First of all, what are parcels? Not the little packages your grandma left on the table in the hall when she came back from shopping. Well, not only that.

In factor analysis, parcels are simply the sum of a small number of items. I prefer using parcels when possible because both basic psychometric theory and common sense tells me that a combination of items will have greater variance and, c.p., greater reliability than a single item.

Just so you know that I learned my share of useless things in graduate school, c.p. is Latin for ceteris paribus which translates to “other things being equal”. The word “etcetera”  meaning other things, has the same root.

Know you know. But I digress. Even more than usual. Back to parcels.

As parcels can be expected to have greater variance and greater reliability, harking back to our deep knowledge of both correlation and test theory we can assume that parcels would tend to have higher correlations than individual items. As factor loadings are simply correlations of a variable (be it item or parcel) with the factor, we would assume that  – there’s that c.p. again – factor loadings of parcels would be higher.

Jeremy Anglim, in a post written several years ago, talks a bit about parceling and concludes that it is less of a problem in a case, like today, where one is trying to determine the number of factors. Actually, he was talking about confirmatory factor analysis but I just wanted you to see that I read other people’s blogs.

The very best article on parceling was called To Parcel or Not to Parcel and I don’t say that just because I took several statistics courses from one of the authors.

 

To recap this post and the last one:

I have a small sample size and due to the unique nature of a very small population it is not feasible to increase it by much.I need to reduce the number of items to an acceptable subject to variables ratio. The communality estimates are quite high (over .6) for the parcels. My primary interest is in the number of factors in the measure and finding an interpretable factor.

So… here we go. The person who provided me the data set went in and helpfully renamed the items that were supposed to measure socializing with people of the same culture ‘social1’, ‘social2’ etc, and renamed the items on language, spirituality, etc. similarly. I also had the original measure that gave me the actual text of each item.

Step 1: Correlation analysis

This was super-simple. All you need is a LIBNAME statement that references the location of your data and then:

PROC CORR DATA = mydataset ;

VAR  firstvar — lastvar ;

In my case, it looked like this

PROC CORR DATA = in.culture ;

VAR social1 — art ;

The double dashes are interpreted as ‘all of the variables in the data set located from var1 to var2 ‘ . This saves you typing if you know all of your variables of interest are in sequence. I could have just used a single dash if they were named the same, like item1 – item17 , and  then it would have used all of the variables named that regardless of their location in the data set. The problem I run into there is knowing what exactly item12 is supposed to measure. We could discuss this, but we won’t. Back to parcels.

Since you want to put together items that are both conceptually related and empirically – that is, the things you think should correlate do- you first want to look at the correlations.

Step 2: Create parcels

The items that were expected to assess similar factors tended to correlate from .42 to .67 with one another. I put these together in a ver simple data step.

data parcels ;
set out.factors ;
socialp1 = social1 + social5 ;
socialp2 = social4 + social3 ;
socialp3 = social2 + social6 + social7 ;
languagep = language2 + language1 ;
spiritualp = spiritual1 + spiritual4 ;
culturep1 = social2 + dance + total;
culturep2 = language3 + art ;

There was one item that asked how often the respondent ate food from the culture, and that didn’t seem to have a justifiable reason for putting with any other item in the measure.

Step 3: Conduct factor analysis

This was also super-simple to code. It is simply

proc factor data= parcels rotate= varimax scree ;
Var socialp1 – socialp3 languagep spiritualp spiritual2 culturep1 culturep2  ;

I actually did this twice, once with and once without the food item. Since it loaded by itself on a separate factor, I did not include it in the second analysis. Both factor analyses yielded two factors that every item but the food item loaded on. It was a very nice simple structure.

Since I have to get back to work at my day job making video games, though, that will have to wait until the next post, probably on Monday.

—–

Be more than ordinary. Take a break. Play Forgotten Trail. I bet you have a computer!

characters traveling on map

Learn and have fun. More productive than fruit crush, candy ninja or whatever the heck else it is you or your kids are playing.

Someone handed me a data set on acculturation that they had collected from a small sample size of 25 people. There was a good reason that the sample was small – think African-American presidents of companies over $100 million in sales or Latina neurosurgeons. Anyway, small sample, can’t reasonably expect to get 500 or 1,000 people.

The first thing I thought about was whether there was a valid argument for a minimum sample size for factor analysis. I came across this very interesting post by Nathan Zhao where he reviews the research on both a minimum sample size and a minimum subjects to variables ratio.

Since I did the public service of reading it so you don’t have to, (though seriously, it was an easy read and interesting), I will summarize:

  1. There is no evidence for any absolute minimum number, be it 100, 500 or 1,000.
  2. The minimum sample size depends on the number of variables and the communality estimates for those variables
  3. “If components possess four or more variables with loadings above .60, the pattern may be interpreted whatever the sample size used .”
  4. There should be at least three measured variables per factor and preferably more.

This makes a lot of sense if you think about factor loadings in terms of what they are, correlations of an item with a factor. With correlations, if you have a very large correlation in the population, you’re going to find statistical significance even with a small sample size. It may not be precisely as large as your population correlation, but it is still going to be significantly different than zero.

So … this data set of 25 respondents that I received originally had 17 items. That seemed clearly too many for me.  I thought there were two factors, so I wanted to reduce the number of variables down to 8, if possible. I also suspected the communality estimates would be pretty high, just based on previous research with this measure.

Here is what I did next :

  • Parceled
  • Parallel analysis
  • Factor Analysis

I can’t believe I haven’t written at all on parceling before and hardly any on the parallel analysis criterion, given the length of time I’ve been doing this blog. I will remedy that deficit this week. Not tonight, though. It’s past midnight, so that will have to wait until the next post.

Update: read post on parcels and the PROC FACTOR code here

—-

My day job is making games that make you smarter. Check out our latest game, Forgotten Trail. Runs on Mac or Windows in any browser. Be more than ordinary.

People on farm

At first, I was thinking it wasn’t right to have a favorite paper, but then I realized that was idiotic. It’s not like these papers (or their presenters) are my children.

My favorite paper was,

Statistical modeling for large complex data: Five new directions from SAS/STAT software

If you’re not a statistician, props to you for reading after that first sentence, especially since some of the lessons apply to any conference.

glm select

  1. You don’t always have to present or attend presentations on whatever is shiny and new. The techniques he presented, like GLMSELECT, a method for selecting the best model is not brand new. I remember when it was first added to SAS/STAT and thinking it was a way cool idea I should use – but, then, I didn’t. As you can see from the graph above, it can be pretty easy to select the best model. Looks a lot like a scree plot, doesn’t it?  This also further supports my point that visual displays of data, like the one above, are everywhere and taking over. Now that I have been reminded of its existence, I’m looking for a use for it so I can really remember it. Unfortunately, this is a method for general linear models and what I am most interested in right now has a binomial outcome, whether a player finished a game or not.
  2. Don’t stop learning when you go home. I remembered that there was also an example in this paper that used HPGENSELECT for generalized linear models, including binomial distributions. So, I am going to try that out with this dataset. One of the areas where I am improving is actually reading all of those papers I mean to get around to when I get home. Whether it is a paper you attended, but is now jumbled around in your brain with the other 25 sessions, or one you could not attend because it conflicted with something else, when you get home, you should read it. Conferences can be expensive and you want to get the most out of that time and money you spent.
  3. Of course, I learned about sparse regression, quantile regression, classification and regression trees and more, which you can, too if you follow my advice from #2.

Okay, well there is a lot more to say about SAS Global Forum and my adventures with HPGENSELECT but we have a new game, Forgotten Trail, coming out for sale tomorrow, so back to work.

———-

7 GENERATION GAMES

Sam and Angie planning their journey

BETTER GAMES, BETTER MATH

 

The nice thing about going to SAS Global Forum is that it’s the gift that keeps on giving. Long after I have gone home, there are still points to ponder.

Visual analytics is big and not just in the sense of there is a product out called that which I have never used but that every presentation, no matter how ‘tech-y’ now makes very effective use of graphics. If I was the type of person to say I told you so, I would mention that I predicted this six years ago after I went to SAS Global Forum in 2010.

In my last post, I mentioned the propensity score graphic with mustaches.

Richard Culter’s presentation on PROC HPSPLIT, which was really excellent, made extensive use of graphics to illustrate fairly complex models.

Nodes in subtree

You can create classification and regression trees (the model you can’t see in this tiny graphic on the left) and you can drill down into sub-trees for further analysis.

Sometimes your classification tree is very easily interpretable. For example, in this case here from the same presentation, each split represents a different type of vegetation/ land surface – water,  two different species of tree, etc.

Classification tree

Speaking of classification, regression and PROC HPSPLIT ….

If you didn’t know, now you know

PROC HPSPLIT is a high performance procedure for fitting and classification now available in SAS/STAT which is useful for data sets where relationships are non-linear. It produces classification and regression trees, includes options for pruning trees and a whole lot more. It is now available on a single computer, not limited to high performance computing clusters. So, yay!

A regression tree is what you get when your dependent variable is continuous, and a classification tree when it is categorical, as in the vegetation example above.

On a semi-related note, graphics can even be used to show when a data set is not suited to a linear model as in the example below, also from Cutler’s presentation. You can see that all of the 1’s are in two quadrants and all of the 0’s in two other quadrants. Yes, you COULD use a regression line to fit this but that is not the best fit of the data.

Also, on a related topic that visualizing data, like all of statistics, really, is a process of iterations, I think this would be more obvious if the quadrants were color coded.


classify

I have a lot more to say on this but I am in North Dakota speaking at the ND STEM conference this weekend and a  kind soul gave me tickets to the hockey game in the president’s box, so, peace, I’m out.

If you did not go to SAS Global Forum this week, here are some things you missed:

Me, rambling on about the 13 techniques all biostatisticians should know, including the answer to:

If McNemar and Kappa are both statistics for handling correlated, categorical data, how can they give you completely different results?

The answer is that the two test different hypotheses, apply different formula and are coded differently.

McNemar tests whether the marginal probabilities are the same. For example, when you switched your patients from drug one to drug two, was there a decrease in the number who experienced side effects? These are correlated data because they are the same people. Can’t get much more correlated than that.

Kappa tests whether the level of agreement of two raters is greater than would be expected by chance. I’ve rambled on it here before, using it to test the level of agreement that our 7 Generation Games raters have when scoring the pretest and post-test we use to assess whether kids are improving as a result of playing our games. Quick answer: Yes.

You also missed Lucy D’Agostino McGowan’s talk on propensity score matching integrating SAS and R.

Random notes from that presentation:

Why would you want to do this? Well, it would be lovely if you could do a randomized control trial and sending your subjects randomly off to treatment or control group.

However, what if your subjects tell you to drop dead they’re not going to be in your stupid treatment group?

In my experience, propensity scores have been commonly used when evaluating special programs that do not randomly receive patients. For example, patients sent to an Intensive Care Unit tend to be sicker than non-ICU patients. How then, do you decide if an ICU has any benefit when people in it are more likely to die?

Observational studies can use propensity scores to get a more unbiased estimate of treatment effects.

Propensity score matching assumes

  1. That there are no unmeasured confounders
  2. Every subject has a non-zero probability of receiving treatment.

Propensity scores are simply predicted values from a logistic regression predicting treatment

Useful rule of thumb:
Use caliper of .2 * pooled standard deviation

Only match people from treatment group to control group if their distance is within the caliper.

Also, I have slide envy because she thought to use mustaches and fedoras in illustrating propensity scores.

Propensity Scores with mustaches

Also with really cool slides I was not quick enough to take a picture before he moved on …

Using Custom Tasks with In-memory statistics and SAS Studio by Steve Ludlow

I was able to find the slides from a related presentation he give in the UK last year. I linked to that one because it gave a little more detail on what SAS in-memory statistics is, how to use it and examples. If you had gone to his presentation, you probably would have wanted to learn more about this proc imstat and custom tasks of which he speaks.

Three points you might have come away with:

  1. Creating custom tasks is really easy
  2. Custom tasks could be really useful for teams sharing a large data base. Say, for example, you are on a longitudinal project study development of at-risk youth from age 12-25. You might have all kinds of people doing similar analyses, maybe looking at predictors of high school dropout, say. You could save your task and re-run it with next year’s data, only for females or in a hundred other ways.
  3. Custom tasks could be super-useful for teaching. Have the students run and inspect tasks you create and then modify these for their own analyses.

Fish lake woman

Okay, off to more sessions. Just a reminder, if you are here and feeling guilt that you left your children/ grandchildren at home, you can buy Fish Lake or Spirit Lake for them to play while you are gone. They’ll get smarter and you will get brownie points from their mom / dad / teacher .

Esteemed statistics guru, Dr. Nathaniel Golden has some sobering news for Democrats. His latest models predict a Republican blow out. As can be seen by the map below, the Republican front-runner has tapped into the mood of resentment in the country’s non-elites. When the dust has settled, only the two highest earning states in the country will remain in the blue column, Maryland and New Jersey (seriously, New Jersey). Code used in creating this map and the statistics behind it can be found below.

Map in all red but 2 states

Step 1: Create a data set

Oh, and April Fool’s !  I just made up these data. If you really do need a data set with state data aligned to SAS maps, though, you can do what I did and pull it from the UCLA Stats Site. If you had real data, say percent of people who use methamphetamine, or whatever, you could just replace the last column there with your data. Since I did not have actual data, I just created a variable that was 40,000 for everything less than 51,000, and 51,000 for everything over. I’m going to use that in the PROC FORMAT below.

Also, even though my data are not nicely aligned here, note that the statename variable has a width of 20 so make sure you align your data like that so that state comes in column 22 or after.

DATA income2000;
INPUT statename $20. state income ;
IF income < 51000 THEN vote = 40000 ;
ELSE vote = 51000 ;
DATALINES ;
Maryland 24 51695
Alaska 2 50746
New Jersey 34 51032
Connecticut 9 50360

— a bunch more data

;

Here’s how you set up a PROC FORMAT for the two categories.

PROC FORMAT
VALUE votfmt low-50000="Republican"
50001-high="Democrat";

*** Making the patterns red and blue ;

pattern1 value=msolid color=red;
pattern2 value=msolid color=blue;

*** Making the map ;

proc gmap data = income2000 map=maps.us;
id state;
choro vote;
format vote votfmt.;

The important thing to keep in mind is if you want a U.S. map with the states that maps.us is in a SAS library named maps. Like the sashelp library, it’s already there, you don’t need to create it or assign it in the LIBNAME statement, you can just reference it. Go look under your libraries. See, I was right.

And don’t forget to vote.  I don’t care how busy you are. You don’t want this, do you?

I can’t believe I haven’t written about this before – I’m going to tell you an easy (yes, easy) way to find and communicate to a non-technical audience standardized mortality rates and relative risk by strata.

It all starts with PROC STDRATE . No, I take that back. It starts with this post I wrote on age-adjusted mortality rates which many cohorts of students have found to be – and this is a technical term here – “really hard”.

walnut

Here is the idea in a nutshell – you want to compare two populations, in my case, smokers and non-smokers, and see if one of them experiences an “event”, in my case, death from cancer, at a higher rate than the other. However, there is a problem. Your populations are not the same in age and – news flash from Captain Obvious here – old people are more likely to die of just about anything, including cancer, than are younger people. I say “just about anything” because I am pretty sure that there are more skydiving deaths and extreme sports-related deaths among younger people.

Captain Obvious wearing her obvious hat

Captain Obvious wearing her obvious hat

So, you compute the risk stratified by age. I happened to have this exact situation here, and if you want to follow along at home, tomorrow I will post how to create the data using the sashelp library’s heart data set.
The code is a piece of cake

cake

PROC STDRATE DATA=std4
REFDATA=std4
METHOD=indirect(af)
STAT=RISK
PLOTS(STRATUM=HORIZONTAL);
POPULATION EVENT=event_e TOTAL=count_e;
REFERENCE EVENT=event_ne TOTAL=count_ne;
STRATA agegroup / STATS;

The first statement gives the data set name that holds your exposed sample data, e.g., the smokers, your reference data set of non-exposed records, in this example, the non-smokers. You don’t need these data to be in two different data sets, and, this example, they happen to be in the same one.  The method used for standardization is indirect. If you’re interested in the different types of standardization, check out this 2013 SAS Global Forum paper by Yang Yuan.

STAT = RISK will actually produce many statistics,  including both crude risk estimates and estimates by strata for the exposed and non-exposed groups, as well as standardized mortality rate – just, a bunch of stuff. Run it yourself and see.  The PLOTS option is what is of interest to me right now. I want plots of the risk by stratum.

The POPULATION statement gives the variable that holds the value for the number of people in the exposed group who had the event, in this case, death by cancer, and the count is the total in the exposed group.

The REFERENCE statement names the variable that holds the value of the number in the non-exposed group who had the event, and the total count in the non-exposed group (both those who died and those who didn’t).

The STRATA statement gives the variable by which to stratify. If you don’t need your data set stratified because there are no confounding variables – lucky you – then just leave this statement out.

Below is the graph

risks by strata
The PLOTS statement produces plots of the crude estimate of the risk by strata, with the reference group risk as a single line. If you look at the graph above you can see several useful measures. First, the blue circles are the risk estimate for the exposed group at each age group and the vertical blue bars represent the 95% confidence limits for that risk. The red crosses are the risk for the reference group at each age group. The horizontal, solid blue line is the crude estimate for the study group, i.e., smokers, and the dashed, red line is the crude estimate of risk for the reference group, in this case, the non-smokers.

Several observations can be made at a glance.

  1. The crude risk for non-smokers is lower than for smokers.
  2. As expected, the younger age groups are below the overall risk of mortality from cancer.
  3. At every age group, the risk is lower for the non-exposed group.
  4. The differences between exposed and non-exposed are significantly different for the two younger age groups only, for the other two groups, the non-smokers, although having a lower risk, do fall within the 95% confidence limits for the exposed group.

There are also a lot more statistics produced in tables but I have to get back to work so maybe more about that later.

I live in opposite world

Speaking of work — my day job is that I make games for 7 Generation Games and for fun I write a blog on statistics and teach courses in things like epidemiology. Actually, though, I really like making adventure games that teach math and since you are reading this, I assume you like math or at least find it useful.

Mom and kid

Share the love! Get your child, grandchild, niece or nephew a game from 7 Generation Games.

One of my favorite emails was from the woman who said that after playing the games several times while visiting her house, her grandson asked her suspiciously,

Grandma, are these games on your computer a really sneaky way to teach me math?

You can check out the games here and if you have no children to visit you or to send one as a gift, you can give one to a school – good karma. (But, hey, what’s with the lack of children in your life? What’s going on?)

SENSITIVITY AND SPECIFICITY – TWO ANSWERS TO “DO YOU HAVE A DISEASE?”

Both sensitivity and specificity address the same question – how accurate is a test for disease – but from opposite perspectives. Sensitivity is defined as the proportion of those who have the disease that are correctly identified as positive. Specificity is the proportion of those who do not have the disease who are correctly identified as negative.

Students and others new to biostatistics often confuse the two, perhaps because the names are somewhat similar. If I was in charge of naming things, I would have named one ‘sensitivity’ and the other something completely different like ‘unfabuloso’. Why I am never consulted on these issues is a mystery to me, too.

Specificity and sensitivity can be computed simultaneously, as shown in the example below using a hypothetical Disease Test. The results are in and the following table has been obtained:

 

  Disease No Disease
Test Positive 240 40
Test Negative 60 160

Results from Hypothetical Screening Test

COMPUTING SENSITIVITY AND SPECIFICITY USING SAS

Step 1 (optional): Reading the data into SAS. If you already have the data in a SAS data set, this step is unnecessary.

The example below demonstrates several SAS statements in reading data into a SAS dataset when only aggregate results are available. The ATTRIB statement sets the length of the result variable to be 10, rather than accepting the SAS default of 8 characters. The INPUT statement uses list input, with a $ signifying character variables.

DATALINES;

a statement on a line by itself, precedes the data. (Trivial pursuit fact : CARDS; will also work, dating back to the days when this statement was followed by cards with the data punched on them.) A semi-colon on a line by itself denotes the end of the data.

DATA diseasetest ;

ATTRIB result LENGTH= $10 ;

INPUT result $ disease $ weight ;

DATALINES ;

positive present 240

positive absent 40

negative present 60

negative absent 160

;

Step 2: PROC FREQ

PROC FREQ DATA= diseasetest ORDER=FREQ ;

TABLES result* disease;

WEIGHT weight ;

Yes,  plain old boring PROC FREQ. The ORDER = FREQ option is not required but it makes the data more readable, in my opinion, because with these data the first column will now be those who had a positive result and did, in fact, have the disease. This is the numerator for the formula for sensitivity, which is:

 

Sensitivity =   (Number tested positive)/ (Total with disease).

 

TABLES variable1*variable2   will produce a cross-tabulation with variable1 as the row variable and variable2 as the column variable.

Weight weightvariable will weight each record by the value of the weight variable. The variable was named ‘weight’ in the example above but any valid SAS name is acceptable. Leaving off this statement will result in a table that only has 4 subjects, 1 subject for each combination of result and disease, corresponding to the data lines above.

Results of the PROC FREQ are shown below. The bottom value in each box is the column percent.

Because the first category happens to be the “tested positive” and the first column is “disease present”, the column percent for the first box in the cross-tabulation – positive test result, disease is present – is the sensitivity, 80%. This is the proportion of those who have the disease (the disease present column) who had a positive test result.

 

Table of result by disease
result disease
Frequency
Percent
Row Pct
Col Pct
present absent Total
positive 240
48.00
85.71
80.00
40
8.00
14.29
20.00
280
56.00
negative 60
12.00
27.27
20.00
160
32.00
72.73
80.00
220
44.00
Total 300
60.00
200
40.00
500
100.00

Output from PROC FREQ for Sensitivity and Specificity

The column percentage for the box corresponding to a negative test result and absence of disease is the value for specificity. In this example, the two values, coincidentally, are both 80%.

Three points are worthy of emphasis here:

  1. While the location of specificity and sensitivity in the table may vary based on how the data and PROC FREQ are coded, the values for sensitivity and specificity will always be diagonal to one another.
  2. This exact table produces four additional values of interest in evaluating screening and diagnostic tests; positive predictive value, negative predictive value, false positive probability and false negative probability. Further details on each of these, along with how to compute the confidence intervals for each can be found in Usage Note 24170 (SAS Institute, 2015).
  3. The same exact procedure produces six different statistics used in evaluating the usefulness of a test. Yes, that is pretty much the same as point number 2, but it bears repeating.

Speaking of that SAS Usage Note, you should really check it out.

In the early part of any epidemiology course, few things throw students as much as computing age-adjusted mortality. It seems really counter-intuitive that two populations could have the exact same mortality rate and yet one is significantly less healthy than the other.

Thinking about it for a moment, though, before diving into computation, makes it pretty clear.

Say you have a class of 30 members of a senior citizens center in Florida and 30  second-graders in Santa Monica. In each group, 4 members died this year. Is the mortality rate the same?Me and my mom in a pool with martinis

Eva in school uniform

This is where age-adjusted mortality comes in. It just so happens that in fact the CRUDE MORTALITY RATE is the same.

Crude mortality rate is simply (# of people who died)/(population at midyear)

We take midyear population because the denominator is the population at risk and if you have already died you cannot die again. Poets talk about dying a thousand deaths but statisticians don’t believe in that crap.

Since, we will assume, no one is joining your community center or class, mid-year population = 28.

How did I get 28? I assumed that people died randomly throughout the year so 1/2 of the year, 2 of your 4 people have died.

So, your crude mortality rate is 143 per 1,000.

Does it bother you that more of the second-graders died? Does that not seem right? That’s because you have some intuitive understanding of age-adjusted mortality.

Age-adjusted mortality is what you get when you apply ACTUAL age specific rates to a HYPOTHETICAL STANDARD POPULATION.

Let’s say we want to compare the mortality rates of two relatively small cities, each with the same size population and in each city, 74 people died in the last year. We are arguing that pollution is causing increased mortality but the main polluter in town points to the fact that City B has no more deaths than City A, on the other side of the state.

To compute the age-adjusted population, we would take the actual mortality rate for each age group for each city, as in the example below. Applying that to a standard population, let’s say each city had 10,000 children born that year, 20,000 ages 1-5 and so on.

Age Group
Standard Population
CITY A Mortality Rates per 100,000
Expected Deaths A
CITY B Mortality Rates per 100,000
Expected Deaths B
< 1 10,000 160 16 70 7
1-5 20,000 20 4 12 2.4
6-40 50,000 30 15 14 7
41-65 10,000 50 5 45 4.5
Over 65 10,000 350 35 300 30
TOTAL 75 50.9

The cities may have different age distributions, so city A, which is a college town, has  a lot more young people than City B. Given the City A mortality rates for each age group, one would expect 75 deaths in a standard population –  that is, with the age distribution given above.

However, given the mortality rates by age in City B, one would expect only 50.9 deaths in a year. So, yes, City A has the same number of people and the same number of deaths, but if the people in City A are much younger, they should have FEWER deaths.

The standardized mortality ratio is the observed number of deaths per year divided by the expected number of deaths.

Let’s say we use the rate for City B, without the polluter, as our expected number

SMR =  75/ 50.9 = 1.47

Usually, we multiply it by 100. So, this says the deaths in City A are 147% of what would be expected for this distribution of ages based on the mortality rate in a city with no polluting plant.

Feel smarter after reading this?

Just need a little R & R now?

Sam is running

Check out my day job, making educational adventure games. Download one for Mac or Windows today.

Policy makers have very good reason for wanting to know how common a condition or disease is. It allows them to plan and budget for treatment facilities, supplies of medication, rehabilitation personnel. There are two broad answers to the question, “How common is condition X?” and, interestingly, both of these use the exact same SAS procedures. Prevalence is the number of persons with a condition divided by the number in the population. It’s often given as per thousand, or per 100,000, depending on how common the condition is. Prevalence is often referred to as a snapshot. It’s how many people have a condition at any given time.

 

Just for fun, let’s take a look at how to compute prevalence with SAS Studio.

Step 1: Access your data set

First, assign a libname so that you can access your data. To do that, you create a new SAS program by clicking on the first tab in the top menu and selecting SAS Program.

Click to create new program

libname mydata "/courses/number/number/" access=readonly;

(Students only have readonly access to data sets in the course directory. This prevents them from accidentally deleting files shared by the whole class. As a professor with many years of experience, let me just tell you that this is a GREAT idea.)

Click on the little running guy at the top of your screen and, voila, your LIBNAME is assigned and the directory is now available for access.

(Didn’t believe me there is a little running guy that means “run”? Ha!)

running guy

Next, in the left window pane, click on Tasks and in the window to the right, click on the icon next to the data field.

window to select library

From the drop down menu of directories, select the one with your data and then click on the file you need to analyze.

list of files in directory

Step 2: Select the statistic that you want and then select the variable. In this case, I selected one-way frequencies, and one cool thing is that SAS will automatically show you ONLY the roles you need for a specific test. If you were doing a two-sample t-test, for example, it would ask for you groups variable and your analysis variable. Since I am doing a one-way frequency, there is only an analysis variable.

select roles

When you click on the plus next to Analysis Variables, all of the variables in your data set pop up and you can select which you want to use. Then, click on your little running guy again, and voila again, results.

Results of proc freq

So … the prevalence of diabetes is about 11% of the ADULT population in California, or about 110 per 1,000.

You can also code it very simply if you would like:
libname mydata “/courses/number/number/” access=readonly;

PROC FREQ DATA = mydata.datasetname ;

TABLE variable ;

Of course, all of this assumes that your data is cleaned and you have a binary variable with has disease/  doesn’t have disease, which is a pretty large assumption.

Now, curiously, the code above is the exact SAME code we used to compute incidence of Down syndrome a few weeks ago. What’s up with that and how can you use the exact same code to compute two different statistics?

Patience, my dear. That is a post for another day.

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