Percentage Points of the Chi-Square Distribution

Keyword(s):  
1980 ◽  
Vol 17 (01) ◽  
pp. 145-153 ◽  
Author(s):  
H. Solomon ◽  
M. A. Stephens

Many random variables arising in problems of geometric probability have intractable densities, and it is very difficult to find probabilities or percentage points based on these densities. A simple approximation, a generalization of the chi-square distribution, is suggested, to approximate such densities; the approximation uses the first three moments. These may be theoretically derived, or may be obtained from Monte Carlo sampling. The approximation is illustrated on random variables (the area, the perimeter, and the number of sides) associated with random polygons arising from two processes in the plane. Where it can be checked theoretically, the approximation gives good results. It is compared also with Pearson curve fits to the densities.


2019 ◽  
Vol 37 (15_suppl) ◽  
pp. e18224-e18224
Author(s):  
Lori Keys Pender ◽  
Haleh Kadkhoda ◽  
Katie S. Lucero ◽  
Patti Repetto ◽  
Charlotte Warren ◽  
...  

e18224 Background: Immune checkpoint inhibitors (ICIs) are increasingly used in oncology care and produce a wide variety of immune-related adverse events (irAEs) that differ from toxicities of other systemic therapies. The objective of this study was to assess trends over time in oncologists’ knowledge, competence, and confidence managing irAEs. Methods: A series of online continuing medical education (CME) activities addressing irAEs was launched beginning in April 2014; 39 included multiple-choice knowledge/competence questions and a confidence question assessed on a 5-point Likert-type scale before and immediately after the activity. Activities that had at least 30 oncologists participate pre/post are included in this analysis. A pre-/post-assessment study design was used, and educational effect was assessed with chi-square tests. Analyses were conducted to examine trends in knowledge, competence, and confidence recognizing, identifying, and managing irAEs over four years on a quarterly basis. Weighted averages in each of the outcomes were calculated by quarter. Results: A total of 187,800 learners participated from April 2014-March 2018, including 96,177 physicians, of whom 25,127 were oncologists. The average increase pre- to post-test for 22 activities that asked a knowledge-based question was 18% (P < 0.001). The absolute increase from pre-test in 2014 (67%) to post-test in 2018 (87%) was 20 percentage points. For 16 activities with competence questions, the average increase from pre- to post-test was 8% (P < 0.001), and the absolute increase from pre-test in 2014 (39%) to post-test in 2017 (87%) was 48 percentage points. For 5 activities with a confidence question, the average increase from pre- to post-test was 8% (P < 0.05), and the mean rating pre-test in 2016 was 2.85 versus 3.53 post-test in 2018. Conclusions: Online CME is effective to improve oncologists’ knowledge, competence, and confidence managing irAEs; however, pre-test outcomes in 2018 demonstrate ongoing knowledge and competence gaps that should be addressed, and post-test confidence data indicate a persistent lack of confidence among oncologists even after participating in online CME.


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