Sampling strategies to evaluate the prognostic value of a new biomarker on a time-to-event end-point

Graziano, Francesca; Valsecchi, Maria Grazia; Rebora, Paola

doi:10.1186/s12874-021-01283-0

BMC Medical Research Methodology

Table 1 Bias, empirical standard error, mean square error, power and design effect of the biomarker regression coefficient estimate (\( {\hat{\beta}}_{BM} \)) for the full cohort and different sampling designs. Accuracy of surrogate: sensitivity (i.e. probability of having a positive surrogate if the biomarker is positive) = 0.7 and specificity (i.e. probability of having a negative surrogate if the biomarker is negative) = 0.7, biomarker common (a) and rare (b)

From: Sampling strategies to evaluate the prognostic value of a new biomarker on a time-to-event end-point

Sampling design	Stratification variable	n*	Bias			SE empirical			MSE			Power (%)			Design effect
			Censoring rate			Censoring rate			Censoring rate			Censoring rate			Censoring rate
			0	0.1	0.4	0	0.1	0.4	0	0.1	0.4	0	0.1	0.4	0	0.1	0.4
a)
Full cohort	–	2000	0.008	−0.015	0.009	0.093	0.095	0.112	0.009	0.009	0.013	99	97	95	–	–	–
1. SRS	–	600	0.004	−0.013	0.006	0.182	0.187	0.206	0.033	0.035	0.042	64	58	53	–	–	–
2. PPS	Event	599	0.007	−0.015	0.007	0.173	0.180	0.199	0.029	0.033	0.039	65	58	54	1.003	1.003	1.005
2a. PPS	Event; Risk factor	598	0.008	−0.016	0.004	0.172	0.175	0.205	0.029	0.031	0.042	65	58	52	1.002	1.003	1.002
2b. PPS	Event; Confounder	598	0.003	−0.015	0.002	0.174	0.179	0.203	0.030	0.032	0.041	65	57	51	0.999	1.002	1.000
2c. PPS	Event; Surrogate	598	0.007	−0.013	0.013	0.161	0.171	0.190	0.026	0.029	0.036	69	64	57	1.106	1.129	1.104
3. CC	Event	600	0.011	−0.008	0.019	0.159	0.158	0.179	0.025	0.025	0.032	74	68	67	1.179	1.219	1.352
3a. CC	Event; Risk factor	600	0.010	−0.009	0.008	0.162	0.166	0.182	0.026	0.028	0.033	72	65	62	1.139	1.176	1.307
3b. CC	Event; Confounder	600	0.012	−0.015	0.010	0.162	0.161	0.175	0.026	0.026	0.031	73	65	66	1.182	1.187	1.354
3c. CC	Event; Surrogate	600	0.008	−0.016	0.012	0.148	0.153	0.170	0.022	0.024	0.029	76	71	69	1.334	1.363	1.495
4. NCC	Event	550	0.008	−0.018	0.014	0.169	0.165	0.175	0.029	0.028	0.031	68	63	67	1.066	1.144	1.378
5. CM	Event; Surrogate	546	−0.044	−0.058	− 0.009	0.151	0.153	0.165	0.025	0.027	0.027	67	61	67	1.379	1.395	1.536
b)
Full cohort	–	2000	−0.028	−0.004	−0.023	0.193	0.199	0.225	0.038	0.039	0.052	52	53	41	–	–	–
1. SRS	–	600	−0.045	− 0.041	−0.093	0.376	0.392	0.802	0.144	0.156	0.652	23	23	19	–	–	–
2 PPS	Event	599	−0.051	−0.023	−0.060	0.380	0.394	0.453	0.147	0.155	0.209	25	24	19	1.079	1.131	1.139
2a. PPS	Event; Risk factor	598	−0.048	−0.039	− 0.081	0.372	0.393	0.721	0.141	0.156	0.526	22	24	21	1.085	1.109	1.145
2b. PPS	Event; Confounder	598	−0.057	−0.033	−0.059	0.381	0.393	0.453	0.148	0.156	0.209	23	23	20	1.077	1.104	1.140
2c. PPS	Event; Surrogate	598	−0.055	−0.022	− 0.073	0.388	0.391	0.597	0.153	0.153	0.362	24	25	19	1.090	1.147	1.158
3. CC	Event	600	−0.003	0.021	0.003	0.332	0.339	0.368	0.110	0.116	0.135	24	26	22	1.257	1.317	1.509
3a. CC	Event; Risk factor	600	−0.011	0.015	0.006	0.345	0.357	0.384	0.119	0.127	0.148	23	24	21	1.193	1.283	1.418
3b. CC	Event; Confounder	600	−0.023	0.024	0.011	0.328	0.344	0.363	0.108	0.119	0.132	23	26	22	1.267	1.329	1.513
3c. CC	Event; Surrogate	565	−0.018	0.011	−0.010	0.311	0.313	0.345	0.097	0.098	0.119	26	29	24	1.419	1.607	1.757
4. NCC	Event	545	−0.020	0.024	−0.000	0.354	0.355	0.363	0.126	0.127	0.132	21	24	21	1.126	1.222	1.513
5. CM	Event; Surrogate	529	−0.057	−0.041	−0.028	0.311	0.315	0.341	0.099	0.101	0.117	26	27	25	1.541	1.679	1.823

Legend: SRS Simple Random Sample, PPS Probability Proportional to size, CC Case-Control, NCC Nested Case-Control, CM Counter-matching; n* mean sample size of the full cohort (first row) and of the phase II sample

Back to article page

ISSN: 1471-2288

Contact us

General enquiries: journalsubmissions@springernature.com