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Re: Comparative effectiveness of prostate cancer treatments: evaluating statistical adjustments for confounding in observational data.

Hadley et al. (1) sought to estimate the efficacy of radical prostatectomy in reducing mortality in men 65 years and older who were diagnosed with early-stage prostate cancer. Using linked Surveillance, Epidemi ology, and End Results and Medicare data from 1995 to 2003, they compared the results of an instrumental variable (IV) analysis with those from a randomized trial. They concluded that: 1) the IV analysis gave results similar to the trial and 2) the particular type of “instrument” chosen—the likelihood of radical prostatectomy having been performed in the previous year among men with localized prostate cancer in the patient’s geographic locale—may prove useful in studies of other cancer treatments. In our opinion, the results presented by the authors do not justify either of these conclusions. We shall start by addressing the first conclusion (point 1). In the randomized trial intent-to-treat analysis (2), men aged 65 years and older who were assigned to receive conservative therapy had a 15% greater likelihood of dying from prostate cancer in the ensuing 12 years than men assigned to radical prostatectomy, an increase of uncertain statistical and clinical significance (Table 1). Approximately 15% of these men did not receive their assigned intervention, so the true increase in mortality associated with receipt of conservative therapy could be greater. Furthermore, in participants of all ages, the relative risk associated with assignment to conservative therapy was 1.54, and it is not clear whether the overall result or that for the smaller number of older men is more applicable. In any event, the IV analysis does not approximate an increase of 15% or 54%, but actually a 27% decrease in prostate cancer mortality associated with receipt of conservative therapy (relative risk = 0.73, 95% confidence interval = 0.08 to 6.73) (Table 1). With regard to the second conclusion (point 2), the authors cite a rule of thumb that the F-statistic, a metric used to test statistical significance of the association between the instrument and the treatment, should be at least 10. This cut point was developed (3) to identify “weak” instruments, which result in finite sample bias and inflated type I error. Although the F-statistic cut point can be considered a necessary condition to avoid these known weak instrument limitations, it is not sufficient to ensure that the IV estimate will be measured with enough precision to be interpretable. As the authors note, an instrument should also account for a “meaningful share” of treatment variation; however, their instrument accounted for only 4.2% of the variation in receipt of radical prostatectomy among the men under study. This low predictive ability resulted in an extremely wide confidence interval. An analysis in which the relative risk cannot be specified within an 80-fold range will not generally provide a result of much value. Also, to the extent that the assumption of a lack of independent association between the instru-