泊松分布95%置信区间计算

如题：
总数  失败数  估计失败率（%，95% CI）
347       7            2.02（0.96-4.23）

code该如何写?

1. data have1;
   
2. y =7; n =347;
   
3. log_n = log(347);
   
4. run;
   
5. ods select Estimates;
   
6. proc genmod;
   
7. model y=/dist =poisson offset =log_n;
   
8. estimate 'rate' intercept 1/exp;
   
9. run;

复制代码

Contrast Estimate Results
                 Mean            Mean                         L'Beta          Standard
Label        Estimate      Confidence Limits     Estimate       Error      Alpha
rate           0.0202         0.0096      0.0423     -3.9034         0.3780      0.05
Exp(rate)                                                        0.0202          0.0076     0.05
                Contrast Estimate Results
                    L'Beta                       Chi-
Label          Confidence Limits     Square    Pr > ChiSq
rate             -4.6442     -3.1626    106.66        <.0001
Exp(rate)     0.0096      0.0423

but I dont think this is exact poisson regression either, while you can count on SAS 9.22 for the newly implemented Exact method in Genmod

data a;
r=7/347;
r_low = cinv(0.025, 2*7)/(2*347);
r_up = cinv(0.975, 2*(7+1))/(2*347);
run;

It is easy if you use R:

poisson.test(7,347)

data a;
r=7/347;z=probit(0.975);
deta=z*sqrt((z/347)**2+4*r/347);
b=2*r+z**2/347;
up=(b+deta)/2;
lo=(b-deta)/2;
proc print;run;

harlon1976 发表于 2010-8-10 07:02
data a;
r=7/347;z=probit(0.975);
deta=z*sqrt((z/347)**2+4*r/347);
b=2*r+z**2/347;
up=(b+deta)/2;
lo=(b-deta)/2;
proc print;run;

这是正态近似法计算，结果为：95%CI（0.9771942-4.1644）,
与想要的结果还有点差距。能否用exact poisson distribution计算呢？

marloneusa 发表于 2010-8-10 04:07
data a;
r=7/347;
r_low = cinv(0.025, 2*7)/(2*347);
r_up = cinv(0.975, 2*(7+1))/(2*347);
run;

It is easy if you use R:

poisson.test(7,347)

The CINV function returns the pth quantile from the chi-square distribution with degrees of freedom df and a noncentrality parameter nc. The probability that an observation from a chi-square distribution is less than or equal to the returned quantile is p. This function accepts a noninteger degrees of freedom parameter df.
If the optional parameter nc is not specified or has the value 0, the quantile from the central chi-square distribution is returned. The noncentrality parameter nc is defined such that if X is a normal random variable with mean and variance 1, X2 has a noncentral chi-square distribution with df=1 and nc = 2.
CAUTION: For large values of nc, the algorithm could fail; in that case, a missing value is returned.   
Note:   CINV is the inverse of the PROBCHI function.  

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