KARL PEARSON'S CHI-SQUARED GOODNESS-OF-FIT TEST

2021 ◽  
Vol 39 (15_suppl) ◽  
pp. e14050-e14050
Author(s):  
Olusola Michael Adeleke ◽  
Rubyyat A Hakim ◽  
Laurence Dean ◽  
Huma Zahid ◽  
Rongyu Lin ◽  
...  

e14050 Background: Historically, metastatic spinal cord compression (MSCC) referrals trend towards a Friday peak in incidence (Koiter E, Radioth Onc 2013). However, data from a single, tertiary centre in the UK showed a reversal in the Friday peak (Adeleke S, Annals of Oncology 2020). This was attributed to early case referrals and quicker treatment decisions. In this new study, we explored whether a similar pattern was apparent in multiple district general hospital (DGH) settings and attempt to identify underlying causes. DGHs manage a larger proportion of cancer patients in the UK. Methods: 1,069 patients between 1 Jan 2015 and 31 Dec 2020 were identified across 4 hospitals in Kent, UK with a population of 1.6 million people. 220, 181, 182, 159, 134 and 193 MSCC patients were identified annually (2015-2020). Commonest cancers were prostate (24.1%), lung (19.3%) and breast (12.3%). Thoracic and lumbar regions constituted 80% of MSCC sites. Kruskal Wallis was used to compare differences in referrals across weekdays. Data was then dichotomised to Fridays only vs. other days of the week combined, as previously reported (De Bono B, Acta Neurochir 2019). Chi squared was used to compare frequency of referrals between the two groups. Chi squared goodness of fit test was conducted to detect if Friday reflected the day with highest referrals across the week. Results: Across the region, 2015 saw the highest number of Friday referrals relative to other days, p= 0.002. Friday referrals continued to drop, year on year, until 2018 with a corresponding increase in mid-week referrals. After 2018, there was a return in trend to a further Friday peak across the region, though p= 0.836. On an individual hospital basis, the persistent Friday peak in the region was driven by two hospitals. Having a 7-day acute oncology service (AOS), 7-day radiology reporting and single referral point of contact in the department, were factors identified that kept the referrals across the week uniform. On another note, a substantial shift towards a single 8Gy fraction vs. 20Gy in 5 fractions was observed across the region. This change coincided with SCORAD III data (Hoskin P, ASCO 2017) and demonstrates adherence to evidence-based practice in the region. Conclusions: This large multi-centre retrospective study shows a differential referral pattern in the region, with hospitals with 7-day AOS/Radiology reporting and single point of referral (e.g, similar to MSCC coordinator role) having a quicker treatment turnaround and uniform referrals across the week. The MSCC coordinator has been shown to streamline service, ensure timely decision-making and improved survival outcomes (Richards L, Spine J 2017). The role is recommended by NICE UK. DGHs should consider appointing an MSCC coordinator when designing/auditing their service. The shift towards single 8Gy fraction can provide a ‘one-stop’ service where patients are scanned, planned and treated on the same day.


Biometrika ◽  
2019 ◽  
Vol 106 (3) ◽  
pp. 716-723
Author(s):  
Mengyu Xu ◽  
Danna Zhang ◽  
Wei Biao Wu

Summary We establish an approximation theory for Pearson’s chi-squared statistics in situations where the number of cells is large, by using a high-dimensional central limit theorem for quadratic forms of random vectors. Our high-dimensional central limit theorem is proved under Lyapunov-type conditions that involve a delicate interplay between the dimension, the sample size, and the moment conditions. We propose a modified chi-squared statistic and introduce an adjusted degrees of freedom. A simulation study shows that the modified statistic outperforms Pearson’s chi-squared statistic in terms of both size accuracy and power. Our procedure is applied to the construction of a goodness-of-fit test for Rutherford’s alpha-particle data.


Biometrics ◽  
2009 ◽  
Vol 66 (2) ◽  
pp. 426-434 ◽  
Author(s):  
Jing Cao ◽  
Ann Moosman ◽  
Valen E. Johnson

2020 ◽  
Author(s):  
Didier de Villiers ◽  
Marc Schleiss ◽  
Marie-Claire ten Veldhuis ◽  
Rolf Hut ◽  
Nick van de Giesen

Abstract. A new type of rainfall sensor (the intervalometer), which counts the arrival of raindrops at a piezo electric element, is implemented during the Tanzanian monsoon season alongside tipping bucket rain gauges and an impact disdrometer. The aim is to test the validity of the Poisson hypothesis underlying the estimation of rainfall rates using Marshall and Palmer’s (1948) exponential raindrop size distribution parameterisation. The latter is defined independently of the scale of observation and therefore implicitly assumes that rainfall is a homogeneous Poisson process. Our results show that 28.3 % of the total observed rainfall patches can reasonably be considered Poisson-distributed and that the main reasons for Poisson deviations of the remaining 71.7 % are non-compliance with the stationarity criterion (45.9 %), the presence of correlations between drop counts (7.0 %), particularly at higher arrival rates (ρa > 500 m−2.s−1) and failing a chi squared goodness of fit test for a Poisson distribution (17.7 %). Our results show that whilst the Poisson hypothesis is likely not strictly true for rainfall that contributes most to the total rainfall amount it is quite useful in practice and may hold under certain rainfall conditions. Despite the non-compliance with the Poisson hypothesis, estimates of total rainfall amount over the entire observational period derived from disdrometer drop counts are within 2 % of co-located tipping bucket measurements. Uncorrected intervalometer estimates of total rainfall amount overestimate the co-located tipping bucket measurements by a factor of approximately 3. The overestimate is most likely due to poor calibration of the minimum detectable drop size (Dmin). Intervalometer estimates of total rainfall when corrected for minimum drop size are within 1 % of co-located tipping bucket measurements. The intervalometer principle shows good potential for use as a rainfall measurement instrument and for determining rough estimates of mean drop size.


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