Stata v 12 Stratified Analysis of K 2x2 tables - UMass Amherst

14 Pages·2013·0.39 MB·English

by  Carol Bigelow

PubHlth 640 – Spring 2013 Stata v 12 Stratified Analysis of K 2x2 Tables

Stratified Analysis of K 2x2 Tables

Is the association of coffee with myocardial infarction different, depending on smoking status (“effect modification”)?
If the association is the same, regardless of smoking status, is there an association of coffee consumption with
myocardial infarction at all? This is an example of a stratified analysis of an exposure-disease relationship.

A stratified analysis of K 2x2 tables is used to assess: (1) evidence of modification of an exposure-disease relationship
by changes in the value of a third (stratifying) variable; or (2) in the absence of modification, a Mantel-Haenszel
analysis of an exposure disease relationship controlling for confounding.

Data Source:

In this illustration, a data set is created in Stata using the data editor tool. The data are in tabular form. The expand
function is used to convert the tabular data into a full data set that contains one record per subject.

The sample size is n = 494.

1. Introduction and Example ………………………………………………………..……..……..… 2

2. Entering Tabular Data ……………………………………………………………………….…… 3

3. Descriptives – Numerical ………………………………………………………………………… 7

4. Descriptives – Graphical …………………………………………………………………………. 10

5. Mantel Haenszel Test of Null: Homogeneity of Odds Ratio ……………………………………. 13

6. Mantel-Haenszel Test of Null: Odds Ratio = 1 ………………………………………….. 14
COMMON

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PubHlth 640 – Spring 2013 Stata v 12 Stratified Analysis of K 2x2 Tables

1. Introduction and Example

Example -
Note – This is a subset of the data used in the Unit 4 (Categorical Data Analysis) practice problems.

. Source: Fisher LD and Van Belle G. Biostatistics: A Methodology for the Health Sciences.
New York: Wiley, 1993. Chapter 6 problem 14, page 235.

Rosenberg et al (1980) performed a retrospective study of the association of coffee drinking (exposure)
and the occurrence of myocardial infarction (MI) (outcome) among n=494. Information on smoking
was also available. The analysis investigated possible modification of the coffee-MI relationship
with smoking status (stratification).

The data are in tabular form.

Stratum 1: FORMER SMOKER
Cups Coffee per day MI Control
> 5 7 18
< 5 20 112

Stratum 2: 1-14 CIGARETTES/DAY
Cups Coffee per day MI Control
> 5 7 24
< 5 33 11

Stratum 3: 35-44 CIGARETTES/DAY
Cups Coffee per day MI Control
> 5 27 24
< 5 55 58

Stratum 4: 45+ CIGARETTES/DAY
Cups Coffee per day MI Control
> 5 30 17
< 5 34 17

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PubHlth 640 – Spring 2013 Stata v 12 Stratified Analysis of K 2x2 Tables

2. Entering Tabular Data

Tabular data is convenient for data entry. The result, however, is data in collapsed form. For example, consider the
first table on the previous page. It shows that there are 7 individuals who are former smokers (stratum=1) who drank
5+ cups of coffee per day and who experienced an MI. We will enter this record just once and keep track of the
frequency of this observation equal to 7 using a variable called tally.

Tip – It is possible to analyze tabular data in Stata. Each profile of variable values is “weighted” by their frequency of
occurrence (in our case by the variable tally). However, there are some analyses that we might want to do that cannot
be performed using tabular data. For this reason, after entering the tabular data, the expand function is used to create a
full data set.

Coding Manual
Tips – (1) Always create a coding manual before creating a data set (2) Use “lower case” only variable names.

Example -
Variable Variable Label Format Format code definitions
smoking Smoking Status smokingf 1 = Former smoker
2 = 1-14 cigs/day
3 = 35-44 cigs/day
4 = 45+ cigs day
coffee Cups Coffee Per Day coffeef 0 = < 5 cups/day
1 = 5+ cups/day
mi Myocardial Infarction mif 0 = control
1 = case (MI)
tally Frequency weight - -

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PubHlth 640 – Spring 2013 Stata v 12 Stratified Analysis of K 2x2 Tables

Tip – Before proceeding, be sure you have started a log of your session in “.log” format!

. *
. ***** Illustration: Entering Tabular Data
. set more off

. *
. ***** Initialize variable names and set initial value to missing.
. generate smoking=.
. generate coffee=.
. generate mi=.
. generate tally=.

. *
. ***** Click on the data editor icon. You should see the following empty spreadsheet.

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PubHlth 640 – Spring 2013 Stata v 12 Stratified Analysis of K 2x2 Tables
. *
. ***** Enter your data.

Note – Enter your table by table, beginning with the first table (smoking =1 for the “Former
smokers”) as follows. For each table, enter the data row by row, beginning with the first row.
When you are done, your completed spreadsheet should be populated exactly as shown below.
Close the data editor window. Don’t worry! Your data is not lost.

. *
. ***** Close the data editor window to return to the command window.

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PubHlth 640 – Spring 2013 Stata v 12 Stratified Analysis of K 2x2 Tables

. *
. ***** Assign variable names. Create value labels. Assign value labels.
. label variable smoking "Stratum of Smoking"
. label variable coffee "Cups of Coffee/Day"
. label variable mi "MI - Myocardial Infarction"
. label define smokingf 1 "Former Smoker" 2 "1-4 cigs/day" 3 "35-44 cigs/day" 4 "45+ cigs/day"
. label define mif 1 "MI" 0 "Non-MI"
. label define coffee 1 “5+cups” 0 “Less”
. label values smoking smokingf
. label values coffee coffeef
. label values mi mif

. *
. ***** Save tabular data in stata data set called coffeemi_tabular.dta
. save "/Users/carolbigelow/Desktop/coffeemi_tabular.dta"
file /Users/carolbigelow/Desktop/coffeemi_tabular.dta saved

. *
. ***** Create expanded data set. Check. Save as coffeemi_full.dta
. expand tally
(478 observations created)

. drop tally
. save "/Users/carolbigelow/Desktop/coffeemi_full.dta"
file /Users/carolbigelow/Desktop/coffeemi_full.dta saved

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PubHlth 640 – Spring 2013 Stata v 12 Stratified Analysis of K 2x2 Tables

3. Descriptives - Numerical

Stata offers several commands for producing descriptives. Some results are more compact than others. The following
are some suggestions.

. *
. ***** 3a) xtab of coffee by mi - OVERALL
. tab2 coffee mi, row column

-> tabulation of coffee by mi

+-------------------+
| Key |
|-------------------|
| frequency |
| row percentage |
| column percentage |
+-------------------+

| MI - Myocardial
Cups of | Infarction
Coffee/Day | Non-MI MI | Total
-----------+----------------------+----------
Less | 198 142 | 340
| 58.24 41.76 | 100.00
| 70.46 66.67 | 68.83
-----------+----------------------+----------
5+ cups | 83 71 | 154
| 53.90 46.10 | 100.00
| 29.54 33.33 | 31.17
-----------+----------------------+----------
Total | 281 213 | 494
| 56.88 43.12 | 100.00
| 100.00 100.00 | 100.00

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. *
. ***** 3b xtab of coffee by mi - by strata of SMOKING
. sort smoking
. by smoking: tab2 coffee mi, row column

-> smoking = Former Smoker
-> tabulation of coffee by mi

+-------------------+
| Key |
|-------------------|
| frequency |
| row percentage |
| column percentage |
+-------------------+

| MI - Myocardial
Cups of | Infarction
Coffee/Day | Non-MI MI | Total
-----------+----------------------+----------
Less | 112 20 | 132
| 84.85 15.15 | 100.00
| 86.15 74.07 | 84.08
-----------+----------------------+----------
5+ cups | 18 7 | 25
| 72.00 28.00 | 100.00
| 13.85 25.93 | 15.92
-----------+----------------------+----------
Total | 130 27 | 157
| 82.80 17.20 | 100.00
| 100.00 100.00 | 100.00

---- some output omitted ----

-> smoking = 45+ cigs/day

| MI - Myocardial
Cups of | Infarction
Coffee/Day | Non-MI MI | Total
-----------+----------------------+----------
Less | 17 34 | 51
| 33.33 66.67 | 100.00
| 50.00 53.12 | 52.04
-----------+----------------------+----------
5+ cups | 17 30 | 47
| 36.17 63.83 | 100.00
| 50.00 46.88 | 47.96
-----------+----------------------+----------
Total | 34 64 | 98
| 34.69 65.31 | 100.00
| 100.00 100.00 | 100.00

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. *
. ***** 3c) Compact display of % experiencing an MI, in each category of smoking and coffee
Wonderful Tip!! Because the variable mi that we created is coded as 0=NON MI and 1=MI, the
value of the sample mean of mi will be equal to the % who experience MI

. tabulate smoking coffee, summarize(mi) means

Means of MI - Myocardial Infarction

Stratum of | Cups of Coffee/Day
Smoking | Less 5+ cups | Total
-----------+----------------------+----------
Former Sm | .15151515 .28 | .17197452
1-4 cigs/ | .75 .22580645 | .53333333
35-44 cig | .48672566 .52941176 | .5
45+ cigs/ | .66666667 .63829787 | .65306122
-----------+----------------------+----------
Total | .41764706 .46103896 | .43117409

Illustration of interpreting this table:

(1) Overall, 43% experienced an MI
(2) Among former smokers whose coffee consumption is “LESS”, 15% experienced an MI
Etc.

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PubHlth 640 – Spring 2013 Stata v 12 Stratified Analysis of K 2x2 Tables

4. Descriptives - Graphical

Stata also offers several graphical options. Two are shown here. One is a bar graph, which is often used but not
always a great choice. The second is a plot of the odds ratios, together with their 95% confidence limits.

. *
. ***** 4a) GRAPH - Bar Graph of % Experiencing MI over coffee and smoking
. set scheme s2color
. graph bar mi, over(coffee, gap(10)) over(smoking, gap(80)) outergap(50) ytitle("Proportion
Experiencing MI") title("Coffee and MI") subtitle("by Smoking Status") ylabel(0(.2)1)
caption("mi_bar.png", size(vsmall))

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