Chapter 13, Section 13.4

 

Muscatine Coronary Risk Factor Study

Marginal Logistic Regression Model

 

use "muscatine.dta"

 

gen cage=age - 12

 

gen cage2=cage*cage

 

tsset id occasion

       panel variable:  id (strongly balanced)

        time variable:  occasion, 1 to 3

                delta:  1 unit

 

xtgee y i.gender cage cage2 i.gender#c.cage i.gender#c.cage2, /// 

     family(binomial) link(logit) corr(unstr) robust

 

Iteration 1: tolerance = .01601043

Iteration 2: tolerance = .00008379

Iteration 3: tolerance = 1.585e-06

Iteration 4: tolerance = 4.164e-08

 

GEE population-averaged model                   Number of obs      =      9856

Group and time vars:           id occasion      Number of groups   =      4856

Link:                                logit      Obs per group: min =         1

Family:                           binomial                     avg =       2.0

Correlation:                  unstructured                     max =         3

                                                Wald chi2(5)       =     71.38

Scale parameter:                         1      Prob > chi2        =    0.0000

 

                                     (Std. Err. adjusted for clustering on id)

------------------------------------------------------------------------------

             |             Semirobust

           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]

-------------+----------------------------------------------------------------

    1.gender |   .1137967   .0711192     1.60   0.110    -.0255943    .2531878

        cage |   .0378425   .0132932     2.85   0.004     .0117884    .0638966

       cage2 |  -.0176874   .0033755    -5.24   0.000    -.0243033   -.0110715

             |

      gender#|

      c.cage |

          1  |   .0071529   .0183061     0.39   0.696    -.0287264    .0430322

             |

      gender#|

     c.cage2 |

          1  |   .0038899   .0046337     0.84   0.401    -.0051919    .0129717

             |

       _cons |  -1.212052   .0505248   -23.99   0.000    -1.311078   -1.113025

------------------------------------------------------------------------------

 

xtcorr

 

Estimated within-id correlation matrix R:

 

        c1      c2      c3

r1  1.0000

r2  0.5978  1.0000

r3  0.4708  0.5479  1.0000

 

test 1.gender#c.cage 1.gender#c.cage2 

 

 ( 1)  1.gender#c.cage = 0

 ( 2)  1.gender#c.cage2 = 0

 

           chi2(  2) =    0.87

         Prob > chi2 =    0.6481

 

 

 

 

xtgee y gender cage cage2,family(binomial) link(logit) corr(unstr) robust

 

Iteration 1: tolerance = .01571011

Iteration 2: tolerance = .0003364

Iteration 3: tolerance = 3.081e-06

Iteration 4: tolerance = 8.681e-08

 

GEE population-averaged model                   Number of obs      =      9856

Group and time vars:           id occasion      Number of groups   =      4856

Link:                                logit      Obs per group: min =         1

Family:                           binomial                     avg =       2.0

Correlation:                  unstructured                     max =         3

                                                Wald chi2(3)       =     71.21

Scale parameter:                         1      Prob > chi2        =    0.0000

 

                                     (Std. Err. adjusted for clustering on id)

------------------------------------------------------------------------------

             |             Semi-robust

           y |      Coef.   StdErr.      z    P>|z|     [95% Conf. Interval]

-------------+----------------------------------------------------------------

      gender |   .1426856   .0626843     2.28   0.023     .0198266    .2655447

        cage |   .0416386   .0091281     4.56   0.000     .0237479    .0595292

       cage2 |  -.0156835   .0023092    -6.79   0.000    -.0202095   -.0111575

       _cons |  -1.226743   .0476951   -25.72   0.000    -1.320223   -1.133262

------------------------------------------------------------------------------

 

 

Clinical Trial of Antibiotics for Leprosy

Marginal Log-linear Regression Model

 

 

use "leprosy.dta"

 

gen id=_n

 

gen antibiotic=0

 

replace antibiotic=1 if (drug != 0)

(20 real changes made)

 

reshape long y, i(id) j(time)

(note: j = 1 2)

 

Data                               wide   ->   long

-----------------------------------------------------------------------------

Number of obs.                       30   ->      60

Number of variables                   5   ->       5

j variable (2 values)                     ->   time

xij variables:

                                  y1 y2   ->   y

-----------------------------------------------------------------------------

 

. label variable y "Count of Leprosy Basilli"

 

xtgee y 2.time i.drug#2.time,family(poisson) link(log) corr(unstr) ///

     robust scale(x2)

 

 

Iteration 1: tolerance = .14470346

Iteration 2: tolerance = .00794855

Iteration 3: tolerance = .00030872

Iteration 4: tolerance = .00004549

Iteration 5: tolerance = 1.450e-06

Iteration 6: tolerance = 2.701e-07

 

GEE population-averaged model                   Number of obs      =        60

Group and time vars:               id time      Number of groups   =        30

Link:                                  log      Obs per group: min =         2

Family:                            Poisson                     avg =       2.0

Correlation:                  unstructured                     max =         2

                                                Wald chi2(3)       =     22.20

Scale parameter:                  3.213811      Prob > chi2        =    0.0001

 

                                     (Std. Err. adjusted for clustering on id)

------------------------------------------------------------------------------

             |             Semirobust

           y |      Coef.   StdErr.      z    P>|z|     [95% Conf. Interval]

-------------+----------------------------------------------------------------

      2.time |  -.0028761   .1596889    -0.02   0.986    -.3158606    .3101085

             |

   drug#time |

        1 2  |  -.5625683   .2257767    -2.49   0.013    -1.005083    -.120054

        2 2  |  -.4952842   .2382042    -2.08   0.038    -.9621559   -.0284125

             |

       _cons |   2.373354   .0815078    29.12   0.000     2.213602    2.533107

------------------------------------------------------------------------------

(Standard errors scaled using square root of Pearson X2-based dispersion)

 

xtcorr    

 

Estimated within-id correlation matrix R:

 

        c1      c2

r1  1.0000

r2  0.7384  1.0000

 

 

test 1.drug#2.time 2.drug#2.time

 

 ( 1)  1.drug#2.time = 0

 ( 2)  2.drug#2.time = 0

 

           chi2(  2) =    7.09

         Prob > chi2 =    0.0288

 

test 1.drug#2.time = 2.drug#2.time

 

 ( 1)  1.drug#2.time - 2.drug#2.time = 0

 

           chi2(  1) =    0.09

         Prob > chi2 =    0.7699

 

 

 

xtgee y 2.time i.antibiotic#2.time,family(poisson) link(log) /// 

     corr(unstr) robust scale(x2)

 

Iteration 1: tolerance = .13032639

Iteration 2: tolerance = .00695181

Iteration 3: tolerance = .00030193

Iteration 4: tolerance = .00003147

Iteration 5: tolerance = 1.506e-06

Iteration 6: tolerance = 1.481e-07

 

GEE population-averaged model                   Number of obs      =        60

Group and time vars:               id time      Number of groups   =        30

Link:                                  log      Obs per group: min =         2

Family:                            Poisson                     avg =       2.0

Correlation:                  unstructured                     max =         2

                                                Wald chi2(2)       =     21.38

Scale parameter:                  3.230823      Prob > chi2        =    0.0000

 

                                     (Std. Err. adjusted for clustering on id)

------------------------------------------------------------------------------

             |             Semirobust

           y |      Coef.   StdErr.      z    P>|z|     [95% Conf. Interval]

-------------+----------------------------------------------------------------

      2.time |   -.002855   .1596885    -0.02   0.986    -.3158387    .3101286

             |

  antibiotic#|

        time |

        1 2  |  -.5278276   .2022255    -2.61   0.009    -.9241823    -.131473

             |

       _cons |   2.373354   .0815078    29.12   0.000     2.213602    2.533107

------------------------------------------------------------------------------

(Standard errors scaled using square root of Pearson X2-based dispersion)

 

 

xtcorr

 

Estimated within-id correlation matrix R:

 

        c1      c2

r1  1.0000

r2  0.7383  1.0000

 

 

 

Arthritis Clinical Trial

Marginal Proportional Odds (Ordinal) Regression Model

 

 

 

 

use "arthritis.dta"

 

reshape long y, i(id) j(time)

(note: j = 1 2 3 4)

 

Data                               wide   ->   long

-----------------------------------------------------------------------------

Number of obs.                      303   ->    1212

Number of variables                   7   ->       5

j variable (4 values)                     ->   time

xij variables:

                           y1 y2 ... y4   ->   y

-----------------------------------------------------------------------------

 

gen month=2*(time-1)

 

gen sqrtmonth=month^0.5

 

drop if y==.

(18 observations deleted)

 

ologit y trt sqrtmonth trt#c.sqrtmonth, cluster(id)

 

Iteration 0:   log pseudolikelihood = -1649.2551  

Iteration 1:   log pseudolikelihood = -1620.2638  

Iteration 2:   log pseudolikelihood = -1620.1446  

Iteration 3:   log pseudolikelihood = -1620.1446  

 

Ordered logistic regression                       Number of obs   =       1194

                                                  Wald chi2(3)    =      72.10

                                                  Prob > chi2     =     0.0000

Log pseudolikelihood = -1620.1446                 Pseudo R2       =     0.0177

 

                                   (Std. Err. adjusted for 303 clusters in id)

------------------------------------------------------------------------------

             |               Robust

           y |      Coef.   StdErr.      z    P>|z|     [95% Conf. Interval]

-------------+----------------------------------------------------------------

         trt |  -.0713875    .193902    -0.37   0.713    -.4514286    .3086535

   sqrtmonth |  -.2481326   .0619707    -4.00   0.000     -.369593   -.1266722

             |

         trt#|

 c.sqrtmonth |

          1  |   -.235426   .0894341    -2.63   0.008    -.4107137   -.0601383

-------------+----------------------------------------------------------------

       /cut1 |  -3.190244   .1996446                      -3.58154   -2.798948

       /cut2 |  -1.204158   .1524371                     -1.502929   -.9053864

       /cut3 |   .5736485   .1474602                      .2846318    .8626652

       /cut4 |   2.477013   .2000607                      2.084901    2.869125

------------------------------------------------------------------------------