Region of Attainable Redaction, an extension of Ellipse of Insignificance analysis for gauging impacts of data redaction in dichotomous outcome trials

Figures

Figure 1

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Figure 2

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Tables

Table 1

Redaction for ${\displaystyle R{R}_e>1}$
	Endpoint positive	Endpoint negative
Experimental group	${\displaystyle a}$	${\displaystyle b+x}$
Control group	${\displaystyle c+y}$	${\displaystyle d}$
Redaction for ${\displaystyle R{R}_e<1}$
	Endpoint positive	Endpoint negative
Experimental group	${\displaystyle a+x}$	${\displaystyle b}$
Control group	${\displaystyle c}$	${\displaystyle d+y}$

Table 2

Statistics for simulated example case
ROAR statistic (${\displaystyle \alpha =0.05}$)	Calculated ROAR value (simulated ${\displaystyle R{R}_E>1}$ data)	Calculated ROAR value (simulated ${\displaystyle R{R}_E<1}$ data)
Total subjects reported ${\displaystyle N}$	200	200
Relative risk (95% CI) ${\displaystyle R{R}_E}$	1.40 (1.11–1.77)	0.60 (0.46–0.76)
FOCK point	${\displaystyle (x_e,y_e)=(6.89,4.79)}$	${\displaystyle (x_e,y_e)=(4.79,6.89)}$
${\displaystyle r_{min}}$	12 subjects	12 subjects
Experimental redaction tolerance ${\displaystyle {\rho }_E}$	9.51% (${\displaystyle \lceil x_c\rceil }$ = 10 subjects)	14.32% (${\displaystyle \lceil x_c\rceil }$ = 14 subjects)
Control redaction tolerance ${\displaystyle {\rho }_C}$	14.32% (${\displaystyle \lceil y_c\rceil }$ = 16 subjects)	9.51% (${\displaystyle \lceil y_c\rceil }$ = 10 subjects)
Total redaction tolerance ${\displaystyle {\rho }_A}$	5.66% (12 subjects)	5.66% (12 subjects)
Statistics for large meta-analysis
ROAR statistic (${\displaystyle \alpha =0.05}$)	Calculated ROAR value
Total subjects reported ${\displaystyle N}$	39,197
Relative risk (95% CI)	0.85 (0.74–0.97)
FOCK point	${\displaystyle (x_e,y_e)=(14.17,0.32)}$
${\displaystyle r_{min}}$	14 subjects
Experimental redaction tolerance ${\displaystyle {\rho }_E}$	0.07% (13 subjects)
Control redaction tolerance ${\displaystyle {\rho }_C}$	3.21% (649 subjects)
Total redaction tolerance ${\displaystyle {\displaystyle {\rho }_A}}$	0.04% (14 subjects)

1. FOCK, Fewest Observations/Censored Knowledge; ROAR, Region of Attainable Redaction.

Additional files

MDAR checklist

https://cdn.elifesciences.org/articles/93050/elife-93050-mdarchecklist1-v2.docx

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Supplementary file 1

Coefficients for ${\displaystyle g(x,y)}$ (Table S1) and related identity ${\displaystyle h(x,y)}$ (Table S2).

https://cdn.elifesciences.org/articles/93050/elife-93050-supp1-v2.pdf

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