pkcross command: 3x3 crossover design

[Laura Brocklebank]

Hello statalist,

Is it possible to analyse a randomised three-period, three-treatment crossover trial using the pkcross command? If so, does anyone know of an example? I wish to look at the period, sequence, treatment and carryover effects.

Thanks

Laura

[Steve Samuels]

Welcome to Statalist, Laura! The first thing to do before you post is try to find the answer in the documentation. (Well, the very first thing you should do is read the FAQ, especially FAQ 12.) Here's an example of pkcross with a 3x3 crossover, based on Example 3 of the Manual entry for pkshape, which has an analysis with anova. pkcross is a more elaborate ANOVA, so it's not surprising that it can analyze the same data. Note that pkcross with no carryover and anova give the same results.

use http://www.stata-press.com/data/r14/applesales, clear
 pkshape id seq p1 p2 p3, order(bca abc cab) ///
 seq(pattern) period(order) treat(displays)

anova outcome pattern order display id|pattern


                         Number of obs =         18    R-squared     =  0.9562
                         Root MSE      =    1.59426    Adj R-squared =  0.9069

                  Source | Partial SS         df         MS        F    Prob>F
              -----------+----------------------------------------------------
                   Model |  443.66667          9   49.296296     19.40  0.0002
                         |
                 pattern |  .33333333          2   .16666667      0.07  0.9370
                   order |  233.33333          2   116.66667     45.90  0.0000
                displays |        189          2        94.5     37.18  0.0001
              id|pattern |         21          3           7      2.75  0.1120
                         |
                Residual |  20.333333          8   2.5416667  
              -----------+----------------------------------------------------
                   Total |        464         17   27.294118  

.
 ** pkcross: no carryover
. pkcross outcome, seq(pattern) treat(displays) period(order) id(id) carry(none)
                                                 sequence variable = pattern
                                                   period variable = order
                                                treatment variable = displays
                                                carryover variable =
                                                       id variable = id
                 Analysis of variance (ANOVA) for a crossover study
     Source of Variation  | Partial SS   df        MS          F     Prob > F
    ----------------------+--------------------------------------------------
     Intersubjects        |
         Sequence effect  |       0.33    2        0.17      0.02      0.9767
                Residuals |      21.00    3        7.00      2.75      0.1120
    ----------------------+--------------------------------------------------
     Intrasubjects        |
         Treatment effect |     189.00    2       94.50     37.18      0.0001
            Period effect |     233.33    2      116.67     45.90      0.0000
                Residuals |      20.33    8        2.54
    ----------------------+--------------------------------------------------
                    Total |     464.00   17

.
. **pkcross with carryover
. pkcross outcome, seq(pattern) treat(displays) period(order) id(id) carry(carry)
                                                 sequence variable = pattern
                                                   period variable = order
                                                treatment variable = displays
                                                carryover variable = carry
                                                       id variable = id
                 Analysis of variance (ANOVA) for a crossover study
     Source of Variation  | Partial SS   df        MS          F     Prob > F
    ----------------------+--------------------------------------------------
     Intersubjects        |
         Sequence effect  |       2.67    2        1.33      0.19      0.8358
                Residuals |      21.00    3        7.00      2.62      0.1451
    ----------------------+--------------------------------------------------
     Intrasubjects        |
         Treatment effect |      31.67    2       15.83      5.94      0.0378
         Carryover effect |       4.33    2        2.17      0.81      0.4872
            Period effect |     221.13    2      110.57     41.46      0.0003
                Residuals |      16.00    6        2.67
    ----------------------+--------------------------------------------------
                    Total |     464.00   17

    Omnibus measure of separability of treatment and carryover =   18.3503%

.