“If the reader is to grasp what the writer means, the writer must understand what the reader needs.

“Science is often hard to read. Most people assume that its difficulties are born out of necessity, out of the extreme complexity of scientific concepts, data and analysis. We argue here that complexity of thought need not lead to impenetrability of expression; we demonstrate a number of rhetorical principles that can produce clarity in communication without oversimplifying scientific issues. The results are substantive, not merely cosmetic: Improving the quality of writing actually improves the quality of thought.”

“This is an introductory course in machine learning (ML) that covers the basic theory, algorithms, and applications. ML is a key technology in Big Data, and in many financial, medical, commercial, and scientific applications. It enables computational systems to adaptively improve their performance with experience accumulated from the observed data. ML has become one of the hottest fields of study today, taken up by undergraduate and graduate students from 15 different majors at Caltech. This course balances theory and practice, and covers the mathematical as well as the heuristic aspects. The lectures below follow each other in a story-like fashion:

What is learning?

Can a machine learn?

How to do it?

How to do it well?

Take-home lessons.

“The 18 lectures are about 60 minutes each plus Q&A.”

Centering continuous independent variables was one of the earliest lessons in my linear regression class. I was recently asked to explain, “what’s the point?” of going through the trouble of centering? I was at a loss, and realized I had been assuming the answer was obvious when it was not.

After a quick google, this article explained the answer well. In short, centering is useful when interpreting the intercept is important. Here example of age of development of language in infants. Her original article has been copied below.

Should You Always Center a Predictor on the Mean?

by Karen Grace-Martin

Centering predictor variables is one of those simple but extremely useful practices that is easily overlooked.

It’s almost too simple.

Centering simply means subtracting a constant from every value of a variable. What it does is redefine the 0 point for that predictor to be whatever value you subtracted. It shifts the scale over, but retains the units.

The effect is that the slope between that predictor and the response variable doesn’t change at all. But the interpretation of the intercept does.

The intercept is just the mean of the response when all predictors = 0. So when 0 is out of the range of data, that value is meaningless. But when you center X so that a value within the dataset becomes 0, the intercept becomes the mean of Y at the value you centered on.

What’s the point? Who cares about interpreting the intercept?

It’s true. In many models, you’re not really interested in the intercept. In those models, there isn’t really a point, so don’t worry about it.

But, and there’s always a but, in many models interpreting the intercept becomes really, really important. So whether and where you center becomes important too.

A few examples include models with a dummy-coded predictor, models with a polynomial (curvature) term, and random slope models.

Let’s look more closely at one of these examples.

In models with a dummy-coded predictor, the intercept is the mean of Y for the reference category—the category numbered 0. If there’s also a continuous predictor in the model, X2, that intercept is the mean of Y for the reference category only when X2=0.

If 0 is a meaningful value for X2 and within the data set, then there’s no reason to center. But if neither is true, centering will help you interpret the intercept.

For example, let’s say you’re doing a study on language development in infants. X1, the dummy-coded categorical predictor, is whether the child is bilingual (X1=1) or monolingual (X1=0). X2 is the age in months when the child spoke their first word, and Y is the number of words in their vocabulary for their primary language at 24 months.

If we don’t center X2, the intercept in this model will be the mean number of words in the vocabulary of monolingual children who uttered their first word at birth (X2=0).

And since infants never speak at birth, it’s meaningless.

A better approach is to center age at some value that is actually in the range of the data. One option, often a good one, is to use the mean age of first spoken word of all children in the data set.

This would make the intercept the mean number of words in the vocabulary of monolingual children for those children who uttered their first word at the mean age that all children uttered their first word.

One problem is that the mean age at which infants utter their first word may differ from one sample to another. This means you’re not always evaluating that mean that the exact same age. It’s not comparable across samples.

So another option is to choose a meaningful value of age that is within the values in the data set. One example may be at 12 months.

Under this option the interpretation of the intercept is the mean number of words in the vocabulary of monolingual children for those children who uttered their first word at 12 months.

The exact value you center on doesn’t matter as long it’s meaningful, holds the same meaning across samples, and within the range of data. You may find that choosing the lowest value or the highest value of age is the best option. It’s up to you to decide the age at which it’s most meaningful to interpret the intercept.

“How not to collaborate with a biostatistician. This is what happens when two people are speaking different research languages! My current workplace is nothing like this, but I think most biostatisticians have had some kind of similar experiences like this in the past!”

Covariance and correlation are two statistical concepts that are closely related, both conceptually and by their name. The excerpts below are from a concise article that differentiates them.

Difference Between Covariance and Correlation

“Correlation is a special case of covariance which can be obtained when the data is standardised. Now, when it comes to making a choice, which is a better measure of the relationship between two variables, correlation is preferred over covariance, because it remains unaffected by the change in location and scale, and can also be used to make a comparison between two pairs of variables.”

Key Differences Between Covariance and Correlation

“The following points are noteworthy so far as the difference between covariance and correlation is concerned:

“A measure used to indicate the extent to which two random variables change in tandem is known as covariance. A measure used to represent how strongly two random variables are related known as correlation.

“Covariance is nothing but a measure of correlation. On the contrary, correlation refers to the scaled form of covariance.

“The value of correlation takes place between -1 and +1. Conversely, the value of covariance lies between -∞ and +∞.

“Covariance is affected by the change in scale, i.e. if all the value of one variable is multiplied by a constant and all the value of another variable are multiplied, by a similar or different constant, then the covariance is changed. As against this, correlation is not influenced by the change in scale.

“Correlation is dimensionless, i.e. it is a unit-free measure of the relationship between variables. Unlike covariance, where the value is obtained by the product of the units of the two variables.”

Before forecasting its future, there is likely merit in explaining what physiatry is.

What is Physiatry/PM&R?

“Physiatry, also known as pain management and rehabilitation (PM&R) is a branch of medicine that aims to enhance and restore functional ability and quality of life to those with physical impairments or disabilities.”

– Wikipedia

Medicine tends to be sterile. When the end goal is reduced to keeping the patient alive, or moving a lab value within its appropriate range, doctors can forget to be human. Resources are stretched thin in a county hospital in a large metropolitan area. Providers are only attending to biological issues because they are prioritizing scarce resources. They are not trained to deal with the more pressing, social issues. What is the point in treating a patient’s asthma, discharging them back to the streets, waiting for another exacerbation, and then rounding on them next week after they’ve been admitted once again from the ER? Patients like these need social work and preventive public health measures. Instead they get expensive medications once every few months. Medical care can feel calloused and at times even cruel.

On the other end of the spectrum, there are fields based entirely in human connection, but they lack teeth. Naturopathy and alternative medicines have either been shown to have no efficacy, or there is no incentive to research them because they are assumed to be entirely based on the placebo effect. Sometimes people need to be heard and feel connected with their provider. These fields take advantage of this, and patients may be happier, albeit less healthy.

PM&R is western medicine that focuses on the patient’s function and quality of life. Chronic pain patients have sifted through the medical system, frustrated by the lack of resolution to their pain. They’ve stumped doctors who cannot do anything for them because all of their lab values are correct and they seem healthy enough by the protocol standards. Surgeons will happily perform surgery, but it seems a drastic move exposing patients to serious risks, which can be minimized or ignored during the pre-op. Surgery may be the best option for some, but certainly not all of these patients. Physiatry can offer medical treatment, alongside physical therapy for a multidisciplinary approach to increasing patient health and quality of life.

But it turns out, not many procedures used by physiatrists have been supported by clinical evidence.

Dr. Braddom Predicts the Future of PM&R

Dr. Randall Braddom is a clinical professor of physiatry. While at Rutgers Medical School in 2014, he gave a 100-Slide PowerPoint presentation that concisely summarizes the field of PM&R and it’s future direction from his perspective. Dr. Braddom acknowledges how worthless predictions of the future often are, but an experienced physician creating a deep portrayal of their specialty is worth far more than SDN forums.

According to Dr. Braddom, the field of physiatry is placing more value on research. One of the reasons is that physiatric procedures have not been validated in randomized clinical trials, and insurance companies are eliminating reimbursements for procedures without scientific evidence supporting their efficacy. The large proportion of physiatrist in clinical practice may see large reductions in their financial reimbursement for some of their procedures, such as sacroiliac and Z-joint (zygapophysial) injections. A whole field of doctors potentially not getting paid for their work may be a powerful force. It seems that clinical research opportunities in PM&R will likely thrive in the near future.

Below are select few slides from Dr. Braddom’s presentation.

PM&R Research will Boom Soon

Trend to Evidence Based Medicine

Evidence Basis of PM&R is Significantly limited due to:

Variability/complexity

Limited research

Distance from molecular biology

Clinical studies lack analytical rigor

Research is Critical for PM&R Practice

Outcome Studies are key to practice survival

Randomized controlled trials (RCT’s)

Almost no other kind of research is taken seriously

Uncontrolled research is only a pilot study, at best

Laboratory moving closer to the bedside

New emphasis on Evidence Based Medicine in Health Care Reform

Few Physiatrists Have Become High Quality Researchers

Physiatric personality: people oriented rather than rat oriented

“It has also been generally agreed that Rehabilitation research has not done well in fulfilling its objective of providing a foundation of knowledge for rehabilitation practice.”

Lieberman (1993)

AAPMR LNA: 2004 Physiatric Effort Report

Outpatient 50%

Inpatient 23%

Administration 10%

Teaching/CME 4%

Research 3%

Miscellaneous 10%

What to Do After Residency

2014 ABPMR Subspecialty Exams for Physiatrists

Sports Medicine

Neuromuscular Medicine

Pain Medicine

Hospice and Palliative Medicine

Pediatric Rehabilitation Medicine

Spinal Cord Injury Medicine

Brain Injury Medicine

What Percentage of Residents Join Orthopedic Groups?

22%

Range from 10-40%

On residents joining Orthopedic groups:

“This is a sin against humanity!”

– PM&R Chair

From reading forums, it sounds like being a physiatrists working in an orthopedic practice may be a horrible experience. Surgeons with large personalities shunt all their conservative preventive care to one physiatrist on the team because it is a waste of their time to do injections when there are more challenging surgeries to be performed.

I personally would not want to spend so much time in training to be looked down upon or taken advantage of financially during my day to day practice. I don’t see the allure to working in orthopedic groups that the 22% of survey respondents said they are doing.

PM&R is a Great Field

Patients appreciate what we do

Not limited by an organ

Jobs of all types available

Population demographics favor us

Good balance of procedure/E&M

Many academic opportunities

Good physiatric profile/nice people

Small (10,000)

PM&R is focused on patient outcomes and quality of life. There are a wide variety of procedures, subspecialties, and practice styles within physiatry. Dr. Braddom presented many trends in the field as of 2014, and where he expects it to head in the future. He underscores the growing research opportunities in PM&R, the breadth of fellowships for sub-specialization, and that working in an orthopedic group may be less than ideal. Regardless of his prophecies, as of now physiatry looks like a promising career path.

Academic medicine training is a long road via internal medicine.

Minimum Training Requirement in the Subspecialty Research Pathway

DISCIPLINE

IM

CLINICAL

TRAINING

SS

CLINICAL

TRAINING

RESEARCH

TRAINING

(80%)

TOTAL

TRAINING

EXAM

ADMINISTRATION

ELIGIBILITY

Adolescent Medicine
Allergy & Immunology
Critical Care Medicine
Endocrinology, Diabetes, & Metabolism
Geriatric Medicine
Hematology
Hospice & Palliative Medicine
Infectious Disease
Nephrology
Medical Oncology
Pulmonary Disease
Rheumatology
Sleep Medicine
Sports Medicine

24 months

12 months

36 months

72 months/

6 years

Fall, PGY-6

Gastroenterology
Hematology/Medical Oncology
Pulmonary/Critical Care Medicine
Rheumatology/Allergy & Immunology

24 months

18 months

36 months

78 months/

6.5 years

Fall, PGY-7

Cardiovascular Disease

24 months

24 months

36 months

84 months/

7 years

Fall, PGY-7

Tertiary certification

Add the minimum clinical requirement of the subspecialty to the Research Pathway

Transplant Hepatology

24 months

30 months

(18 GI +

12 T-HEP)

36 months

90 months/

7.5 years

Fall, PGY-8

Advance Heart Failure & Transplant Cardiology

24 months

36 months

(24 CVD +

12 AHFTC)

36 months

96 months/

8 years

Fall, PGY-8

Interventional Cardiology

24 months

36 months

(24 CVD +

12 ICARD)

36 months

96 months/

8 years

Fall, PGY-8

Adult Congenital Heart Disease

24 months

42 months

(24 CVD +

18 ACHD)

36 months

102 months/

8.5 years

Fall, PGY-9

Clinical Cardiac Electrophysiology

24 months

48 months

(24 CVD +

24 CCEP)

36 months

108 months/

9 years

Fall, PGY-9

Internal medicine training requires 20 months direct patient responsibility

Ambulatory clinics during research training (10%) ½ day per week

IM exam administration eligibility, Summer PGY-4

All other standard ABIM requirements for ABIM initial certification eligibility must be met

The Importance of Stupidity in Scientific Research

“Science makes me feel stupid too. It’s just that I’ve gotten used to it. So used to it, in fact, that I actively seek out new opportunities to feel stupid. I wouldn’t know what to do without that feeling. I even think it’s supposed to be this way.”

The more comfortable we become with being stupid, the deeper we will wade into the unknown and the more likely we are to make big discoveries.

“Productive stupidity means being ignorant by choice. Focusing on important questions puts us in the awkward position of being ignorant. One of the beautiful things about science is that it allows us to bumble along, getting it wrong time after time, and feel perfectly fine as long as we learn something each time. No doubt, this can be difficult for students who are accustomed to getting the answers right. No doubt, reasonable levels of confidence and emotional resilience help, but I think scientific education might do more to ease what is a very big transition: from learning what other people once discovered to making your own discoveries. The more comfortable we become with being stupid, the deeper we will wade into the unknown and the more likely we are to make big discoveries.”