A simulation study on estimating biomarker–treatment interaction effects in randomized trials with prognostic variables

Haller, Bernhard; Ulm, Kurt

doi:10.1186/s13063-018-2491-0

Trials

Table 3 Proportions of rejected null hypotheses and numbers of included covariates for scenarios with K=24

From: A simulation study on estimating biomarker–treatment interaction effects in randomized trials with prognostic variables

K	Σ	β _k	Censoring	Main	True	AIC_A	AIC_B	Significance	Full
No interaction
24	Σ ₁	β _eq	Low	0.044	0.049	0.065	0.053	0.048	0.049
24	Σ ₁	β _v	Low	0.055	0.069	0.074	0.065	0.060	0.069
24	Σ ₂	β _eq	Low	0.087	0.052	0.063	0.046	0.052	0.052
24	Σ ₂	β _v	Low	0.068	0.071	0.081	0.066	0.071	0.071
24	Σ ₃	β _eq	Low	0.068	0.049	0.061	0.052	0.055	0.049
24	Σ ₃	β _v	Low	0.066	0.056	0.061	0.053	0.054	0.056
24	Σ ₁	β _eq	High	0.035	0.056	0.069	0.054	0.046	0.056
24	Σ ₁	β _v	High	0.051	0.071	0.076	0.059	0.068	0.076
24	Σ ₂	β _eq	High	0.073	0.066	0.074	0.056	0.066	0.066
24	Σ ₂	β _v	High	0.060	0.054	0.066	0.048	0.056	0.056
24	Σ ₃	β _eq	High	0.062	0.058	0.073	0.047	0.059	0.058
24	Σ ₃	β _v	High	0.059	0.068	0.079	0.060	0.057	0.066
Quantitative interaction
24	Σ ₁	β _eq	Low	0.114	0.142	0.158	0.137	0.122	0.142
24	Σ ₁	β _v	Low	0.106	0.138	0.150	0.132	0.125	0.143
24	Σ ₂	β _eq	Low	0.119	0.135	0.148	0.130	0.135	0.135
24	Σ ₂	β _v	Low	0.111	0.124	0.145	0.117	0.126	0.126
24	Σ ₃	β _eq	Low	0.121	0.136	0.145	0.128	0.141	0.136
24	Σ ₃	β _v	Low	0.121	0.136	0.157	0.141	0.134	0.136
24	Σ ₁	β _eq	High	0.088	0.100	0.117	0.091	0.093	0.100
24	Σ ₁	β _v	High	0.085	0.104	0.110	0.096	0.094	0.111
24	Σ ₂	β _eq	High	0.094	0.109	0.122	0.094	0.109	0.109
24	Σ ₂	β _v	High	0.113	0.096	0.116	0.088	0.100	0.100
24	Σ ₃	β _eq	High	0.082	0.098	0.109	0.097	0.103	0.098
24	Σ ₃	β _v	High	0.100	0.091	0.109	0.086	0.098	0.098
Qualitative interaction
24	Σ ₁	β _eq	Low	0.630	0.697	0.686	0.658	0.632	0.697
24	Σ ₁	β _v	Low	0.547	0.678	0.688	0.656	0.615	0.685
24	Σ ₂	β _eq	Low	0.349	0.610	0.619	0.595	0.610	0.610
24	Σ ₂	β _v	Low	0.358	0.590	0.608	0.584	0.578	0.578
24	Σ ₃	β _eq	Low	0.443	0.596	0.620	0.582	0.587	0.596
24	Σ ₃	β _v	Low	0.465	0.632	0.651	0.621	0.636	0.631
24	Σ ₁	β _eq	High	0.448	0.457	0.463	0.424	0.412	0.457
24	Σ ₁	β _v	High	0.384	0.453	0.466	0.425	0.420	0.464
24	Σ ₂	β _eq	High	0.276	0.364	0.387	0.340	0.364	0.364
24	Σ ₂	β _v	High	0.292	0.397	0.423	0.378	0.411	0.411
24	Σ ₃	β _eq	High	0.355	0.387	0.405	0.356	0.382	0.387
24	Σ ₃	β _v	High	0.338	0.408	0.409	0.377	0.404	0.408
Mean number of prognostic covariates included
		β _eq	Low	0	24	13.2	13.7	17.5	24
		β _v	Low	0	16	12.7	13.1	17.8	24
		β _eq	High	0	24	10.2	10.7	16.5	24
		β _v	High	0	16	10.6	11.0	16.8	24

For the scenarios with no true biomarker–treatment interaction, results for methods/strategies with an observed type I error probability above 7% are in italics. For scenarios with a true biomarker–treatment interaction, the observed power is in bold if the type I error probability did not exceed 7%

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ISSN: 1745-6215

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