Overstay2 scoring model for Grace Hospital

This page describes the Overstay2 scoring model for Grace Hospital for the Project Overstay2, one of the site-based Overstay2 scoring models. The model and the Data definition for factor candidates for the Overstay2 project it uses were developed in Re-analysis and generation of Overstay2 model and is used to generate the Overstay2 colour, which in turn drives the Overstay2 processes on the units to reduce discharge delay.

Data elements and assigned coefficients

The binary logistic regression Y (Overstay GE 10 Days) which gave the AUC C-index =0.832 implying better predicted model and Hosmer and Lemeshow Goodness of fit test Chi-Square value of 5.049 (prob=0.7523) is :

LN(OS/1-OS) = Y

Y = Intercept Estimate + sum of all the rest of (the Parameter values multiplied by the Estimate) listed below:

Parameter	Estimate	Prob > ChiSq
Intercept	-10.192235	<.0001
Age	0.030877	<.0001
Homeless	0.835548	0.093
PCH/Chronic Care	-3.600816	<.0001
FromNonWpgFacility	1.744535	0.0612
InterImplantDevice	0.909939	0.0004
Dementia	1.167700	<.0001
CHF	0.273869	0.0263
Plegia	0.261490	0.0547
GCS_Motor	0.448897	0.0131
ADL_bath	0.386783	<.0001
ADL_toilet	0.159622	0.0029
ADL_continence	0.156504	<.0001
ADL_Adlmean_age	-0.000647	0.0087

Where OS is the likelihood to overstay 10 days and beyond.

How to calculate OS:

• OS = exp(Y) / (1 + exp(Y)

• The model gave a 0.076 optimum cut-off probability for OS GE 10 Days with sensitivity = 74.2%, the rate of identifying OS GE 10d out of the patients who actually have OS GE 10d and with specificity = 74.3%, the rate of identifying OS LT 10d out of the patients who actually have OS LT 10d. This cut-off point of 0.076 will result to 25.7% rate of identifying OS GE 10d out of the patients who actually have OS LT 10d. Increasing the cut off predicted probability of (Overstay >= 10 days) to 0.094 resulted to sensitivity = 67.2%, thus reducing the rate of identifying OS GE 10d out of the patients who actually have OS LT 10d to 21.0%. Thus a predicted probability of (Overstay >= 10 days) of 0.094 is going to be used to classify patients into two groups; Overstay >= 10 days and Overstay < 10 days. See more discussion on Overstay2 colour.

• The model has been validated using the data from the validation set of same period. The AUC C-index = 0.815, the Hosmer and Lemeshow Goodness of fit test Chi-Square value = 8.4318 (prob=0.4002) and the optimum cut-off probability for OS = 0.079 with sensitivity = 74.4% and specificity = 74.5%.

• The model was again validated using the data from Jan to June 17, 2025. The AUC C-index = 0.784, the Hosmer and Lemeshow Goodness of fit test Chi-Square value = 13.7139 (prob=0.0918) and the cut-off probability for OS = 0.088 with sensitivity = 73.6% and specificity = 74.3%.

Model files

• files describing the model and records of discussion about it are at

S:\MED\Med_CCMED\​Julie\MedProjects\Overstay_Project_2025\BySite_TrainingValidation\GRA\GGH_FinalModel_25June2025S:\MED\Med_CCMED\Julie\MedProjects\Overstay_Project_2025\BySite_TrainingValidation\GRA\GGH_FinalModel_25June2025

Log

• 2025-06-25 - The definition of Opioids factor has been revisited and broken done between Chronic Addiction and Acute/Overdose Toxicity. The new fitted model from the training data set did not show significant estimates on these factors. The new model is similar to the May 20, 2025 model but without the factor Chronic Addiction and validated in the two data sets of Oct 2020 to Dec 2024 and Jan -June 2025 periods.
• 2025-06-18 - the May 20, 2025 model has been validated using recent data from Jan 1 to June 17, 2025.
• 2025-05-20 - the Feb 21, 2025 model has been revisited and refitted deleting the factor Age*Age. Found a model from the training data set and also validated using a different data set of the same period Oct 2020 to Dec 2024.
• 2025-02-21 - Initial decision on a model - We will use Model 8 at cut-off of 0.069