How many dentists are there in New York?

I will take a bottom-to-top approach here. 

Let's calculate supply bandwidth. 

A dentist will work for 8hrs/Day, 40 hrs/week and 40*53Weeks = 2120 hrs a year. Considering the efficiency is 75%, total working hours -> 2120*75% ~= 1600 hours/year. Hence one doctor will work for 1600 hours a year. 

Lets calculate demand. 

Newyork city have an 8M population, 

A rough beakdown can be

0 10% population 

age>70 -> 10% population

5 80% population

Considering population only between 5-70 age group will take dentist services. 

A target population of 8M*80% = 6.4M might need a dentist, 

But it is not true that everybody needs a dentist every year, some people might not need a dentist throughout their life. Hence It is safe to assume only 60% of users will need a dentist regularly. (I still feel this is on the higher side), But overall ~40M people will need dentists for multiple users, 

One user visits a denstist 2 times a year for 30 mins. They visit a densits for 1hour/year.

total hours needed = 40M * 1hour/year = 40M hours

hence total dentist in newyork = (40M hours/Year )/(1600 hours) = 2500 dentist. 

How many dentists are there in New York?

Some clarifications questions to start off - (may have more on the way as we work through)

1/ Dentists for who -> Humans or animals -> Humans

1.1/ Humans -> Kids, adults, seniors? adults

2/ Private practice or part of a hospital -> Does not matter

3/ Generalist or a specialist, where generalist is a dentists we go for a annual checkup and get cleaning and other high level work done and specialists are like root canals, or other surgery, or teeth correction or trauma specialists -> Generalists

4/ In that generalists category, are we focusing on ones who take private insurance, or ones who work with public health departments to cater to less privileged, or ones who work with public insurance (medicare/medicaids) -> private insurance

5/ New york or New your city? NYC

Ok that you for the clarifications - 

Now let me lay the structure - 

First lets go through the factors that matter - 

1/ Potential user base

2/ General checkups in a year per each user base

3/ Unplanned checkups in a year per each user base

1/ Working days in a year

2/ Working hours in a year

3/ Appt size/duration in a sitting for a general appt

4/ Appt size/duration in a sitting ad hoc appt

That will tell us how many dentists we need.

Formula -

# of dentists (A) = ( # of appts per day (B) / # of appts a dentists can do per day (C) ) / %of dentists active in a day

(B) -> # of appts per day = # of general appointments per day (B1) + # of ad-hoc appointments per day (B2)

(B1) -> # of general appointments per day = # of appts per year / working days in a year

=> # of appts per year = # of patient per year * # of appts in a year per patient

=> # of patients per year = total population * % kids *%patient + total population * % adults * %patient + total population * % seniors *%adults

=>  # of patients per year = 8MM * 15% * 50% + 8MM * 50% * 30% + 8MM * 20% * 20%

                                                      = 8MM * (7.5% + 15% + 4%)

                                          = 8MM * (30%) (approx) = 2.5MM

=>  # of appts in a year per patient =  2

   => # of appts per year = 2.5MM * 2 = 5MM

=> working days in a year = 250 days

(B1) -> 5MM/250 = 500*10,000/250 = 20,000

(B2) -> # of ad-hoc appointments per day  = Genetal appts * % of adhoc (10%) = 2,000

 B -> # of appts per day (B) -> 22,000

C ->  # of appts a dentists can do per day = 10 hrs working time * (# of hygienists  + specialists)   * duration of 1 appt = 10 * (3 + 2) * 3/4hour = 10 * 5 * .75 = 37.5 ~ 40

# of dentists (A) = 22,000/40 = 550 active dentists in a day

If we assume that 20% of overall dentists population is active in a day, then today dentists population is -> 550/.2 = 2750.

A. Clarifying  Questions

·     Male/Female-Both

·     Retired/Practising-Practising

·     Private/Government-Both

·     Dentist student/Passed out(Graduated)-Graduated

·     New York City and Not New York state-City

B. Approach- Top Down

C. Assumption & Calculation

·        Total New York city population-800K

·        Age group-

Ø  0-22 years=30%-Excluded

Ø  22-60 years=60%=800k*60%=500k

Ø  60-80 years=10%- Excluded

·     Employment

Ø Employed-80%=400K

Ø Unemployed-20%=100K- Excluded

·     Employed

Ø Other-90%=400k*90%=360k- Excluded

Ø Doctors-10%=40k

·     Doctors

Ø Other doctor-90%=36k- Excluded

Ø Dentist-10%=4k

D. Result

·     Total dentist in New York city is 4000

E. Sanity Check

People per dentist -800k/4k=200 people/dentist-Ok

Bijan, would like to have your feedback on this, please.Thanks

📌 Clarifying Questions

1. When we say NewYork do we mean NewYork City or the state of NewYork- In NewYork City
2. When we say Dentist do we count those having personal clinic or in a hospital or both- Count in General

 Creating the Equation

Number of Dentists =

Number of total visits in a year to the dentist / Number of patients handled by a dentist in a year

📌 Solving

1. The population of New York City is 10 million
2. The average life expectancy in New York is assumed to be 80 years due to good and advanced medical services.

Now divide this number into the age groups:

1. 4 years - 15 years → (15%) → 1.5 million
2. 15 years - 55 years → (50%) → 5 million
3. 55 years - 80+ years → (30%) → 3 million

Children between 4 years to 15 years has a high proportion to visit doctor because of toothaches and the change that takes place. children eat a lot of chocolate resulting in a chance of higher infection and go for a dental checkup in every 3 months to avoid any kind of infection. So it is safe to consider that 80% can have healthy teeth and 20% are having issues with teeth that too because o genetic or any accident or not because of proper care. The ones having issues go more frequently assuming they go in every 1.5 months.

Adults between 15 years - 55 years are generally grown-up kids and working professionals and they go for their regular checkup of mouth every 6 months. but some have got some infection or dental issues in the mouth due to the bad eating habits etc. So it is safe to consider that 60% can have healthy teeth and 40% are having issues with teeth. The ones having issues go more frequently assuming they go in every 3 months. Generally, these segments don't have enough time so it is safe to consider 3 months and 6 months for the same.

Adults above 55 years have more issues in teeth compared to any changes. There are teeth problems that arise due to increasing age thus increasing the number of people with defects in teeth. It is safe to consider defected teeth percentage to 70% and healthy to 30%. The frequency of the visits increased compared to the previous segment because of the free time but also not much due to the age factor. so it is safe to consider in every 4 months a healthy person goes to the dentist and every 2 months, a person with the problem goes.

The likeliness to go to the dentist at the assumed time will decrease for the person who has the healthiest teeth compared to the one having problem teeth. Some of the factors like distance between the hospital, workload, and income will play role in determining the likeliness and need.\

So it is safe to consider the likeliness of unhealthy people 80% and healthy people 60%

📊 The total number of visits in a year to a dentist is 13.5 million * 0.6 + 23 million * 0.8 million = 8.1 million + 18.4 million → 26.5 million ~ 26 million

Now the working hour of a dentist in a year is calculated by the following techniques →

Total working hours in a day = 8 hours.

Average time to cover 1 patient = 45 minutes. ( It includes the average of time taken to attend to healthy and unhealthy patients)

The number of patients in a day = 10 patients.

The number of working days in a year = 52 weeks * 5 working days → 260 days.

Total number of patients in a year attended = 260 * 10 = 2600 patients.

 ⭐ The total number of dentists needed= 26 million/ 2600 = 10,000 dentists

 📌 Sanity Check

The number of the total dentist comes out to be 10,000 and the total population is 10 Million.

So on average 1 dentist attends 1000 people and it seems to be in acceptable range.

📌 Clarifying Questions

1. When we say NewYork do we mean NewYork City or the state of NewYork- In NewYork City
2. When we say Dentist do we count those having personal clinic or in a hospital or both- Count in General

 Creating the Equation

Number of Dentists =

Number of total visits in a year to the dentist / Number of patients handled by a dentist in a year

📌 Solving

1. The population of New York City is 10 million
2. The average life expectancy in New York is assumed to be 80 years due to good and advanced medical services.

Now divide this number into the age groups:

1. 4 years - 15 years → (15%) → 1.5 million
2. 15 years - 55 years → (50%) → 5 million
3. 55 years - 80+ years → (30%) → 3 million

Children between 4 years to 15 years has a high proportion to visit doctor because of toothaches and the change that takes place. children eat a lot of chocolate resulting in a chance of higher infection and go for a dental checkup in every 3 months to avoid any kind of infection. So it is safe to consider that 80% can have healthy teeth and 20% are having issues with teeth that too because o genetic or any accident or not because of proper care. The ones having issues go more frequently assuming they go in every 1.5 months.

Adults between 15 years - 55 years are generally grown-up kids and working professionals and they go for their regular checkup of mouth every 6 months. but some have got some infection or dental issues in the mouth due to the bad eating habits etc. So it is safe to consider that 60% can have healthy teeth and 40% are having issues with teeth. The ones having issues go more frequently assuming they go in every 3 months. Generally, these segments don't have enough time so it is safe to consider 3 months and 6 months for the same.

Adults above 55 years have more issues in teeth compared to any changes. There are teeth problems that arise due to increasing age thus increasing the number of people with defects in teeth. It is safe to consider defected teeth percentage to 70% and healthy to 30%. The frequency of the visits increased compared to the previous segment because of the free time but also not much due to the age factor. so it is safe to consider in every 4 months a healthy person goes to the dentist and every 2 months, a person with the problem goes.

The likeliness to go to the dentist at the assumed time will decrease for the person who has the healthiest teeth compared to the one having problem teeth. Some of the factors like distance between the hospital, workload, and income will play role in determining the likeliness and need.\

So it is safe to consider the likeliness of unhealthy people 80% and healthy people 60%

📊 The total number of visits in a year to a dentist is 13.5 million * 0.6 + 23 million * 0.8 million = 8.1 million + 18.4 million → 26.5 million ~ 26 million

Now the working hour of a dentist in a year is calculated by the following techniques →

Total working hours in a day = 8 hours.

Average time to cover 1 patient = 45 minutes. ( It includes the average of time taken to attend to healthy and unhealthy patients)

The number of patients in a day = 10 patients.

The number of working days in a year = 52 weeks * 5 working days → 260 days.

Total number of patients in a year attended = 260 * 10 = 2600 patients.

 ⭐ The total number of dentists needed= 26 million/ 2600 = 10,000 dentists

 📌 Sanity Check

The number of the total dentist comes out to be 10,000 and the total population is 10 Million.

So on average 1 dentist attends 1000 people and it seems to be in acceptable range.

1. Clarifying Questions

   1. Are we talking about number of dentist practicing in New York -Yes

   2. Are we talking about dentist doing private private practice or someone associated with a hospital — Both

   3. We can estimate total number of hospital*avg no of dentist + private clinics* average no of dentist

   4. We can go both ways either from demand side or supply side

   5. Let me take the approach of demand side as demand drives the supply

   6. Are we only talking about OPD consultation or surgical process as well- OPD + minor process i.e scaling, RCT

2. What we know 

   1. Population of new York - 20 million

   2. Demographic distribution –assuming life expectancy of 80 years. Assuming equal distribution of population 

      1. 1-20 years → 5 million → visits a year

         1. Regular  – 4 times a year – 20% 

         2. Occasional  –2 times a year -50% 

         3. Rare - once in two years  - 30%

2. 20-40 -  5million – 

   1. Regular  – 2 times a year – 20% 

   2. Occasional  –1 times a year -50% 

   3. Rare - once in two years  - 30%

3. 40-60 - 5 million – 

   1. Regular  – 4 times a year – 20% 

   2. Occasional  –2 times a year -50% 

   3. Rare - once in two years  - 30%

4. 60+ - 5million - 

   1. Regular  – 4 times a year – 50% 

   2. Occasional  –2 times a year -30% 

   3. Rare - once in two years  - 20%

3. Total number of dentist visits → 5*[(4*20%+2*50%+0.5*30%) +(2*20%+1*50%+0.5*30%) + (4*20%+2*50%+0.5*30%) +(4*50%+2*30%+0.5*30%)

   1. 5*[(0.8+1+0.15)+(0.4+0.5+0.15)+(0.8+1+0.15)+(2+0.6+0.15)]=

   2. 5*(1.95+1.05+1.95+2.75)= 5*(7.7) =38.5 million visits annually

   3. 105479 visits daily ~ 100k visits daily

4. Assuming peak and off peak period 

   1. Average consultation runs for 20 mins

   2. No of consultation/ hour/denstist = 3 consultation

   3. Average working hours = 8 hours

      1. Assuming half of this is peak and half is non peak 

      2. During peak hours - no of consultations per hour = 3

      3. During off peak hours - no of consultation per hour =1

   4. Total number of consultation/denstist/day = 3*4 +1+4= 16

   5. No of dentist needed for 100k  patients = 100000/8= 12500dentist

New York population - 8 million

Dentist working hours 8 hours for 5 days a week = 40 hours per week

Avg time per patient ~ 1 hour (Routine checkups takes 30 min or less and procedures takes 1.5 to 2 hours, hence 1 hrs per patient is a good estimate)

With lunch breaks and refreshments, a dentist will be able to see a maximum of 6 patients a day

Hence, on an average, a dentist sees  6*5 = 30 patients weekly

Assuming a dentist takes 6 weeks off on account of annual leaves and public holidays that leaves us with 46 weeks.

In a year a dentist will see 46 * 30 = 1380 patients

No. of dentists required = 14.5m/1380 ~ 10000

Now we know that the health industry is heavily understaffed and so the actual number is going to be far less than 10,000

Hi everyone, 

I didn't look at any of the answers but somehow followed a completely different path: 

Scoping: 

• Normal dentistry (not incl. specialized)
• NYC (not NY state)
• # of Dentists (not # of dental clinics)

• 0-10= 10%
• 11-23= 15
• 24-34= 20
• 35-50= 20
• 50-64= 20
• 64-100= %15

1. Clarify

Are you referring to New York city? 

Any particular type of dentist? General dentist or a specialist? I'll go with a general dentist who does services like regular cleaning/scaling

So I will calculate # of general dentists in New York City who patients go to for regular cleaning

2. Equation

# of dentists in NYC = # of visits in a year / # of visits one dentist can take in a year 

I will estimate how many patient visits occur in a year, then estimate how many visits can a single dentist take in a year. Dividing the 2 should give me a total number of dentists required in NYC - assuming that's how many dentists are there in NYC

3. Calculation

Estimate # of patient visits in a year

Population of NYC ~8M , assuming life expectancy of 80 years and uniform distribution 

Estimate # of visits per dentist in a year

 I will estimate # of visits per dentist per week and use it to estimate for a year

Assumptions - 

Avg time required per visit = 2 hours (incl. breaks)

Dentist typically works 8-6 pm Mon to Fri, 12-4 on Sat, closed on sunday. That is a total of 74 hours per week 

# of appointments per week = 74/2 = 37

# of weeks in a year = 52

Accounting for 2 weeks of vacation every year, thas 50 working weeks in a year. So a dentist can take 50*37 = 1850 appointments every year

So for a total ~7M appointments in a year, NYC must have ~3800 dentists

Clarification

Is this NY state or NY city? Assuming NY city here.

Equation/Forumla

No. of Dentists in YK = Total # of patients have dental problem / # of patients treated by dentists

Calculation

NY city population ≈ 10M

Let's bifurcate the 10M into age groups:

1. 0-20 years = 20% = 2M
2. 20-40 years = 30% = 3M
3. 40-60 years = 30% = 3M
4. Above 60 years = 20% = 2M

Now let's calculate how many could have dental problems;

1. 0-20 years = Assume 2 visits a year as this is growing age and parents are often more concerned about their body changes. Therefore taking 50% of this population = 2M
2. 20-40 years = Assume 2 visits a year as this is the mature population. Therefore taking 30% of this population = 1.8M
3. 40-60 years = Assume 2 visits a year as this is mid of the age, hence, taking 40% of this population = 2.4M
4. Above 60 years = Assume 2 visits per year as this is the senior citizen age and teeth start creating problems. Therefore taking 50% of this population = 2M

Number of dentist:

1. Total population : 8 Million. Approximately 100,000 per year

2. Number of People who would like to see a dentist:

Assunption:

1. Kids under 5 dont need to see a doctor

2. Kids between 5-15 dont need any special work and just bimonthly visits

3. Adults between 15-70 needs atleast 2 visit for check up and 1 visit for 2 hours for cavity/orthodentist work

Averaging out to 1 hour per visit (2*.5+ 2)/3

4. People above 70 would need just one visit per year

Denitist 

Daily working hours: 8 

Weekly working hour: 8*5= 40

Total Work weeks= 50  ( 50* 40= 2000 hours)

Total dentist: 18,500,000/ 2000 = 9,250 dentist

Assumptions:

• New York Dentists Serve Local New York Patients Only.
• The average salary of a dentist is $117,000 and the overhead is the same (cost of equipment, licensing, etc).
• 70% of New Yorkers can afford a dentist.

Main equation:

• (Salary + Overhead)  = (Total people needing medical in NYC in a year * Average dental price)   / (Total number of dentists)

Breaking down unknowns into simpler equations:

• Total people needing medical in NYC = Population of NYC * 70% of New Yorkers can afford a dentist * 1 visit a year.
• Average dental price = Assuming an average of $200 (I am from India and assuming these values after conversion and increasing cost).
• (Salary + Overhead)  = Population of NYC * 70% of New Yorkers can afford a dentist * 1 visit a year * $200  / (Total number of dentists)

Calculate:

•  (Total number of dentists) =  ( 15 Million Population * 70% of New Yorkers can afford a dentist * 1 visit a year * $200 average cost of visit )  / $134,000
• Total number of dentists = 15,671 dentists.

Do a sanity check:

• Average dental sessions for a top dentist who does 20% more patients a day than average = 2.8.
• This seems kind of less and I would assume around double. 
• I guestimate 9,000 dentists in NYC.

Clarifying Questions :

1. Are we talking about the number of dental clinics or number of dentists in new york ? - number of dental clinics
2. there are different types of dentists. general dental clinics, speciality clinics for implants, ornamental surgeries etc. Can we assume that we can take those clinics out of this calculation ? - Yes
3. Are we talking about the entire New York state or just the Manhattan area ? - Lets calculate for the New York metro area that includes Manhattan and other areas.

Analysis :

OK.. Lets collect or make assumptions about some data

I assume that average lifespan of people in new york is 80 years.

Total Population of new york metropolitan area : New York is the most populated metro area in the US. If i remember correctly population of San Francisco Bay area is around 8 million and New York is much densely populated than bay area. I would say it is atleast twice as big in terms of number of people than bay area. A conservative guess would be somewhere between 18 to 22 million. Lets take 20 million for our calculation.

Total population of New York - 20 million.

How Many people need dental care : I remember taking my son to dental care for the for the first time when he was 5 years old. So I would assume that children between 0 to 5 does not visit a dentist usually.

If we make a uniform distribution of population that would be around 6% of the population.

So the total population needing dental care is = 20*.94 = 18.8 → round it up to 19 million.

People from 5 to 50 will typically have healthy teeth and visits a dentist for regular checkup twice a year.

If we do an even distribution for this population there will be around 10.8 million in this age range.

Among this population not everyone will be disciplined or lack insurance to go to a dentist.

I am not sure if Obama care covers dental insurance. I would assume that around 30% of the new york population are not covered by dental insurance.

So total number of people less than 50 going to dentist - 7.5

So number dental visits required by this population will be - 15 million.

People above 50 requires more frequent dental visits - If we make an even distribution there will be around 7.2 million people in this group

These people need frequent dental visits . We can assume 2.5 visits per person per year.

30 % does not have insurance - so 5 million people will go to dentist every year.

Total number of dental visits for this group - 12.5 million.

So total dental visit : 15+12.5 = 27.5 → Lets round up to 25 million.

One dentist can see 3 patients in an hr . So considering and 2000hr work year one dentist can handle 6000 visits per year.

So total number of dentist required for 25 million visits = 25,000,000/6000 = 4200 dentists.

Assuming there are around 20% shortages of dentist

Total number of dentist in new york is 3200.

• 1.      We need to count all the dentists, practising and non practising.
• 2.      There are around 10 med-schools in New York and all the students get passed.
• 3.      Each medical schools has 500 seats for medical students.
• 4.     Life expectancy of new York is 80 years

I see that previous posts have used the number of dental visits / year to answer this question. I approached the problem differently and would love to hear if this approach seems acceptable too. I'm not sure if I made too many assumptions. 

1. CLARIFYING QUESTIONS:
   1. Is it OK to assume that we are only referring to living, practicing dentists (i.e. not images of dentists, retired dentists, or orthodotists)? Assume yes.
   2. Is it OK to assume present day population? Assume yes.
   3. Do we need to factor dentists traveling into the state (though with COVID, there isn't much travel)? Assume no. 
   4. Is it OK to exclude dental students who have not completed their dental education? Assume yes.
2. CREATE EQUATION:
   1. Number of dentists in NY can be derived by:
      1. Calculating the number of adults in NY eliglble to be dentists 
      2. Calculating the % doctors of these adults
      3. Calculating the % dentists of these doctors
3. BREAKDOWN UNKNOWNS:
   1. Number of adults in NY eligible to be dentists: 
      1. The total population of NY state is ~ 20M. 
      2. Assuming the average lifespan is 0-80 with an even distribution every 10 years, approximately 2.5M people within each 10 year age group bracket. 
         1. There are 8 age brackets from 0-80 (0-9, 10-19, 20-29, etc.)
         2. 20M / 8 = 2.5M
      3. The number of adults eligible to be practicing dentistry are those who have completed dental school (4 years after college) up until age 65 (retirement). 

         1. Age Group	Eligble to be dentist? (Y/N)	Population eligible to be dentist
            0-9	N	N/A
            10-19	N	N/A
            20-29	Y (a little less than half population due to school - i.e. 26-29 years old)	1M (2.5M / 10 = .25M for each year; .25M * 4 age groups = 1 M (age 26-29)
            30-39	Y	2.5M
            40-49	Y	2.5M
            50-59	Y	2.5M
            60-69	Y (half popuation due to retirement)	1.25M
            70-80	N	N/A

         2. Total adults eliglble to be dentists: 1M + 2.5M(3) + 1.25M = 9.75M
4. Number of doctors of the eligible adults: Many different professions that adults can have. Dentistry requires both a college and a graduate school degree. 
   1. Assume 6/10 adults finish college: .6(9.75M) = 5.85M adults finish college
   2. Assume 1/10 college graduates go to medical school: .1(5.85M) = .585M or 585K go to medical school (assumes all types of doctor professions, including dentristry)
5. Number of dentists out of doctors: There are many specialities someone can have within the field of medicine. 
   1. Assume 1/20 doctors are dentists: .05(585K) = 29,250 practicing dentists in NY state
6. GUT CHECK: 
   1. ~1 dentist for every 684 people in NY state (20M / 29,250).
   2. Not everyone goes to the dentist. Assume 70% of people go to the dentist. 1 dentist sees ~ 479 people / year, which doesn't seem too far off given that there are 365 days in a year. Although the dentist will not work every day of the year, they see more than 1 patient a day.
   3. 5 days a week * 52 weeks / year = 260 working days (assuming a dentist only works business days)
   4. If the dentist takes vacation (say they take 20 days paid vacation), they have 240 days a year of working.
   5. 240 days / year allows them to see ~ 2 patients / day (479 / 240 = ~2) if the patients were only seeing the dentist 1 time / year.
   6. We know that dentists see more than 2 patients a day - at least double if not more (based on my experience going to the dentist), and patients may see the dentist more than once. There seems to be a reasonable amount of time left in the day for the dentist to see more patients than the 2 (assuming the average visit takes about 1 hour and the workday is 7.5 hours long with 30 minutes for lunch break).
   7. Note: I'd ask the interviewer if they would want more detail in regards to a gut check with the time estimates on patient visits. Assuming no, I'd stick with the 29,250 practicing dentists in the state of NY.

A: 

Does this include orthodontists? Interviewer says no, just a family dentist. Okay got it. And do you mean NYC or New York State? Interviewer says NYC is fine. Okay. 

Estimate = population of NYC * percent on a health plan / avg # of patients on a doctor’s patient panel 

= 8M * 0.8 / 50

= 13k

As a sanity check, 13k sounds reasonable given there are approximately 40k optomistrists in the city.