Geodesic
Goodness-of-fit for the Cox model from left truncated and right censored data
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 7-19

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We propose a test for the proportional hazards (Cox) model which is oriented against wide classes of alternatives including monotone hazard ratios and crossings of survival functions and can be used when data are left truncated and right censored. The limit distribution of the test statistics is derived. The results are applied for statistical analysis of classical data considered by Stablein and Koutrouvelis [19], Klein and Moeschberger [12], Hosmer and Lemeshow [7], Hosmer, Lemeshow and May [8]. Bibl. – 20 titles. 
@article{ZNSL_2009_368_a1,
     author = {V. Bagdonavi\v{c}ius and R. Levulien\'e and M. S. Nikulin},
     title = {Goodness-of-fit for the {Cox} model from left truncated and right censored data},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--19},
     publisher = {mathdoc},
     volume = {368},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a1/}
}
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V. Bagdonavičius; R. Levuliené; M. S. Nikulin. Goodness-of-fit for the Cox model from left truncated and right censored data. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 15, Tome 368 (2009), pp. 7-19. http://geodesic.mathdoc.fr/item/ZNSL_2009_368_a1/