Sir,

We thank Tian et al (2015) for their comments on our paper (Korn et al, 2015). They appear to agree with us that their analytic methods proposed in Tian et al (2014) do not work unless the following two assumptions hold: (1) the treatments have approximately equal efficacy in the overall population; and (2) the treatments the patients received were essentially assigned randomly (and not associated with factors that have prognostic importance). We note that these two assumptions are very strong, and, following Tian et al (2015), we review their plausibility in the context of recurrent ovarian cancer considered by Rutherford et al (2013). For assumption (1), one might question whether single-agent cisplatin or carboplatin works as well as the other treatments (e.g., combinations with platinum) on the population studied by Rutherford et al (2013), which contains ∼45% of patients who were resistant to their initial platinum chemotherapy. If single-agent platinum drugs do not work as well, then assumption (1) is violated.

Assumption (2) allows one to treat observational data as if it were from a randomised clinical trial. It is impossible to prove that this assumption is satisfied, as there may always be important unmeasured prognostic characteristics of the patients that clinicians are implicitly using to help decide which treatments have to be given to which patients. However, it is possible to show that the assumption is questionable by finding a known important prognostic variable that is associated with the treatment the patients received. In the present case, consider the recognised important prognostic variable defined by whether patients are platinum sensitive or platinum resistant to their initial platinum chemotherapy (Jayson et al, 2014). It is known that patients with platinum-sensitive recurrent disease are more likely to be treated with combination of drugs including a platinum agent, whereas patients with platinum-resistant recurrent disease are more likely treated with a single (non-platinum) drug (Jayson et al, 2014). Indeed, this appears to be the case with data analysed by Rutherford et al (2013), where 27% of the platinum-sensitive patients received (non-platinum) single drugs whereas 50% of the platinum-resistant patients did (Table 1). This suggests a violation of assumption (2) that patients had their treatment chosen randomly.

Table 1 Distribution of patients cross classified by treatment received and platinum status (data are abstracted from Supplementary Table S1 of Rutherford et al (2013))
Full size table

It can be difficult to assess in any given clinical situation whether the required assumptions for the analytic methods of Tian et al (2014) are reasonable. In particular, the required assumptions seem questionable in this recurrent ovarian cancer setting.