Dataset Information

Quantification of errors in ordinal outcome scales using shannon entropy: effect on sample size calculations.

ABSTRACT:

Objective

Clinical trial outcomes often involve an ordinal scale of subjective functional assessments but the optimal way to quantify results is not clear. In stroke, the most commonly used scale, the modified Rankin Score (mRS), a range of scores ("Shift") is proposed as superior to dichotomization because of greater information transfer. The influence of known uncertainties in mRS assessment has not been quantified. We hypothesized that errors caused by uncertainties could be quantified by applying information theory. Using Shannon's model, we quantified errors of the "Shift" compared to dichotomized outcomes using published distributions of mRS uncertainties and applied this model to clinical trials.

Methods

We identified 35 randomized stroke trials that met inclusion criteria. Each trial's mRS distribution was multiplied with the noise distribution from published mRS inter-rater variability to generate an error percentage for "shift" and dichotomized cut-points. For the SAINT I neuroprotectant trial, considered positive by "shift" mRS while the larger follow-up SAINT II trial was negative, we recalculated sample size required if classification uncertainty was taken into account.

Results

Considering the full mRS range, error rate was 26.1%±5.31 (Mean±SD). Error rates were lower for all dichotomizations tested using cut-points (e.g. mRS 1; 6.8%±2.89; overall p<0.001). Taking errors into account, SAINT I would have required 24% more subjects than were randomized.

Conclusion

We show when uncertainty in assessments is considered, the lowest error rates are with dichotomization. While using the full range of mRS is conceptually appealing, a gain of information is counter-balanced by a decrease in reliability. The resultant errors need to be considered since sample size may otherwise be underestimated. In principle, we have outlined an approach to error estimation for any condition in which there are uncertainties in outcome assessment. We provide the user with programs to calculate and incorporate errors into sample size estimation.

SUBMITTER: Mandava P

PROVIDER: S-EPMC3702531 | biostudies-literature | 2013

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Quantification of errors in ordinal outcome scales using shannon entropy: effect on sample size calculations.

Mandava Pitchaiah P Krumpelman Chase S CS Shah Jharna N JN White Donna L DL Kent Thomas A TA

PloS one 20130705 7

<h4>Objective</h4>Clinical trial outcomes often involve an ordinal scale of subjective functional assessments but the optimal way to quantify results is not clear. In stroke, the most commonly used scale, the modified Rankin Score (mRS), a range of scores ("Shift") is proposed as superior to dichotomization because of greater information transfer. The influence of known uncertainties in mRS assessment has not been quantified. We hypothesized that errors caused by uncertainties could be quantifie ...[more]

PMID: 23861800

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Project description:Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2) these measures connect directly to the rich predictive mathematics of information theory; (3) Shannon entropy is completely additive and has an explicitly hierarchical nature; and (4) Shannon entropy-based differentiation measures obey strong monotonicity properties that heterozygosity-based measures lack. We derive simple new expressions for the expected values of the Shannon entropy of the equilibrium allele distribution at a neutral locus in a single isolated population under two models of mutation: the infinite allele model and the stepwise mutation model. Surprisingly, this complex stochastic system for each model has an entropy expressable as a simple combination of well-known mathematical functions. Moreover, entropy- and heterozygosity-based measures for each model are linked by simple relationships that are shown by simulations to be approximately valid even far from equilibrium. We also identify a bridge between the two models of mutation. We apply our approach to subdivided populations which follow the finite island model, obtaining the Shannon entropy of the equilibrium allele distributions of the subpopulations and of the total population. We also derive the expected mutual information and normalized mutual information ("Shannon differentiation") between subpopulations at equilibrium, and identify the model parameters that determine them. We apply our measures to data from the common starling (Sturnus vulgaris) in Australia. Our measures provide a test for neutrality that is robust to violations of equilibrium assumptions, as verified on real world data from starlings.

Dataset Information

Quantification of errors in ordinal outcome scales using shannon entropy: effect on sample size calculations.

Objective

Methods

Results

Conclusion

Publications

Quantification of errors in ordinal outcome scales using shannon entropy: effect on sample size calculations.

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