Testing ratio of means from 2 samples.

[Sumedha Gupta]

Dear All,
I have an individual-month level panel with a treatment and a control group.

input float(treated outcome month ID)
0 1  1  766
0 2 12  548
0 1 10 1380
0 4  5 1248
0 5  6  773
0 3  4   66
1 1  3 1122
1 3  8  865
0 5  2 1354
1 3  2  650
0 2 11  282
0 6  8 1030
0 1  1 1381
0 3  9  431
0 1  7  250
1 6  9  104
1 2  1  544
0 5  2 1426
1 3  6 1035
0 3 11  938
0 2 10  368
0 2 10  442
0 5  4  718
0 4  1   39
0 6  4  709
0 1  2 1372
0 5  6  827
0 2  3  201
0 7  3 1286
0 2  3   67
0 3 10  776
1 2  6  593
0 3  6   26
0 4  1  962
0 5  4 1215
0 4  2  586
0 4  6  290
0 5  7   83
0 3  8  416
0 6  4  166
0 1  8  410
0 1  8  483
0 1  9  329
1 4 10 1383
0 1 11  629
0 1  5 1161
0 2  6  238
0 3  5  915
0 1  5  788
1 5  6  125
0 2 10 1330
0 4  5 1318
0 6 12 1229
0 3  5  714
0 5 11  678
0 0 12  429
0 2 10 1258
0 3 11  503
0 1  4  900
0 2  9 1305
0 3 12  901
0 4 10  268
0 2  6  694
0 1 12    9
0 2 12  587
1 4  4  135
0 2  1  682
1 2  4  320
0 1  3  663
0 2  3  423
0 4  2  730
0 1  4  496
1 3  7  324
0 5  1 1025
0 4 11  535
0 4  9  954
0 3  5  620
1 1  9  196
0 1  3  635
0 2  7 1300
0 3 12  762
0 2  5  729
0 4  5  252
1 2  6 1095
0 5  7  235
1 2 11  277
0 4  5  751
0 0 10  245
0 0  7  784
0 3  3  701
0 2  1 1275
0 2 10   13
0 4  9  869
0 4 12 1174
0 7 11  241
1 4 10 1057
0 4  7 1325
0 7  1  391
0 3  1  219
0 2  9  350
end

[/CODE]

I want to make a monthly plot of the ratio of the mean outcome (mean_outcome_treated/mean_outcome_control) by treatment status. I tried the following:

. mean outcome, over(treated month)

Mean estimation                              Number of obs   =      1,453

-------------------------------------------------------------------------
                        |       Mean   Std. Err.     [95% Conf. Interval]
------------------------+------------------------------------------------
c.outcome@treated#month |
                  0  1  |   2.914063   .1349519      2.649341    3.178784
                  0  2  |   2.913978   .1658389      2.588669    3.239288
                  0  3  |   2.831933   .1534484      2.530929    3.132937
                  0  4  |   2.990654   .1645196      2.667933    3.313376
                  0  5  |   2.738095   .1586365      2.426914    3.049276
                  0  6  |       3.19   .1685919       2.85929     3.52071
                  0  7  |   3.008696   .1770578      2.661379    3.356012
                  0  8  |    3.00885   .1641434      2.686866    3.330833
                  0  9  |   3.012658   .1876534      2.644558    3.380759
                  0 10  |   2.877551   .1736147      2.536988    3.218114
                  0 11  |   2.905263   .1802535      2.551678    3.258848
                  0 12  |    2.77686   .1536909       2.47538    3.078339
                  1  1  |        3.9   .3395043      3.234029    4.565971
                  1  2  |   2.666667   .5270463      1.632813     3.70052
                  1  3  |   2.333333   .4143877      1.520471    3.146196
                  1  4  |   3.555556   .5555556      2.465778    4.645333
                  1  5  |   3.454545   .5454545      2.384582    4.524509
                  1  6  |        2.6   .5206833      1.578628    3.621372
                  1  7  |   3.263158   .3138341      2.647541    3.878775
                  1  8  |   3.076923   .4593967      2.175771    3.978075
                  1  9  |       3.25   .4330127      2.400603    4.099397
                  1 10  |        3.2   .4163332      2.383321    4.016679
                  1 11  |          3    .438529      2.139782    3.860218
                  1 12  |          3   .5773503       1.86747     4.13253
-------------------------------------------------------------------------

. testnl (1.treated#1.month/0.treated#1.month)=1

  (1)  (1.treated#1.month/0.treated#1.month) = 1
       Constraint (1) dropped

               chi2(0) =        0.00
           Prob > chi2 =             .

I am looking for an estimate, with confidence interval, of the ratio to plot on a graph comparing the mean of the treated and control group in each month of the study period.

I will be grateful for any help you may be able to offer.
Many thanks in advance.
Sumedha.

[Clyde Schechter]

collapse (mean) outcome, by(treated month)
reshape wide outcome, i(month) j(treated)
gen ratio = outcome1/outcome0
graph twoway connected ratio month

Added: Sorry, that doesn't get you any confidence interval. So, this is better:

mean outcome, over(treated month)
frame create for_graph int month float(ratio se)
forvalues i = 1/12 {
    nlcom _b[[email protected]#`i'.month]/_b[[email protected]#`i'.month]
    frame post for_graph (`i') (r(b)[1,1]) (r(V)[1,1])
}

frame change for_graph
gen ll = ratio - invnormal(.975)*se
gen ul = ratio + invnormal(.975)*se
graph twoway (connect ratio month) (rcap ll ul month)

[Sumedha Gupta]

Thank you for your guidance, Prof. Schechter. Your code helps me get the estimated ratio but unfortunately not the CI's I am seeking. Is there a way I can also get the confidence intervals for the ratio at each month as well?

[Clyde Schechter]

See edits to #1.

[Sumedha Gupta]

You're the best! Thank you Prof. Schechter!