• 2 x 2 and 2 x 2 stratified table for longitudinal, cohort study, case-control, and matched case-control data
  • odds ratio, incidence ratio, risk ratio, risk difference, and attributable fraction
  • confidence intervals for the above
  • chi-squared, Fishers's exact, and Mantel–Haenszel tests
  • tests for homogeneity
  • choice of weights for stratified tables: Mantel–Haenszel, standardized, or user-specified
  • exact McNemar test for matched case-control data
  • tabulated odds and odds ratios
  • score test for linear trend

Stata has a set of commands for dealing with 2 x 2 tables, including stratified tables, known collectively as the epitab commands. In order to calculate appropriate statistics and suppress inappropriate statistics, these commands are organized in the way 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. 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, are calculated.

All of 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 is 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 repeatedly exposed to multiple X-ray fluoroscopies and those not so 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       |  1.005722     3.60942  (exact)
 Attr. frac. ex. |         .4611368       |   .005689    .7229472  (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) reports results from Doll and Hill (1966) on age-specific coronary disease deaths among British male doctors by 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 this data into Stata: 
. list

           age     smokes     deaths     pyears 
  1.     35-44          1         32      52407  
  2.     35-44          0          2      18790  
  3.     45-54          1        104      43248  
  4.     45-54          0         12      10673  
  5.     55-64          1        206      28612  
  6.     55-64          0         28       5710  
  7.     65-74          1        186      12663  
  8.     65-74          0         28       2585  
  9.     75-84          1        102       5317  
 10.     75-84          0         31       1462
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     1.704242   33.62016      1.472169  (exact)
           45-54 |   2.138812     1.274529   3.813215      9.624747  (exact)
           55-64 |    1.46824     1.044925   2.110463      23.34176  (exact)
           65-74 |    1.35606     .9625995   1.953472      23.25315  (exact)
           75-84 |   .9047304     .6375086   1.305422      24.31435  (exact)
-----------------+-------------------------------------------------
           Crude |   1.719823     1.437554   2.068803                (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) obtains 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 the table is stratified, and istandard to specify 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     1.704242   33.62016         52407  (exact)
           45-54 |   2.138812     1.274529   3.813215         43248  (exact)
           55-64 |    1.46824     1.044925   2.110463         28612  (exact)
           65-74 |    1.35606     .9625995   1.953472         12663  (exact)
           75-84 |   .9047304     .6375086   1.305422          5317  (exact)
-----------------+-------------------------------------------------
           Crude |   1.719823     1.437554   2.068803                (exact)
 I. Standardized |   1.417609     1.186541   1.693676
If we wanted the externally standardized ratio (weights proportional to the population of the unexposed group), we would substitute estandard for istandard in the command above.

References

Boice, J. D. and R. R. Monson. 1977.
Breast cancer in women after repeated fluoroscopic examinations of the chest. Journal of the National Cancer Institute 59: 823-832.

Doll, R. and A. B. Hill. 1966.
Mortality of British doctors in relation to smoking: observations on coronary thrombosis. In Epidemiological Approaches to the Study of Cancer and Other Chronic Diseases, ed. W. Haenszel. National Cancer Institute Monograph 19: 205-268.

Rothman, K. J. and S. Greenland. 1998.
Modern Epidemiology. 2d ed. Philadelphia: Lippincott–Raven.

© Copyright 2005 Stata Corporation.