Hello, Alessandro.

Indeed, if you plot martingale residuals (Y-axis) versus continuous covariates (X-axis), you may check functional form and the possibility of nonlinearity in a CoxReg. The model may be correct, but the cloud may show an unevenly distribution, asymmetrically around zero, likely with a tail to the right. Local linear regression (LOESS) curve is usually parallel to zero line.

Anyway, you are right, there are no clear explanations.

Have a look at:

http://www.mwsug.org/proceedings/2006/stats/MWSUG-2006-SD08.pdf

Regards.

This is an output, martingale plot, from a study we conducted on postmenopausal women, with LOESS line. The assumption of linearity was fullfilled.

Dear Emilio Pariente.

Thank you for your help. Here attached the Martingale residuals versus tumor diameter of hepatocellular carcinoma with LOESS line. Do you think that assumption of linearity is fulfilled? That is because most, if not all, residuals are between -1.0 and +1.0?

Many thanks again. Sincerely yours.

Alessandro:

Martingale residuals may present any value in the range (-∞, +1). A range between (-1, +1) is of interest in the assessment of deviance residuals, which may be calculated from martingale residuals. Their plot is easier to evaluate than that of martingale because of this optimal range.

In my opinion, your martingale plot seems to be uniform, with a tail to the right and LOESS line shows no trend along the values.

Covariate of interest shows a correct functional form, provides a good fit and fulfills the assumption of linearity (more correctly, non-linearity is slight)

Regards

Isn't there a clear cluster structure in the residuals, maybe due to an omitted grouping factor?

Dear Emilio, thank you very much for your help.. effectively (I read more in deep my statistical notes) the range is of interest if I check deviance residuals...

In conclusion, the more the LOESS line is parallel to zero line the more the non-linearity can be excluded.

For Eik... the cluster is represented by censored patients versus dead patients.

Hello, Eik.

You may be right and perhaps there is a cluster structure, due to a hidden factor.

However, it is also possible an overlapping: martingale residuals for incomplete observations will have negative values, whereas complete observations may show from very negative values (longer surviving values) to +1 (earlier deaths).

As far as I know, smoothing the plot with LOESS is key for its interpretation.

Regards.

Dear Cucchetti, this is helpful to me too. Thank you.

Dear Bernard.

Emilio Pariente-Rodrigo explained me how to interpret Martingales...

This has been useful to me too. Thanks Emilio.