Simply Statistics


Rafa's citations above replacement in statistics journals is crazy high.

Editor's note:  I thought it would be fun to do some bibliometrics on a Friday. This is super hacky and the CAR/Y stat should not be taken seriously. 

I downloaded data on the 400 most cited papers between 2000-2010 in some statistical journals from Web of Science. Here is a boxplot of the average number of citations per year (from publication date - 2015) to these papers in the journals Annals of Statistics, Biometrics, Biometrika, Biostatistics, JASA, Journal of Computational and Graphical Statistics, Journal of Machine Learning Research, and Journal of the Royal Statistical Society Series B.




There are several interesting things about this graph right away. One is that JASA has the highest median number of citations, but has fewer "big hits" (papers with 100+ citations/year) than Annals of Statistics, JMLR, or JRSS-B. Another thing is how much of a lottery developing statistical methods seems to be. Most papers, even among the 400 most cited, have around 3 citations/year on average. But a few lucky winners have 100+ citations per year. One interesting thing for me is the papers that get 10 or more citations per year but aren't huge hits. I suspect these are the papers that solve one problem well but don't solve the most general problem ever.

Something that jumps out from that plot is the outlier for the journal Biostatistics. One of their papers is cited 367.85 times per year. The next nearest competitor is 67.75 and it is 19 standard deviations above the mean! The paper in question is: "Exploration, normalization, and summaries of high density oligonucleotide array probe level data", which is the paper that introduced RMA, one of the most popular methods for pre-processing microarrays ever created. It was written by Rafa and colleagues. It made me think of the statistic "wins above replacement" which quantifies how many extra wins a baseball team gets by playing a specific player in place of a league average replacement.

What about a "citations /year above replacement" statistic where you calculate for each journal:

Median number of citations to a paper/year with Author X - Median number of citations/year to an average paper in that journal

Then average this number across journals. This attempts to quantify how many extra citations/year a person's papers generate compared to the "average" paper in that journal. For Rafa the numbers look like this:

  • Biostatistics: Rafa = 15.475, Journal = 1.855, CAR/Y =  13.62
  • JASA: Rafa = 74.5, Journal = 5.2, CAR/Y = 69.3
  • Biometrics: Rafa = 4.33, Journal = 3.38, CAR/Y = 0.95

So Rafa's citations above replacement is (13.62 + 69.3 + 0.95)/3 =  27.96! There are a couple of reasons why this isn't a completely accurate picture. One is the low sample size, the second is the fact that I only took the 400 most cited papers in each journal. Rafa has a few papers that didn't make the top 400 for journals like JASA - which would bring down his CAR/Y.



Data analysis subcultures

Roger and I responded to the controversy around the journal that banned p-values today in Nature. A piece like this requires a lot of information packed into very little space but I thought one idea that deserved to be talked about more was the idea of data analysis subcultures. From the paper:

Data analysis is taught through an apprenticeship model, and different disciplines develop their own analysis subcultures. Decisions are based on cultural conventions in specific communities rather than on empirical evidence. For example, economists call data measured over time 'panel data', to which they frequently apply mixed-effects models. Biomedical scientists refer to the same type of data structure as 'longitudinal data', and often go at it with generalized estimating equations.

I think this is one of the least appreciated components of modern data analysis. Data analysis is almost entirely taught through an apprenticeship culture with completely different behaviors taught in different disciplines. All of these disciplines agree about the mathematical optimality of specific methods under very specific conditions. That is why you see methods like randomized trials re-discovered across multiple disciplines.

But any real data analysis is always a multi-step process involving data cleaning and tidying, exploratory analysis, model fitting and checking, summarization and communication. If you gave someone from economics, biostatistics, statistics, and applied math an identical data set they'd give you back very different reports on what they did, why they did it, and what it all meant. Here are a few examples I can think of off the top of my head:

  • Economics calls longitudinal data panel data and uses mostly linear mixed effects models, while generalized estimating equations are more common in biostatistics (this is the example from Roger/my paper).
  • In genome wide association studies the family wise error rate is the most common error rate to control. In gene expression studies people frequently use the false discovery rate.
  • This is changing a bit, but if you learned statistics at Duke you are probably a Bayesian and if you learned at Berkeley you are probably a frequentist.
  • Psychology has a history of using parametric statistics, genomics is big into empirical Bayes, and you see a lot of Bayesian statistics in climate studies.
  • You see homoskedasticity tests used a lot in econometrics, but that is hardly ever done through formal hypothesis testing in biostatistics.
  • Training sets and test sets are used in machine learning for prediction, but rarely used for inference.

This is just a partial list I thought of off the top of my head, there are a ton more. These decisions matter a lot in a data analysis.  The problem is that the behavioral component of a data analysis is incredibly strong, no matter how much we'd like to think of the process as mathematico-theoretical. Until we acknowledge that the most common reason a method is chosen is because, "I saw it in a widely-cited paper in journal XX from my field" it is likely that little progress will be made on resolving the statistical problems in science.


A blessing of dimensionality often observed in high-dimensional data sets

Tidy data sets have one observation per row and one variable per column.  Using this definition, big data sets can be either:

  1. Wide - a wide data set has a large number of measurements per observation, but fewer observations. This type of data set is typical in neuroimaging, genomics, and other biomedical applications.
  2. Tall - a tall data set has a large number of observations, but fewer measurements. This is the typical setting in a large clinical trial or in a basic social network analysis.

The curse of dimensionality tells us that estimating some quantities gets harder as the number of dimensions of a data set increases - as the data gets taller or wider. An example of this was nicely illustrated by my student Prasad (although it looks like his quota may be up on Rstudio).

For wide data sets there is also a blessing of dimensionality. The basic reason for the blessing of dimensionality is that:

No matter how many new measurements you take on a small set of observations, the number of observations and all of their characteristics are fixed.

As an example, suppose that we make measurements on 10 people. We start out by making one measurement (blood pressure), then another (height), then another (hair color) and we keep going and going until we have one million measurements on those same 10 people. The blessing occurs because the measurements on those 10 people will all be related to each other. If 5 of the people are women and 5 or men, then any measurement that has a relationship with sex will be highly correlated with any other measurement that has a relationship with sex. So by knowing one small bit of information, you can learn a lot about many of the different measurements.

This blessing of dimensionality is the key idea behind many of the statistical approaches to wide data sets whether it is stated explicitly or not. I thought I'd make a very short list of some of these ideas:

1. Idea: De-convolving mixed observations from high-dimensional data. 

How the blessing plays a role: The measurements for each observation are assumed to be a mixture of values measured from different observation types. The proportion of each observation type is assumed to be fixed across measurements, so you can take advantage of the multiple measurements to estimate the mixing percentage and perform the deconvolution. (Wenyi Wang came and gave an excellent seminar on this idea at JHU a couple of days ago, which inspired this post).

2. Idea: The two groups model for false discovery rates.

How the blessing plays a role:  The models assume that a hypothesis test is performed for each observation and that the probability any observation is drawn from the null, the null distribution, and the alternative distributions are common across observations. If the null is assumed known, then it is possible to use the known null distribution to estimate the common probability that an observation is drawn from the null.


3. Idea: Empirical Bayes variance shrinkage for linear models

How the blessing plays a role:  A linear model is fit for each observation and the means and variances of the log ratios calculated from the model are assumed to follow a common distribution across observations. The method estimates the hyper-parameters of these common distributions and uses them to adjust any individual measurement's estimates.


4. Idea: Surrogate variable analysis

How the blessing plays a role:  Each observation is assumed to be influenced by a single variable of interest (a primary variable) and multiple unmeasured confounders. Since the observations are fixed, the values of the unmeasured confounders are the same for each measurement and a supervised PCA can be used to estimate surrogates for the confounders. (see my JHU job talk for more on the blessing)


The blessing of dimensionality I'm describing here is related to the idea that Andrew Gelman refers to in this 2004 post.  Basically, since increasingly large number of measurements are made on the same observations there is an inherent structure to those observations. If you take advantage of that structure, then as the dimensionality of your problem increases you actually get better estimates of the structure in your high-dimensional data - a nice blessing!


Teaser trailer for the Genomic Data Science Specialization on Coursera


We have been hard at work in the studio putting together our next specialization to launch on Coursera. It will be called the "Genomic Data Science Specialization" and includes a spectacular line up of instructors: Steven Salzberg, Ela Pertea, James Taylor, Liliana Florea, Kasper Hansen, and me. The specialization will cover command line tools, statistics, Galaxy, Bioconductor, and Python. There will be a capstone course at the end of the sequence featuring an in-depth genomic analysis. If you are a grad student, postdoc, or principal investigator in a group that does genomics this specialization is for you. If you are a person looking to transition into one of the hottest areas of research with the new precision medicine initiative this is for you. Get pumped and share the teaser-trailer with your friends!


A surprisingly tricky issue when using genomic signatures for personalized medicine

My student Prasad Patil has a really nice paper that just came out in Bioinformatics (preprint in case paywalled). The paper is about a surprisingly tricky normalization issue with genomic signatures. Genomic signatures are basically statistical/machine learning functions applied to the measurements for a set of genes to predict how long patients will survive, or how they will respond to therapy. The issue is that usually when building and applying these signatures, people normalize across samples in the training and testing set.

An example of this normalization is to mean-center the measurements for each gene in the testing/application stage, then apply the prediction rule. The problem is that if you use a different set of samples when calculating the mean you can get a totally different prediction function. The basic problem is illustrated in this graphic.


Screen Shot 2015-03-19 at 12.58.03 PM


This seems like a pretty esoteric statistical issue, but it turns out that this one simple normalization problem can dramatically change the results of the predictions. In particular, we show that the predictions for the same patient, with the exact same data, can change dramatically if you just change the subpopulations of patients within the testing set. In this plot, Prasad made predictions for the exact same set of patients two times when the patient population varied in ER status composition. As many as 30% of the predictions were different for the same patient with the same data if you just varied who they were being predicted with.

Screen Shot 2015-03-19 at 1.02.25 PM


This paper highlights how tricky statistical issues can slow down the process of translating ostensibly really useful genomic signatures into clinical practice and lends even more weight to the idea that precision medicine is a statistical field.


A simple (and fair) way all statistics journals could drive up their impact factor.


If every method in every stats journal was implemented in a corresponding R package (easy), was required to have a  companion document that was a tutorial on how to use the software (easy), included a reference to how to cite the paper if you used the software (easy) and the paper/tutorial was posted to the relevant message boards for the communities of interest (easy) that journal would see a dramatic bump in its impact factor.


Data science done well looks easy - and that is a big problem for data scientists

Data science has a ton of different definitions. For the purposes of this post I'm going to use the definition of data science we used when creating our Data Science program online. Data science is:

Data science is the process of formulating a quantitative question that can be answered with data, collecting and cleaning the data, analyzing the data, and communicating the answer to the question to a relevant audience.

In general the data science process is iterative and the different components blend together a little bit. But for simplicity lets discretize the tasks into the following 7 steps:

  1. Define the question of interest
  2. Get the data
  3. Clean the data
  4. Explore the data
  5. Fit statistical models
  6. Communicate the results
  7. Make your analysis reproducible

A good data science project answers a real scientific or business analytics question. In almost all of these experiments the vast majority of the analyst's time is spent on getting and cleaning the data (steps 2-3) and communication and reproducibility (6-7). In most cases, if the data scientist has done her job right the statistical models don't need to be incredibly complicated to identify the important relationships the project is trying to find. In fact, if a complicated statistical model seems necessary, it often means that you don't have the right data to answer the question you really want to answer. One option is to spend a huge amount of time trying to tune a statistical model to try to answer the question but serious data scientist's usually instead try to go back and get the right data.

The result of this process is that most well executed and successful data science projects don't (a) use super complicated tools or (b) fit super complicated statistical models. The characteristics of the most successful data science projects I've evaluated or been a part of are: (a) a laser focus on solving the scientific problem, (b) careful and thoughtful consideration of whether the data is the right data and whether there are any lurking confounders or biases and (c) relatively simple statistical models applied and interpreted skeptically.

It turns out doing those three things is actually surprisingly hard and very, very time consuming. It is my experience that data science projects take a solid 2-3 times as long to complete as a project in theoretical statistics. The reason is that inevitably the data are a mess and you have to clean them up, then you find out the data aren't quite what you wanted to answer the question, so you go find a new data set and clean it up, etc. After a ton of work like that, you have a nice set of data to which you fit simple statistical models and then it looks super easy to someone who either doesn't know about the data collection and cleaning process or doesn't care.

This poses a major public relations problem for serious data scientists. When you show someone a good data science project they almost invariably think "oh that is easy" or "that is just a trivial statistical/machine learning model" and don't see all of the work that goes into solving the real problems in data science. A concrete example of this is in academic statistics. It is customary for people to show theorems in their talks and maybe even some of the proof. This gives people working on theoretical projects an opportunity to "show their stuff" and demonstrate how good they are. The equivalent for a data scientist would be showing how they found and cleaned multiple data sets, merged them together, checked for biases, and arrived at a simplified data set. Showing the "proof" would be equivalent to showing how they matched IDs. These things often don't look nearly as impressive in talks, particularly if the audience doesn't have experience with how incredibly delicate real data analysis is. I imagine versions of this problem play out in industry as well (candidate X did a good analysis but it wasn't anything special, candidate Y used Hadoop to do BIG DATA!).

The really tricky twist is that bad data science looks easy too. You can scrape a data set off the web and slap a machine learning algorithm on it no problem. So how do you judge whether a data science project is really "hard" and whether the data scientist is an expert? Just like with anything, there is no easy shortcut to evaluating data science projects. You have to ask questions about the details of how the data were collected, what kind of biases might exist, why they picked one data set over another, etc.  In the meantime, don't be fooled by what looks like simple data science - it can often be pretty effective.


Editor's note: If you like this post, you might like my pay-what-you-want book Elements of Data Analytic Style:



De-weaponizing reproducibility

A couple of weeks ago Roger and I went to a conference on statistical reproducibility held at the National Academy of Sciences. The discussion was pretty wide ranging and I love that the thinking about reproducibility is coming back to statistics. There was pretty widespread support for the idea that prevention is the right way to approach reproducibility.
It turns out I was the last speaker of the whole conference. This is an unenviable position to be in with so many bright folks speaking first as they covered a huge amount of what I wanted to say. My talk focused on three key points:
  1. The tools for reproducibility already exist, the barrier isn't tools
  2. We need to de-weaponize reproducibility
  3. Prevention is the right approach to reproducibility


In terms of the first point, tools like iPython, knitr, and Galaxy can be used to all but the absolutely largest analysis reproducible right now.  Our group does this all the time with our papers and so do many others. The problem isn't a lack of tools.

Speaking to point two, I think many people would agree that part of the issue is culture change. One issue that is increasingly concerning to me is the "weaponization" of reproducibility.  I have been noticing is that some of us (like me, my students, other folks at JHU, and lots of particularly junior computational people elsewhere) are trying really hard to be reproducible. Most of the time this results in really positive reactions from the community. But when a co-author of mine and I wrote that paper about the science-wise false discovery rate, one of the discussants used our code (great), improved on it (great), identified a bug (great), and then did his level best to humiliate us both in front of the editor and the general public because of that bug (not so great).

I have seen this happen several times. Most of the time if a paper is reproducible the authors get a pat on the back and their code is either ignored, or used in a positive way. But for high-profile and important problems, people  largely use eproducibility to:
  1.  Impose regulatory hurdles in the short term while people transition to reproducibility. One clear example of this is the Secret Science Reform Act which is a bill that imposes strict reproducibility conditions on all science before it can be used as evidence for regulation.
  2. Humiliate people who aren't good coders or who make mistakes in their code. This is what happened in my paper when I produced reproducible code for my analysis, but has also happened to other people.
  3. Take advantage of people's code to plagiarize/straight up steal work. I have stories about this I'd rather not put on the internet


Of the three, I feel like (1) and (2) are the most common. Plagiarism and scooping by theft I think are actually relatively rare based on my own anecdotal experience. But I think that the "weaponization" of reproducibility to block regulation or to humiliate folks who are new to computational sciences is more common than I'd like it to be. Until reproducibility is the standard for everyone - which I think is possible now and will happen as the culture changes -  the people who are the early adopters are at risk of being bludgeoned with their own reproducibility. As a community, if we want widespread reproducibility adoption we have to be ferocious about not allowing this to happen.


The elements of data analytic style - so much for a soft launch

Editor's note: I wrote a book called Elements of Data Analytic Style. Buy it on Leanpub or Amazon! If you buy it on Leanpub, you get all updates (there are likely to be some) for free and you can pay what you want (including zero) but the author would be appreciative if you'd throw a little scratch his way. 

So uh, I was going to soft launch my new book The Elements of Data Analytic Style yesterday. I figured I'd just quietly email my Coursera courses to let them know I created a new reference. It turns out that that wasn't very quiet. First this happened:


and sure enough the website was down:


Screen Shot 2015-03-02 at 2.14.05 PM



then overnight it did something like 6,000+ units:





So lesson learned, there is no soft open with Coursera. Here is the post I was going to write though:


### Post I was gonna write

I have been doing data analysis for something like 10 years now (gulp!) and teaching data analysis in person for 6+ years. One of the things we do in my data analysis class at Hopkins is to perform a complete data analysis (from raw data to written report) every couple of weeks. Then I grade each assignment for everything from data cleaning to the written report and reproducibility. I've noticed over the course of teaching this class (and classes online) that there are many common elements of data analytic style that I don't often see in textbooks, or when I do, I see them spread across multiple books.

I've posted on some of these issues in some open source guides I've posted to Github like:

But I decided that it might be useful to have a more complete guide to the "art" part of data analysis. One goal is to summarize in a succinct way the most common difficulties encountered by practicing data analysts. It may be a useful guide for peer reviewers who could refer to section numbers when evaluating manuscripts, for instructors who have to grade data analyses, as a supplementary text for a data analysis class, or just as a useful reference. It is modeled loosely in format and aim on the Elements of Style by William Strunk. Just as with the EoS, both the checklist and my book cover a small fraction of the field of data analysis, but my experience is that once these elements are mastered, data analysts benefit most from hands on experience in their own discipline of application, and that many principles may be non-transferable beyond the basics. But just as with writing, new analysts would do better to follow the rules until they know them well enough to violate them.

The book includes a basic checklist that may be useful as a guide for beginning data analysts or as a rubric for evaluating data analyses. I'm reproducing it here so you can comment/hate/enjoy on it.


The data analysis checklist

This checklist provides a condensed look at the information in this book. It can be used as a guide during the process of a data analysis, as a rubric for grading data analysis projects, or as a way to evaluate the quality of a reported data analysis.
I Answering the question

1. Did you specify the type of data analytic question (e.g. exploration, assocation causality) before touching the data?
2. Did you define the metric for success before beginning?
3. Did you understand the context for the question and the scientific or business application?
4. Did you record the experimental design?
5. Did you consider whether the question could be answered with the available data?

II Checking the data

1. Did you plot univariate and multivariate summaries of the data?
2. Did you check for outliers?
3. Did you identify the missing data code?

III Tidying the data

1. Is each variable one column?
2. Is each observation one row?
3. Do different data types appear in each table?
4. Did you record the recipe for moving from raw to tidy data?
5. Did you create a code book?
6. Did you record all parameters, units, and functions applied to the data?

IV Exploratory analysis

1. Did you identify missing values?
2. Did you make univariate plots (histograms, density plots, boxplots)?
3. Did you consider correlations between variables (scatterplots)?
4. Did you check the units of all data points to make sure they are in the right range?
5. Did you try to identify any errors or miscoding of variables?
6. Did you consider plotting on a log scale?
7. Would a scatterplot be more informative?

V Inference

1. Did you identify what large population you are trying to describe?
2. Did you clearly identify the quantities of interest in your model?
3. Did you consider potential confounders?
4. Did you identify and model potential sources of correlation such as measurements over time or space?
5. Did you calculate a measure of uncertainty for each estimate on the scientific scale?

VI Prediction

1. Did you identify in advance your error measure?
2. Did you immediately split your data into training and validation?
3. Did you use cross validation, resampling, or bootstrapping only on the training data?
4. Did you create features using only the training data?
5. Did you estimate parameters only on the training data?
6. Did you fix all features, parameters, and models before applying to the validation data?
7. Did you apply only one final model to the validation data and report the error rate?

VII Causality

1. Did you identify whether your study was randomized?
2. Did you identify potential reasons that causality may not be appropriate such as confounders, missing data, non-ignorable dropout, or unblinded experiments?
2. If not, did you avoid using language that would imply cause and effect?

VIII Written analyses

1. Did you describe the question of interest?
2. Did you describe the data set, experimental design, and question you are answering?
3. Did you specify the type of data analytic question you are answering?
4. Did you specify in clear notation the exact model you are fitting?
5. Did you explain on the scale of interest what each estimate and measure of uncertainty means?
6. Did you report a measure of uncertainty for each estimate on the scientific scale?

IX Figures

1. Does each figure communicate an important piece of information or address a question of interest?
2. Do all your figures include plain language axis labels?
3. Is the font size large enough to read?
4. Does every figure have a detailed caption that explains all axes, legends, and trends in the figure?

X Presentations

1. Did you lead with a brief, understandable to everyone statement of your problem?
2. Did you explain the data, measurement technology, and experimental design before you explained your model?
3. Did you explain the features you will use to model data before you explain the model?
4. Did you make sure all legends and axes were legible from the back of the room?

XI Reproducibility

1. Did you avoid doing calculations manually?
2. Did you create a script that reproduces all your analyses?
3. Did you save the raw and processed versions of your data?
4. Did you record all versions of the software you used to process the data?
5. Did you try to have someone else run your analysis code to confirm they got the same answers?

XI R packages

1. Did you make your package name "Googleable"
2. Did you write unit tests for your functions?
3. Did you write help files for all functions?
4. Did you write a vignette?
5. Did you try to reduce dependencies to actively maintained packages?
6. Have you eliminated all errors and warnings from R CMD CHECK?



Navigating Big Data Careers with a Statistics PhD

Editor's note: This is a guest post by Sherri Rose. She is an Assistant Professor of Biostatistics in the Department of Health Care Policy at Harvard Medical School. Her work focuses on nonparametric estimation, causal inference, and machine learning in health settings. Dr. Rose received her BS in statistics from The George Washington University and her PhD in biostatistics from the University of California, Berkeley, where she coauthored a book on Targeted Learning. She tweets @sherrirose.

A quick scan of the science and technology headlines often yields two words: big data. The amount of information we collect has continued to increase, and this data can be found in varied sectors, ranging from social media to genomics. Claims are made that big data will solve an array of problems, from understanding devastating diseases to predicting political outcomes. There is substantial “big data” hype in the press, as well as business and academic communities, but how do upcoming, current, and recent statistical science PhDs handle the array of training opportunities and career paths in this new era? Undergraduate interest in statistics degrees is exploding, bringing new talent to graduate programs and the post-PhD job pipeline.  Statistics training is diversifying, with students focusing on theory, methods, computation, and applications, or a blending of these areas. A few years ago, Rafa outlined the academic career options for statistics PhDs in two posts, which cover great background material I do not repeat here. The landscape for statistics PhD careers is also changing quickly, with a variety of companies attracting top statistics students in new roles.  As a new faculty member at the intersection of machine learning, causal inference, and health care policy, I've already found myself frequently giving career advice to trainees.  The choices have become much more nuanced than just academia vs. industry vs. government.

So, you find yourself inspired by big data problems and fascinated by statistics. While you are a student, figuring out what you enjoy working on is crucial. This exploration could involve engaging in internship opportunities or collaborating with multiple faculty on different types of projects. Both positive and negative experiences can help you identify your preferences.

Undergraduates may wish to spend a couple months at a Summer Institute for Training in Biostatistics or National Science Foundation Research Experience for Undergraduates. There are also many MOOC options to get a taste of different areas ofstatistics. Selecting a graduate program for PhD study can be a difficult choice, especially when your interests within statistics have yet to be identified, as is often the case for undergraduates. However, if you know that you have interests in software and programming, it can be easy to sort which statistical science PhD programs have a curricular or research focus in this area by looking at department websites. Similarly, if you know you want to work in epidemiologic methods, genomics, or imaging, specific programs are going to jump right to the top as good fits. Getting advice from faculty in your department will be important. Competition for admissions into statistics and biostatistics PhD programs has continued to increase, and most faculty advise applying to as many relevant programs as is reasonable given the demands on your time and finances. If you end up sitting on multiple (funded) offers come April, talking to current students, student alums, and looking at alumni placement can be helpful. Don't hesitate to contact these people, selectively. Most PhD programs genuinely do want you to end up in the place that is best for you, even if it is not with them.

Once you're in a PhD program, internship opportunities for graduate students are listed each year by the American Statistical Association. Your home department may also have ties with local research organizations and companies with openings. Internships can help you identify future positions and the types of environments where you will flourish in your career. Lauren Kunz, a recent PhD graduate in biostatistics from Harvard University, is currently a Statistician at the National Heart, Lung, and Blood Institute (NHLBI) of the National Institutes of Health. Dr. Kunz said, "As a previous summer intern at the NHLBI, I was able to get a feel for the day to day life of a biostatistician at the NHLBI. I found the NHLBI Office of Biostatistical Research to be a collegial, welcoming environment, and I soon learned that NHLBI biostatisticians have the opportunity to work on a variety of projects, very often collaborating with scientists and clinicians. Due to the nature of these collaborations, the biostatisticians are frequently presented with scientifically interesting and important statistical problems. This work often motivates methodological research which in turn has immediate, practical applications. These factors matched well with my interest in collaborative research that is both methodological and applied."

Industry is also enticing to statistics PhDs, particularly those with an applied or computational focus, like Stephanie Sapp and Alyssa Frazee. Dr. Sapp has a PhD in statistics from the University of California, Berkeley, and is currently a Quantitative Analyst at Google. She also completed an internship there the summer before she graduated. In commenting about her choice to join Google, Dr. Sapp said,  "I really enjoy both academic research and seeing my work used in practice.  Working at Google allows me to continue pursuing new and interesting research topics, as well as see my results drive more immediate impact."  Dr. Frazee just finished her PhD in biostatistics at Johns Hopkins University and previously spent a summer exploring her interests in Hacker School.  While she applied to both academic and industry positions, receiving multiple offers, she ultimately chose to go into industry and work for Stripe: "I accepted a tech company's offer for many reasons, one of them being that I really like programming and writing code. There are tons of opportunities to grow as a programmer/engineer at a tech company, but building an academic career on that foundation would be more of a challenge. I'm also excited about seeing my statistical work have more immediate impact. At smaller companies, much of the work done there has visible/tangible bearing on the product. Academic research in statistics is operating a lot closer to the boundaries of what we know and discovering a lot of cool stuff, which means researchers get to try out original ideas more often, but the impact is less immediately tangible. A new method or estimator has to go through a lengthy peer review/publication process and be integrated into the community's body of knowledge, which could take several years, before its impact can be fully observed."  One of Dr. Frazee, Dr. Sapp, and Dr. Kunz's considerations in choosing a job reflects many of those in the early career statistics community: having an impact.

Interest in both developing methods and translating statistical advances into practice is a common theme in the big data statistics world, but not one that always leads to an industry or government career. There are also academic opportunities in statistics, biostatistics, and interdisciplinary departments like my own where your work can have an impact on current science.  The Department of Health Care Policy (HCP) at Harvard Medical School has 5 tenure-track/tenured statistics faculty members, including myself, among a total of about 20 core faculty members. The statistics faculty work on a range of theoretical and methodological problems while collaborating with HCP faculty (health economists, clinician researchers, and sociologists) and leading our own substantive projects in health care policy (e.g., Mass-DAC). I find it to be a unique and exciting combination of roles, and love that the science truly informs my statistical research, giving it broader impact. Since joining the department a year and a half ago, I've worked in many new areas, such as plan payment risk adjustment methodology. I have also applied some of my previous work in machine learning to predicting adverse health outcomes in large datasets. Here, I immediately saw a need for new avenues of statistical research to make the optimal approach based on statistical theory align with an optimal approach in practice. My current research portfolio is diverse; example projects include the development of a double robust estimator for the study of chronic disease, leading an evaluation of a new state-wide health plan initiative, and collaborating with department colleagues on statistical issues in all-payer claims databases, physician prescribing intensification behavior, and predicting readmissions. The larger statistics community at Harvard also affords many opportunities to interact with statistics faculty across the campus, and university-wide junior faculty events have connected me with professors in computer science and engineering. I feel an immense sense of research freedom to pursue my interests at HCP, which was a top priority when I was comparing job offers.

Hadley Wickam, of ggplot2 and Advanced R fame, took on a new role as Chief Scientist at RStudio in 2013. Freedom was also a key component in his choice to move sectors: "For me, the driving motivation is freedom: I know what I want to work on, I just need the freedom (and support) to work on it. It's pretty unusual to find an industry job that has more freedom than academia, but I've been noticeably more productive at RStudio because I don't have any meetings, and I can spend large chunks of time devoted to thinking about hard problems. It's not possible for everyone to get that sort of job, but everyone should be thinking about how they can negotiate the freedom to do what makes them happy. I really like the thesis of Cal Newport's book So Good They Can't Ignore You - the better you are at your job, the greater your ability to negotiate for what you want."

There continues to be a strong emphasis in the work force on the vaguely defined field of “data science,” which incorporates the collection, storage, analysis, and interpretation of big data.  Statisticians not only work in and lead teams with other scientists (e.g., clinicians, biologists, computer scientists) to attack big data challenges, but with each other. Your time as a statistics trainee is an amazing opportunity to explore your strengths and preferences, and which sectors and jobs appeal to you. Do your due diligence to figure out which employers are interested in and supportive of the type of career you want to create for yourself. Think about how you want to spend your time, and remember that you're the only person who has to live your life once you get that job. Other people's opinions are great, but your values and instincts matter too. Your definition of "best" doesn't have to match someone else's. Ask questions! Try new things! The potential for breakthroughs with novel flexible methods is strong. Statistical science training has progressed to the point where trainees are armed with thorough knowledge in design, methodology, theory, and, increasingly, data collection, applications, and computation.  Statisticians working in data science are poised to continue making important contributions in all sectors for years to come. Now, you just need to decide where you fit.