Presenting results after using tvc

[Marko Deinders]

I would like to continue on a previous post http://www.statalist.org/forums/foru...rical-variable

I will summarize what I did.

1) I used xi: stcox to find the HR's for 'i.fi' (categorical variable) which resulted in

          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]

      _Ifi_2 |    1.30246   .3043983     1.13   0.258     .8238155    2.059202
      _Ifi_3 |   1.227158   .2705795     0.93   0.353     .7965566    1.890533
      _Ifi_4 |   1.265197   .2959124     1.01   0.315     .7999703     2.00098
    confoun1 |   1.020096   .0205274     0.99   0.323     .9806459    1.061133
    confoun2 |   .1285151   .0386602    -6.82   0.000     .0712679    .2317471
    confoun3 |   1.866878   .2851363     4.09   0.000     1.383911    2.518394

2) After using stphtest there was an indication of a PH violation for '_Ifi3 & 4'. Therefore, I included a tvc for these variables.

                  
               Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]

main         |
      _Ifi_2 |    1.42097   .6583137     0.76   0.448     .5731079     3.52317
      _Ifi_3 |   2.467073   1.011836     2.20   0.028     1.104265    5.511765
      _Ifi_4 |   2.806306   1.203235     2.41   0.016     1.211081     6.50275
    confoun1 |   1.020374   .0205202     1.00   0.316     .9809375    1.061396
    confoun2 |     .12806   .0385377    -6.83   0.000     .0709998    .2309773
    confoun3 |   1.873243   .2861077     4.11   0.000     1.388631    2.526978
-------------+----------------------------------------------------------------
tvc          |
      _Ifi_3 |   .9271744   .0341732    -2.05   0.040     .8625582    .9966312
      _Ifi_4 |   .9149631   .0368545    -2.21   0.027     .8455073    .9901245

There is a statistically significant interaction with time for '_Ifi_3 & 4'.

How to present the results in a scientific article? '

This is the way I have done it, but not sure about this.

Haz. Ratio
Q1 = 1 (ref)
Q2 = 1.42 [0.57 - 3.52]
Q3 = 0.93 [0.86 - 0.99]
Q4 = 0.91 [0.84 - 0.99]

[Maarten Buis]

That is incorrect. The hazard ratio of fi3 is 2.47 at t=0 and declines by 1.3% every unit of time. Just like when you add a regular interaction you can no longer summarize "the" effect with one number, instead the effect changes depending on the value of the variable with which it is interacted. So you need to report and discuss both the main effect and the interaction term and/or present a graph.

[Marko Deinders]

Hi Maarten,

Thank you for your clear answer.

The articles that I have read simply present the initial results (without tvc) and use a footnote to indicate a violation ('The PH assumption was violated for this variable' ...)They do not report the main effect/interaction term.

1. Do you think this way of reporting is sufficient?
2. Can you provide an article that does report the main effect/interaction term or graph in case there was a PH violation?

[Steve Samuels]

In my opinion, the articles you describe are scientifically irresponsible; publication itself is certainly no justification. What would you think of a published multiple linear regression that reported the presence of interactions, but did nothing to describe them? In the case of stcox, the interactions are with time, as Maarten said.


Maarten has shown you one way of interpreting the interaction terms.

In Stata, stphplot is an ideal graph for describing non-proportionality of hazards for discrete groups. It stratifies by group, then plots log cumulative hazards adjusted for covariates (centered, so that zero is a reasonable value). Parallel curves have proportional hazards. To create a publishable graph, you can add any plot options you'd like.make the graph publishable. The manual has good examples. If the log cumulative hazard curves cross, then stphkm will show crossing survival curves.

You can model the hazard function with time interactions most easily with stpm2 (Lambert and Royston, 2009) (findit) fits flexible models, as time is an explicit variable in the model. However stpm2 is sensitive to the exact times, whereas stcox only depends on their rank.

See also Hess (1994) and Hosmer and Royston (2002), which I haven't tried.

Some other comments:

1.You have assumed that linear terms in your covariates provide the best fit? How do you know? Minimally, one approach is to run linktest after stcox. A broader approach is to find the best fitting flexible polynomial terms with fp or mfp.

2. If your covariates interact with time, they might also interact with each other. Have you checked for that possibility?

3. tvc and texp options are used time-varying coefficients. If you also have time-varying covariates, then other issues arise.


References:

Hess, K. 1994. Assessing time-by-covariate interactions in proportional hazards regression models using cubic spline models. Statistics in Medicine 13: 1045–1062.


Hosmer, David W, and Patrick Royston. 2002. Using Aalen’s linear hazards model to investigate time-varying effects in the proportional hazards regression model. The Stata Journal 2, 331-350.
available at: http://www.stata-journal.com/article.html?article=st0024


Lambert, Paul C, and Patrick Royston. 2009. Further development of flexible parametric models for survival analysis. Stata Journal 9, no. 2: 265.
http://www.stata-journal.com/article...article=st0165

[Eric Weisbrod]

That is incorrect. The hazard ratio of fi3 is 2.47 at t=0 and declines by 1.3% every unit of time. Just like when you add a regular interaction you can no longer summarize "the" effect with one number, instead the effect changes depending on the value of the variable with which it is interacted. So you need to report and discuss both the main effect and the interaction term and/or present a graph.

Maarten how did you get 1.3%? Do you mean 7.3%? (1 - .9271744 coefficient?) Otherwise I feel a bit lost.

Thanks if you see this and have time to follow up.

[Maarten Buis]

-7.3% is correct, thanks.