Participation and performance trends in elderly marathoners in four of the world’s largest marathons during 2004–2011

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Table 1 Results of mixed effects regression analyses for race time for all, the annual fastest and the annual three fastest finishers

Parameter	Estimate	SE	df	t	p value
All finishers
Constant term	−17,025.92	1334.69	921.87	−12.75	<0.0001
(Gender = f)	23.34	8.10	775.06	2.87	0.004
Calendar year	8.65	0.66	922.02	13.01	<0.0001
Cage	5.21	1.06	808.90	4.91	<0.0001
Cage²	−0.12	0.09	595.08	−1.32	0.187
(Gender = f) × cage	−7.43	3.83	787.02	−1.93	0.053
(Gender = f) × cage²	1.22	0.53	773.14	2.31	0.021
Annual fastest
Constant term	−10,780.25	5967.83	41.83	−1.80	0.078
(Gender = f)	29.01	22.49	42.56	1.28	0.204
Calendar year	5.48	2.97	41.81	1.84	0.072
Cage	9.57	11.76	31.11	0.81	0.422
Cage²	−1.22	0.68	22.00	−1.78	0.088
(Gender = f) × cage	0.53	15.83	30.26	0.03	0.973
(Gender = f) × cage²	0.83	1.65	39.67	0.50	0.617
(Gender = f) × (age group = 85–89)	97.22	97.18	43.08	1.00	0.323
(Gender = f) × (age group = 80–84)	27.35	39.34	43.96	0.69	0.491
(Gender = m) × (age group = 95–99)	481.64	182.05	15.84	2.64	0.018
(Gender = m) × (age group = 90–94)	234.69	102.33	19.55	2.29	0.033
(Gender = m) × (age group = 85–89)	209.87	86.63	25.08	2.42	0.023
(Gender = m) × (age group = 80–84)	15.55	45.97	17.64	0.33	0.739
Annual three fastest
Constant term	−8462.10	3487.14	98.90	−2.42	0.017
(Gender = f)	−107.05	47.30	60.97	−2.26	0.027
Calendar year	4.42	1.73	98.83	2.55	0.012
Cage	11.21	5.17	53.16	2.16	0.035
Cage²	−1.69	0.41	36.57	−4.05	<0.0001
(Gender = f) × cage	0.27	7.20	47.77	0.03	0.969
(Gender = f) × cage²	1.55	0.87	58.95	1.76	0.082
(Gender = f) × (age group = 75–79)	−11.01	17.29	36.53	−0.637	0.528
(Gender = m) × (age group = 75–79)	−181.52	42.53	55.53	−4.26	<0.0001
(Gender = m) × (age group = 80–84)	−149.15	31.73	69.43	−4.70	<0.0001