Hospitals Calculations

1. HOSPITAL STATISTICS
Col Zulfiquer Ahmed Amin
M Phil, MPH, PGD (Health Economics), MBBS
Armed Forces Medical Institute (AFMI)

2. Definition
Information obtained from hospital indoor and
outdoor facilities regarding quality of care,
utilization of services, quantity of services
delivered, workload and other hospital related
administrative and logistic affairs is called
Hospital Statistics.

3. Uses of Hospital Statistics
• Measure of evaluation of quality of care
• Helps in planning
• Allocation of resources in different areas
• Identify deficiencies at various levels; ie. Input,
process and outcome o services
• Evaluate effectiveness and efficiency of the
administration

4. Types of Hospital Statistics
1. Reports related to hospital beds
Daily Census
Daily Average Attendance
Bed Occupancy Rate
Bed Turn Over Interval
Bed Turn Over Rate
Total Patient Days Care
Vacancy Rate
Hospital Beds
Sanctioned Beds
Functional bed
Bed Supply Rate

5. 2. Reports Related to Admission/ Discharge/ Death
Admission:
Daily Admission
Total Admission over a period
Discharge:
Daily Discharge
Total Discharge over a period
Average length of stay
Deaths
Daily number of deaths
Total deaths over a period
Total deaths over 48 hours
Total deaths under 48 hours
Net death rate
Gross death rate
Post Operative death rate
Anaesthetic death rate

6. 3. Work load statistics
Total number of outputs
New cases/ Repeat cases
Total number of operations
Total number of X-Rays
Average OPD patients per day
Total caesarean sections per day
Average number of food served per day

7. 4. Hospital care Evaluation Statistics
HAI Rate
Post Operative complication rate
Autopsy rate
Percentage of agreement between final
and pathological diagnosis
Gross result of treatment; ie. Patients
recovered, improved or not relieved

8. 5. Indices related to population at risk
Admission Rate
Hospitalization Rate per person
Bed-Population Index

9. Other type of classification
• Patient movement statistics- Admission,
discharge, deaths
• Morbidity statistics- Patients under various
diagnosis
• Administrative statistics- Manpower, material,
money-finance
• Hospital service statistics- No of operations,
utilization indicators

10. Hospital Utilization Statistics

11. Admission
The formal acceptance by a hospital or other inpatient health
care facility of a patient who is to be provided with room, and
continuous nursing service in an area of the hospital or facility
where patients generally reside at least overnight.
Admission Rate
Number of admission per 1000 population in a year.
Discharge
Discharge from the hospital is the point at which the patient
leaves the hospital and either returns home or is transferred
to another facility such as one for rehabilitation or to a
nursing home. Discharge involves the medical instructions
that the patient will need to fully recover.

12. Hospital Beds
WHO defines a hospital bed as a bed that is regularly maintained
and staffed for the accommodation and full-time care of a
succession of inpatients and is situated in wards or a part of the
hospital where continuous medical care for inpatients is
provided. Total number of beds excludes bed compliments of the
hospital for normal, healthy newborn babies in maternity ward;
but includes incubators used for premature babies.
Sanctioned Bed
It is the official bed capacity of the hospital.
CMH Dhaka: 1100 beds (Soon to upgrade to 1500 beds)
Functional Bed
This is the actual functional status of beds in a hospital.

13. Bed-days or Patient-days
A bed-day is a day during which a person is confined to a bed
and in which the patient stays overnight in a hospital. It is the
unit of measure denoting the services rendered to one in-patient
day in the hospital. One full day is counted when admission
before mid-day and discharge after mid-day. Patient-day should
not include data for healthy new born infants.
Bed Supply Rate (Bed to population ratio)
BSR = (No of Beds available ÷ No of population served) x 1000
Bangladesh: 0.6 beds/1000 population
WHO Standard: 5 beds/ 1000 population
Vacancy Rate = 100% - Occupancy Rate

14. Bed Turnover Rate
Average number of patients cared for a bed during a given
period.
BTR= (No of discharges including deaths for a given period of
time ÷ Average bed count for that period of time) x 100
Indicates:
An important measure of hospital utilization indices.
Gives the net effect of changes in Occupancy Rate and Average
Length of Stay (ALS)
Example:
In a particular hospital, there were 2358 discharges in the year
2009.
Number of beds in that hospital in 2009 was 300.
Hospital Bed turnover rate = 2358/300 = 7.86

15. Average Bed Occupancy
Average number of days during which the bed is occupied by a
patient in the course of a given period of time.
Average Daily Census (ADC)
Average number of patients in the hospital at a given time per
day. This is the ratio of the total number of in-patient days
(Excluding new born) to total number of days in the same period.
ADC= Total Patient Days ÷ Number of calendar days in a period.
For example, the total number of inpatient service days provided
for the 1st week of May is 1729. Average daily census is 1729/7 =
247.

16. Average Length of Stay (ALOS)
Length of stay is a term which is used to calculate a patient's day
of admission in the hospital till the day of discharge i.e. the
number of days a patient stayed in a hospital for treatment.
Formula for calculating average length of stay:
(TOTAL INPATIENT DAYS OF CARE / TOTAL Discharges) = AVERAGE
LENGTH OF STAY (IN DAYS)
- The average length of stay in hospitals (ALOS) is often used as
an indicator of efficiency.
- All other things being equal, a shorter stay will reduce the cost
per discharge

17. Total Length of stay = 6 + 11 + 5 + 8
= 30 days
Average Length of Stay
= Total length of stay / Total
number of discharges
= 30 / 4
= 7.5 days
Given,
Number of patients = 4

18. Number of patients' day (service days) in a year
Number of beds x 365
X 100
Bed Occupancy Rate (BOR)
BOR is the average occupancy of hospital beds in percentage. It is
the ratio between beds used and beds provided. The beds
occupancy rate is calculated based on the midnight bed census at
each hospital. [For example, the BOR for Monday is based on the
bed census taken at 0000 hrs Tuesday].
- 80-85% BOR is ideal for good quality of patient care.
- 15-20% beds are vacant for emergency, maternity, isolation,
intensive care (Dead Space Beds).
- 100% occupancy means over-utilization.
- Occupancy less than 80% is uneconomical

19. Example :
In the month of June 4000 inpatients days were served in a
hospital with 150 beds .
Given,
Total number of inpatient days = 4000. Available beds = 150. June
has 30 days. So, number of days in the period = 30
BOR = Total number of inpatient days for a given period x 100 /
Available beds x Number of days in the period
= 4000 x 100 / 150 x 30
= 400000 / 4500
= 88.889 %

20. Bed Turn Over Interval (TOI)
Turnover interval (TOI):
Average length of time (in days) that elapses between the
discharge of one inpatient and the admission of the next
inpatient to the same bed. It is the average period in days, that a
bed remains empty.

21. Calculation of Turnover interval (TOI):
TOI = (Available staffed bed days – Occupied bed days) /
Inpatient discharges.
Inpatient discharges include deaths, transfers out to other
specialties/significant facilities and transfers out to other
hospitals.
Interpretation:
- Negative TOI indicates scarcity of beds and over-utilization.
- Long positive TOI s indicative of under-utilization because of
defective admission procedures or poor quality medical care.
- Short positive TOI is indicative of optimum utilization.
- TOI is ‘zero’ when Bed Occupancy Rate is 100%.

22. Gross Death Rate:
Ratio of total deaths to total discharges including deaths. In
general hospital, it should not exceed 3%.
Gross Death Rate= (Total death in a period ÷ Total discharge)
x 100
Formula:
r = ( n / t ) * 100
Where,
r = (Hospital) Gross Death rate
n = Number of Deaths of Inpatients in a Period
t = Number of Discharges ( Including Deaths ) in the Same Period

23. Net Death Rate:
A death rate, also known as the institutional death rate, that
does not include deaths, which occur within 48 hours of
admission (24 hours of admission in some countries).
Anaesthetic death rate = (No of deaths due to anaesthesia ÷ No
of patients anaesthesized during that period) x 5000
It should be less than 1 in 5000
Post Operative death rate = (Deaths within 10 days of surgery ÷
Total operations during that period) x 100
Usual value is 1-2% (Depending on nature of surgery)

24. Autopsy Rate = (Number of pathological autopsies performed ÷
Number of deaths during that period) x 100
Patients who are dead on arrival (DOA) at the hospital and fetal
deaths are excluded from both the numerator and the
denominator. Autopsy Rate more than 15-20% indicates enquiry
type of medical staff, progressive in outlook.
Caesarean Section Rate = (Total CS performed ÷ Total live-births
during that period) x 100
- Normal value is 3-4%.
- Between 2004 and 2014, the C-section rate in Bangladesh
increased from 4% to 23%.
- A higher CS should be enquired into.