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How do viewers interpret graphs that abstract away from individual-level data to present only summaries of data such as means, intervals, distribution shapes, or effect sizes? Here, focusing on the mean bar graph as a prototypical example of such an abstracted presentation, we contribute three advances to the study of graph interpretation. First, we distill principles for Measurement of Abstract-Graph Interpretation (MAGI principles) to guide the collection of valid interpretation data from viewers who may vary in expertise. Second, using these principles, we create the Draw Datapoints on Graphs (DDoG) measure, which collects drawn readouts (concrete, detailed, visuospatial records of thought) as a revealing window into each person’s interpretation of a given graph. Third, using this new measure, we discover a common, categorical error in the interpretation of mean bar graphs: the Bar-Tip Limit (BTL) error. The BTL error is an apparent conflation of mean bar graphs with count bar graphs. It occurs when the raw data are assumed to be limited by the bar-tip, as in a count bar graph, rather than distributed across the bar-tip, as in a mean bar graph. In a large, demographically diverse sample, we observe the BTL error in about one in five persons; across educational levels, ages, and genders; and despite thoughtful responding and relevant foundational knowledge. The BTL error provides a case-in-point that simplification via abstraction in graph design can risk severe, high-prevalence misinterpretation. The ease with which our readout-based DDoG measure reveals the nature and likely cognitive mechanisms of the BTL error speaks to the value of both its readout-based approach and the MAGI principles that guided its creation. We conclude that mean bar graphs may be misinterpreted by a large portion of the population, and that enhanced measurement tools and strategies, like those introduced here, can fuel progress in the scientific study of graph interpretation.

Background: Numerous germline single-nucleotide polymorphisms increase susceptibility to prostate cancer, some lying near genes involved in cellular radiation response. This study investigated whether prostate cancer patients with a high genetic risk have increased toxicity following radiotherapy. Methods: The study included 1560 prostate cancer patients from four radiotherapy cohorts: RAPPER (n=533), RADIOGEN (n=597), GenePARE (n=290) and CCI (n=150). Data from genome-wide association studies were imputed with the 1000 Genomes reference panel. Individuals were genetically similar with a European ancestry based on principal component analysis. Genetic risks were quantified using polygenic risk scores. Regression models tested associations between risk scores and 2-year toxicity (overall, urinary frequency, decreased stream, rectal bleeding). Results were combined across studies using standard inverse-variance fixed effects meta-analysis methods. Results: A total of 75 variants were genotyped/imputed successfully. Neither non-weighted nor weighted polygenic risk scores were associated with late radiation toxicity in individual studies (P>0.11) or after meta-analysis (P>0.24). No individual variant was associated with 2-year toxicity. Conclusion: Patients with a high polygenic susceptibility for prostate cancer have no increased risk for developing late radiotherapy toxicity. These findings suggest that patients with a genetic predisposition for prostate cancer, inferred by common variants, can be safely treated using current standard radiotherapy regimens.

What's known on the subject? and What does the study add? While the frequencies and severity of late toxicities following prostate brachytherapy are well known, less has been published with regard to time to first onset. Several series with limited median follow-up have published time to onset. An extensive analysis of timing to late toxicity following brachytherapy for cervical cancer has also been published. This study is the largest of its kind with the longest median follow-up to capture very late events. It can provide a basis for physician and patient education about when late toxicities can reasonably be expected to occur. The study also shows that a significant amount of erectile dysfunction might be more age related than radiation induced.• To assess the timing of first onset of late rectal bleeding, late haematuria and erectile dysfunction (ED) following brachytherapy with or without external beam radiation therapy (EBRT) for prostate adenocarcinoma. • To identify treatment factors and patient characteristics that affect the time to first onset.• In all, 2046 patients were definitively treated for prostate adenocarcinoma with a full (125) I or (103) Pd implant or a partial (103) Pd implant followed by EBRT with 6 years median follow-up (range 2-17 years). • Patients were selected for an event of Radiation Therapy Oncology Group (RTOG) grade 2 or greater rectal bleeding, ≥RTOG grade 2 haematuria, or a drop in the Mount Sinai Erectile Dysfunction Score from potent to impotent (excluding patients who received androgen deprivation therapy). • Life tables were generated to calculate actuarial incidence rates of toxicity. • Wilcoxon rank sum and Cox regression were utilized to identify treatment factors affecting time to onset.• The incidence rate per 1000 patients for 0-2 years, 2-5 years and 5-10 years following radiation for rectal bleeding is 14.3, 15.9 and 6.5, respectively; for haematuria, 14.0, 8.2 and 1.3, respectively; and for ED, 82.4, 48.2 and 42.2, respectively. • Just 5% of rectal bleeding occurs after 5 years from radiation vs 18% of haematuria cases and 22% of ED. • On multivariate analysis, time to first onset of rectal bleeding was affected by the addition of EBRT only whereas the time to onset of haematuria was affected by the biological effective dose of the radiation and the addition of EBRT. • The only factor on multivariate analysis to affect time to onset of ED was the age of the patient at treatment, independent of radiation dose or technique.• Unique temporality to first onset of selected toxicities was observed in patients after radioactive implant for prostate adenocarcinoma with or without EBRT. • Clinicians and patients should be counselled when to expect late toxicities. • The only factor to affect time to onset of ED is the age of the patient, suggesting possible over-reporting of radiation-induced ED in the light of normal age-related events.