Answers Epidemiology

There were 1000 people with osteosarcoma and the population at risk was 50 million. So:

Prevalence = $\frac{1000}{50000000}=\frac{20}{1000000}$ = 20 per million

At the start of the year there were 1000 cases of osteosarcoma. 200 new cases were diagnosed and 75 patients with osteosarcoma died. On 1^st January 2001 there were therefore:

1000 + 200 – 75 = 1125 patients with osteosarcoma. So:

Prevalence = $\frac{1125}{50000000}=\frac{22.5}{1000000}$ = 22.5 per million

There were 200 new cases of osteosarcoma in the year. The Incidence is therefore:

Incidence = $\frac{200}{50000000}=\frac{4}{1000000}$ = 4 per million

The two by two table is as follows:

Kienböck’s No Kienböck’s

Neg Ulnar Var 12 138

No Neg Ulnar Var 3 347
The relative risk is:

	Kienböck’s	No Kienböck’s
Neg Ulnar Var	12	138
No Neg Ulnar Var	3	347

Absolute Risk 1 = $\frac{12}{150}$ = 0.08

Absolute Risk 2 = $\frac{3}{350}\approx$ 0.00857

Relative Risk = $\frac{12 \over 150}{ 3 \over 350}\approx 9.33$

The odds ratio is:

Odds Ratio = $\frac{12 \times 347}{138 \times 3}\approx 10.06$

First construct a two by two table:

	Died	Survived
	1517	706	2223
Men	1347	336	1683
Women & Children	170	370	540

In the JGR / R console 1 :

library(epiR)
mat<-matrix(c(1347,170,336,370),ncol=2)
mat
     [,1] [,2]
[1,] 1347 336
[2,] 170 370
epi.2by2(mat)
             Outcome +    Outcome –      Total        Inc risk *        Odds
Exposed +         1347          336       1683              80.0    4.009
Exposed –            170          370       540              31.5        0.459
Total           1517          706       2223              68.2        2.149

Point estimates and 95 % CIs:
———————————————————
Inc risk ratio                               2.54 (2.24, 2.89)
Odds ratio                                   8.71 (6.98, 10.91)
Attrib risk *                                48.55 (44.20, 52.91)
Attrib risk in population *                  36.76 (32.39, 41.13)
Attrib fraction in exposed (%)               60.67 (55.35, 65.35)
Attrib fraction in population (%)            53.87 (48.34, 58.81)
———————————————————
* Cases per 100 population units

The package epiR 1 should be installed.

The odds ratio provided is the maximum likelihood estimate that is different from the cross product ratio. To obtain the cross product ratio :

summary(epi.tests(mat))
               est     lower      upper
aprev    0.7570850 0.7387012 0.7747887
tprev    0.6824112 0.6626028 0.7017375
se       0.8879367 0.8709769 0.9033774
sp       0.5240793 0.4864967 0.5614599
diag.acc 0.7723797 0.7543719 0.7896666
diag.or 8.7253151 7.0204403 10.8442094
nnd      2.4270900 2.1512902 2.7974095
youden   0.4120160 0.3574736 0.4648373
ppv      0.8003565 0.7804454 0.8192143
npv      0.6851852 0.6441513 0.7241780
plr      1.8657242 1.7232384 2.0199914
nlr      0.2138289 0.1825536 0.2504622

The absolute risk for men dying is 80 %

The absolute risk for women and children dying is 31.5 %

The odds for men dying is 4.009

The odds for women and children dying is 0.459

The odds ratio is 8.73 ; 95% confidence interval: 7.02 – 10.84

To obtain the cross product odds ratio with a 99% confidence interval:

summary(epi.tests(mat,conf.level=0.99))
               est     lower      upper
aprev    0.7570850 0.7328916 0.7801648
tprev    0.6824112 0.6563789 0.7076541
se       0.8879367 0.8655122 0.9078798
sp       0.5240793 0.4749263 0.5729024
diag.acc 0.7723797 0.7486736 0.7949055
diag.or 8.7253151 6.5568681 11.6108976
nnd      2.4270900 2.0799435 2.9373883
youden   0.4120160 0.3404385 0.4807823
ppv      0.8003565 0.7741208 0.8248692
npv      0.6851852 0.6312886 0.7357534
plr      1.8657242 1.6807535 2.0710513
nlr      0.2138289 0.1737045 0.2632217

The odds ratio is 8.73 ; 99% confidence interval: 6.56 – 11.61

First construct the two by two table:

	Died	Survived
	832	492	1324
1st / 2nd Class	296	318	614
3rd Class	536	174	710

library(epiR)
mat<-matrix(c(296,536,318,174),ncol=2)
mat
     [,1] [,2]
[1,] 296 318
[2,] 536 174
epi.2by2(mat)
             Outcome +    Outcome –      Total        Inc risk *        Odds
Exposed +          296          318        614              48.2       0.931
Exposed –       536          174        710              75.5       3.080
Total                832          492       1324              62.8       1.691

Point estimates and 95 % CIs:
———————————————————
Inc risk ratio                               0.64 (0.58, 0.70)
Odds ratio                                   0.30 (0.24, 0.38)
Attrib risk *                                -27.28 (-32.35, -22.22)
Attrib risk in population *                  -12.65 (-16.75, -8.56)
Attrib fraction in exposed (%)               -56.60 (-71.70, -42.82)
Attrib fraction in population (%)            -20.14 (-24.39, -16.03)
———————————————————
* Cases per 100 population units

The absolute risk for third class passengers dying is 75.5 %

The absolute risk for first and second class passengers dying is 48.2 %

The odds for third class passengers dying is 3.08

The odds for first and second class passengers dying is 0.93

The odds ratio is 0.3 ; 95% confidence interval: 0.24 – 0.38

The package epiR 1 should be installed.

The odds ratio provided is the maximum likelihood estimate that is different from the cross product ratio. To obtain the cross product ratio :

summary(epi.tests(mat))
                est      lower      upper
aprev     0.4637462 0.4366131 0.4910407
tprev     0.6283988 0.6017300 0.6544962
se        0.3557692 0.3231978 0.3893667
sp        0.3536585 0.3113859 0.3977019
diag.acc 0.3549849 0.3291785 0.3814368
diag.or   0.3021684 0.2393570 0.3814626
nnd      -3.4414851 -4.6963489 -2.7366048
youden   -0.2905722 -0.3654163 -0.2129314
ppv       0.4820847 0.4419150 0.5224274
npv       0.2450704 0.2138415 0.2784340
plr       0.5504354 0.4919185 0.6159133
nlr       1.8216180 1.6000518 2.0738655

First construct a two by two table:

	Prostate Cancer	Control
	149	125
Bald	46	72
Hairy	103	53

library(epiR)
mat<-matrix(c(46,103,72,53),ncol=2)
mat
     [,1] [,2]
[1,]   46   72
[2,] 103   53
epi.2by2(mat)
             Outcome +    Outcome –      Total        Inc risk *        Odds
Exposed +           46           72        118              39.0       0.639
Exposed –          103           53        156              66.0       1.943
Total             149          125        274              54.4       1.192

Point estimates and 95 % CIs:
———————————————————
Inc risk ratio                               0.59 (0.46, 0.76)
Odds ratio                                   0.33 (0.19, 0.56)
Attrib risk *                                -27.04 (-38.56, -15.52)
Attrib risk in population *                  -11.65 (-21.13, -2.16)
Attrib fraction in exposed (%)               -69.37 (-117.96, -31.61)
Attrib fraction in population (%)            -21.42 (-31.94, -11.73)
———————————————————
* Cases per 100 population units

The odds of developing prostate cancer for bald patients is 0.639

The odds of developing prostate cancer for hairy patients is 1.943

The odds ratio is 0.33 ; 95% confidence interval: 0.2 – 0.54

The package epiR 1 should be installed.

The odds ratio provided is the maximum likelihood estimate that is different from the cross product ratio. To obtain the cross product ratio :

summary(epi.tests(mat))
          est       lower      upper
aprev     0.4306569   0.3712342 0.4915959
tprev     0.5437956   0.4827946 0.6038392
se        0.3087248   0.2356959 0.3895415
sp        0.4240000   0.3361237 0.5155619
diag.acc 0.3613139   0.3043858 0.4212781
diag.or   0.3287487   0.2000696 0.5401904
nnd      -3.7414624 -10.5377855 -2.3354642
youden   -0.2672752 -0.4281804 -0.0948966
ppv       0.3898305   0.3014051 0.4839246
npv       0.3397436   0.2659238 0.4197827
plr       0.5359806   0.4036857 0.7116308
nlr       1.6303660   1.2943610 2.0535949



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    1. 
Stevenson M, Nunes T, Heuer C, Marshall J, Sanchez J, Thornton R, et al. epiR: Tools for the Analysis of Epidemiological Data [Internet]. 2015. (R package). Available from: http://cran.r-project.org/package=epiR