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Tables for epidemiologists
Stata has a set of commands for dealing with 2 x 2 tables, including stratified tables, known collectively as the epitab commands. To calculate appropriate statistics and suppress inappropriate statistics, these commands are organized in the same way that epidemiologists conceptualize data. Stata’s ir command is used with incidence-rate (incidence density or person-time) data; point estimates and confidence intervals for the incidence-rate ratio and difference are calculated, along with the attributable or prevented fractions for the exposed and total populations. Stata’s cs command is used with cohort study data with equal follow-up time per subject. Risk is then the proportion of subjects who become cases. Point estimates and confidence intervals for the risk difference, risk ratio, and (optionally) the odds ratio are calculated, along with attributable or prevented fractions for the exposed and total population. Stata’s cc command is used with case–control and cross-sectional data. Point estimates and confidence intervals for the odds ratio are calculated along with attributable or prevented fractions for the exposed and total population. mcc is used with matched case–control data. It calculates McNemar’s chi-squared, point estimates, and confidence intervals for the difference, ratio, and relative difference of the proportion with the factor, along with the odds ratio. All these commands come in two flavors: their normal forms and an “immediate” form. In their normal forms, the commands form counts by summing the dataset in use. In their immediate forms, the data are specified on the command line. For instance, Boice and Monson (1977 and reprinted in Rothman and Greenland 1998, 238) reported on breast cancer cases and person-years of observations for women with tuberculosis who were repeatedly exposed to multiple X-ray fluoroscopies and for those not exposed: X-ray fluoroscopy
Exposed Unexposed
-------------------------------------------
Breast cancer cases 41 15
Person years 28,010 19,017
Using the immediate form of ir, you specify the values in the table following the command: . iri 41 15 28010 19017
| Exposed Unexposed | Total
-----------------+------------------------+------------
Cases | 41 15 | 56
Person-time | 28010 19017 | 47027
-----------------+------------------------+------------
| |
Incidence Rate | .0014638 .0007888 | .0011908
| |
| Point estimate | [95% Conf. Interval]
|------------------------+------------------------
Inc. rate diff. | .000675 | .0000749 .0012751
Inc. rate ratio | 1.855759 | 1.005684 3.6093 (exact)
Attr. frac. ex. | .4611368 | .0056519 .722938 (exact)
Attr. frac. pop | .337618 |
+-------------------------------------------------
(midp) Pr(k>=41) = 0.0177 (exact)
(midp) 2*Pr(k>=41) = 0.0355 (exact)
The grander ir command itself can work with individual-level or aggregate data and also work with stratified data. Rothman and Greenland (1998, 259) report results from Doll and Hill (1966) on age-specific coronary disease deaths among British male doctors in relation to cigarette smoking: Smokers Nonsmokers
Age Deaths Person-years Deaths Person-years
-------------------------------------------------------
35-44 32 52,407 2 18,790
45-54 104 43,248 12 10,673
55-64 206 28,612 28 5,710
65-74 186 12,663 28 2,585
75-84 102 5,317 31 1,462
We have entered these data into Stata: . list, separator(0)
+-----------------------------------+
| age smokes deaths pyears |
|-----------------------------------|
1. | 35-44 1 32 52,407 |
2. | 35-44 0 2 18,790 |
3. | 45-54 1 104 43,248 |
4. | 45-54 0 12 10,673 |
5. | 55-64 1 206 28,612 |
6. | 55-64 0 28 5,710 |
7. | 65-74 1 186 12,663 |
8. | 65-74 0 28 2,585 |
9. | 75-84 1 102 5,317 |
10. | 75-84 0 31 1,462 |
+-----------------------------------+
We can obtain the Mantel–Haenszel combined estimate of the incidence-rate ratio, along with 90% confidence intervals, by typing . ir deaths smokes pyears, by(age) level(90)
age | IRR [90% Conf. Interval] M-H Weight
-----------------+-------------------------------------------------
35-44 | 5.736638 1.704271 33.61646 1.472169 (exact)
45-54 | 2.138812 1.274552 3.813282 9.624747 (exact)
55-64 | 1.46824 1.044915 2.110422 23.34176 (exact)
65-74 | 1.35606 .9626026 1.953505 23.25315 (exact)
75-84 | .9047304 .6375194 1.305412 24.31435 (exact)
-----------------+-------------------------------------------------
Crude | 1.719823 1.437544 2.0688 (exact)
M-H combined | 1.424682 1.194375 1.699399
-------------------------------------------------------------------
Test of homogeneity (M-H) chi2(4) = 10.41 Pr>chi2 = 0.0340
Rothman and Greenland (1998, 264) obtain the standardized incidence-rate ratio and 90% confidence intervals, weighting each age category by the population of the exposed group, thus producing the standardized mortality ratio (SMR). This calculation can be reproduced by specifying by(age) to indicate that the table is stratified, and istandard to specify that we want the internally standardized rate: . ir deaths smokes pyears, by(age) level(90) istandard
age | IRR [90% Conf. Interval] Weight
-----------------+-------------------------------------------------
35-44 | 5.736638 1.704271 33.61646 52407 (exact)
45-54 | 2.138812 1.274552 3.813282 43248 (exact)
55-64 | 1.46824 1.044915 2.110422 28612 (exact)
65-74 | 1.35606 .9626026 1.953505 12663 (exact)
75-84 | .9047304 .6375194 1.305412 5317 (exact)
-----------------+-------------------------------------------------
Crude | 1.719823 1.437544 2.0688 (exact)
I. Standardized | 1.417609 1.186541 1.693676
If we want the externally standardized ratio (weights proportional to the population of the unexposed group), we can substitute estandard for istandard in the command above. See New in Stata 10 for more about what was added in Stata Release 10. References
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