Odds Ratio, Risk Ratio, and Prevalence Ratio

Odds Ratio, Risk Ratio, and Prevalence Ratio

Deddens (2008). Approaches for estimating prevalence ratios.

Petersen (2008). A comparison of two methods for estimating prevalence ratios.
Lumley (2006). Relative Risk Regression in Medical Research: Models, Contrasts,Estimators, and Algorithms.

Spiegelman (2005). Easy SAS calculations for risk or prevalence ratios and differences.
Santos (2008). Estimating adjusted prevalence ratio in clustered cross-sectional epidemiological data.
Savu (2009). Estimation of relative risk and prevalence ratio (pdf).
Barros (2003). Alternatives for logistic regression in cross-sectional studies. (using Stata)
Lee (1993). Estimation of prevalence rate ratios for cross sectional data: an example in occupational epidemiology, and (1994) Use of the prevalence ratio v the prevalence odds ratio as a measure of risk in cross sectional studies.
Thompson (1998). Prevalence odds ratio or prevalence ratio in the analysis of cross sectional data: what is to be done?

How can I estimate relative risk using glm for common outcomes in cohort studies using Stata or SAS? Source: UCLA Statistical Computing.

Understanding RR Ratios in Multinomial Logistic Regression. Source: UCLA Statistical Computing.

Special issue on lipotoxicity

Special Issue on Lipotoxicity

Source: Biochimica et Biophysica Acta 2010;1801(3)

Editors: A. Vidal-Puig & R.Unger

“It was sometime in March 2009 when our colleague Fritz Spener first proposed a special issue of BBA Molecular and Cell Biology of Lipids focused on the concept of lipotoxicity and its relevance as an integrative pathogenic mechanism of the metabolic syndrome. Although we might have hesitated a little initially, this did not last long as we realised that: a) ours would be a unique, high quality publication addressing the topic in depth and globally; b) this is an important area of research with enormous implications for metabolic disease and, in our opinion, its relevance is underestimated and relatively unknown among both the biomedical community and general public; and c) the great opportunities offered by new technologies and experimental models to understand the role of lipotoxicity in common metabolic diseases makes this a very timely issue. And also, of course, we expected strong support from the “lipotoxic community”. Certainly we have not been disappointed. In fact our colleagues have provided enormous support and their generosity has made this issue viable. Our only regret is that we have not been able to involve as many of the key experts as we wanted due to space constrains and the time scale of the project, and we hope this will not be the cause of any lost friendships!”


Here is the special issue: Special issue on lipotoxicity.

This issue isn’t new. I have got the similar hypothesis after I attended a lecture by J. Denis McGarry in 2001 (In memory of Dr. John Denis McGarry. His article "What if Minkowski Had Been Ageusic?"  is on the wall of my office all the time). I put this special issue on my blog to remind me keeping work on this hypothesis.

In Dieting, Magic Isn’t a Substitute for Science

In Dieting, Magic Isn't a Substitute for Science

By GINA KOLATA

 "Is a calorie really just a calorie? Do calories from a soda have the same effect on your waistline as an equivalent number from an apple or a piece of chicken?"

 Read full article here: In Dieting, Magic Isn't a Substitute for Science

Studies of Human Microbiome Yield New Insights

Studies of Human Microbiome Yield New Insights
Source: NYTimes.com by Carl Zimmer
"For a century, doctors have waged war against bacteria, using antibiotics as their weapons. But that relationship is changing as scientists become more familiar with the 100 trillion microbes that call us home - collectively known as the microbiome.
...". Read full article here.
There is also a story about Zhao Liping combines traditional Chinese medicine and studies of gut microbes to understand and fight obesity on the Nature: My Microbiome and Me.

Revolutions: The role of Statistics in the Higgs Boson discovery

The role of Statistics in the Higgs Boson discovery
Source: Revolution Analytics
News is starting to leak that the Large Hadron Collider may have accomplished its primary mission of confirming the existence of the hypothesised and heretofore elusive subatomic particle, the Higgs Boson. And sure, billions of Euros worth of state-of-the-art high-energy machinery and an army of experimental and theoretical physicists probably had something to do with the discovery. But did you know Statistics played a part as well? Check out this explainer video from PhD comics, below (an R chart even appears at the 00:27 mark):
Full text: here

What's in the world is a Higgs Boson? Source: NYTimes.com


The Higgs Boson Explained from PHD Comics on Vimeo.

Stata articles

Stata Articles

• Cummings (2009). Methods for estimating adjusted risk ratios (pdf).
• Multiple imputation of missing values: further update of ice, with an emphasis on interval censoring (2007).
• Royston (2001). Flexible parametric alternatives to the Cox model, and more (stpm) (pdf).
• Lambert & Royston (2009). Further development of flexible parametric models for survival analysis (stpm2) (pdf).
• ...

How to Get Into Stanford with B’s on Your Transcript

How to Get Into Stanford with B's on Your Transcript
Source: Study Hacks by Cal Newport
"Let's try a simple experiment. Imagine that you're an admissions officer at a competitive college, and you're evaluating the following two applicants:
•David — He is captain of the track team and took Japanese calligraphy lessons throughout high school; he wrote his application essay on the challenge of leading the track team to the division championship meet.
•Steve — He does marketing for a sustainability-focused NGO; he wrote his application essay about lobbying delegates at the UN climate change conference in Johannesburg, South Africa.
Who impresses you more?
..."
This is an article recommended by my daughter. You can find the full text here: How to Get Into Stanford with B's on Your Transcript

"...

Lassiter’s Insight

What happened inside your brain when you read the descriptions of David and Steve? According to a clever series of experiments conducted by G. Daniel Lassiter, a psychology professor at the University of Ohio, your first response was to look into the proverbial mirror. Or, as Lassiter describes it, somewhat more formally,  in his 2002 paper on the subject: we have a “pervasive tendency…to use the self as a standard of comparison in [our] dispassionate judgments of others.”

Put another way, to evaluate a person’s accomplishments, we imagine ourselves attempting the same feat, allowing your own capabilities to provide a convenient benchmark for assessing others’.

(In Lassiter’s experiments, students took tests made up of difficult mathematical puzzles. He showed that when a student was asked to rate the intelligence of another student, this judging student used a self-assessment of his own intelligence, combined with how well he did on the test, to construct the rating.)

Let’s walk through the logic here. When you first encountered David and Steve, your brain began to compare them to yourself. In essence, your brain asked: “Could I do that? And if so, what would it require?”

...:

This is my test run using GoogleVis, a R! package

My test-run using GoogleVis, a R! package

This week, I attended a R! training class instructed by Dr. Aedin Culhane, a wonderful teacher. I was taught that I can use the GoogleVis, a R! package, to draw a moving bubble plot. It's amazing. Here is the output we used in the class.
    R! Codes: library(googleVis)
             M <- gvisMotionChart(Fruits, "Fruit", "Year")
             plot(M)
             cat(M$html$chart, file="tmp.html")
Here is the more information about: Using the Google Visualisation API with R

Data: Fruits • Chart ID: MotionChartIDed077347ee8
R version 2.15.0 (2012-03-30) • googleVis-0.2.16 • Google Terms of Use • Data Policy

FW: A Firm Diagnosis of Frailty - NYTimes.com

A Firm Diagnosis of Frailty
Source: NYTimes.com


... After years of observing and working with older patients, Dr. Fried recognized objective hallmarks of frailty, and in the 1990s developed a definition of frailty in people 65 and older that called for the diagnosis when three or more of the following five criteria were present: unintentional weight loss of 10 pounds or more in the past year, self-reported exhaustion, weakness as measured by grip strength, slow walking speed and low physical activity. The presence of one or two of those criteria would identify a person as "pre-frail."

Update on the alternative to HOMA-IR and HOMA-b

Update on the HOMA-IR and HOMA-b
Source:  iHOMA2
iHOMA2 is an interactive, 24-variable, HOmeostatic Model of Assessment with the baseline default characteristics of the HOMA2 computer model of fasting insulin:glucose interaction. iHOMA2 enables the mathematical functions describing the organs and tissues involved in the glucose and hormonal compartments to be modified using simple visual analogue controls. The model can be used to evaluate therapeutic agents and predict effects on fasting glucose and insulin and on beta cell function and insulin sensitivity.

Here is the main URL for the iHOMA2 website.

I am not a fan of iHOMA2; I post it here as a future reference.

Joslin's Diabetes Deskbook, A Guide for Primary Care Providers, Updated 2nd Ed., Excerpt 2: Do You Know the Conditions that May Cause Inaccurate Results from the A1C Test?

Joslin's Diabetes Deskbook, A Guide for Primary Care Providers, Updated 2nd Ed., Excerpt 2: Do You Know the Conditions that May Cause Inaccurate Results from the A1C Test?
By Richard S. Beaser, M.D.


"... With respect to the testing methodology, when HPLC laboratory techniques are used to perform measurements, the number of things that can affect the test results is limited. Using this methodology, the most common factors that can affect A1C measurements are:

• Hemolytic anemias Carbamylated and acetylated hemoglobins (rare).
• "Fast" migrating hemoglobins, most commonly hemoglobins D, J, and N, can lower readings.
• Fetal hemoglobin greater than 25% interferes with hemoglobin A1c measurement and cannot be corrected for.
• True beta-thalassemia will interfere with some HPLC methods, but the patient has to be symptomatic at the time for the effect to be significant.
• Severe lipemia in some patients can interfere with measurements. Interference can be reduced by washing red cells and making an offline dilution to report out the A1C value
• Taking medications such as salicylates can have an effect, though rarely ..."

Fatty Liver Disease in Diabetes: Good and Bad?

Fatty Liver Disease in Diabetes: Good and Bad?


When the enzyme called histone deacetylase 3 (HDAC3) was removed, the mice had massively fatty livers, but lower blood sugar, and were thus protected from glucose intolerance and insulin resistance....


The findings demonstrate that fat itself is not necessarily all bad. "It matters a lot how fat is handled and stored," notes Lazar. "It also highlights the importance of complying with our internal circadian clock. For example, since our body does not anticipate food at night and is preparing to generate more glucose, night-time eating is likely to shoot up blood sugar and thus may contribute to diabetes."


The full text here.
The original article here.

Metabolic surgery for type 2 diabetes and obesity related - Nature Medicine

Metabolic surgery for type 2 diabetes

David E Cummings

Clinicians note that bariatric operations can dramatically resolve type 2 diabetes, often before and out of proportion to postoperative weight loss. Now two randomized controlled trials formally show superior results from surgical compared with medical diabetes care, including among only mildly obese patients. The concept of 'metabolic surgery' to treat diabetes has taken a big step forward.

Full Text | PDF

Topic: Guts over glory - why diets fail

Rachel Larder and Stephen O'Rahilly

Losing weight can pose a challenge, but how to avoid putting those pounds back on can be a real struggle. A major health problem for obese people is that diseases linked to obesity, such as type 2 diabetes and cardiovascular disease, put their lives at risk, even in young individuals. Although bariatric surgery[mdash]a surgical method to reduce or modify the gastrointestinal tract[mdash]was originally envisioned for the most severe cases of obesity, evidence suggests that the benefit of this procedure may not be limited to the staggering weight loss it causes. Endogenous factors released from the gut, and modified after surgery, may explain why bariatric surgery can be beneficial for obesity-related diseases and why operated individuals successfully maintain the weight loss. In 'Bedside to Bench,' Rachel Larder and Stephen O'Rahilly peruse a human study with dieters who regained weight despite a successful diet. Appetite-regulating hormones in the gut may be responsible for this relapse in the long term. In 'Bench to Bedside,' Keval Chandarana and Rachel Batterham examine how two different methods of bariatric surgery highlight the relevance of gut-derived hormones not only in inducing sustained weight loss but also in improving glucose homeostasis. These insights may open new avenues to bypass the surgery and obtain the same results with targeted drugs.

Full Text | PDF

Topic: Metabolic insights from cutting the gut

Keval Chandarana and Rachel L Batterham

Losing weight can pose a challenge, but how to avoid putting those pounds back on can be a real truggle. A major health problem for obese people is that diseases linked to obesity, such as type 2 diabetes and cardiovascular disease, put their lives at risk, even in young individuals. Although bariatric surgery[mdash]a surgical method to reduce or modify the gastrointestinal tract[mdash]was originally envisioned for the most severe cases of obesity, evidence suggests that the benefit of this procedure may not be limited to the staggering weight loss it causes. Endogenous factors released from the gut, and modified after surgery, may explain why bariatric surgery can be beneficial for obesity-related diseases and why operated individuals successfully maintain the weight loss. In 'Bedside to Bench,' Rachel Larder and Stephen O'Rahilly peruse a human study with dieters who regained weight despite a successful diet. Appetite-regulating hormones in the gut may be responsible for this relapse in the long term. In 'Bench to Bedside,' Keval Chandarana and Rachel Batterham examine how two different methods of bariatric surgery highlight the relevance of gut-derived hormones not only in inducing sustained weight loss but also in improving glucose homeostasis. These insights may open new avenues to bypass the surgery and obtain the same results with targeted drugs.

Full Text | PDF 

Stata: useful and Interesting user-written ado programs

Stata: Useful and Interesting User-written ado Programs/packages
Manage the ado programs

• Stata Syntax-highlighting for Notepad++ or download from the Notepad++ website
• Syntax Highlight Packages (Dynamic documents in Stata: MarkDoc, Ketchup, and Weaver): Synlight, Weaver, MarkDoc
• Determine build-in command or ado-file: which command
• Check codes: viewsource command or type "directory\xxx.ado"
• list of the packages: ado dir
• Install: ssc install package [,replace]
• ssc describe { pkgname | letter }: Describe a specified package at SSC
• check update: adooupdate
• update: adoupdate, update
• uninstall: ado uninstall package|[#]
• re-run profile.do: do profile.do

A list of ado packages I am using (. ssc install -package-)

• -groups- Stata module to list group frequencies. Speaking Stata (2017): Tables as Lists: The Groups Command. groups updated on SSC
• -fre- Stata module to display one-way frequency table
• -vioplot- Stata module to produce violin plots with current graphics
• -qqplot3- Stata module to plot the unweighted and weighted quantiles of one variable against the corresponding quantiles of another
• -qreg2- Stata module to perform quantile regression with robust and clustered standard errors
• -intcens- Stata module to perform interval-censored survival analysis, which is a program that fits parametric _continuous_ survival time distributions to interval-censored survival time data. The program doesn't allow
  time-varying covariates.
• -midiagplots-, a user-written ado, makes diagnostic plots for multiple imputations created by mi impute.
• -fitstat-, a user-written program is to compute fit statistics for single equation regression models.
• -mgof-, a user-written goodness-of-fit tests for the distribution/multinomial data, can deals with the survey design svy(). Jann (2008).Multinomial goodness–of–fit
• -relrank- is to generate relative data (Relative Distribution Methods in Stata)
• -svr- is a user-written program to comupte estimates with survey replication based standard errors. The -survwgt- command creates brr, jk1, jk2 and jkn replicate weights.
• -somersd- is a package to calculate Kendall's tau-a, Somers'D, AUC (Harrell's c). It can deal with the complex survey design. UCLA idre
• -st0314- Attributable and unattributable risks and fractions and other scenario comparisons (can deal with complex sampled data)
• -svylorenz-, -sumdist- Jenkins (2006): calculate Gini/Lorenz/inequality from complex survey data, summary of income distributions
• -stpm2- (slides), a extension of - stpm -, include improvement in the way time-dependent covariates are modeled; the ability to incorporate expected mortality and thus fit relative survival models; and a superior predict command that enables simple quantification of differences between any two covariate patterns through calculation of time-dependent hazard ratios, hazard differences, and survival differences. stpm has a option "left(leftvar)" to dealing with interval-censored data, and stpm2 does not have an option to deal with interval censoring (checked @ 04/016/2016, wish they could have added it).
• -tabstat- Stata module to produce and export table of results in a matricial format.
• -univar- How can I get descriptive statistics and the five number summary on one line?
• -outreg2- The 'outreg2' is based on the earlier package 'outreg' but has much more features.
• -tabout- is a table building program for oneway and twoway tables of frequencies and percentages, and for summary tables.
• -estout- How can I use -estout- to make regression tables that look like those in journal articles?
• -renvar- Stata module to rename variables
• -wridit- Stata module to generate weighted ridits
• -gtools- Faster Stata for big data. This packages uses C plugins and hashes to provide a massive speed improvements to common Stata commands.
• -ftools- A faster Stata for large datasets (Sergio's slides)
• -psmatch2- implements full Mahalanobis matching and a variety of propensity score matching methods
• -psmatch2- vs. - teffects psmatch- 

Other Resources for adding features to Stata by Stata

R Is Not Enough For "Big Data"

R Is Not Enough For "Big Data"

by Douglas Merrill

“… // Side note 1: I was an undergraduate at the University of Tulsa, not a school that you’ll find listed on any list of the best undergraduate schools.  I did pretty well at Princeton in my doctoral studies.  I’ve hired a lot of people from “bad” schools — like Washington State University — that have been very successful.  Although school is a decent proxy for intellectual horsepower, it’s only a proxy — I believe that the top 1% at any school will likely be pretty awesome.  The hard part is finding that 1%, because there’s likely a material difference between the mean of a second-rate school and the mean of a, say, Harvard. //

// Side note 3: OK, I’m about to take some real liberties with the math here, to help make my point.  All the real mathematicians out there are going to experience almost uncontrollable body twitches over the next few paragraphs.  Breathe deeply, it will pass.  //

// Side note 3: There are all kinds of mathematical problems with most regression models, notably that few things are linearly related and that many things have “correlated errors”, but I’ll leave that to Wikipedia if you’re interested. // …”

Full text here

In pursuit of scientific excellence: sex matters

In pursuit of scientific excellence: sex matters
by Virginia M. Miller
The comments of this article is from the perspective of biology, but may help us to understand existed sex/gender arguments from the perspective of public health.
"...
In the era of physiological genomics and individualized medicine, the presence of an XX or XY chromosomal complement is fundamental to the genome of an individual person, animal, tissue, or cell. Every cell has a sex.
Therefore, based on existing knowledge, it is inappropriate to assume that results from studies conducted on only one sex apply to the other (13). For some studies of neonates and embryos, cells derived from males and females are mixed in a single culture and should be reported as such. The scientific community needs to determine whether this technique is valid by providing sufficient data to control and confirm survival, differentiation, and function of cells of each sex. Similarly, cell-based therapies need to validate survival and function of the cell graft in the same- and opposite-sexed recipients.
...
How then should the sex of experimental material be reported? Use of the terms "sex" and "gender" has evolved over the last decade. According to definitions proposed by the Institute of Medicine (23), "sex" is a biological construct dictated by the presence of sex chromosomes and in animals and humans the presence of functional reproductive organs. "Gender" is a cultural construct and refers to behaviors that might be directed by specific stimuli (visual, olfactory, etc.) or by psychosocial expectations that result from assigned or perceived sex. Gender, thus, can influence biological outcomes. In most studies conducted on isolated cells, tissues can be classified as male or female by the sex chromosomal complement and for experimental animals by the sex chromosomal complement and anatomical features. Similar information may be available for humans. However, humans may self-report their sex according to gender and some studies in animals can be designed to address influences of psychosocial (gender) constructs on physiological outcomes (12). The new editorial policy for all APS journals requires the reporting of sex for cells, tissues, and experimental animals and humans (i.e., male and female) or gender where appropriate. The investigator must decide based on the experimental design which terms are most appropriate for a given study.
..."
Full text of article

In defence of white rice | BMJ

In defence of white rice
by Kadoch
The finding of an increased risk of type 2 diabetes with higher consumption of white rice1 is not surprising because suboptimal results are to be expected whenever a whole plant food is refined. This is especially true with other poor lifestyle practices. Nevertheless, I worry that we are losing the forest among the trees.
White rice has been the staple of the Asian diet for thousands of years. For most of that time it produced some of the most slender people in history. Western diseases such as diabetes and coronary artery disease were almost unheard of in this region.2 Only after the comparatively recent adoption of high fat Western dietary habits, focused primarily on animal products and highly processed junk foods, have these illnesses become more prevalent in Asia.
Diets centred on white rice have, in fact, produced some of the most dramatic health benefits reported in the medical literature. The rice diet, as pioneered by Walter Kempner, has repeatedly been shown to drastically reduce hypertension, insulin resistance, and obesity.3 Low fat diets emphasising starch have reversed diabetes and coronary artery disease.4 5 These remarkable studies were all inspired by the traditional Asian cuisine.
Encouraging patients to choose intact whole grains such as brown rice is certainly warranted. However, to rescue the Asian population from a mounting epidemic of chronic lifestyle diseases, most effort should be focused on removing the cause-the toxic Western diet. This may even justify promoting a return to white rice, instead of condemning it outright.
Full text of article

R Tips

R! Tips

• R Tips: A lot of R tips - Paul E. Johnson  the latest html version is here and the PDF version is here.
• R Tips and Links - Howard Seltman.
• Set user and default R library folder when R starting?
• in RStudio, which is my favorite open source integrated development environment (IDE) for R
• in the R console, type ".libPaths()" to find the default library folder(s).
• go to "\RStudio\R".
• edit file "Options.R".
• add ".libPaths(c("../RStudio/R/library","x:/MyRLib"))".
• save the change.
• Find argument in a function using "args()" for example: args(ls). The three-dots construct in R
• Set user's R library folders as the first library after R started?
• in the R console, type ".libPaths(c("xxx/MyRLibrary1"," xxx/MyRLibrary2"))"
• or, in the RStudio, go to the "\R\" under the RStudio, edit file "Options.R", add one line ".libPaths(c("c:/myRlibsxxxx", .libPaths())", and save it.
• Customize startup of R! (Where to setup R startup environment)
• you can change options through RStudio File -> Tools - > Options
• or,
• open or create file named 'Rprofile.site' under the "..\etc\"
• add options line you want:
• options(digits = 5)           # to set decimal place
• option(width = 100)
• ".First" function will run at the start of the R: 
• .First<-function() {library(a); library(b)}
• ".Last" function will run at the end of the session ( I don't use this usually): 
• .Last <-function(){
• xxx
• }. 
• Do Basic Calculus Using R!
• RMarkdown: Generate a color-coded/formatted Word file of R! using RStudio
• 10 Tips for making your R graphics look their best
• Quantile Regression for Complex Survey Data
• Piecewise/Segmented Regression Related
• How to get orthogonal polynomial coefficient/vector/codes

Diabetes diet: What to eat when you have diabetes - Chicago Tribune

Decoding the diabetic diet
Source: Chicago Tribune.


"A focus on carb- and portion-control should be top priority, but that doesn't mean the occasional treat is out of the question."


Eat more

• Fish
• Nuts
• Nonstarchy vegetables
• Magnesium-rich foods (spinach, almonds, broccoli, lentils, tofu, pumpkin seeds, sunflower seeds)
• Foods rich in omega-3s (flaxseed, walnuts, salmon, tuna, sardines)
• Whole grains (quinoa, brown rice, wild rice, amaranth)
• Whole fruit (in servings the size of a tennis ball)
• Nonfat or low-fat Greek yogurt
• Olive oil
• Cinnamon
• Vinegar

Eat less

• Stick margarine, butter, shortening or lard
• Fried foods
• Refined grains (white bread, white rice, white flour)
• Sugary drinks (soda, fruit juices, sweetened ice teas, sports drinks)
• Fruity yogurts
• High-fat meats (sausage, bacon, hot dog, scrapple)

Full text here.

Matrix of Stata

Matrix of Stata

• Define a -matrix- or -mat- in short: matrix matrixname = matrix_expression.
• matrix define mymat = (1,2\3,4)
• Or, matrix mymat = (1,2\3,4)
• mat list mymat
• Print a matrix: 
• matrix list matrix_name
• -matlist-: Display a matrix and control its format: 
• matlist r(table)'*100, tw(20) format(%8.2f)
• Matrix rename: .matrix rename oldname newname
• Rename col/row names: 
• matrix colnames A = names
• matrix rownames A = names
• Convert variables to matrix and vice versa: 
• mkmat varlist
• svmat  [type] A [, names(col|eqcol|matcol|string)] // with -preserve-, -drop _all-and -restore-.
• Matrix addition & subtraction:
• mat matrix_a + matrix_b
• mat matrix_a - matrix_b
• Matrix multiplication:
• mat matrix_a * matrix_b
• Transpose of a matrix
• mat matrix_t = matrix_a'
• Inverse of a matrix, matrix function are defined by using parentheses ():
• mat matrix_inv = inv(matrix_a)
• A\B adds row of B after the rows of A; A,B adds columns B to matrix A. For example:
• mat RTab=r(table)'
• mat R1=RTab[1...,"b"]
• mat R2=RTab[1...,"ll".."ul"]
• mat RDisp=R1,R2
• The usual way to obtain matrices after a command that produces matrices is simply to refer to the returned matrix in the standard way. (source: Stata manual) Or 'get()' matrix function obtains a copy of an internal Stata system matrix.
• For instance all estimation commands return
• e(b) coefficient vector
• e(V) variance-covariance matrix of the estimates (VCE)
• And these matrices can be referenced directly. For examples:
• matrix list e(b)
• mattrix myE = e(b)*100
• matrix myV = e(V)*100
• matrix myVget=get(_b)
• Then, you can use
• "ereturn post myE myV" to Change coefficient vector and variance-covariance matrix.
• And "ereturn display" to create and display a coefficient table: "r(table)" that have been previously posted using "ereturn post" or "repost". "r(table)" is a matrix containing all the data displayed in the coefficient table (including b, se, t, pvalue, ll, ul, df, crit, and eform).
• Reset row/column names of matrix
• mat A = (1,2,3\ 4,5,6\ 7,8,9)
• matrix rownames A = myrow1 myrow2 myrow3
• mat colnames A = mycol1 mycol2 mycol3
• refix the column names of A with equation names eq1, eq2, and eq3: mat coleq A = eq1 eq2 eq3
• Matrix utilities:
• matrix dir - List the currently defined matrices
• matrix list - Display the contents of a matrix
• matrix rename - Rename a matrix
• matrix drop - Drop a matrix
• Matrix Subscripting:
• Referring to a matrix's element/cell using numbers of row and column or using the names of row and column or using mixed ways:
• disp matrix_name [r,c]
• matrix A = A/A[1,1]
• gen newvar = oldvar/A[2,2]
• mat B = V["price","price"]
• gen sdif = dif/sqrt(V["price","price"])
• Create a matrix B having the first through fifth rows and first through fifth columns of A, using two periods:
• matrix B = A[1..5,1..5]
• Create a matrix B having the all rows and first column of A, use three periods: 
• matrix B = A[1...,1]
• mat B=A[1...,"b"]
• Define an element of a maxtrix:
• mat A[1,2] = sqrt(2)
• Abstract row and column names from a matrix (-rownames- and -colnames-: Macro extended function related to matrices). Also, we can use -rowfullnames matname-, and -colfullnames matname-
• sysuse auto,clear
• regress mpg price weight length
• local rn :rownames r(table)
• local cn :colnames r(table)
• disp "`w1'" // price
• disp "`:word 1 of `:colnames r(table)''" // price
• disp "rownames = `rn'" _n "columnnames = `cn'"
• disp `:word count `cn'' // 4
• disp "`:word count `:colnames r(table)''" // 4
• disp "`:colsof r(table)'" // 4
• disp "`:rowsof r(table)'" // 9
• forval i = 1/`:word count `cn'' {
•   local varn: word `i' of `cn'
•   disp "`varn'"
•   }
• Find out number of row and column (-colsof(matname)- and -rowsof(matname)-): Matrix functions
• disp "number of row = " rowsof(r(table)) 
• disp "number of column = " colsof(r(table)) 
• How to do element-by-element operation
• mata, the new matrix language of Stata (since version 9), can do element-by-element operation easily. (read more here)
• Colon operations perform element-by-element operations: addition(:+), subtraction(:-), multiplication(:*), division(:/), power(:^), equality(:==), inequality(:!=), greater than(:>), greater than or equal to(:>=), less than(:<), less than or equal to(:<=), and(:&), or(:|)
• If you apply the exponential function on each element:
• . mata
• : x=(0,1\2,3)
• : exp(x) // x = (1,2.7\7.4,20.1)
• : exp((0,1\2,3)) // (1,2.7\7.4,20.1)
• : x:/2 // x = (0,0.5\1, 1.5)
• : end
• mata can use a Stata matrix
• matrix A=r(table)'
• mata: exp(st_matrix("A")) // display only
• mata: st_matrix("se",sqrt(diagonal(st_matrix("V")))) // create a matrix of standard deviation
• mata: st_matrix("expA", exp(st_matrix("A"))) // create a new matrix, expA
• matrix eformtab=expA[1..., "b"], expA[1...,"ll".."ul"], expA[1...,"se"]
• matlist eformtab*100, tw(30) format(%8.1f)
• More about mata
• create row vector: row=(1,2,3) or row=(1..3)
• create column vector: col=(1\2\3) or col=(1::3)
• transpose a matrix: m2=(0,1\2,3)'
• scalar functions will operate on elements: sqrtrow=sqrt(row)
• SSCC: an introduction to Mata

• Articles
• Watson (2005). Further processing of estimation results: Basic programming with matrices. (pdf).
• Mill (2009). Expedited Introduction to Stata, Programming Basics, Automating Tables and Monte Carlo Simulations