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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.

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Should I stay or should I go?

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  1. 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

  2. Presentation Outline • Introduction • Descriptive Statistics • Statistical Tests • Survival Analysis & Conclusion

  3. The Variables • 7 Variables • Admission reason • Urine Incontinence • Stroke • Rehab • Other • Diabetic • Fall • Decreased Mobility • Confusion • Age • Sex • Year of admission • 1994 / 1995 / 1996 / 1997 • Barthel score • Destination (when leaving hospital) • Length of stay (LOS) in hospital.

  4. 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

  5. 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.

  6. Descriptive Statistics By Tara O’Hare

  7. 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)

  8. 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

  9. Graph to show Number of Patients in each Admin Group Frequency Key for Admin groups 1=Urine Incontinence 2=Stroke 3=Rehab 4=Other 5=Diabetes 6=Fall 7=Decreased Mobility 8=Confusion 1 2 3 4 5 6 7 8 999 Admin group

  10. Destination of Patients Bar Chart to show Destination of patients Frequency Table to show median values for different Destinations Key 1=Died 2=Home 3=Transfer 1 2 3 999 Destination

  11. 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

  12. Length of stay Box plots to show the LOS for the different Admin groups • 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 LOS 1 2 3 4 5 6 7 8 999 Admin group

  13. Barthel Scores for the different Los groups • 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

  14. Statistical Tests By Lisa Mc Crink

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

  16. 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.

  17. 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 • procfreqdata=work.elderly; • tables los*barthel/chisq; • run; Each variable has significant association with the length of stay of a patient.

  18. 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.

  19. 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. Table of Chi Squared Values for Males Only: Table of Chi Squared Values for Females Only:

  20. 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.

  21. 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. • procnpar1way data=work.elderly; • class destinat; • var los; • run;

  22. Interpreting Results of Kruskal-Wallis Test Table of Kruskal-Wallis values for whole data set: • The subgroups of each variable have significant difference in a patients median length of stay.

  23. 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.

  24. Further Investigation Into Length of Stay of patients with Different Destinations Bar Chart of the Destination of patients whose length of stay was 14 days or less 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 Key 1=Died 2=Home 3=Transfer

  25. 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:

  26. Further Investigation Into Length of Stay of patients with Different Destinations • 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.

  27. Survival Analysis& Conclusion By Mike Rigby

  28. 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

  29. 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

  30. 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(Tt) = 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)

  31. 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

  32. 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;

  33. 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;

  34. 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;

  35. 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;

  36. 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;

  37. 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;

  38. 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;

  39. The Long Way: sasuser.sacf

  40. The Long Way: sasuser.sacf

  41. The Long Way: The Survival Function

  42. 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; NB: ODS graphics are experimental in this release of SAS

  43. The SAS Way The Long Way

  44. Survival Function - Stratified by Barthel Score

  45. Survival Function - Stratified by Barthel ScoreZOOMED

  46. 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.

  47. 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.

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