should i stay or should i go?

Should I stay or should I go?

An examination of the factors effecting the length of stay of patients in a Geriatric Medicine

Department of a London Hospital

Presentation Outline Introduction

Descriptive Statistics

Statistical Tests

Survival Analysis & Conclusion

The Variables 7 Variables

Admission reason1. Urine Incontinence2. Stroke3. Rehab4. Other5. Diabetic6. Fall7. Decreased Mobility8. Confusion

Age Sex Year of admission

1994 / 1995 / 1996 / 1997 Barthel score Destination (when leaving hospital) Length of stay (LOS) in hospital.

Rationale for focusing on LOS Our research highlighted that the key variable

was length of stay. Length of Stay is a contentious issue in the NHS

– the economical advantages are clear but Ministers, hospital staff, patients and the public are concerned that patients should not be discharged until they are ready.

Budgets £400/day per patient Outpatient programmes

The Task To assess the effects of a patient’s

admission reason, age, sex, year of admission, Barthel score, destination (when leaving hospital), on their length of stay in hospital.

Descriptive StatisticsBy Tara O’Hare

Basic Information about the elderly dataset

● There are 4722 patients in our data, of which,

● 1537 are male● 3185 are female

● 7 Variables

● Admin group● Age● Sex● Year● Barthel Score● Destination● Length of Stay (LOS)

Descriptive Statistics● The average age of patients in data set is:

● 81.1 years for males● 83.52 years for females

● 21 patients where under the age of 48 years old.

● Approx 71% went home after departure from hosptial

● One year old girl was admitted to the geriatric ward, Admin reason was confusion

Age Barthel LOS

Mean 82.74 8.97 85.41

Median 84 9 17

Mode 84 0 15

Range of values

1 - 106 1 - 20 1 - 10453

Key for Admin groups

1=Urine Incontinence2=Stroke3=Rehab4=Other5=Diabetes6=Fall7=Decreased Mobility8=Confusion

Admin group 1 2 3 4 5 6 7 8 999

Frequency

Graph to show Number of Patients in each Admin Group

Destination of Patients

Destination 1 2 3 999

Frequency

Key

1=Died

2=Home

3=Transfer

Bar Chart to show Destination of patients

Age Barthel LOS

Died 84 2.05 16

Home 83 16 16

Transfer 85 6.97 34.5

999 83 0 959

Table to show median values for different Destinations

● 1097 Patients have a Barthel score of 19 or 20

● LOS : median=14 mode=8

● 0.64% of patients died

● 93.98% of patients went home

● 4.56% of patients where transferred

● 2022 Patients have a Barthel score of 0 or 1

● LOS : median= 17 mode= 15

● 40.36% of patients died.

● 41.59% of patients went home

● 9.35% of patients where transferred

Analysis of Barthel, LOS and Destination

Length of stay

● Outliers present in LOS

● Looked at extreme values for LOS>9677 days.

●13 Patients had a LOS > 9677 days

●The Year in which these patients were admitted is missing

Admin group

LOS

Box plots to show the LOS for the different Admin groups

1 2 3 4 5 6 7 8 999

Barthel Scores for the different Los groups

Los ≤ 14 Los 15 - 48 Los > 48

Mean 9.54 9.48 5.90

Median 11 11 0

Mode 0 0 0

Patients with an LOS of greater than 48 days are very dependent, evident as both median and mode are zero

The mean value for the barthel score decreases as the LOS increases for the different groups

Statistical TestsBy Lisa Mc Crink

By inspection of the graph, the data is not Normally Distributed. Thus, can not use ANOVA or t-tests.

Kolmogorov-Smirnov Test: H0: Data set is normally Distributed H1: Data set is not normally distributed This gave us a P-value<0.01. Thus, the test is significant at 5% level of

significance. We reject H0, in favour of H1. The data is not normally distributed.

The Chi-Squared Distribution H0: No association between the variables and length of stay of a Geriatric

patient H1: Association between each variable and length of stay

Variable Chi Squared Degrees of P-ValueValue Freedom

Destination 3990 822 <0.0001Admgrp 3497 2192 <0.0001Barthel 6501.9 5280 <0.0001

Sex 321.6 274 0.0254Year 965.5 783 <0.0001Age 47712.1 15618 <0.0001

Each variable has significant association with the length of stay of a patient.

proc freq data=work.elderly;tables los*barthel/chisq;run;

Interpreting Results of Chi-Squared Distribution

We are 99.9% confident that each variable, excluding sex, has an association with a patient’s length of stay.

Sex has a P-Value greater than that of other variables, indicating that association between sex of a patient and their length of stay is not as significant as that of other variables.

From this, it is evident that each variable effects a patients length of stay and so would be important to include in any model to predict a patients length of stay.

Separating Data into Male and Female Subgroups By inspection, for both

subgroups, year hasn’t as significant an association to a patients length of stay.

For females only, at a significance level of 5%, year is not significant. Thus, no association between year of admission and the length of stay of a female patient.

However, as this P-Value is very close to 0.05, more investigation into this is required.


Destination 1648.3 504 <0.0001Admgrp 1566.3 1176 <0.0001Barthel 4298.9 3280 <0.0001Year 583.2 495 0.0038Age 12027.4 7392 <0.0001

Table of Chi Squared Values for Females Only:


Destination 2716.8 666 <0.0001Admgrp 2868.5 1776 <0.0001Barthel 5213.1 4300 <0.0001Year 693.4 636 0.0569Age 33938 11988 <0.0001

Table of Chi Squared Values for Males Only:

The Importance of Year to the Length of Stay of Patients

In fact, this is contrary to previous research completed on this. Over the last century, there is a dramatic increase in the proportion

of elderly people in the population. Due to this, Geriatric units are struggling to provide enough beds for

those who need them. Previous research indicates that hospitals are actively trying to

decrease the length of stay of patients in an aid to solve the bed capacity problems.

The result we obtained can be explained due to the data being collected over a short duration from 1994 to 1997.

The Kruskal-Wallis Test It is a non-parametric test which is applied when ANOVA normality

assumptions may not apply. H0: Median length of stay of different subgroups of variables are

equal H1: Median length of stay of different subgroups vary

As the data is skewed, it is more useful to test for significant differences in the median instead of the mean length of stay of patients. This test was chosen for this purpose.

proc npar1way data=work.elderly;class destinat;

var los;

run;

Interpreting Results of Kruskal-Wallis Test

The subgroups of each variable have significant difference in a patients median length of stay.

Variable Kruskal-Wallis Degrees of P-ValueValue Freedom

Destination 403.52 3 <0.0001Admgrp 230.37 8 <0.0001Barthel 265.6 20 <0.0001

Sex 9.8288 1 0.0017Year 43.4469 3 <0.0001Age 128.02 57 <0.0001

Table of Kruskal-Wallis values for whole data set:

Interpreting Results of Kruskal-Wallis Test

As each variable, excluding sex, has a p-value<0.0001, there is a 99.9% level of confidence in this difference in median length of stay.

Sex is shown not to have as significant a difference between the median length of stay of the different subgroups.

For example, the median length of stay of males and females separately is less significantly different than the median length of stay of patients admitted due to confusion and those admitted due to a stroke.

Further Investigation Into Length of Stay of patients with Different Destinations

Bar Chart of the Destination of patients whose length of stay was between 15 and 48 days

Bar Chart of the Destination of Patients whose length of stay was greater than 49 days

Bar Chart of the Destination of patients whose length of stay was 14 days or less

Key

1=Died

2=Home

3=Transfer

Further Investigation Into Length of Stay of patients with Different Destinations There is a significant difference in the length of stay of transfer

patients and patients who either were sent home or died in hospital.

By testing this using the Kruskal-Wallis test, we found:

Variables Being Tested Kruskal-Wallis Value Degrees of Freedom P-ValueDead, Home and Transfer 234.2141 2 <0.0001

Dead and Transfer 144.04 1 <0.0001Home and Transfer 228.1389 1 <0.0001Dead and Home 4.979 1 0.0257

It is evident that there is less significance in the difference between median length of stay of patients who were sent home or died than that of transfer patients, and this is supported by the graphs.

This agrees with previous studies, in which it was found that transfer patients had increased lengths of stays when compared to those who died or were sent home.

Further Investigation Into Length of Stay of patients with Different Destinations

Survival Analysis& Conclusion

By Mike Rigby

Survival Analysis

What is Survival Analysis?

Basic Survival Analysis functions

How does Survival Analysis apply to our problem?

Survival Analysis and SAS The long way and the SAS way

Survival functions

What is Survival Analysis?

What is Survival Analysis? A branch of statistics that deals with death in

biological organisms and failure in mechanical systems.

Death or failure is called an ‘event’ Time to event models

Basic Survival Analysis Functions

The Survival Function S(t) = P(T>t) Where t is some time and T is the time of death That is the probability of surviving longer than time t. Usually assume S(0)=1 S(t)0 as t

Lifetime Distribution Function F(t) = P(Tt) = 1 - P(T>t) = 1 - S(t)

Event Density Function f(t) = F’(t) Rate of Death per unit time

Hazard Function and Cumulative Hazard Function (t)dt = P(t < T ≤ t+dt | T>t)

How does Survival Analysis apply to our problem?

In Survival Analysis terms: Our time variable is length of stay Our ‘event’ is departure

Our Survival Function S(t) = P(T > t) Where t is some length of stay and T is the total length of stay at

departure That is the probability that a patient’s length of stay is longer than t. Both are measured in Days

The Long Way:Converting Raw Data into Survival Data

/******************************* Use proc freq to output cum % freq to data table sacf *******************************/ TITLE 'Survival Analysis'; PROC FREQ data=sasuser.elderly; TABLES los / outcum out=sasuser.sacf; RUN; QUIT; DATA sasuser.survival; SET sasuser.sacf; /*Set S as the values of the Survival Function*/ S=1-(CUM_PCT/100); /*Set F as the values of the Lifetime Function*/ F=CUM_PCT/100; /*Set C as the coded log length of stay*/ C=log(los); RUN;

The Long Way: sasuser.sacf

The Long Way: The Survival Function

The SAS Way: The Survival Function ods html; ods graphics on;

proc lifetest data=sasuser.elderly notable;

time los; label los='Length of Stay

(Days)'; run;

ods graphics off; ods html close;

The Long Way

The SAS Way

Survival Function - Stratified by Barthel Score

Survival Function - Stratified by Barthel Score

ZOOMED

Conclusion After initial examination and discussion we identified length of stay as

the main variable because its analysis could help hospital managers with resource management.

We examined the elderly dataset with particular attention to the effects of other variables on the response variable, length of stay, for this reason.

Length of Stay The Frequency Barchart indicated a positively skewed distribution. Non-normality was confirmed by the Kolmogorov Smirnov Test Non-normality informed the decision to use non-parametric tests,

survival analysis and the median. Wilcoxon, even though a non-parametric test, was out of reach as it

requires a symmetric p.d.f.

Kruskal-Wallis told us that the median length of stay for each of the other 6 variables (Admission Reason, Age, Barthel Score, Destination, Sex, Year of Admission ) is not the same.

Conclusion Discretising Length of Stay into classes of 1-14 days, 15-48 days, 49+ days revealed

that those patients who stay in hospital for a long time (49+) are much more likely to be transferred than those who stay in hospital for a shorter stint (48 days or less).

Survival Analysis Survival Functions stratified by Barthel Score surprisingly told us that those with a

Barthel score of 12 were more likely to stay in hospital for up to around 1400 days than any other Barthel score, including low Barthel scores, which indicate highly dependent patients. That said, after 1400 days in hospital those with low Barthel scores, were the most likely to stay in hospital.

ReferencesBooks Lindsey, J.K., Statistical Analysis of Stochastic Processes in Time, (2004), Cambridge University

Press, Chapter 3 - Survival Processes, pp39-70 Spiegel, M.R., et al., Schaum’s Outlines: Statistics, (1999), 3rd ed., McGraw Hill

Journals Marshall, A., et al., Modelling Patient Duration of Stay to Facilitate Resource Management of

Geriatric Hospitals, Health Care Management Science 5, 313-319, (2002) Marshall, A., et al., Developing a Bayesian belief network for the management of geriatric hospital

care, Health Care Management Science 4, 25-30, (2001)

Web http://www.reducinglengthofstay.org.uk / http://www.patient.co.uk/showdoc/40001654/ - Barthel Score http://en.wikipedia.org/wiki/Survival_analysis http://en.wikipedia.org/wiki/Weibull_distribution

Miscellaneous SAS Help Lecture Notes

http://www.reducinglengthofstay.org.uk/



http://www.patient.co.uk/showdoc/40001654/

http://en.wikipedia.org/wiki/Survival_analysis

http://en.wikipedia.org/wiki/Survival_analysis

http://en.wikipedia.org/wiki/Weibull_distribution

http://en.wikipedia.org/wiki/Weibull_distribution

For more information, including a download ofthis powerpoint presentation, which includes

research references and web links, visit:

www.mikerigby.net

Thanks for Listening!

From Team Elderly

Santa loves SAS!

Survival Analysis

Why use Survival Analysis for the elderly data? The data is heavily positively skewed. Answer questions about the data

What fraction of the population will survive past a certain time? Death Rates for those who survive. Taking into account multiple causes of death

Survival Function - Stratified by Admission Reason

ZOOMED

should i stay or should i go?

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