate model, each additional minute of triage wait is associated with lower odds of hospitalization (OR 0.878, 95% CI 0.871 to 0.885, p <0.001). Rescaled to 60 minutes, the OR is 0.000 (95% CI 0.000 to 0.001). This association is statistically significant.

3.10 Physician wait

\[ \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) = \beta_0 + \beta_{\mathrm{PhysWait}}\,\mathrm{PhysWait}_i \]

Physician wait alone
Term Odds ratio 95% CI P value
Physician wait 0.942 0.939 to 0.945 <0.001
Physician wait, per 60 minutes 0.028 0.023 to 0.034 <0.001

In this single-covariate model, each additional minute of physician wait is associated with lower odds of hospitalization (OR 0.942, 95% CI 0.939 to 0.945, p <0.001). Rescaled to 60 minutes, the OR is 0.028 (95% CI 0.023 to 0.034). This association is statistically significant.

3.11 Total emergency stay and CTAS

This model replaces pre-disposition stay with total emergency stay. It is shown so the two stay measures can be compared. It is not the primary result.

\[ \begin{aligned} \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) &= \beta_0 + \beta_{\mathrm{LOS}}\,\mathrm{LOS}_i + \beta_{2}\,\mathbf{1}(\mathrm{CTAS}_i = 2) \\ &\quad {}+ \beta_{3}\,\mathbf{1}(\mathrm{CTAS}_i = 3) + \beta_{4}\,\mathbf{1}(\mathrm{CTAS}_i = 4) \\ &\quad {}+ \beta_{5}\,\mathbf{1}(\mathrm{CTAS}_i = 5) \end{aligned} \]

Hospitalization on total emergency stay and CTAS
Term Odds ratio 95% CI P value
Emergency department length of stay 1.003 1.003 to 1.004 <0.001
Emergency department length of stay, per 60 minutes 1.224 1.200 to 1.250 <0.001
CTAS level: 2 vs 1 0.489 0.449 to 0.531 <0.001
CTAS level: 3 vs 1 0.277 0.253 to 0.302 <0.001
CTAS level: 4 vs 1 0.141 0.126 to 0.158 <0.001
CTAS level: 5 vs 1 0.078 0.066 to 0.093 <0.001

After adjustment for the other covariates in this model, each additional minute of emergency department length of stay is associated with higher odds of hospitalization (OR 1.003, 95% CI 1.003 to 1.004, p <0.001). Rescaled to 60 minutes, the OR is 1.224 (95% CI 1.200 to 1.250). This association is statistically significant.

After adjustment for the other covariates in this model, compared with CTAS 1, CTAS 2 is associated with lower odds of hospitalization (OR 0.489, 95% CI 0.449 to 0.531, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with CTAS 1, CTAS 3 is associated with lower odds of hospitalization (OR 0.277, 95% CI 0.253 to 0.302, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with CTAS 1, CTAS 4 is associated with lower odds of hospitalization (OR 0.141, 95% CI 0.126 to 0.158, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with CTAS 1, CTAS 5 is associated with lower odds of hospitalization (OR 0.078, 95% CI 0.066 to 0.093, p <0.001). This association is statistically significant.

3.12 All selected covariates

This exploratory model includes pre-disposition stay, CTAS, and the other selected covariates. It does not include total emergency stay. Each odds ratio is adjusted for the other covariates. With 5,810 hospitalized visits, this model has many parameters, so its adjusted estimates are less stable than those of the primary model.

\[ \begin{aligned} \operatorname{logit}\bigl(\Pr(Y_i = 1)\bigr) &= \beta_0 + \beta_{2}\,\mathbf{1}(\mathrm{CTAS}_i = 2) + \beta_{3}\,\mathbf{1}(\mathrm{CTAS}_i = 3) \\ &\quad {}+ \beta_{4}\,\mathbf{1}(\mathrm{CTAS}_i = 4) + \beta_{5}\,\mathbf{1}(\mathrm{CTAS}_i = 5) \\ &\quad {}+ \beta_{\mathrm{Age}}\,\mathrm{Age}_i + \beta_{\text{M}}\,\mathbf{1}(\mathrm{Sex}_i = \text{M}) \\ &\quad {}+ \beta_{\text{Calgary}}\,\mathbf{1}(\mathrm{Zone}_i = \text{Calgary}) + \beta_{\text{Central}}\,\mathbf{1}(\mathrm{Zone}_i = \text{Central}) \\ &\quad {}+ \beta_{\text{North}}\,\mathbf{1}(\mathrm{Zone}_i = \text{North}) + \beta_{\text{South}}\,\mathbf{1}(\mathrm{Zone}_i = \text{South}) \\ &\quad {}+ \beta_{\text{Ground ambulance}}\,\mathbf{1}(\mathrm{Arrival}_i = \text{Ground ambulance}) + \beta_{\mathrm{Injury}}\,\mathrm{Injury}_i \\ &\quad {}+ \beta_{\mathrm{MH}}\,\mathrm{MH}_i + \beta_{\mathrm{Pain}}\,\mathrm{Pain}_i \\ &\quad {}+ \beta_{\mathrm{TriageWait}}\,\mathrm{TriageWait}_i + \beta_{\mathrm{PhysWait}}\,\mathrm{PhysWait}_i \\ &\quad {}+ \beta_{\mathrm{PreLOS}}\,\mathrm{PreLOS}_i \end{aligned} \]

Hospitalization on pre-disposition stay, CTAS, and the other covariates
Term Odds ratio 95% CI P value
CTAS level: 2 vs 1 0.512 0.467 to 0.561 <0.001
CTAS level: 3 vs 1 0.310 0.279 to 0.345 <0.001
CTAS level: 4 vs 1 0.175 0.152 to 0.203 <0.001
CTAS level: 5 vs 1 0.118 0.095 to 0.146 <0.001
Age 1.034 1.032 to 1.036 <0.001
Sex: M vs F 1.144 1.074 to 1.218 <0.001
Health zone: Calgary vs Edmonton 0.812 0.752 to 0.876 <0.001
Health zone: Central vs Edmonton 0.823 0.741 to 0.913 <0.001
Health zone: North vs Edmonton 0.860 0.764 to 0.969 0.013
Health zone: South vs Edmonton 1.429 1.281 to 1.594 <0.001
Arrival mode: Ground ambulance vs Walk-in 0.966 0.886 to 1.053 0.430
Injury indicator 0.853 0.759 to 0.959 0.008
Mental health indicator 0.671 0.566 to 0.796 <0.001
Pain score 1.003 0.993 to 1.013 0.585
Triage wait 1.012 1.000 to 1.024 0.045
Physician wait 0.994 0.989 to 0.999 0.016
Pre-disposition stay 1.000 1.000 to 1.001 0.097

Interpretation

The sentences below describe the adjusted associations. Sentences highlighted in yellow are statistically significant; the others are not.

After adjustment for the other covariates in this model, compared with CTAS 1, CTAS 2 is associated with lower odds of hospitalization (OR 0.512, 95% CI 0.467 to 0.561, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with CTAS 1, CTAS 3 is associated with lower odds of hospitalization (OR 0.310, 95% CI 0.279 to 0.345, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with CTAS 1, CTAS 4 is associated with lower odds of hospitalization (OR 0.175, 95% CI 0.152 to 0.203, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with CTAS 1, CTAS 5 is associated with lower odds of hospitalization (OR 0.118, 95% CI 0.095 to 0.146, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, each additional year of age is associated with higher odds of hospitalization (OR 1.034, 95% CI 1.032 to 1.036, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with F, M is associated with higher odds of hospitalization (OR 1.144, 95% CI 1.074 to 1.218, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with Edmonton, Calgary is associated with lower odds of hospitalization (OR 0.812, 95% CI 0.752 to 0.876, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with Edmonton, Central is associated with lower odds of hospitalization (OR 0.823, 95% CI 0.741 to 0.913, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with Edmonton, North is associated with lower odds of hospitalization (OR 0.860, 95% CI 0.764 to 0.969, p 0.013). This association is statistically significant.

After adjustment for the other covariates in this model, compared with Edmonton, South is associated with higher odds of hospitalization (OR 1.429, 95% CI 1.281 to 1.594, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, compared with Walk-in, Ground ambulance is associated with lower odds of hospitalization (OR 0.966, 95% CI 0.886 to 1.053, p 0.430). This association is not statistically significant.

After adjustment for the other covariates in this model, a value of 1 on the injury indicator, compared with 0, is associated with lower odds of hospitalization (OR 0.853, 95% CI 0.759 to 0.959, p 0.008). This association is statistically significant.

After adjustment for the other covariates in this model, a value of 1 on the mental health indicator, compared with 0, is associated with lower odds of hospitalization (OR 0.671, 95% CI 0.566 to 0.796, p <0.001). This association is statistically significant.

After adjustment for the other covariates in this model, each additional point on the pain score is associated with higher odds of hospitalization (OR 1.003, 95% CI 0.993 to 1.013, p 0.585). This association is not statistically significant.

After adjustment for the other covariates in this model, each additional minute of triage wait is associated with higher odds of hospitalization (OR 1.012, 95% CI 1.000 to 1.024, p 0.045). Rescaled to 60 minutes, the OR is 2.030 (95% CI 1.017 to 4.052). This association is statistically significant.

After adjustment for the other covariates in this model, each additional minute of physician wait is associated with lower odds of hospitalization (OR 0.994, 95% CI 0.989 to 0.999, p 0.016). Rescaled to 60 minutes, the OR is 0.706 (95% CI 0.531 to 0.938). This association is statistically significant.

After adjustment for the other covariates in this model, each additional minute before the disposition decision is associated with higher odds of hospitalization (OR 1.000, 95% CI 1.000 to 1.001, p 0.097). Rescaled to 60 minutes, the OR is 1.019 (95% CI 0.997 to 1.041). This association is not statistically significant.

4 Shared release

This memo uses unified synthetic release 2.0-2026-10-09, built from the same NACRS/DAD source files as A07–A09. Hospital location and patient residence are separate variables. See A00 for definitions and provenance.

These legacy descriptive regression specifications use conventional model-based standard errors. They do not account for the hospital clustering introduced in release 2.0, so their significance tests are for illustration only. A07–A09 explicitly handle the hospital structure for the asthma questions.