The sixth annual (and first virtual) “New York” R Conference took place August 5-6 & 12-15. Almost 300 attendees, and 30 speakers, plus a stand-up comedian and a whiskey masterclass leader, gathered remotely to explore, share, and inspire ideas.

We had many awesome speakers, many new and some, returning: Dr. Rob J Hyndman (Monash University), Dr. Adam Obeng (Facebook), Ludmila Janda (Amplify), Emily Robinson (Warby Parker), Daniel Chen (Virginia Tech, Lander Analytics), Dr. Jon Krohn (untapt), Dr. Andrew Gelman (Columbia University), David Smith (Microsoft), Laura Gabrysiak (Visa), Brooke Watson (ACLU), Dr. Sebastian Teran Hidalgo (Vroom), Catherine Zhou (Codecademy), Dr. Jacqueline Nolis (Brightloom), Sonia Ang (Microsoft), Emily Dodwell (AT&T Labs Research), Jonah Gabry (Columbia University, Stan Development Team), Wes MckKinney and Dr. Neal Richardson (Ursa Labs), Dr. Thomas Mock (RStudio), Dr. David Robinson, (Heap), Dr. Max Kuhn (RStudio), Dr. Erin LeDell (H2O.ai), Monica Thieu (Columbia University), Camelia Hssaine (Codecademy), and myself and, coming soon, a bonus talk by Heather Nolis (T-Mobile) which will be shared on YouTube as soon as our team is done editing them, along with all the other talks.

Let’s take a look at some of the highlights from the conference:

Andrew Gelman Gave Another 40-Minute Talk (no slides, as always)

Our favorite quotes from Andrew Gelman’s talk, Truly Open Science: From Design and Data Collection to Analysis and Decision Making, which had no slides, as usual:

“Everyone training in statistics becomes a teacher.”

“The most important thing you should take away — put multiple graphs on a page.”

“Honesty and transparency are not enough.”

“Bad science doesn’t make someone a bad person.”

Laura Gabrysiak Shows us We Are Driven By Experience, and not Brand Loyalty…Hope you Folks had a Good Experience!

Laura’s talk on re-Inventing customer engagement with machine learning went through several interesting use cases from her time at Visa. In addition to being a data scientist, she is an active community organizer and the co-founder of R-Ladies Miami.

Adam Obeng Delivered a Talk on Adaptive Experimentation

One of my former students at Columbia University, Adam Obeng, gave a great presentation on his adaptive experimentation. We learned that adaptive experimentation is three things: The name of (1) a family of techniques, (2) Adam’s team at Facebook, and (3) an open source package produced by said team. He went through the applications which are hyper-parameter optimization for ML, experimentation with multiple continuous treatments, and physical experiments or manufacturing.

Dr. Jacqueline Nolis Invited Us to Crash Her Viral Website, Tweet Mashup

Jacqueline asked the crowd to crash her viral website,Tweet Mashup, and gave a great talk on her experience building it back in 2016. Her website that lets you combine the tweets of two different people. After spending a year making it in .NET, when she launched the site it became an immediate sensation. Years later, she was getting more and more frustrated maintaining the F# code and decided to see if I could recreate it in Shiny. Doing so would require having Shiny integrate with the Twitter API in ways that hadn’t been done by anyone before, and pushing the Twitter API beyond normal use cases.

Attendees Participated in Two Virtual Happy Hours Packed with Fun

At the Friday Happy Hour, we had a mathematical standup comedian for the first time in R Conference history. Comic and math major Rachel Lander (no relationship to me!) entertained us with awesome math and stats jokes.

Following the stand up, we had a Whiskey Master Class with our Vibe Sponsor Westland Distillery, and another one on Saturday with Bruichladdich Distillery (hard to pronounce and easy to drink). Attendees and speakers learned and drank together, whether it be their whiskey, matchas, soda or water.

All Proceeds from the A(R)T Auction went to the R Foundation Again

A newer tradition, the A(R)T Auction, took place again! We featured pieces by artists in the R Community, and all proceeds were donated to the R Foundation. The highest-selling piece at auction was Street Cred (2020) by Vivian Peng (Lander Analytics and Los Angeles Mayor’s Office, Innovation Team). The second highest was a piece by Jacqueline Nolis (Brightloom, and Build a Career in Data Science co-author), R Conference speaker, Designed by Allison Horst, artist in residence at RStudio. 

 

The R-Ladies Group Photo Happened, Even Remotely!

As per tradition, we took an R-Ladies group photo, but, for the first time, remotely– as a screenshot! We would like to note that many more R-Ladies were present in the chat, but just chose not to share video.

Jon Harmon, Edna Mwenda, and Jessica Streeter win Raspberri Pis, Bluetooth Headphones, and Tenkeyless Keyboards for Most Active Tweeting During the Conference

This year’s Twitter Contest, in Malorie’s words, was a “ruthless but noble war.” You can see the NYR 2020 Dashboard here. A custom started that DCR 2018 by our Twitter scorekeeper Malorie Hughes (@data_all_day) has returned every year by popular demand, and now she’s stuck with it forever! Congratulations to our winners!

50+ Conference Attendees Participated in Pre-Conference Workshops Before

For the first time ever, workshops took place over the course of several days to promote work-life balance, and to give attendees the chance to take more than one course. We ran the following seven workshops:

Recreating the In-Person Experience

We recreated as much of the in-person experience as possible with attendee networking sessions, the speaker walk-on songs and fun facts, abundant prizes and giveaways, the Twitter contest, an art auction, and happy hours. In addition to all of this, we mailed conference programs, hex stickers, and other swag to each attendee (in the U.S.), along with discount codes from our Vibe Sponsors, MatchaBar, Westland Distillery and Bruichladdich Distillery.

Thank you, Lander Analytics Team!

Even though it was virtual, there was a lot of work that went into the conference, and I want to thank my amazing team at Lander Analytics along with our producer, Bill Prickett, for making it all come together. 

Looking Forward to D.C. and Dublin
If you attended, we hope you had an incredible experience. If you did not, we hope to see you at the virtual DC R Conference in the fall, and at the first Dublin R Conference and the NYR next year!

Related Posts



Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.

Health Insurance Calculations
Health Insurance Calculations

The costs involved with a health insurance plan can be confusing so I perform an analysis of different options to find which plan is most cost effective

My wife and I recently brought a new R programmer into our family so we had to update our health insurance. Becky is a researcher in neuroscience and psychology at NYU so we decided to choose an NYU insurance plan.

Our son sporting a New York R Conference shirt.
Our son sporting a New York R Conference shirt.

For families there are two main plans: Value and Advantage. The primary differences between the plans are the following:

Item Explanation Value Plan Amount Advantage Plan Amount
Bi-Weekly Premiums The amount we pay every other week in order to have insurance $160 ($4,160 annually) $240 ($6,240 annually)
Deductible Amount we pay directly to health providers before the insurance starts covering costs $1,000 $800
Coinsurance After the deductible is met, we pay this percentage of medical bills 20% 10%
Out-of-Pocket Maximum This is the most we will have to pay to health providers in a year (premiums do not count toward this max) $6,000 $5,000

We put them into a tibble for use later.

# use tribble() to make a quick and dirty tibble
parameters <- tibble::tribble(
    ~Plan, ~Premiums, ~Deductible, ~Coinsurance, ~OOP_Maximum,
    'Value', 160*26, 1000, 0.2, 6000,
    'Advantage', 240*26, 800, 0.1, 5000
)

Other than these cost differences, there is not any particular benefit of either plan over the other. That means whichever plan is cheaper is the best to choose.

This blog post walks through the steps of evaluating the plans to figure out which to select. Code is included so anyone can repeat, and improve on, the analysis for their given situation.

Cost

In order to figure out which plan to select we need to figure out the all-in cost, which is a function of how much we spend on healthcare in a year (we have to estimate our annual spending) and the aforementioned premiums, deductible, coinsurance and out-of-pocket maximum.

\[ \text{cost} = f(\text{spend}; \text{premiums}, \text{deductible}, \text{coinsurance}, \text{oop_maximum}) = \\ \text{min}(\text{oop_maximum}, \text{deductible} + \text{coinsurance}*(\text{spend}-\text{deductible}))+\text{premiums} \]

This can be written as an R function like this.

#' @title cost
#' @description Given healthcare spend and other parameters, calculate the actual cost to the user
#' @details Uses the formula above to caluclate total costs given a certain level of spending. This is the premiums plus either the out-of-pocket maximum, the actual spend level if the deductible has not been met, or the amount of the deductible plus the coinsurance for spend above the deductible but below the out-of-pocket maximum.
#' @author Jared P. Lander
#' @param spend A given amount of healthcare spending as a vector for multiple amounts
#' @param premiums The annual premiums for a given plan
#' @param deductible The deductible for a given plan
#' @param coinsurance The coinsurance percentage for spend beyond the deductible but below the out-of-pocket maximum
#' @param oop_maximum The maximum amount of money (not including premiums) that the insured will pay under a given plan
#' @return The total cost to the insured
#' @examples
#' cost(3000, 4160, 1000, .20, 6000)
#' cost(3000, 6240, 800, .10, 5000)
#'
cost <- function(spend, premiums, deductible, coinsurance, oop_maximum)
{
    # spend is vectorized so we use pmin to get the min between oop_maximum and (deductible + coinsurance*(spend - deductible)) for each value of spend provided
    pmin(
      # we can never pay more than oop_maximum so that is one side
      oop_maximum, 
      # if we are under oop_maximum for a given amount of spend,
      # this is the cost
      pmin(spend, deductible) + coinsurance*pmax(spend - deductible, 0)
    ) + 
    # we add the premiums since that factors into our cost
    premiums
}

With this function we can see if one plan is always, or mostly, cheaper than the other plan and that’s the one we would choose.

R Packages

For the rest of the code we need these R packages.

library(dplyr)
library(ggplot2)
library(tidyr)
library(formattable)
library(readr)
library(readxl)

Spending

To see our out-of-pocket cost at varying levels of healthcare spend we build a grid in $1,000 increments from $1,000 to $70,000.

spending <- tibble::tibble(Spend=seq(1000, 70000, by=1000))

We call our cost function on each amount of spend for the Value and Advantage plans.

spending <- spending %>% 
    # use our function to calcuate the cost for the value plan
    mutate(Value=cost(
        spend=Spend, 
        premiums=parameters$Premiums[1], 
        deductible=parameters$Deductible[1], 
        coinsurance=parameters$Coinsurance[1], 
        oop_maximum=parameters$OOP_Maximum[1]
    )
    ) %>% 
    # use our function to calcuate the cost for the Advantage plan
    mutate(Advantage=cost(
        spend=Spend, 
        premiums=parameters$Premiums[2], 
        deductible=parameters$Deductible[2], 
        coinsurance=parameters$Coinsurance[2], 
        oop_maximum=parameters$OOP_Maximum[2]
    )
    ) %>% 
  # compute the difference in costs for each plan
  mutate(Difference=Advantage-Value) %>% 
  # the winner for a given amount of spend is the cheaper plan
  mutate(Winner=if_else(Advantage < Value, 'Advantage', 'Value'))

The results are in the following table, showing every other row to save space. The Spend column is a theoretical amount of spending with a red bar giving a visual sense for the increasing amounts. The Value and Advantage columns are the corresponding overall costs of the plans for the given amount of Spend. The Difference column is the result of AdvantageValue where positive numbers in blue mean that the Value plan is cheaper while negative numbers in red mean that the Advantage plan is cheaper. This is further indicated in the Winner column which has the corresponding colors.

Spend Value Advantage Difference Winner
$2,000 $5,360 $7,160 1800 Value
$4,000 $5,760 $7,360 1600 Value
$6,000 $6,160 $7,560 1400 Value
$8,000 $6,560 $7,760 1200 Value
$10,000 $6,960 $7,960 1000 Value
$12,000 $7,360 $8,160 800 Value
$14,000 $7,760 $8,360 600 Value
$16,000 $8,160 $8,560 400 Value
$18,000 $8,560 $8,760 200 Value
$20,000 $8,960 $8,960 0 Value
$22,000 $9,360 $9,160 -200 Advantage
$24,000 $9,760 $9,360 -400 Advantage
$26,000 $10,160 $9,560 -600 Advantage
$28,000 $10,160 $9,760 -400 Advantage
$30,000 $10,160 $9,960 -200 Advantage
$32,000 $10,160 $10,160 0 Value
$34,000 $10,160 $10,360 200 Value
$36,000 $10,160 $10,560 400 Value
$38,000 $10,160 $10,760 600 Value
$40,000 $10,160 $10,960 800 Value
$42,000 $10,160 $11,160 1000 Value
$44,000 $10,160 $11,240 1080 Value
$46,000 $10,160 $11,240 1080 Value
$48,000 $10,160 $11,240 1080 Value
$50,000 $10,160 $11,240 1080 Value
$52,000 $10,160 $11,240 1080 Value
$54,000 $10,160 $11,240 1080 Value
$56,000 $10,160 $11,240 1080 Value
$58,000 $10,160 $11,240 1080 Value
$60,000 $10,160 $11,240 1080 Value
$62,000 $10,160 $11,240 1080 Value
$64,000 $10,160 $11,240 1080 Value
$66,000 $10,160 $11,240 1080 Value
$68,000 $10,160 $11,240 1080 Value
$70,000 $10,160 $11,240 1080 Value

Of course, plotting often makes it easier to see what is happening.

spending %>% 
    select(Spend, Value, Advantage) %>% 
    # put the plot in longer format so ggplot can set the colors
    gather(key=Plan, value=Cost, -Spend) %>% 
    ggplot(aes(x=Spend, y=Cost, color=Plan)) + 
        geom_line(size=1) + 
        scale_x_continuous(labels=scales::dollar) + 
        scale_y_continuous(labels=scales::dollar) + 
        scale_color_brewer(type='qual', palette='Set1') + 
        labs(x='Healthcare Spending', y='Out-of-Pocket Costs') + 
        theme(
          legend.position='top',
          axis.title=element_text(face='bold')
        )
Plot of out-of-pocket costs as a function of actual healthcare spending. Lower is better.
Plot of out-of-pocket costs as a function of actual healthcare spending. Lower is better.

It looks like there is only a small window where the Advantage plan is cheaper than the Value plan. This will be more obvious if we draw a plot of the difference in cost.

spending %>% 
    ggplot(aes(x=Spend, y=Difference, color=Winner, group=1)) + 
        geom_hline(yintercept=0, linetype=2, color='grey50') + 
        geom_line(size=1) + 
        scale_x_continuous(labels=scales::dollar) + 
        scale_y_continuous(labels=scales::dollar) + 
        labs(
          x='Healthcare Spending', 
          y='Difference in Out-of-Pocket Costs Between the Two Plans'
        ) + 
        scale_color_brewer(type='qual', palette='Set1') + 
        theme(
          legend.position='top',
          axis.title=element_text(face='bold')
        )
Plot of the difference in overall cost between the Value and Advantage plans. A difference greater than zero means the Value plan is cheaper and a difference below zero means the Advantage plan is cheaper.
Plot of the difference in overall cost between the Value and Advantage plans. A difference greater than zero means the Value plan is cheaper and a difference below zero means the Advantage plan is cheaper.

To calculate the exact cutoff points where one plan becomes cheaper than the other plan we have to solve for where the two curves intersect. Due to the out-of-pocket maximums the curves are non-linear so we need to consider four cases.

  1. The spending exceeds the point of maximum out-of-pocket spend for both plans
  2. The spending does not exceed the point of maximum out-of-pocket spend for either plan
  3. The spending exceeds the point of maximum out-of-pocket spend for the Value plan but not the Advantage plan
  4. The spending exceeds the point of maximum out-of-pocket spend for the Advantage plan but not the Value plan

When the spending exceeds the point of maximum out-of-pocket spend for both plans the curves are parallel so there will be no cross over point.

When the spending does not exceed the point of maximum out-of-pocket spend for either plan we set the cost calculations (not including the out-of-pocket maximum) for each plan equal to each other and solve for the amount of spend that creates the equality.

To keep the equations smaller we use variables such as \(d_v\) for the Value plan deductible, \(c_a\) for the Advantage plan coinsurance and \(oop_v\) for the out-of-pocket maximum for the Value plan.

\[ d_v + c_v(S – d_v) + p_v = d_a + c_a(S – d_a) + p_a \\ c_v(S – D_v) – c_a(S-d_a) = d_a – d_v + p_a – p_v \\ c_vS – c_vd_v – c_aS + c_ad_a = d_a – d_v + p_a – p_v \\ S(c_v – c_a) = d_a – c_ad_a – d_v + c_vd_v + p_a – p_v \\ S(c_v – c_a) = d_a(1 – c_a) – d_v(1 – c_v) + p_a – p_v \\ S = \frac{d_a(1 – c_a) – d_v(1 – c_v) + p_a – p_v}{(c_v – c_a)} \]

When the spending exceeds the point of maximum out-of-pocket spend for the Value plan but not the Advantage plan, we set the out-of-pocket maximum plus premiums for the Value plan equal to the cost calculation of the Advantage plan.

\[ oop_v + p_v = d_a + c_a(S – d_a) + p_a \\ d_a + c_a(S – d_a) + p_a = oop_v + p_v \\ c_aS – c_ad_a = oop_v + p_v – p_a – d_a \\ c_aS = oop_v + p_v – p_a + c_ad_a – d_a \\ S = \frac{oop_v + p_v – p_a + c_ad_a – d_a}{c_a} \]

When the spending exceeds the point of maximum out-of-pocket spend for the Advantage plan but not the Value plan, the solution is just the opposite of the previous equation.

\[ oop_a + p_a = d_v + c_v(S – d_v) + p_v \\ d_v + c_v(S – d_v) + p_v = oop_a + p_a \\ c_vS – c_vd_v = oop_a + p_a – p_v – d_v \\ c_vS = oop_a + p_a – p_v + c_vd_v – d_v \\ S = \frac{oop_a + p_a – p_v + c_vd_v – d_v}{c_v} \]

As an R function it looks like this.

#' @title calculate_crossover_points
#' @description Given healthcare parameters for two plans, calculate when one plan becomes more expensive than the other.
#' @details Calculates the potential crossover points for different scenarios and returns the ones that are true crossovers.
#' @author Jared P. Lander
#' @param premiums_1 The annual premiums for plan 1
#' @param deductible_1 The deductible plan 1
#' @param coinsurance_1 The coinsurance percentage for spend beyond the deductible for plan 1
#' @param oop_maximum_1 The maximum amount of money (not including premiums) that the insured will pay under plan 1
#' @param premiums_2 The annual premiums for plan 2
#' @param deductible_2 The deductible plan 2
#' @param coinsurance_2 The coinsurance percentage for spend beyond the deductible for plan 2
#' @param oop_maximum_2 The maximum amount of money (not including premiums) that the insured will pay under plan 2
#' @return The amount of spend at which point one plan becomes more expensive than the other
#' @examples
#' calculate_crossover_points(
#' 160, 1000, 0.2, 6000,
#' 240, 800, 0.1, 5000
#' )
#'
calculate_crossover_points <- function(
    premiums_1, deductible_1, coinsurance_1, oop_maximum_1,
    premiums_2, deductible_2, coinsurance_2, oop_maximum_2
)
{
    # calculate the crossover before either has maxed out
    neither_maxed_out <- (premiums_2 - premiums_1 + 
                              deductible_2*(1 - coinsurance_2) - 
                              deductible_1*(1 - coinsurance_1)) /
        (coinsurance_1 - coinsurance_2)
    
    # calculate the crossover when one plan has maxed out but the other has not
    one_maxed_out <- (oop_maximum_1 + 
                          premiums_1 - premiums_2 +
                          coinsurance_2*deductible_2 -
                          deductible_2) /
        coinsurance_2
    
    # calculate the crossover for the reverse
    other_maxed_out <- (oop_maximum_2 + 
                            premiums_2 - premiums_1 +
                            coinsurance_1*deductible_1 -
                            deductible_1) /
        coinsurance_1
    
    # these are all possible points where the curves cross
    all_roots <- c(neither_maxed_out, one_maxed_out, other_maxed_out)
    
    # now calculate the difference between the two plans to ensure that these are true crossover points
    all_differences <- cost(all_roots, premiums_1, deductible_1, coinsurance_1, oop_maximum_1) - 
        cost(all_roots, premiums_2, deductible_2, coinsurance_2, oop_maximum_2)
    
    # only when the difference between plans is 0 are the curves truly crossing
    all_roots[all_differences == 0]
}

We then call the function with the parameters for both plans we are considering.

crossovers <- calculate_crossover_points(
    parameters$Premiums[1], parameters$Deductible[1], parameters$Coinsurance[1], parameters$OOP_Maximum[1],
    parameters$Premiums[2], parameters$Deductible[2], parameters$Coinsurance[2], parameters$OOP_Maximum[2]
)

crossovers
## [1] 20000 32000

We see that the Advantage plan is only cheaper than the Value plan when spending between $20,000 and $32,000.

The next question is will our healthcare spending fall in that narrow band between $20,000 and $32,000 where the Advantage plan is the cheaper option?

Probability of Spending

This part gets tricky. I’d like to figure out the probability of spending between $20,000 and $32,000. Unfortunately, it is not easy to find healthcare spending data due to the opaque healthcare system. So I am going to make a number of assumptions. This will likely violate a few principles, but it is better than nothing.

Assumptions and calculations:

  • Healthcare spending follows a log-normal distribution
  • We will work with New York State data which is possibly different than New York City data
  • We know the mean for New York spending in 2014
  • We will use the accompanying annual growth rate to estimate mean spending in 2019
  • We have the national standard deviation for spending in 2009
  • In order to figure out the standard deviation for New York, we calculate how different the New York mean is from the national mean as a multiple, then multiply the national standard deviation by that number to approximate the New York standard deviation in 2009
  • We use the growth rate from before to estimate the New York standard deviation in 2019

First, we calculate the mean. The Centers for Medicare & Medicaid Services has data on total and per capita medical expenditures by state from 1991 to 2014 and includes the average annual percentage growth. Since the data are bundled in a zip with other files, I posted them on my site for easy access.

spend_data_url <- 'https://jaredlander.com/data/healthcare_spending_per_capita_1991_2014.csv'
health_spend <- read_csv(spend_data_url)

We then take just New York spending for 2014 and multiply it by the corresponding growth rate.

ny_spend <- health_spend %>% 
  # get just New York
  filter(State_Name == 'New York') %>% 
  # this row holds overall spending information
  filter(Item == 'Personal Health Care ($)') %>% 
  # we only need a few columns
  select(Y2014, Growth=Average_Annual_Percent_Growth) %>% 
  # we have to calculate the spending for 2019 by accounting for growth
  # after converting it to a percentage
  mutate(Y2019=Y2014*(1 + (Growth/100))^5)

ny_spend
Y2014 Growth Y2019
9778 5 12479.48

The standard deviation is trickier. The best I can find was the standard deviation on the national level in 2009. In 2013 the Centers for Medicare & Medicaid Services wrote in Volume 3, Number 4 of Medicare & Medicaid Research Review an article titled Modeling Per Capita State Health Expenditure Variation: State-Level Characteristics Matter. Exhibit 2 shows that the standard deviation of healthcare spending was $1,241 for the entire country in 2009. We need to estimate the New York standard deviation from this and then account for growth into 2019.

Next, we figure out the difference between the New York State spending mean and the national mean as a multiple.

nation_spend <- health_spend %>% 
  filter(Item == 'Personal Health Care ($)') %>% 
  filter(Region_Name == 'United States') %>% 
  pull(Y2009)

ny_multiple <- ny_spend$Y2014/nation_spend

ny_multiple
## [1] 1.418746

We see that the New York average is 1.4187464 times the national average. So we multiply the national standard deviation from 2009 by this amount to estimate the New York State standard deviation and assume the same annual growth rate as the mean. Recall, we can multiply the standard deviation by a constant.

\[ \begin{align} \text{var}(x*c) &= c^2*\text{var}(x) \\ \text{sd}(x*c) &= c*\text{sd}(x) \end{align} \]

ny_spend <- ny_spend %>% 
  mutate(SD2019=1241*ny_multiple*(1 + (Growth/100))^10)

ny_spend
Y2014 Growth Y2019 SD2019
9778 5 12479.48 2867.937

My original assumption was that spending would follow a normal distribution, but New York’s resident agricultural economist, JD Long, suggested that the spending distribution would have a floor at zero (a person cannot spend a negative amount) and a long right tail (there will be many people with lower levels of spending and a few people with very high levels of spending), so a log-normal distribution seems more appropriate.

\[ \text{spending} \sim \text{lognormal}(\text{log}(12479), \text{log}(2868)^2) \]

Visualized it looks like this.

draws <- tibble(
  Value=rlnorm(
    n=1200, 
    meanlog=log(ny_spend$Y2019), 
    sdlog=log(ny_spend$SD2019)
  )
)

ggplot(draws, aes(x=Value)) + geom_density() + xlim(0, 75000)
The log-normal distribution has a long right tail.
The log-normal distribution has a long right tail.

We can see that there is a very long right tail which means there are many low values and few high values.

Then the probability of spending between $20,000 and $32,000 can be calculated with plnorm().

plnorm(crossovers[2], meanlog=log(ny_spend$Y2019), sdlog=log(ny_spend$SD2019)) - 
  plnorm(crossovers[1], meanlog=log(ny_spend$Y2019), sdlog=log(ny_spend$SD2019))
## [1] 0.02345586

So we only have a 2.35% probability of our spending falling in that band where the Advantage plan is more cost effective. Meaning we have a 97.65% probability that the Value plan will cost less over the course of a year.

We can also calculate the expected cost under each plan. We do this by first calculating the probability of spending each (thousand) dollar amount (since the log-normal is a continuous distribution this is an estimated probability). We multiply each of those probabilities against their corresponding dollar amounts. Since the distribution is log-normal we need to exponentiate the resulting number. The data are on the thousands scale, so we multiply by 1000 to put it back on the dollar scale. Mathematically it looks like this.

\[ \mathbb{E}_{\text{Value}} \left[ \text{cost} \right] = 1000*\text{exp} \left\{ \sum p(\text{spend})*\text{cost}_{\text{Value}} \right\} \\ \mathbb{E}_{\text{Advantage}} \left[ \text{cost} \right] = 1000*\text{exp} \left\{ \sum p(\text{spend})*\text{cost}_{\text{Advantage}} \right\} \]

The following code calculates the expected cost for each plan.

spending %>% 
  # calculate the point-wise estimated probabilities of the healthcare spending
  # based on a log-normal distribution with the appropriate mean and standard deviation
  mutate(
    SpendProbability=dlnorm(
      Spend, 
      meanlog=log(ny_spend$Y2019), 
      sdlog=log(ny_spend$SD2019)
    )
  ) %>% 
  # compute the expected cost for each plan
  # and the difference between them
  summarize(
    ValueExpectedCost=sum(Value*SpendProbability),
    AdvantageExpectedCost=sum(Advantage*SpendProbability),
    ExpectedDifference=sum(Difference*SpendProbability)
  ) %>% 
  # exponentiate the numbers so they are on the original scale
  mutate_each(funs=exp) %>% 
  # the spending data is in increments of 1000
  # so multiply by 1000 to get them on the dollar scale
  mutate_each(funs=~ .x * 1000)
ValueExpectedCost AdvantageExpectedCost ExpectedDifference
5422.768 7179.485 1323.952

This shows that overall the Value plan is cheaper by about $1,324 dollars on average.

Conclusion

We see that there is a very small window of healthcare spending where the Advantage plan would be cheaper, and at most it would be about $600 cheaper than the Value plan. Further, the probability of falling in that small window of savings is just 2.35%.

So unless our spending will be between $20,000 and $32,000, which it likely will not be, it is a better idea to choose the Value plan.

Since the Value plan is so likely to be cheaper than the Advantage plan I wondered who would pick the Advantage plan. Economist Jon Hersh invokes behavioral economics to explain why people may select the Advantage plan. Some parts of the Advantage plan are lower than the Value plan, such as the deductible, coinsurance and out-of-pocket maximum. People see that under certain circumstances the Advantage plan would save them money and are enticed by that, not realizing how unlikely that would be. So they are hedging against a low probability situation. (A consideration I have not accounted for is family size. The number of members in a family can have a big impact on the overall spend and whether or not it falls into the narrow band where the Advantage plan is cheaper.)

In the end, the Value plan is very likely going to be cheaper than the Advantage plan.

Try it at Home

I created a Shiny app to allow users to plug in the numbers for their own plans. It is rudimentary, but it gives a sense for the relative costs of different plans.

Thanks

A big thanks to Jon Hersh, JD Long, Kaz Sakamoto, Rebecca Martin and Adam Hogan for reviewing this post.

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Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.

Data scientists and R enthusiasts gathered for the 5th annual New York R Conference held on May 9th-11th. In front of a crowd of more than 300 attendees, 24 speakers gave presentations on topics ranging from deep learning and building packages in R to football and hockey analytics.

Speakers included: Andrew Gelman, Emily Robinson, Max Kuhn, Dan Chen, Jared Lander, Namita Nandakumar, Mike Band, Soumya Kalra, Brooke Watson, David Madigan, Jacqueline Nolis, Heather Nolis, Gabriela Hempfling, Wes McKinney, Noam Ross, Jim Savage, Ludmila Janda, Emily Dodwell, Michelle Gill, Krista Watts, Elizabeth Sweeney, Adam Chekroud, Amanda Dobbyn and Letisha Smith.

This year marked the ten-year anniversary of the New York Open Statistical Programming Meetup. It has been incredible to see the growth of meetup over the years. We now have over 10,000 members around the world!

Members Over Time

Let’s take a look at some of the highlights from the conference:

Jonah Gabry Kicked Off “R” Week at the New York Open Statistical Programming Meetup with a Talk on Using Stan in R

Jonah Gabry kicking off R Week with a talk about the Stan ecosystem

Jonah Gabry from the Stan Development Team kicked off “R” week with a talk on making Bayes easier in the R ecosystem. Jonah went over the packages (rstanarm, rstantools, bayesplot and loo) which emulate other R model-fitting functions, unify function naming across Stan-based R packages, and develop plotting functions using ggplot objects.

50 Conference Attendees Participated in Pre-Conference Workshops on Thursday before the Conference

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People learning about machine learning from Max Kuhn during the pre-conference workshops

On the Thursday before the two-day conference, more than 50 conference attendees arrived at Work-Bench a day early for a full day of workshops. This was the first year of the R Conference Workshop Series. Max Kuhn, Dan Chen, Elizabeth Sweeney and Kaz Sakamoto each led a workshop which covered the following topics:

  • Machine Learning with Caret (Max Kuhn)
  • Git for Data Science (Dan Chen)
  • Introduction to Survival Analysis (Elizabeth Sweeney)
  • Geospatial Statistics and Mapping in R (Kaz Sakamoto)

The Growth of R-Ladies Summed Up in Three Pictures…

A group of people posing for a photo

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We are so excited to see the growth of the R-Ladies community and we appreciate their support for the NY R Conference over the years. Congratulations ladies!

Dr. Andrew Gelman Delivers Keynote Speech on the Fallacy of P-Values and Thinking like a Statistician—All Without Slides

A person standing in front of a curtain

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Andrew Gelman wowing the crowd as usual

There wasn’t a soul in the crowd who wasn’t hanging on every word from Columbia professor Dr. Andrew Gelman. The only speaker with a 40-minute time slot, and the only speaker to not use slides, Dr. Gelman talked about life as a statistician, warned of the perils of p-values and stressed the importance of simulation—before data collection—to improve our understanding of possible real-life scenarios. “Only through simulating fake data, can you really have statistical confidence about whatever performance metric you’re aiming for,” Gelman noted.

While we try not to pick a favorite speaker, Dr. Gelman runs away with that title every time he comes to speak at the New York R Conference.

Jacqueline and Heather Nolis Taught Us to Not to Be Afraid of Deep Learning and Model Deployment in Production

A group of people standing in a room

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Jacqueline Nolis showing how fun and easy deep learning can be

The final talk on day one was perhaps the most entertaining and insightful from the weekend. Jacqueline Nolis taught us how developing a deep learning model is easier than we thought and how humor can help us understand a complex idea in a simple form. Our top five favorite neural network-generate pet names: Dia, Spok, Jori, Lule, and Timuse!

On Saturday morning, Heather Nolis showed us how we can deploy the model into production. Heather walked through the steps involved in preparing an R model for production using containers (Docker) and container orchestration (Kubernetes) to share models throughout an organization or for the public. How can we put a model into production without your laptop running 24/7? By running the code safely on a server in the cloud!

Emily Robinson and Honey Berk Win Headphones for Most Tweets During the Conference

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Emily Robinson winning the tweeting grand prize

If you’re not following Emily Robinson (@robinson_es) and Honey Berk (@honeyberk), you’re missing out! Emily and Honey led all conference attendees in Twitter mentions according to our Twitter scorekeeper Malorie Hughes (@data_all_day). Because of Emily and Honey’s presence on Twitter, those who were unable to attend the conference were able to follow along with all of our incredible speakers throughout the two-day event.

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Tweet stats dashboard created by Malorie Hughes

Jared Lander Debuts New-Born R Package Hex Sticker T-Shirts: Congratulations to Jared and Rebecca on the Birth of their Son, Lev

Baby themed hex sticker shirts designed by Vivian Peng

During my talk I debuted a custom R package hex sticker t-shirt with my wife Rebecca and son Lev. We R a very nerdy family.

Looking Forward to 2020

If you attended the 2019 New York R Conference, we hope you had an incredible experience. If you did not attend the conference, we hope to see you next year!

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Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.

Pi Cake 2019
Pi Cake 2019

On Pi Day this year I was giving a keynote talk at DataFest in Scotland, so we celebrated Pi Day a week later, on the 21st. While it wasn’t the exact date, there’s never a bad time to eat pizza and Pi Cake.

This was the tenth Pi Cake, and it’s pretty hard to beat the Einstein design on last year’s Pi Cake, so Empire Cakes gave created us a cake with the actual definition of pi: The ratio of a circle’s circumference to its diameter.

For pizza we went to the new Lombardi’s in Chelsea. They use an amazing electric oven instead of coal, so if you look closely you can tell the difference, but the pizza was still great and the decor was fantastic. 

And now Pi Cake throughout the years:

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Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.

2018 New York R Conference

The 2018 New York R Conference was the biggest and best yet. This is both in terms of the crowd size and content.  The speakers included some of the R community’s best such as Hadley Wickham, David Robinson, Jennifer Hill, Max Kuhn, Andreas Mueller (ok, a little Python), Evelina Gabasova, Sean Taylor and Jeff Ryan. I am proud to say we were almost at gender parity for both attendees and speakers which is amazing for a tech conference. Brooke Watson even excitedly noted that we had a line for the women’s room.

Particularly gratifying for me was seeing so many of my students speak. Eurry Kim, Dan Chen and Alex Boghosian all gave excellent talks.

Some highlights that stuck out to me are:

Emily Robinson Shows There is More to the Tidyverse than Hadley

The Expanded Tidyverse

Emily Robinson, otherwise known as ERob, gave an excellent talk showing how the Tidyverse is so much more than just Hadley and that there are many people inspired by him to contribute in the Tidy way.

Sean Taylor Forecasted the Future with Prophet

Sean Taylor

Sean Taylor, former New Yorker and unrepentant Eagles fan, demonstrate his powerful R and Python, package Prophet, for forecasting time series data. Facebook open sourced his work so we could all benefit.

OG Data Mafia Founder Drew Conway Popped In

Giving away a data mafia shirt

A lucky fan got an autographed NYC Data Mafia t-shirt from Drew Conway.

David Smith Playing Minecraft Through R

Minecraft in R

David Smith played Minecraft through R, including building objects and moving through the world.

Evelina Gabasova Used Social Network Analysis to Break Down Star Wars

It's a Trap

Evelina Gabasova wowed the audience with her fun talk and detailed analysis of character interaction in Star Wars.

Dusty Turner Represented West Point

Dusty Talking Army Sports

Dusty Turner taught us how the United States Military Academy uses R for both student instruction and evaluation.

Hadley Wickham Delved into the Nitty Gritty of R

Hadley shows off objects are stored in memory

Hadley Wickham showed us how to get into the internals of R and figure out how to examine objects from a memory perspective.

Jennifer Hill Demonstrated Awesome Machine Learning Techniques for Causal Inference

Jennifer Hill Explaining Causal Inference

Following her sold-out meetup appearance in March, Jennifer continued to push the boundaries of causal inference.

I Made the Authors of Caret and scitkit-learn Show That R and Python Can Get Along

Caret and Scikit-learn in one place

While both Andreas and Max gave great individual talks, I made them pose for this peace-making photo.

David Robinson Got the Upper Hand in a Sibling Twitter Duel

DRob Teaching

Given only about 30 minutes notice, David put together an entire slideshow on how to livetweet and how to compete with your sibling.

In the End Emily Robinson Beat Her Brother For Best Tweeting

Emily won the prize for best tweeting

Despite David’s headstart Emily was the best tweeter (as calculated by Max Kuhn and Mara Averick) so she won the WASD Code mechanical keyboard with MX Cherry Clear switches.

Silent Auction of Data Paintings

The Robinson Family bought the Pizza Data painting for me

Thomas Levine made paintings of famous datasets that we auctioned off with the proceeds supporting the R Foundation and the Free Software Foundation. The Robinson family very graciously chipped in and bought the painting of the Pizza Poll data for me! I’m still floored by this and in love with the painting.

Ice Cream Sandwiches

Ice Cream Sandwiches

In addition to bagels and eggs sandwiches from Murray’s Bagels, Israeli food from Hummus and Pita Company, avocado toast and coffee from Bluestone Lane Coffee and pizza from Fiore’s, we also had ice creams sandwiches from World’s Best Cookie Dough.

All the Material

To catch up on all the presentations check out Mara Averick’s excellent notes:

Or check out all of Brooke’s drawings, collated by Dan Chen.

Videos and Upcoming Events

The videos will be posted at rstats.nyc in a few weeks for all to enjoy.

There are a number of other events coming up including:

We are already beginning plans for next year’s conference and are working on bringing it to DC as well! Stay tuned for all that and more.

Dan loves his mug

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Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.

Pi Day 2018

It’s Pi Day, when we celebrate all things round by eating pizza and Pi Cake. This is the ninth year we have celebrated Pi Day and the fourth year in a row we got the Pi Cake from Empire Cakes. This year’s pizza place was Arturo’s on Thompson and Houston. Arturo’s is a great example of old New York pizza with an oven dating to the 1920’s.

In addition to the traditional Pi Symbol atop the cake we added Albert Einstein since today is also his birthday. It seems fitting that we lost one of the world’s other greatest physicists, Stephen Hawking on the same math holiday.

Pi Cake 2018

The crew has grown quite large from the five of us who celebrated our first pie day almost a decade ago.

Some more pictures from this fun night.

And now Pi Cake throughout the years:

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Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.

Snowstorm Stella impacted both our numbers and our location, but last night a smaller crew braved the cold weather and messy streets to celebrate Pi Day with pizza and Pi Cake at Ribalta.

We naturally ate a lot of round pies and even a rectangular pie to honor Hippocrates’ squaring the lune.

This year’s Pi Cake came from Empire Cakes for the third year in a row.  It was their Brooklyn Blackout cake with Chocolate frosting, a blue Pi symbol on top and blue circles with red radii around the sides.

Some pictures from last night:

IMG_20170314_224825_430 IMG_20170314_225301_523 IMG_1967 IMG_20170314_201119 IMG_20170314_205344

And all the years’ Pi Cakes:

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Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.

Highlights from the 2016 New York R Conference

Originally posted on www.work-bench.com.

image

You might be asking yourself, “How was the 2016 New York R Conference?”

Well, if we had to sum it up in one picture, it would look a lot like this (thank you to Drew Conway for the slide & delivering the battle cry for data science in NYC):

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Our 2nd annual, sold-out New York R Conference was back this year on April 8th & 9th at Work-Bench. Co-hosted with our friends at Lander Analytics, this year’s conference was bigger and better than ever, with over 250 attendees, and speakers from Airbnb, AT&T, Columbia University, eBay, Etsy, RStudio, Socure, and Tamr. In case you missed the conference or want to relive the excitement, all of the talks and slides are now live on the R Conference website.

With 30 talks, each 20 minutes long and two forty-minute keynotes, the topics of the presentations were just as diverse as the speakers. Vivian Peng gave an emotional talk on data visualization using non-visual senses and “The Feels.” Bryan Lewis measured the shadows of audience members to demonstrate the pros and cons of projection methods, and Daniel Lee talked about life, love, Stan, and March Madness. But, even with 32 presentations from a diverse selection of speakers, two dominant themes emerged: 1) Community and 2) Writing better code.

Given the amazing caliber of speakers and attendees, community was on everyone’s mind from the start. Drew Conway emoted the past, present, and future of data science in NYC, and spoke to the dangers of tearing down the tent we built. Joe Rickert from Microsoft discussed the R Consortium and how to become involved. Wes McKinney talked about community efforts in improving interoperability between data science languages with the new Feather data frame file format under the Apache Arrow project. Elena Grewal discussed how Airbnb’s data science team made changes to the hiring process to increase the number of female hires, and Andrew Gelman even talked about how your political opinions are shaped by those around you in his talk about Social Penumbras.

Writing better code also proved to be a dominant theme throughout the two day conference. Dan Chen of Lander Analytics talked about implementing tests in R. Similarly, Neal Richardson and Mike Malecki of Crunch.io talked about how they learned to stop munging and love tests, and Ben Lerner discussed how to optimize Python code using profilers and Cython. The perfect intersection of themes came from Bas van Schaik of Semmle who discussed how to use data science to write better code by treating code as data. While everyone had some amazing insights, these were our top five highlights:

JJ Allaire Releases a New Preview of RStudio

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JJ Allaire, the second speaker of the conference, got the crowd fired up by announcing new features of RStudio and new packages. Particularly exciting was bookdown for authoring large documents, R Notebooks for interactive Markdown files and shared sessions so multiple people can code together from separate computers.

Andrew Gelman Discusses the Political Impact of the Social Penumbra

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As always, Dr. Andrew Gelman wowed the crowd with his breakdown of how political opinions are shaped by those around us. He utilized his trademark visualizations and wit to convey the findings of complex models.

Vivian Peng Helps Kick off the Second Day with a Punch to the Gut

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On the morning of the second day of the conference, Vivian Peng gave a heartfelt talk on using data visualization and non-visual senses to drive emotional reaction and shape public opinion on everything from the Syrian civil war to drug resistance statistics.

Ivor Cribben Studies Brain Activity with Time Varying Networks

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University of Alberta Professor Ivor Cribben demonstrated his techniques for analyzing fMRI data. His use of network graphs, time series and extremograms brought an academic rigor to the conference.

Elena Grewal Talks About Scaling Data Science at Airbnb

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After a jam-packed 2 full days, Elena Grewal helped wind down the conference with a thoughtful introspection on how Airbnb has grown their data science team from 5 to 70 people, with a focus on increasing diversity and eliminating bias in the hiring process.

See the full conference videos & presentations below, and sign up for updates for the 2017 New York R Conference on www.rstats.nyc. To get your R fix in the meantime, follow @nyhackr, @Work_Bench, and @rstatsnyc on Twitter, and check out the New York Open Programming Statistical Meetup or one of Work-Bench’s upcoming events!

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Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.

Last night we celebrated Rounded Pi Day by rounding at the 10,000’s digit to get 3.1416 which nicely works with the date 3/14/16.  This was great after Mega Pi Day worked out so perfectly last year.  And this all built upon previous years’ celebrations.

We ate a large quantity of pizza at Lombardi’s. and for the second year in a row we got the Pi Cake from Empire Cakes with peanut butter and chocolate flavors.  The base was inscribed with historic approximations of Pi:  25/8, 256/81, 339/108, 223/71, 377/120, 3927/1250, 355/113, 62832/20000, 22/7.

Some pictures from the fantastic night:

IMG_20160314_193523 IMG_20160314_203411 IMG_20160314_203443

Previous year’s Pi Cakes:

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Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.


I R NY
On April 24th and 25th Lander Analytics and Work-Bench coorganized the (sold-out) inaugural New York R Conference. It was an amazing weekend of nerding out over R and data, with a little Python and Julia mixed in for good measure. People from all across the R community gathered to see rockstars discuss their latest and greatest efforts.

Highlights include:


BryanLewis
Bryan Lewis wowing the crowd (there were literally gasps) with rthreejs implemented with htmlwidgets.


HilaryParker
Hilary Parker receiving spontaneous applause in the middle of her talk about reproducible research at Etsy for her explainr, catsplainr and mansplainr packages.


JamesPowell
James Powell speaking flawless Mandarin in a talk tangentially about Python.


VivianPeng
Vivian Peng also receiving spontaneous applause for her discussion of storytelling with data.


WesMcKinney
Wes McKinney showing love for data.frames in all languages and sporting an awesome R t-shirt.


DanChen
Dan Chen using Shiny to study Ebola data.


AndyGelman
Andrew Gelman blowing away everyone with his keynote about Bayesian methods with particular applications in politics.

Videos of the talks are available at http://www.rstats.nyc/#speakers with slides being added frequently.

A big thank you to sponsors RStudio, Revolution Analytics, DataKind, Pearson, Brewla Bars and Twillory.


Next year’s conference is already being planned for April. To inquire about sponsoring or speaking please get in touch.

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Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.