The Impact of Small Sample Size on Selecting Appropriate Distributions for Parametric Survival Extrapolations Models: A Methodological Commentary and Simulation Study

OBJECTIVES: This simulation study explored the impact of sample size on parametric survival extrapolation model selection guided using statistical criteria and the potential effect of erroneous extrapolation on economic evaluations.

METHODS: Weibull survival data were simulated using ‘simsurv’ package in R, applying scale parameter 1.0 and consecutive shape parameters 0.5, 1.5, and 5.0. Datasets were randomly sampled with sample sizes increasing from 25 to 250 and extrapolated using seven functional forms 1000 times per sample size. The concordance between the actual and selected parametric survival distribution was evaluated at each sample size. Akaike information criterion (AIC) and Bayesian information criterion (BIC) were used to identify the best fitting distributions. Differences compared using the restricted mean survival time (RMST).

RESULTS: The Weibull distribution was the most probable distribution selected at all sample sizes using BIC but was selected only 31.3%, 51.9%, and 35.6% during 1000 simulations at n=25, for shape parameters 0.5, 1.5, and 5.0, respectively. Weibull selection increased linearly with each n=25 increment, by 6.15% (p=0.01), 6.38% (p<0.01), and 4.49% (p=0.01), for shape parameters 0.5, 1.5, and 5.0, respectively. AIC demonstrated similar trends to BIC apart from increasing generalized gamma selection at sample sizes greater than n=125 (p>0.05). The relative differences in the RMST to the sampled data were greatest in the log-normal and log-logistic distributions. These distributions were selected more frequently when the sample size was small and the shape parameter less than 1.0 resulting in an overestimation of the RMST by 151%.

CONCLUSIONS: Sample size influences the probability of selecting the appropriate parametric survival extrapolation distribution to model survival outcomes when informed by statistical criteria. An incorrect extrapolation of the sampled data can lead to under- and overestimation of the RMST, directly impacting the calculation of the benefits and costs in an economic evaluation.