sample size for multivariate logistic regression

[Yoshiro Nagao]

Dear Experts

First let me apologise for buzzing you with a layman's question.

I have a hypothesis that the amount of a certain virus in our blood (i.e. viral_load) is associated with the development of a certain illness .

We coded the development of illness and sex as binary variables.

A pilot study with a small sample size (n=59) showed that::

. sum viral_load sex illness

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
  viral_load |        59     4.30339    1.557403          0        7.3
         sex |        59    .5254237    .5036396          0          1
     illness |        51    .1764706    .3850134          0          1

. sum sex viral_load if illness == 0

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
         sex |        42     .452381    .5037605          0          1
  viral_load |        42    4.204762    1.593577          0        7.3

. sum sex viral_load if illness == 1

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
         sex |         9    .7777778    .4409586          0          1
  viral_load |         9    4.966667     .952628          4        6.9

. logistic illness sex viral_load

Logistic regression                               Number of obs   =         51
                                                  LR chi2(2)      =       5.35
                                                  Prob > chi2     =     0.0690
Log likelihood = -21.091878                       Pseudo R2       =     0.1125

------------------------------------------------------------------------------
     illness | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         sex |   4.314489    3.80492     1.66   0.097     .7660555    24.29957
  viral_load |   1.560802    .518568     1.34   0.180     .8138436    2.993332
       _cons |   .0108567   .0200497    -2.45   0.014     .0002909     .405189
------------------------------------------------------------------------------

The P value for the viral_load was marginal (P=0.18). The above result shows that we have to consider the effect of sex (1 for male, 0 for female in this dataset).

How can I estimate the sample size to adequately test the hypothesis in a multivariate analysis which considers the effect of sex?
alpha and beta should be the default.

I am using Stata 13. Since I am not experienced in programming for Stata, I would like to do the work by a command or a wizard, if possible.

Your assistance would be appreciated.

Yoshi

[Carlo Lazzaro]

Yoshi:
1) you probably want to run a multiple (and not a multivariate, that implies >1 dependent variable) logistic regression;
2) you should probably interact your predictors (I assume that in your research sex is a n-level categorical varable):

logistic illness i.sex##c.viral_load

3) see https://blog.stata.com/2019/08/13/ca...ic-regression/