Basics of Biostatistics for Health ResearchSession 3 – February 21, 2013

Dr. Scott Patten, Professor of EpidemiologyDepartment of Community Health Sciences

& Department of Psychiatry

patten@ucalgary.ca

Some General Principles of Data Analysis

• Data cleaning, checking is always the first step after data entry.

• Start with “univariate” analysis (frequencies and their CIs.

• Progress to “bivariate” analysis – does a “dependent” variable differ depending on an “independent” variable

• The next stage is “multivariate”

Statistical Errors

• Go to “www.ucalgary.ca/~patten” www.ucalgary.ca/~patten

• Scroll to the bottom.

• Right click to download the files described as being “for PGME Students”– One is a dataset– One is a data dictionary

• Save them on your desktop

Open the Datafile

Comparing Proportions

• We’ve looked at two procedures (e.g. for obesity in men vs. women):

generate obese = bmi

recode obese 0/30=0 30.001/1000=1

prtest obese, by(sex)

Generate Commands Using Logic

generate obese2 = .

recode obese2 .=0 if bmi <= 30

recode obese2 .=1 if bmi > 30

tab obese obese2

prtest obese2, by(sex)

Generate as a Recode Subcommand

recode bmi (0/30=0) (30.01/1000=1), gen(obese3)

tab obese obese3

Alternative to prtest

• Can use tab with the subcommand “exact”

tab obese sex, exact

Epitab Commands

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3

2

Risk Ratios

“risk” in the “exposed”

“risk” in the “non-exposed”RR =

Odds Ratios

Odds in the “exposed”

Odds in the “non-exposed”OR =

Measures of Association

• The most common ones are ratios..– RR– OR– PR– IR

• You’ll sometimes see differences as well..– Risk Difference

Another Alternative…

• The “cs” command is for “cross-sectional” and will give you risk ratios or risk differences

• However, it requires 0 and 1 values.

recode sex (1=0) (2=1), gen(female)

cs obese female, exact

Odds and Proportions

• In our sample, there are…– 1560 obese– 10,015 non-obese– (and 52 missing)

• The frequency of obesity (prevalence) is 1,560/(1,560 + 10,015)

• The odds are: 1,560/10,015

Odds and Proportions

• In other words…– If ‘a’ means “have disease” and b means “does

not have the disease” then…– Proportion = a / a+b– Odds = a / b

Another Alternative…

• The “cc” command is for “case-control” and will give you odds ratios

• However, it requires 0 and 1 values.

cc obese female, exact

As Task for You…• What is the prevalence of diabetes? (provide a 95%

confidence interval for your estimate)

• What is the prevalence of diabetes in men and women (hint: use “by” in the dialogue box)

• What is the odds ratio for the association of diabetes and obesity?

• What is the risk ratio for the association of diabetes and obesity?

• Is the association statistically significant?

A More Complex Problem..

• The prevalence of obesity is said to be associated with lower levels of education

Two-way Tables

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3

A Two-way Table

Pearson chi2(3) = 136.4094 Pr = 0.000

Total 4,663 3,395 1,883 1,341 11,282

1 813 417 162 112 1,504

0 3,850 2,978 1,721 1,229 9,778

obese 1 2 3 4 Total

grad+

0-11 years, hs or ged, some coll, coll

. tabulate obese educ, chi2

Bar Graphs

• It is under the graphics menu, the dialogue box…

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3

Select Categories..

1

2

0.0

5.1

.15

.2m

ean

of o

bese

1 2 3 4

Histograms, with “by”

• The pattern of obesity by education is different than that of mean BMI.

• Your Task: use the “by” subcommand with the histogram command to look at the distribution of BMI by eduation.

Does BMI Differ by Education?

• If we had two groups we’ld use a t-test.

• Our null would be Mean(1) = Mean(2), or as Stata says: Mean(1) – Mean(2) = 0

• But we have > 2 groups, so could try to use ANOVA– Can think of this test as an extension of the two

group t-test– Assumes normal distribution and equal variances

(like the t-test it is “parametric”)

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2

3

One-Way ANOVA

STATA Warns of a Problem

Bartlett's test for equal variances: chi2(3) = 195.1798 Prob>chi2 = 0.000

Total 189524.965 11281 16.8003692

Within groups 184631.134 11278 16.370911

Between groups 4893.83027 3 1631.27676 99.64 0.0000

Source SS df MS F Prob > F

Analysis of Variance

. oneway bmi educ

The Kruskal-Wallis Test

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3

Kruskal-Wallis Output

probability = 0.0001

chi-squared with ties = 294.008 with 3 d.f.

probability = 0.0001

chi-squared = 294.007 with 3 d.f.

4 1341 6.93e+06

3 1883 9.29e+06

2 3395 1.83e+07

1 4663 2.91e+07

educ Obs Rank Sum

Kruskal-Wallis equality-of-populations rank test

. kwallis bmi, by(educ)

Non-Parametric Tests• Kruskall-Wallis and its 2 sample version (Wilcoxon

Rank Sum Test) require that…– The variable can be meaningfully ordered, and– Has a roughly/loosely bell shaped frequency

distribution (should have a central tendency)

• Your task: Repeat our analysis from last week in which we compared BMI in men and women, but use Kruskall-Wallis and Wilcoxon’s Rank Sum test.– Do you get equivalent results?

Comparing Proportions?

Yes No

Fisher’s Exact Test Parametric Assumptions?

Yes No

Multiple Groups? Multiple Groups?

Yes NoYes No

ANOVA t-test Kruskall-Wallis Wilcoxon’s-Rank Sum

Prevalence of Diabetes

Your Task: try this command: cii 11627 530, exact

Total 11,627 100.00

1 530 4.56 100.00

0 11,097 95.44 95.44

y/n Freq. Percent Cum.

diabetic

. tab diabetes

(Does your estimate resemble what you get with ci diabetes, exact?)

The CI Calculator

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The “CC” Calculator

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The CC Calculator

Your Task: Try the cci command to obtain the OR

chi2(1) = 122.89 Pr>chi2 = 0.0000

Attr. frac. pop .1368591

Attr. frac. ex. .7042266 .6248288 .7652318 (exact)

Odds ratio 3.380966 2.66545 4.25952 (exact)

Point estimate [95% Conf. Interval]

Total 842 10785 11627 0.0724

Controls 739 10358 11097 0.0666

Cases 103 427 530 0.1943

Exposed Unexposed Total Exposed

Proportion

. cc diabetes prevchd

Your Task: Can you reproduce these CIs with an immediateCommand?

Diagnostic Test Metrics

• Sensitivity

• Specificity

• Positive Predictive Value

• Negative Predictive Value

Common Notation for Test Metrics

Formulas for Test Metrics…

Let’s make formulas for Se, Sp, PPV and NPV using this terminology.

(In Class) Assignment for Today

• Our database has random blood glucose (they call it “casual”)

• In these units (mg/dl) about 140 may be used as a cut-point for an “elevated” level

• Create a variable for “elevated” glucose and determine its Se, Sp, PPV and NPV as a diagnostic test for diabetes

• Calculate a confidence interval for each parameter.