Table 5: Open in new tab Result of the...

Endpoint (a)
Colorectal	Vitamin D quintile
	2	0.153	0.211	(–0.262, 0.567)	0.297	0.192	(–0.079, 0.672)	1.22
	3	–0.085	0.217	(–0.510, 0.341)	0.150	0.196	(–0.234, 0.534)	1.23
	4	–0.223	0.225	(–0.663, 0.217)	0.124	0.205	(–0.278, 0.526)	1.20
	5	–0.394	0.241	(–0.868, 0.079)	–0.095	0.218	(–0.523, 0.333)	1.22
	BMI $>$ 25	0.007	0.161	(–0.308, 0.321)	0.085	0.150	(–0.210, 0.380)	1.14
	Diabetes	0.470	0.260	(–0.039, 0.979)	0.602	0.237	(0.137, 1.067)	1.20
Prostate	Vitamin D quintile
	2	–0.006	0.188	(–0.373, 0.362)	–0.091	0.181	(–0.446, 0.264)	1.07
	3	0.521	0.173	(0.182, 0.859)	0.385	0.166	(0.060, 0.710)	1.08
	4	0.571	0.188	(0.203, 0.939)	0.347	0.177	(–0.001, 0.693)	1.13
	5	0.262	0.180	(–0.091, 0.615)	0.096	0.173	(–0.244, 0.435)	1.08
	BMI $>$ 25	–0.050	0.126	(–0.297, 0.196)	–0.094	0.120	(–0.328, 0.141)	1.10
	Diabetes	–0.066	0.231	(–0.519, 0.387)	–0.162	0.216	(–0.584, 0.261)	1.15
Proportionality^b	Intercept				3.438	0.551	(2.357, 4.518)
	t				–0.519	0.588	(–1.672, –0.634)
	$t^{2}$				–0.307	0.157	(–0.616, 0.001)

Endpoint (a)

{\tilde{L}}_{1} (β)

{\tilde{L}}_{F U, I C} (β)

Parameter^a

Estimate

95% CI

Estimate

95% CI

RE^c

Colorectal

Vitamin D quintile

0.153

0.211

(–0.262, 0.567)

0.297

0.192

(–0.079, 0.672)

1.22

–0.085

0.217

(–0.510, 0.341)

0.150

0.196

(–0.234, 0.534)

1.23

–0.223

0.225

(–0.663, 0.217)

0.124

0.205

(–0.278, 0.526)

1.20

–0.394

0.241

(–0.868, 0.079)

–0.095

0.218

(–0.523, 0.333)

1.22

BMI

>

0.007

0.161

(–0.308, 0.321)

0.085

0.150

(–0.210, 0.380)

1.14

Diabetes

0.470

0.260

(–0.039, 0.979)

0.602

0.237

(0.137, 1.067)

1.20

Prostate

Vitamin D quintile

–0.006

0.188

(–0.373, 0.362)

–0.091

0.181

(–0.446, 0.264)

1.07

0.521

0.173

(0.182, 0.859)

0.385

0.166

(0.060, 0.710)

1.08

0.571

0.188

(0.203, 0.939)

0.347

0.177

(–0.001, 0.693)

1.13

0.262

0.180

(–0.091, 0.615)

0.096

0.173

(–0.244, 0.435)

1.08

BMI

>

–0.050

0.126

(–0.297, 0.196)

–0.094

0.120

(–0.328, 0.141)

1.10

Diabetes

–0.066

0.231

(–0.519, 0.387)

–0.162

0.216

(–0.584, 0.261)

1.15

Proportionality^b

Intercept

3.438

0.551

(2.357, 4.518)

–0.519

0.588

(–1.672, –0.634)

t^{2}

–0.307

0.157

(–0.616, 0.001)

Endpoint (a)
Colorectal	Vitamin D quintile
	2	0.153	0.211	(–0.262, 0.567)	0.297	0.192	(–0.079, 0.672)	1.22
	3	–0.085	0.217	(–0.510, 0.341)	0.150	0.196	(–0.234, 0.534)	1.23
	4	–0.223	0.225	(–0.663, 0.217)	0.124	0.205	(–0.278, 0.526)	1.20
	5	–0.394	0.241	(–0.868, 0.079)	–0.095	0.218	(–0.523, 0.333)	1.22
	BMI $>$ 25	0.007	0.161	(–0.308, 0.321)	0.085	0.150	(–0.210, 0.380)	1.14
	Diabetes	0.470	0.260	(–0.039, 0.979)	0.602	0.237	(0.137, 1.067)	1.20
Prostate	Vitamin D quintile
	2	–0.006	0.188	(–0.373, 0.362)	–0.091	0.181	(–0.446, 0.264)	1.07
	3	0.521	0.173	(0.182, 0.859)	0.385	0.166	(0.060, 0.710)	1.08
	4	0.571	0.188	(0.203, 0.939)	0.347	0.177	(–0.001, 0.693)	1.13
	5	0.262	0.180	(–0.091, 0.615)	0.096	0.173	(–0.244, 0.435)	1.08
	BMI $>$ 25	–0.050	0.126	(–0.297, 0.196)	–0.094	0.120	(–0.328, 0.141)	1.10
	Diabetes	–0.066	0.231	(–0.519, 0.387)	–0.162	0.216	(–0.584, 0.261)	1.15
Proportionality^b	Intercept				3.438	0.551	(2.357, 4.518)
	t				–0.519	0.588	(–1.672, –0.634)
	$t^{2}$				–0.307	0.157	(–0.616, 0.001)

Endpoint (b)
Colorectal	Vitamin D quintile
	2	0.124	0.213	(–0.293, 0.541)	0.281	0.193	(–0.097, 0.658)	1.22
	3	-0.097	0.218	(–0.523, 0.330)	0.095	0.195	(–0.287, 0.478)	1.24
	4	-0.234	0.225	(–0.675, 0.207)	0.102	0.205	(–0.299, 0.504)	1.20
	5	-0.397	0.242	(–0.871, 0.078)	-0.096	0.219	(–0.526, 0.334)	1.22
	BMI $>$ 25	-0.001	0.161	(–0.316, 0.314)	0.089	0.151	(–0.207, 0.384)	1.13
	Diabetes	0.468	0.260	(–0.040, 0.977)	0.633	0.239	(0.165, 1.102)	1.18
Prostate	Vitamin D quintile
	2	0.003	0.186	(–0.362, 0.367)	-0.084	0.182	(–0.441, 0.272)	1.05
	3	0.434	0.170	(0.100, 0.768)	0.344	0.166	(0.019, 0.669)	1.06
	4	0.482	0.179	(0.131, 0.833)	0.289	0.171	(–0.046, 0.624)	1.10
	5	0.302	0.176	(–0.043, 0.647)	0.144	0.170	(–0.189, 0.477)	1.07
	BMI $>$ 25	-0.018	0.129	(–0.270, 0.234)	-0.078	0.122	(–0.318, 0.161)	1.11
	Diabetes	0.043	0.237	(–0.422, 0.508)	-0.091	0.221	(–0.525, 0.342)	1.15
Proportionality²	Intercept				3.384	0.555	(2.296, 4.472)
	t				-0.510	0.592	(–1.670, 0.651)
	$t^{2}$				-0.309	0.159	(–0.620, 0.002)

Endpoint (b)

{\tilde{L}}_{1} (β)

{\tilde{L}}_{F U, I C} (β)

Parameter¹

Estimate

95% CI

Estimate

95% CI

{RE}^{3}

Colorectal

Vitamin D quintile

0.124

0.213

(–0.293, 0.541)

0.281

0.193

(–0.097, 0.658)

1.22

-0.097

0.218

(–0.523, 0.330)

0.095

0.195

(–0.287, 0.478)

1.24

-0.234

0.225

(–0.675, 0.207)

0.102

0.205

(–0.299, 0.504)

1.20

-0.397

0.242

(–0.871, 0.078)

-0.096

0.219

(–0.526, 0.334)

1.22

BMI

>

-0.001

0.161

(–0.316, 0.314)

0.089

0.151

(–0.207, 0.384)

1.13

Diabetes

0.468

0.260

(–0.040, 0.977)

0.633

0.239

(0.165, 1.102)

1.18

Prostate

Vitamin D quintile

0.003

0.186

(–0.362, 0.367)

-0.084

0.182

(–0.441, 0.272)

1.05

0.434

0.170

(0.100, 0.768)

0.344

0.166

(0.019, 0.669)

1.06

0.482

0.179

(0.131, 0.833)

0.289

0.171

(–0.046, 0.624)

1.10

0.302

0.176

(–0.043, 0.647)

0.144

0.170

(–0.189, 0.477)

1.07

BMI

>

-0.018

0.129

(–0.270, 0.234)

-0.078

0.122

(–0.318, 0.161)

1.11

Diabetes

0.043

0.237

(–0.422, 0.508)

-0.091

0.221

(–0.525, 0.342)

1.15

Proportionality²

Intercept

3.384

0.555

(2.296, 4.472)

-0.510

0.592

(–1.670, 0.651)

t^{2}

-0.309

0.159

(–0.620, 0.002)

Endpoint (b)
Colorectal	Vitamin D quintile
	2	0.124	0.213	(–0.293, 0.541)	0.281	0.193	(–0.097, 0.658)	1.22
	3	-0.097	0.218	(–0.523, 0.330)	0.095	0.195	(–0.287, 0.478)	1.24
	4	-0.234	0.225	(–0.675, 0.207)	0.102	0.205	(–0.299, 0.504)	1.20
	5	-0.397	0.242	(–0.871, 0.078)	-0.096	0.219	(–0.526, 0.334)	1.22
	BMI $>$ 25	-0.001	0.161	(–0.316, 0.314)	0.089	0.151	(–0.207, 0.384)	1.13
	Diabetes	0.468	0.260	(–0.040, 0.977)	0.633	0.239	(0.165, 1.102)	1.18
Prostate	Vitamin D quintile
	2	0.003	0.186	(–0.362, 0.367)	-0.084	0.182	(–0.441, 0.272)	1.05
	3	0.434	0.170	(0.100, 0.768)	0.344	0.166	(0.019, 0.669)	1.06
	4	0.482	0.179	(0.131, 0.833)	0.289	0.171	(–0.046, 0.624)	1.10
	5	0.302	0.176	(–0.043, 0.647)	0.144	0.170	(–0.189, 0.477)	1.07
	BMI $>$ 25	-0.018	0.129	(–0.270, 0.234)	-0.078	0.122	(–0.318, 0.161)	1.11
	Diabetes	0.043	0.237	(–0.422, 0.508)	-0.091	0.221	(–0.525, 0.342)	1.15
Proportionality²	Intercept				3.384	0.555	(2.296, 4.472)
	t				-0.510	0.592	(–1.670, 0.651)
	$t^{2}$				-0.309	0.159	(–0.620, 0.002)

Table 5:

Open in new tab

Result of the combined analysis of two case-control studies nested in the PLCO cohort.

Endpoint (a)
		${\tilde{L}}_{1} (β)$			${\tilde{L}}_{F U, I C} (β)$
	Parameter^a	Estimate	SE	95% CI	Estimate	SE	95% CI	RE^c
Colorectal	Vitamin D quintile
	2	0.153	0.211	(–0.262, 0.567)	0.297	0.192	(–0.079, 0.672)	1.22
	3	–0.085	0.217	(–0.510, 0.341)	0.150	0.196	(–0.234, 0.534)	1.23
	4	–0.223	0.225	(–0.663, 0.217)	0.124	0.205	(–0.278, 0.526)	1.20
	5	–0.394	0.241	(–0.868, 0.079)	–0.095	0.218	(–0.523, 0.333)	1.22
	BMI $>$ 25	0.007	0.161	(–0.308, 0.321)	0.085	0.150	(–0.210, 0.380)	1.14
	Diabetes	0.470	0.260	(–0.039, 0.979)	0.602	0.237	(0.137, 1.067)	1.20
Prostate	Vitamin D quintile
	2	–0.006	0.188	(–0.373, 0.362)	–0.091	0.181	(–0.446, 0.264)	1.07
	3	0.521	0.173	(0.182, 0.859)	0.385	0.166	(0.060, 0.710)	1.08
	4	0.571	0.188	(0.203, 0.939)	0.347	0.177	(–0.001, 0.693)	1.13
	5	0.262	0.180	(–0.091, 0.615)	0.096	0.173	(–0.244, 0.435)	1.08
	BMI $>$ 25	–0.050	0.126	(–0.297, 0.196)	–0.094	0.120	(–0.328, 0.141)	1.10
	Diabetes	–0.066	0.231	(–0.519, 0.387)	–0.162	0.216	(–0.584, 0.261)	1.15
Proportionality^b	Intercept				3.438	0.551	(2.357, 4.518)
	t				–0.519	0.588	(–1.672, –0.634)
	$t^{2}$				–0.307	0.157	(–0.616, 0.001)

Endpoint (a)
		${\tilde{L}}_{1} (β)$			${\tilde{L}}_{F U, I C} (β)$
	Parameter^a	Estimate	SE	95% CI	Estimate	SE	95% CI	RE^c
Colorectal	Vitamin D quintile
	2	0.153	0.211	(–0.262, 0.567)	0.297	0.192	(–0.079, 0.672)	1.22
	3	–0.085	0.217	(–0.510, 0.341)	0.150	0.196	(–0.234, 0.534)	1.23
	4	–0.223	0.225	(–0.663, 0.217)	0.124	0.205	(–0.278, 0.526)	1.20
	5	–0.394	0.241	(–0.868, 0.079)	–0.095	0.218	(–0.523, 0.333)	1.22
	BMI $>$ 25	0.007	0.161	(–0.308, 0.321)	0.085	0.150	(–0.210, 0.380)	1.14
	Diabetes	0.470	0.260	(–0.039, 0.979)	0.602	0.237	(0.137, 1.067)	1.20
Prostate	Vitamin D quintile
	2	–0.006	0.188	(–0.373, 0.362)	–0.091	0.181	(–0.446, 0.264)	1.07
	3	0.521	0.173	(0.182, 0.859)	0.385	0.166	(0.060, 0.710)	1.08
	4	0.571	0.188	(0.203, 0.939)	0.347	0.177	(–0.001, 0.693)	1.13
	5	0.262	0.180	(–0.091, 0.615)	0.096	0.173	(–0.244, 0.435)	1.08
	BMI $>$ 25	–0.050	0.126	(–0.297, 0.196)	–0.094	0.120	(–0.328, 0.141)	1.10
	Diabetes	–0.066	0.231	(–0.519, 0.387)	–0.162	0.216	(–0.584, 0.261)	1.15
Proportionality^b	Intercept				3.438	0.551	(2.357, 4.518)
	t				–0.519	0.588	(–1.672, –0.634)
	$t^{2}$				–0.307	0.157	(–0.616, 0.001)

Endpoint (b)
		${\tilde{L}}_{1} (β)$			${\tilde{L}}_{F U, I C} (β)$
	Parameter¹	Estimate	SE	95% CI	Estimate	SE	95% CI	${RE}^{3}$
Colorectal	Vitamin D quintile
	2	0.124	0.213	(–0.293, 0.541)	0.281	0.193	(–0.097, 0.658)	1.22
	3	-0.097	0.218	(–0.523, 0.330)	0.095	0.195	(–0.287, 0.478)	1.24
	4	-0.234	0.225	(–0.675, 0.207)	0.102	0.205	(–0.299, 0.504)	1.20
	5	-0.397	0.242	(–0.871, 0.078)	-0.096	0.219	(–0.526, 0.334)	1.22
	BMI $>$ 25	-0.001	0.161	(–0.316, 0.314)	0.089	0.151	(–0.207, 0.384)	1.13
	Diabetes	0.468	0.260	(–0.040, 0.977)	0.633	0.239	(0.165, 1.102)	1.18
Prostate	Vitamin D quintile
	2	0.003	0.186	(–0.362, 0.367)	-0.084	0.182	(–0.441, 0.272)	1.05
	3	0.434	0.170	(0.100, 0.768)	0.344	0.166	(0.019, 0.669)	1.06
	4	0.482	0.179	(0.131, 0.833)	0.289	0.171	(–0.046, 0.624)	1.10
	5	0.302	0.176	(–0.043, 0.647)	0.144	0.170	(–0.189, 0.477)	1.07
	BMI $>$ 25	-0.018	0.129	(–0.270, 0.234)	-0.078	0.122	(–0.318, 0.161)	1.11
	Diabetes	0.043	0.237	(–0.422, 0.508)	-0.091	0.221	(–0.525, 0.342)	1.15
Proportionality²	Intercept				3.384	0.555	(2.296, 4.472)
	t				-0.510	0.592	(–1.670, 0.651)
	$t^{2}$				-0.309	0.159	(–0.620, 0.002)

Endpoint (b)
		${\tilde{L}}_{1} (β)$			${\tilde{L}}_{F U, I C} (β)$
	Parameter¹	Estimate	SE	95% CI	Estimate	SE	95% CI	${RE}^{3}$
Colorectal	Vitamin D quintile
	2	0.124	0.213	(–0.293, 0.541)	0.281	0.193	(–0.097, 0.658)	1.22
	3	-0.097	0.218	(–0.523, 0.330)	0.095	0.195	(–0.287, 0.478)	1.24
	4	-0.234	0.225	(–0.675, 0.207)	0.102	0.205	(–0.299, 0.504)	1.20
	5	-0.397	0.242	(–0.871, 0.078)	-0.096	0.219	(–0.526, 0.334)	1.22
	BMI $>$ 25	-0.001	0.161	(–0.316, 0.314)	0.089	0.151	(–0.207, 0.384)	1.13
	Diabetes	0.468	0.260	(–0.040, 0.977)	0.633	0.239	(0.165, 1.102)	1.18
Prostate	Vitamin D quintile
	2	0.003	0.186	(–0.362, 0.367)	-0.084	0.182	(–0.441, 0.272)	1.05
	3	0.434	0.170	(0.100, 0.768)	0.344	0.166	(0.019, 0.669)	1.06
	4	0.482	0.179	(0.131, 0.833)	0.289	0.171	(–0.046, 0.624)	1.10
	5	0.302	0.176	(–0.043, 0.647)	0.144	0.170	(–0.189, 0.477)	1.07
	BMI $>$ 25	-0.018	0.129	(–0.270, 0.234)	-0.078	0.122	(–0.318, 0.161)	1.11
	Diabetes	0.043	0.237	(–0.422, 0.508)	-0.091	0.221	(–0.525, 0.342)	1.15
Proportionality²	Intercept				3.384	0.555	(2.296, 4.472)
	t				-0.510	0.592	(–1.670, 0.651)
	$t^{2}$				-0.309	0.159	(–0.620, 0.002)

The reference levels of the covariates are the first vitamin D quintile, BMI $\leq 25$ and no diabetes.

The proportionality factor is modeled as a linear function of t, where t is the case time in days divided by 1000.

Relative efficiency is the ratio of the variance of an estimate from ${\tilde{L}}_{1} (β)$ to the variance of the corresponding estimate from ${\tilde{L}}_{F U, I C} (β)$ ⁠.

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