A research notebook entry on an important paper follows. I’ve left out quite a bit that is more tutorial. So, the paper is more accessible than it may seem.
All quotes from Hadley, J., Yabroff, K. R., Barrett, M. J., Penson, D. F., Saigal, C. S., & Potosky, A. L. (2010). Comparative effectiveness of prostate cancer treatments: evaluating statistical adjustments for confounding in observational data. Journal of the National Cancer Institute, 102(23), 1780-1793:
We selected 14,302 early-stage prostate cancer patients who were aged 66–74 years and had been treated with radical prostatectomy or conservative management from linked Surveillance, Epidemiology, and End Results–Medicare data from January 1, 1995, through December 31, 2003. Eligibility criteria were similar to those from a clinical trial used to benchmark our analyses. Survival was measured through December 31, 2007, by use of Cox proportional hazards models. We compared results from the benchmark trial with results from models with observational data by use of traditional multivariable survival analysis, propensity score adjustment, and instrumental variable analysis.
This is an important exercise. Here’s why:
The randomized controlled trial is considered the most valid methodology for assessing treatments’ efficacy. However, randomized controlled trials are costly, time consuming, and frequently not feasible because of ethical constraints. Moreover, some randomized controlled trial results have limited generalizability because of differences between randomized controlled trial study populations, who may be screened for eligibility on the basis of age and comorbidities, and community populations, who are likely to be much more heterogeneous with regard to health conditions and socioeconomic characteristics.
To this, add that RCTs are often under-powered for stratification by key patient characteristics. This is where observational studies shine. Of course, biased selection is the principal concern with observational studies.
Patient selection into specific treatments is an important consideration in all observational studies, but particularly for those in prostate cancer, because incidence is highest in the elderly who are also most likely to have multiple comorbidities.
Observational study techniques are not equivalent in their ability to address the selection problem.
Observational studies (1,11–13) have previously used traditional regression and propensity score methods to evaluate associations between specific prostate cancer treatments with survival. In these studies, the propensity score methods did not completely balance (ie, equalize) important patient characteristics such as tumor grade, size, and comorbidities across treatment groups. Furthermore, patients who received active treatment had better survival for noncancer causes of death than patients who received conservative management, indicating that unobserved differences between groups affected both treatment choice and survival.
Instrumental variable analysis is a statistical technique that uses an exogenous variable (or variables), referred to as an “instrument,” that is hypothesized to affect treatment choice but not to be related to the health outcome (14–17). Variations in treatment that result from variations in the value of the instrument are considered to be analogous to variations that result from randomization and so address both observed and unobserved confounding. Instrumental variable analysis has been used with observational data to investigate clinical treatment effects among patients with breast cancer (18–20), lung cancer (21), or prostate cancer (5,22).
The study findings support the use of instrumental variables.
Propensity score adjustments resulted in similar patient characteristics across treatment groups, and survival was similar to that of traditional multivariable survival analyses. The instrumental variable approach, which theoretically equalizes both observed and unobserved patient characteristics across treatment groups, differed from multivariable and propensity score results but were consistent with findings from a subset of elderly patient with early-stage disease in the randomized trial.
The authors’ preferred instrument captures practice pattern variation.
We constructed the primary instrumental variable for treatment received by use of a two-step process. First, we used the entire dataset (n = 17,815) to estimate the probability of receiving conservative management as a function of patients’ clinical characteristics (tumor stage and grade, NCI comorbidity index, and Medicare reimbursements for medical care in the previous year), demographics (age, race, ethnicity, and marital status), year of diagnosis, and all possible interactions among these variables. Second, we calculated the difference between the actual proportion of patients receiving conservative management and the average predicted probability of receiving conservative management (generated from the logistic regression model) in each hospital referral region by year. Areas with relatively large positive differences between the actual and predicted proportions of patients receiving conservative management favor a conservative management treatment pattern, and areas with large negative differences between the actual and predicted proportions of patients receiving conservative management favor a radical prostatectomy treatment pattern. We then lagged this measure of the local area treatment pattern by 1 year and linked it to each patient in the analysis to enhance the instrument’s independence from patients’ current health and unobserved characteristics.
Treatment propensity (ie, the predicted probability of receiving conservative management) for the propensity score analysis and for constructing the lagged area treatment pattern for the instrumental variable analysis was estimated with logistic regression. The survival models were estimated with Cox proportional hazard models. Visual inspection of the parallelism of the Kaplan–Meier plots of the logarithms of the estimated cumulative survival models by treatment supported the proportionality assumption. The instrumental variable version of the Cox hazard model was estimating with the two-stage residual inclusion method (38), which has been shown to be appropriate for nonlinear outcome models. [...]
[The instrument's] independence of the survival outcomes was confirmed by its lack of statistical significance as an independent variable in an alternative version (data not shown) of the Cox survival models.
One acknowledged limitation, among many, is that PSA values were not available to the researchers. Another is that
a complete statistical assessment of the Cox hazard model’s proportionality assumption indicated that the effects of some covariates may not be time invariant, especially in the analysis of all-cause mortality. Although a sensitivity analysis of the effects of allowing time-varying covariates did not alter the principle findings with regard to treatment effects, further analysis of time-varying effects may be warranted.
All in all, a very nice paper. It’s worth a full read by observational researchers.