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  • Deviance residuals in survival model

    Dear all,
    I thank you in advance.
    I have a question.
    It is the first time I run a frailty survival model to account for the clustering of patients within different hospitals.
    I used "linktest" to assess the model specification and I got bad results (I wished for a significant _hat).

    Code:
    ------------------------------------------------------------------------------
              _t | Haz. ratio   Std. err.      z    P>|z|     [95% conf. interval]
    -------------+----------------------------------------------------------------
            _hat |   3.442834   2.606742     1.63   0.103     .7806006     15.1846
          _hatsq |   2.431289   12.82696     0.17   0.866     .0000785    75264.97
           _cons |   .9794605   .0972407    -0.21   0.834     .8062687    1.189855
    ------------------------------------------------------------------------------
    Note: _cons estimates baseline hazard.

    So I tried to look at the distribution of deviance residuals against predicted values.

    I got this strange pattern.

    Click image for larger version

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    How would you interpret it? In other survival models I got more homogeneous distribuitons of deviance reisduals.

    The model I ran was the following:

    Code:
    . xi: streg ib3.AED_aggiunto Età i.Sesso i.EventiYN i.dicOutcome N_AED_prima_reclutamento Mesi_da_diagnosi_epilessia, 
    > distribution(exponential) frailty(gamma) shared(Prefisso_Centro) nolog forceshared
    i.Sesso           _ISesso_0-1         (naturally coded; _ISesso_0 omitted)
    i.EventiYN        _IEventiYN_0-1      (naturally coded; _IEventiYN_0 omitted)
    i.dicOutcome      _IdicOutcom_0-1     (naturally coded; _IdicOutcom_0 omitted)
    
            Failure _d: OutYN==0
      Analysis time _t: cs
    
    Exponential PH regression
    Gamma shared frailty                                Number of obs     =    807
    Group variable: Prefisso_C~o                        Number of groups  =     23
                                                        Obs per group:   
    No. of subjects =      807                                        min =      1
    No. of failures =      157                                        avg =     35
    Time at risk    = 159.0404                                        max =     80
                                                        LR chi2(10)       =   1.81
    Log likelihood = -483.1438                          Prob > chi2       = 0.9976
    
    --------------------------------------------------------------------------------------------
                            _t | Haz. ratio   Std. err.      z    P>|z|     [95% conf. interval]
    ---------------------------+----------------------------------------------------------------
                  AED_aggiunto |
                            1  |   .9841484   .2479838    -0.06   0.949     .6005877    1.612667
                            2  |   1.018387   .3468174     0.05   0.957     .5224341    1.985155
                            4  |   .9716402   .2861077    -0.10   0.922     .5455844     1.73041
                            5  |   .9941576   .3782271    -0.02   0.988     .4716456    2.095534
                               |
                           Età |   .9993997   .0059959    -0.10   0.920     .9877168    1.011221
                     _ISesso_1 |   .9968113   .1654504    -0.02   0.985     .7199972    1.380051
                  _IEventiYN_1 |   1.193334   .2336239     0.90   0.367     .8130531     1.75148
                 _IdicOutcom_1 |   .8259511   .1780857    -0.89   0.375     .5412828     1.26033
      N_AED_prima_reclutamento |   .9920639   .0687574    -0.11   0.908     .8660541    1.136408
    Mesi_da_diagnosi_epilessia |   1.000015   .0002245     0.07   0.947     .9995748    1.000455
                         _cons |    1.06081   .4599163     0.14   0.892     .4535211    2.481291
    ---------------------------+----------------------------------------------------------------
                      /lntheta |  -1.039067   .5173458    -2.01   0.045    -2.053046   -.0250876
    ---------------------------+----------------------------------------------------------------
                         theta |   .3537847    .183029                      .1283434    .9752245
    --------------------------------------------------------------------------------------------
    Note: Estimates are transformed only in the first equation to hazard ratios.
    Note: _cons estimates baseline hazard.
    LR test of theta=0: chibar2(01) = 16.01                Prob >= chibar2 = 0.000
    Attached Files
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