Comparison of exclusion, imputation and modelling of missing binary outcome data in frequentist network meta-analysis

Table 1 Scenarios considered for the simulation set-up

Number of trials per comparison
typical loop^a	NO = 1, NP = 3, OP = 4
double	NO = 2, NP = 6, OP = 8
Trial size
placebo-controlled trials	Unif(102, 187)
old-controlled trials	Unif(128, 241)
Initial event rates of control arm
placebo-controlled trials	Unif(0.27, 0.40)
old-controlled trials	Unif(0.63, 0.76)
Balanced risk of missing outcome data
low	Unif(0, 0.04)
moderate	Unif(0.05, 0.20)
large	Unif(0.21, 0.40)
Unbalanced risk of missing outcome data
low	Unif(0, 0.04)^b
moderate	Unif(0.05, 0.10) for E, Unif(0.11, 0.20) for C
large	Unif(0.21, 0.30) for E, Unif(0.31, 0.40) for C
Missingness mechanisms via log (IMOR)
informative	TN(μ = − ln (2), σ² = 1, a = ln (1)) for Placebo
informative	TN(μ = ln (2), σ² = 1, a = ln (1)) for New and Old
missing at random	N(0, 1) for all interventions
Treatment effects
basic comparisons	LOR_NP = ln (2), LOR_OP = ln (1.5)
functional comparison	LOR_NO = LOR_NP − LOR_OP + IF
Loop inconsistency
inconsistency factor (IF)^c	IF = absent IF = moderate
Common between-trial variance
predictive distribution^d	τ² = 0.02 (small) τ² = 0.08 (substantial)
Surface under cumulative ranking curve
new intervention	96 and 88% for small and substantial τ², respectively
old intervention	54 and 58% for small and substantial τ², respectively
placebo	0 and 4% for small and substantial τ², respectively

Note: C control arm, E experimental arm, IF consistency factor, IMOR informative missingness odds ratio, LOR log odds ratio, N normal distribution, NO New intervention versus Old intervention, NP New intervention versus Old intervention, OP Old intervention versus Placebo, TN truncated-normal distribution, Unif uniform distribution
^aAs defined in Veroniki et al. [46]
^bIn the presence of low missing outcome data, imbalance of missing outcome data in the compared arms is negligible, and therefore, in both arms the risk of missingness was generated from U(0, 0.04) irrespectively the type of intervention
^cAbsent and moderate inconsistency refer to the mean of t-distributions t(μ = 0, σ² = 0.44², df = 3) and t(μ = 1, σ² = 0.44², df = 3), respectively
^dSmall and substantial τ² refer to the predictive log-normal distributions LΝ(−3.95, 1.34²) for all-cause mortality and LΝ(−2.56, 1.74²) for generic health setting, respectively [40]

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