Hi colleagues,
I am designing a hospital-based case-control study to evaluate the performance of a diagnostic panel, called urine circulating tumor DNA (ctDNA), against Computed Tomography (CT) scanning in diagnosing liver cancer. Cases are defined as those with liver cancer, while controls are people without liver cancer. After using the sample size formula to measure Receiver Operating Characteristics (ROC) curves suggested by Machin et al. (1), I came up with 60 cases and 120 controls.
In the next step, I must consider another issue: the performance stratified by Alpha-Fetoprotein (AFP) levels of 20 ng/ml. This is because previous studies showed the performance of ctDNA may vary by AFP levels. Consequently, cases should be divided in half: one group with liver cancer patients with AFP levels > 20 ng/ml and the other with AFP levels < 20 ng/ml.
So, my question is:
a) Shall I keep the sample size as computed earlier, recruit 30 liver cancer cases with AFP > 20 ng/ml and the other 30 cases with AFP < 20 ng/ml while recruiting 120 controls regardless of their AFP levels?
b) Shall I double the sample size as computed earlier, which will become 120 cases and 240 controls. After this, I will recruit 60 liver cancer cases with AFP > 20ng/ml and the other 60 cases with AFP > 20 ng/ml while recruiting 240 controls regardless of their AFP levels.
Thank you very much for helping me.
Reference
(1) Machin, D., Campbell, M.J., Tan, S.B. and Tan, S.H., 2018. Chapter 21: Reference Intervals and Receiver Operating Curves.Sample sizes for clinical, laboratory, and epidemiology studies. John Wiley & Sons.
Hi Thanh,
Definitely not an expert here, but since you asked. Sample size calculation for ROC curve really depends on which question you're asking (and thus, which testing / comparison you're making). Sample size calculation for constructing a confidence interval is different from that for testing a hypothesis (such as the ROC AUC is > 50%).
This problem is more complicated under stratification. Your question may be whether the ROC curves of strata are different, or stratification is simply used to account for the heterogeneity in predictive values of ctDNA. Also, we should concern whether stratification will be done in cases, controls, or both; note that this is decided based on your substantive knowledge. In your case, I believe we should stratify on both cases and controls.
Shukhatme (1994) has an excellent article on diagnostic studies with stratification [1]. In this article, the author described different stratified models, and how standard errors of the ROC AUC are calculated. I'm not trained on order statistics, so I don't really get all the concepts in here; but one thing I get from the article is that under proportional allocation, the variance of stratified samples is smaller than the variance of unstratified samples. My understanding is that, under proportional allocation, you can guarantee the sample size calculated for unstratified samples has enough power for stratified analysis. Proportional allocation means your sample has the same strata weights as those from the target population, which means you should not sample patients in your two strata with a 1:1 ratio.
Looking forward to answers from people who are familiar with this.
References
1. Sukhatme S, Beam CA. Stratification in nonparametric ROC studies. Biometrics. 1994;50(1):149-163.
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