Assumptions of an Accelerated Failure Time model?

Question

I have an AFT model, comparing the adjusted survival of 5 groups and seeming to give reasonable results. As I do not feel confident in survival modelling, does this model has assumptions that need to be tested before publishing its results?

If there are assumptions, how should I test them? Only thing that I have found is this: “the QQ plot approximates well to a straight line from the origin, indicating that the AFT approach may provide a suitable model” (Figure 4 in article https://doi.org/10.1002/pst.213). As I have 5 groups, I have to make multiple comparisons (A vs B, A vs C etc). Should the points draw a fully straight line or some deviations are acceptable?

MODEL

    m = flexsurvreg(Surv(time, status) ~ group + sex + age + 
                    comorbidity, dist="lnorm", data = data)

SUMMARY

    Call:
    flexsurvreg(formula = Surv(time_12m, status_12m) ~ group + sex + 
        age + comorbidity, data = data, dist = "lnorm")
    
    Estimates: 
                                                                                data mean  est       L95%      U95%      se        exp(est)  L95%      U95%    
    meanlog                                                                           NA   12.24216  11.66464  12.81969   0.29466        NA        NA        NA
    sdlog                                                                             NA    2.36049   2.29609   2.42670   0.03331        NA        NA        NA
    groupB                                                                       0.01036    0.21074  -0.36563   0.78712   0.29407   1.23459   0.69376   2.19705
    groupC                                                                       0.03170   -2.47406  -2.73891  -2.20922   0.13513   0.08424   0.06464   0.10979
    groupD                                                                       0.02000   -1.90413  -2.24392  -1.56435   0.17336   0.14895   0.10604   0.20922
    groupE                                                                       0.00545   -0.93920  -1.63303  -0.24537   0.35400   0.39094   0.19534   0.78241
    sexMale                                                                      0.28116   -0.72137  -0.85427  -0.58847   0.06781   0.48609   0.42560   0.55517
    age                                                                         78.71304   -0.09784  -0.10443  -0.09125   0.00336   0.90679   0.90084   0.91279
    comorbidity                                                                  1.65045   -0.22674  -0.25970  -0.19378   0.01682   0.79713   0.77128   0.82384
    
    N = 11200,  Events: 3346,  Censored: 7854
    Total time at risk: 105996.2
    Log-likelihood = -13337.38, df = 9
    AIC = 26692.76

score 1 · Accepted Answer · answered Mar 09 '21 at 22:38

In general, for a parametric survival model one should in particular:

verify that the assumption of linearity in the coefficients holds, as for any (generalized) linear model;
check that the assumed parametric form of the model adequately represents the data;
validate the model by resampling to guard against overfitting; and
check the calibration of the model by comparing predicted and observed survival probabilities at specific times of interest.

These are essentially the same for any survival regression model, except that point 2 for a Cox proportional-hazards (PH) model would be to check the PH assumption rather than a particular parametric form.

This question is very broad, so I'd recommend that you study the detailed presentation on building and validating parametric survival models in Chapters 18 and 19 of Harrell's Regression Modeling Strategies book or freely available course notes. Those presentations use the rms package in R, which provides more built-in tools for model assessment than does the flexsurv package; its psm() function fits parametric survival models. There is a bit of a steep initial learning curve with rms, but it's quite worth the effort if you do much regression modeling of any type.

For your own benefit, you should become much more familiar with survival modeling, or engage a collaborator with some experience in it, before you submit for publication. Otherwise, the way that you present results might lead to unnecessary criticisms from reviewers that could be difficult to address.

Assumptions of an Accelerated Failure Time model?

1 Answers1