Calculate z scores from p-values to get SEs

[Yuki Ishikawa]

Hi, all

I am trying to calculate z scores from p-values to get SEs using a logistic regression summary statistics data, a part of which is presented below.

SNP	P	P(R)	OR	OR(R)	Q	I
rs3094315	0.4913	0.4913	0.9420	0.9420	0.3873	0.00
rs12562034	0.9737	0.9737	1.0022	1.0022	0.5991	0.00

This is a meta-analysis data conducted by others.
P is p value and (R) indicates random effect models. Q is Q statistic and I I² index to assess the heterogeneity of the data.

Since they did not provide SEs or 95% CIs in this summary statistics, I am using the following formulas to get SEs:
SE=beta/z=ln(OR)/invnormal(p)
beta=ln(OR)
z=invnormal(p)

Then, I got these results.

SNP	β	z	z(R)	SE	SE(R)
rs3094315	-0.05975	-0.021809	-0.021809	2.739642	2.739642
rs12562034	0.0021976	1.938190	1.938190	0.001134	0.001134

I am wondering whether my calculation is correct or not, because the same calculations using a different data set, such as 1978 Automobile data, gave me completely different results.

logistic foreign price mpg rep78

Logistic regression                             Number of obs     =         69
                                                LR chi2(3)        =      34.08
                                                Prob > chi2       =     0.0000
Log likelihood = -25.362394                     Pseudo R2         =     0.4018

------------------------------------------------------------------------------
     foreign | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       price |   1.000141   .0001379     1.03   0.305     .9998712    1.000412
         mpg |    1.18063   .0966693     2.03   0.043     1.005583    1.386148
       rep78 |   5.321595   2.656576     3.35   0.001     2.000398    14.15687
       _cons |   .0000112    .000032    -4.00   0.000     4.23e-08    .0029816
------------------------------------------------------------------------------

If I am wrong, could you point out what is wrong about my calculations, please?

I will really appreciate any help and comments.

[Yuki Ishikawa]

Now I figure out I was stupid.
Considering p=2*(1-norm|z|), |z|=invnorm(1-p/2) is the correct function. Am I right?