Poisson regression
Stata's poisson command fits
maximum-likelihood models of the number of occurrences (counts) of an event.
In a Poisson regression model, the incidence rate for the jth observation is
assumed to be given by
r_j = exp(b_0 + b_1*x_(1,j) + ... + b_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) + b_0 + b_1*x_(1,j) + ... + b_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 a2-a5, 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
a2 | 4.410584 .8605197 7.61 0.000 3.009011 6.464997
a3 | 13.8392 2.542638 14.30 0.000 9.654328 19.83809
a4 | 28.51678 5.269878 18.13 0.000 19.85177 40.96395
a5 | 40.45121 7.775511 19.25 0.000 27.75326 58.95885
pyears | (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.
Stata can perform stepwise Poisson regression, too. Also, Stata
provides Cox regression,
exponential, Weibull, and other parametric survival models, as well as
logistic regression
and stepwise variants of these procedures.
See
New in Stata 10
for more about what was added in Stata Release 10.
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