3 types of analytics
1) descriptive- known data- getting a pic of he data so you can find a pattern which will help
you to the predictive data
2) predicitive- unknown data- you try to predict the future eight he data
3) prescriptive - decision model- helps us to take action
a multi class queuing model with abandonments (the chart with the vendalators)
- there are K allocation eligible classes of patient
- pk 1= survival probability with ventilator
- Pk 0= probability of staying alive after t periods while waiting for a vendaltor
- LOU K- vendetta or length of use
- VK (T)- the number of class K patients who used a ventilator by time T
- Ak (T)- the number of class K patients who died
- Qk (T)
priority rule: (a1, a2,…, ak)
Decison= who gets priority
- ask E (0,1) indicates if a class k patient us assigned to the red queue or not
- the optimal ventilator allocation policy maximizes
prediction in this case
- ex: predictions for PK1
- we find higher mortality risk for patients with kidney disease, high BMI, suffering from
hypoxemia, etc
Existing and proposed allocation procedures
- SOFA score based prioritization= assighns patients with sufficiently low “sofa scores” tp
the red queue
- incremenrtal survivial priority (ISP)= assighns patients whose “estimated survival
probability” is above a threshold to the red queue
(The graph in my camera roll)
- Use the formula on the side to calculate which u should use for data and highest number
is the right data to use
phase 2: performance comparison (why?)
- expected number of surviving patients: ISP-LU > ISP > SOFA-P
- detah risk while waiting for a ventilator: ISP-LU < SOFA-P < ISP
conclusion
- facing resources shortages and necessity to ration scarves capacity triage teams should
1) use patient specific criteria beyond SOFA scores to better predict survivial probabilities
2) utilize a priority scheme that emphasizes both survivial and
, 02/05
sampling distributions and estimation
population vs sample
- sample mean= X bar
- sample standard deviation= S
- sample proportion= P
- these are also called random variables. They may vary based on the sample collected
- mue sigma and pie are population proportions
- N= population/ sample size
- Mue= the mean
- sigma= stabndrd deviation
- pi= Proportion
-
central limit theorem
- r bar N(mu, sigma over n squared)
- sample mean X bar is a good estimator for mu
- but it is still a point estimate
- but we can not use CLT to construct an interval estimate
- population mean falls between X bar- Z alfa/2 sigma over n squared and X bar + z a/2
sigma over n squared with probability 1-a
- In order to get Z a/2= NORMSINV 100- the confidence interval percent and that will give
u ur Alfa so 100-90 Alfa will be 10
- plug into excel NOMSINV (1- the Alfa divided by 2)
- so do 100- the confidence interval and then take that number and divide it by two and
that should give you the alfa
- ex is confidence interval is 90 you do 100-90 is 10 and then 10 divided by 2 is 5 and
then u would plug 5 into NORMSINV (1- 5/2)
central limit theorem for T
(get notes from sldies)
central limit theorem fir proportions
- ratio of yes observations (X) to sample size (N)
- sample mean p=X/N is a good estimator for pi
- we can assume normality if NP is greater than or equal to 10 and N(1-p) is greater than
or equal to 10
- P- Z a/2 then multiple the entire square of P(1-p)/ N
Attendance 1 ( Z a/2)
Standard deviation= 2.5
Mean= 18
random sample= 100
1) descriptive- known data- getting a pic of he data so you can find a pattern which will help
you to the predictive data
2) predicitive- unknown data- you try to predict the future eight he data
3) prescriptive - decision model- helps us to take action
a multi class queuing model with abandonments (the chart with the vendalators)
- there are K allocation eligible classes of patient
- pk 1= survival probability with ventilator
- Pk 0= probability of staying alive after t periods while waiting for a vendaltor
- LOU K- vendetta or length of use
- VK (T)- the number of class K patients who used a ventilator by time T
- Ak (T)- the number of class K patients who died
- Qk (T)
priority rule: (a1, a2,…, ak)
Decison= who gets priority
- ask E (0,1) indicates if a class k patient us assigned to the red queue or not
- the optimal ventilator allocation policy maximizes
prediction in this case
- ex: predictions for PK1
- we find higher mortality risk for patients with kidney disease, high BMI, suffering from
hypoxemia, etc
Existing and proposed allocation procedures
- SOFA score based prioritization= assighns patients with sufficiently low “sofa scores” tp
the red queue
- incremenrtal survivial priority (ISP)= assighns patients whose “estimated survival
probability” is above a threshold to the red queue
(The graph in my camera roll)
- Use the formula on the side to calculate which u should use for data and highest number
is the right data to use
phase 2: performance comparison (why?)
- expected number of surviving patients: ISP-LU > ISP > SOFA-P
- detah risk while waiting for a ventilator: ISP-LU < SOFA-P < ISP
conclusion
- facing resources shortages and necessity to ration scarves capacity triage teams should
1) use patient specific criteria beyond SOFA scores to better predict survivial probabilities
2) utilize a priority scheme that emphasizes both survivial and
, 02/05
sampling distributions and estimation
population vs sample
- sample mean= X bar
- sample standard deviation= S
- sample proportion= P
- these are also called random variables. They may vary based on the sample collected
- mue sigma and pie are population proportions
- N= population/ sample size
- Mue= the mean
- sigma= stabndrd deviation
- pi= Proportion
-
central limit theorem
- r bar N(mu, sigma over n squared)
- sample mean X bar is a good estimator for mu
- but it is still a point estimate
- but we can not use CLT to construct an interval estimate
- population mean falls between X bar- Z alfa/2 sigma over n squared and X bar + z a/2
sigma over n squared with probability 1-a
- In order to get Z a/2= NORMSINV 100- the confidence interval percent and that will give
u ur Alfa so 100-90 Alfa will be 10
- plug into excel NOMSINV (1- the Alfa divided by 2)
- so do 100- the confidence interval and then take that number and divide it by two and
that should give you the alfa
- ex is confidence interval is 90 you do 100-90 is 10 and then 10 divided by 2 is 5 and
then u would plug 5 into NORMSINV (1- 5/2)
central limit theorem for T
(get notes from sldies)
central limit theorem fir proportions
- ratio of yes observations (X) to sample size (N)
- sample mean p=X/N is a good estimator for pi
- we can assume normality if NP is greater than or equal to 10 and N(1-p) is greater than
or equal to 10
- P- Z a/2 then multiple the entire square of P(1-p)/ N
Attendance 1 ( Z a/2)
Standard deviation= 2.5
Mean= 18
random sample= 100
