Stata’s poisson fits maximum-likelihood models of the number of occurrences (counts) of an event. In a Poisson regression model, the incidence rate for the \(j\)th observation is assumed to be given by
\(r_j = exp(\beta_0 + \beta_1 x_{1,j} +{...}+ \beta_k x_{k,j}) \)
If \(E_j\) is the exposure, the expected number of events \(C_j\) will be
\(C_j = E_j r_j\)
\(\;\;\;\;\:= exp[\;ln(E_j) + \beta_0 + \beta_1 x_{1,j} +{...}+ \beta_k x_{k,j}\;]\)
This is the model fitted by poisson. \(E_j\) may be specified or, if not specified, is assumed to be \(1\).
. poisson deaths smokes i.agecat, exposure(pyears) irr
Iteration 0: Log likelihood = -33.823284
Iteration 1: Log likelihood = -33.600471
Iteration 2: Log likelihood = -33.600153
Iteration 3: Log likelihood = -33.600153
Poisson regression Number of obs = 10
LR chi2(5) = 922.93
Prob > chi2 = 0.0000
Log likelihood = -33.600153 Pseudo R2 = 0.9321
| deaths | IRR Std. Err. z P>|z| [95% Conf. Interval] | |
| smokes | 1.425519 .1530638 3.30 0.001 1.154984 1.759421 | |
| agecat | ||
| 45-54 | 4.410584 .8605197 7.61 0.000 3.009011 6.464997 | |
| 55-64 | 13.8392 2.542638 14.30 0.000 9.654328 19.83809 | |
| 65-74 | 28.51678 5.269878 18.13 0.000 19.85177 40.96395 | |
| 75-84 | 40.45121 7.775511 19.25 0.000 27.75326 58.95885 | |
| _cons | .0003636 .0000697 -41.30 0.000 .0002497 .0005296 | |
| ln(pyears) | 1 (exposure) | |
The syntax of all estimation commands is the same: the name of the dependent variable is followed by the names of the independent variables, which are followed by a comma and any options. In this case, we controlled for the exposure (person-years recorded in the variable pyears) and asked that results be displayed as incidence-rate ratios rather than as coefficients.
svy: poisson can be used to analyze complex survey data, and the mi estimate: poisson command performs estimation using multiple imputations. Also, Stata provides Cox regression, exponential, Weibull, and other parametric survival models, as well as logistic regression, and all can be used to analyze complex survey data or to perform estimation using multiple imputations.
