Tarea 3.pdf

Tarea 3 Fundamentos de An´alisis Epidemiol´ogico II 3009373 Diego Alejandro Mu˜ noz Gaviria Catalina Ot´alvaro Ram´ırez 23 de marzo de 2019

10.5 Swan (1986) gives the following data from a study of infant respiratory disease. Each cell of the table shows the number out of so many observed children who developed bronchitis or pneumonia in their first year of life, classified by sex and type of feeding (with the risk in parentheses). Sex Boys Girls

Bottle only 77/458 (0.17) 48/384 (0.13)

Breast + supplement 19/147 (0.13) 16/127 (0.13)

Breast only 47/494 (0.10) 31/464 (0.07)

The major question of interest is whether the risk of illness is affected by the type of feeding. Also, is the risk the same for both sexes and, if there are differences between the feeding groups, are they the same for boys and girls? (i) Fit all possible linear logistic regression models to the data. Use your results to answer all the preceding questions through significance testing. Summarize your findings using odds ratios with 95 % confidence intervals. Existe la posibilidad de ajustar 3 modelos diferentes para encontrar tales diferencias, uno en el cual solo se tenga en cuenta tipo de alimentaci´on, otro para g´enero y otro en el cual se eval´ uen las dos covariables. The LOGISTIC Procedure Model Information Data Set

ADE.SIRS

Response Variable (Events)

illness

Response Variable (Trials)

total

Model

binary logit

Optimization Technique

Fisher's scoring

Number of Observations Read

6

Number of Observations Used

6

Sum of Frequencies Read

2074

Sum of Frequencies Used

2074

Response Profile Ordered Value

Binary Outcome

1

Event

2

Nonevent

Total Frequency 238 1836

Class Level Information Class

Value

feeding

1

1

2

0

1

3

-1

-1

1

Design Variables 0

Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied.

Number of Observations Read

6

Number of Observations Used

6

Sum of Frequencies Read

2074

Sum of Frequencies Used

2074

Response Profile Ordered Value

Total Frequency

Binary Outcome

Modelo ajustado al tipo de alimentaci´ 1 = Bottle only, feeding 1 Eventon donde: feeding 238 1836 2 = Breast + supplement, feeding2 3Nonevent = Breast only. Class Level Information Class

Value

feeding

1

Design Variables 1

2

0

1

3

-1

-1

0

Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics Intercept and Covariates Criterion

Intercept Only

Log Likelihood

Full Log Likelihood

AIC

1480.102

1463.426

43.217

SC

1485.739

1480.338

60.129

-2 Log L

1478.102

1457.426

37.217

Testing Global Null Hypothesis: BETA=0 Test

Chi-Square

DF

Pr > ChiSq

Likelihood Ratio

20.6763

2

<.0001

Score

20.3480

2

<.0001

Wald

19.8447

2

<.0001

Type 3 Analysis of Effects Effect feeding

DF

Wald Chi-Square

Pr > ChiSq

2

19.8447

<.0001

Analysis of Maximum Likelihood Estimates

Parameter Intercept

DF

Estimate

Standard Error

Wald Chi-Square

Pr > ChiSq

1

-2.0304

0.0790

661.2600

<.0001

feeding

1

1

0.2836

0.0968

8.5877

0.0034

feeding

2

1

0.1092

0.1310

0.6958

0.4042

Odds Ratio Estimates Effect

Point Estimate

95% Wald Confidence Limits

feeding 1 vs 3

1.967

1.458

2.654

feeding 2 vs 3

1.652

1.082

2.524

Association of Predicted Probabilities and Observed Responses Percent Concordant

39.1

Somers' D

0.163

Percent Discordant

22.8

Gamma

0.263

Percent Tied

38.1

Tau-a

0.033

c

0.581

Pairs

436968

ˆ f eeding,13 = 1.967 como estimaci´on para la En este modelo ajustado se obtiene Ψ raz´ on de odds, fijando como nivel de referencia el nivel 3, Breast only; lo que quiere decir es que los ni˜ nos que se alimentan Bottle only tienen aproximadamente 1.97 veces m´ as riesgo de sufrir una enfermedad respiratoria comparado con los bebes alimentados Breast only; este riesgo se considera significativo ya que su intervalo de confianza no contiene el 1, (1.458, 2.654).

2

Model Information Data Set

ADE.SIRS

Response Variable (Events)

illness

Response Variable (Trials)

total

Model

binary logit

Optimization Technique

Fisher's scoring

Number of Observations Read

6

ˆ f eeding,23 = 1.652, seNumber Siendo Ψ tienen para Used decir que los ni˜ nos que reciben una of Observations 6 Sum of Frequencies Read 2074 alimentaci´ on Breast + supplement tienen un riesgo 1.65 veces mayor de sufrir Sum of Frequencies Used 2074 de una enfermedad respiratoria que los bebes alimentados Breast only; este riesgo se considera significativo ya queResponse su intervalo de confianza no contiene el 1 Profile Ordered Total (1.082, 2.524). Value

Binary Outcome

1

Frequency

Event

238

Nonevent Modelo ajustado al g´enero donde:2 sex 1 = Boys, 1836 sex 2 = Girls Class Level Information Class

Value

sex

1

Design Variables 1

2

-1

Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics Intercept and Covariates Criterion

Intercept Only

Log Likelihood

Full Log Likelihood

AIC

1480.102

1476.626

56.417

SC

1485.739

1487.900

67.692

-2 Log L

1478.102

1472.626

52.417

Testing Global Null Hypothesis: BETA=0 Test

Chi-Square

DF

Pr > ChiSq

Likelihood Ratio

5.4761

1

0.0193

Score

5.4324

1

0.0198

Wald

5.3975

1

0.0202

Type 3 Analysis of Effects Effect sex

DF

Wald Chi-Square

Pr > ChiSq

1

5.3975

0.0202

Analysis of Maximum Likelihood Estimates Parameter

DF

Estimate

Standard Error

Wald Chi-Square

Pr > ChiSq

1

-2.0629

0.0702

864.0594

<.0001

1

0.1630

0.0702

5.3975

0.0202

Intercept sex

1

Odds Ratio Estimates Effect

Point Estimate

sex 1 vs 2

1.386

95% Wald Confidence Limits 1.052

1.824

Association of Predicted Probabilities and Observed Responses Percent Concordant

28.8

Somers' D

0.080

Percent Discordant

20.8

Gamma

0.162

Percent Tied

50.4

Tau-a

0.016

c

0.540

Pairs

436968

ˆ Boys,Girls = 1.386 como estimaci´on para la Al ajustar este modelo se obtiene Ψ raz´ on de odds, fijando como nivel de referencia el nivel asociado a Girls; Boys tienen un riesgo 1.386 veces mayor de sufrir de una enfermedad respiratoria, comparado con Girls. Este riesgo se considera significativo ya que su intervalo de confianza no contiene el 1 (1.386, 1.824). 3

Number of Observations Read

6

Number of Observations Used

6

Sum of Frequencies Read

2074

Sum of Frequencies Used

2074

Response Profile Ordered Value

Total Frequency

Binary Outcome

1

Event

238

2 Nonevent 1836 Modelo ajustado al tipo de alimentaci´ on y g´enero. Class Level Information Class

Value

sex

1

1

2

-1

1

1

2

0

1

3

-1

-1

feeding

Design Variables

0

Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics Intercept and Covariates Criterion

Intercept Only

Log Likelihood

Full Log Likelihood

AIC

1480.102

1460.449

40.240

SC

1485.739

1482.998

62.789

-2 Log L

1478.102

1452.449

32.240

Testing Global Null Hypothesis: BETA=0 Test

Chi-Square

DF

Pr > ChiSq

Likelihood Ratio

25.6534

3

<.0001

Score

25.2344

3

<.0001

Wald

24.6148

3

<.0001

Type 3 Analysis of Effects DF

Wald Chi-Square

sex

1

4.9109

0.0267

feeding

2

19.3786

<.0001

Effect

Pr > ChiSq

Analysis of Maximum Likelihood Estimates Parameter Intercept

DF

Estimate

Standard Error

Wald Chi-Square

Pr > ChiSq

1

-2.0496

0.0801

654.9727

<.0001

sex

1

1

0.1563

0.0705

4.9109

0.0267

feeding

1

1

0.2806

0.0969

8.3844

0.0038

feeding

2

1

0.1081

0.1311

0.6791

0.4099

Odds Ratio Estimates Effect

Point Estimate

95% Wald Confidence Limits

sex 1 vs 2

1.367

1.037

1.802

feeding 1 vs 3

1.953

1.447

2.636

feeding 2 vs 3

1.643

1.075

2.512

Association of Predicted Probabilities and Observed Responses Percent Concordant

50.2

Somers' D

0.196

Percent Discordant

30.6

Gamma

0.243

Percent Tied

19.2

Tau-a

0.040

c

0.598

Pairs

436968

Con este modelo sin interacci´on entre Sex y Feeding se obtienen los verdaderos valores de los par´ ametros estimados cuando intervienen como variebles sin tener interacci´ on, sus razones de odds e intervalos de confianza, as´ı: Comparaci´ on Boys : Girls Bottle : Breast Mixed : Breast

4

Odds ratio 1.37 1.95 1.64

IC 95 % (1.04,1.80) (1.45,2.51) (1.08,2.05)

(ii) Fit the model with explanatory variables sex and type of feeding (but no interaction). Calculate the residuals, deviance residuals and standardised deviance residuals and comment on the results. Luego de realizar el ajuste del modelo con el PROC LOGISTIC se buscaron los residuales en el PROC GENMOD con la opci´on output que arroja la siguiente tabla: Sex Boy Boy Boy Girl Girl Girl

Feed Bottle Mixed Breast Bottle Mixed Breast

Resid 0.8742 -2.1175 1.2433 -0.8742 2.1175 -1.2433

Dev Resid 0.1096 -0.5052 0.1922 -0.1342 0.5896 -0.2284

St Dev Resid 0.2462 -0.8579 0.3670 -0.2473 0.8279 -0.3707

Programa SAS /*

Study of Infant Respiratory Disease

*/

data ADE.SIRS; input illness total sex$ feeding$; cards; 77 458 1 1 19 147 1 2 47 494 1 3 48 384 2 1 16 127 2 2 31 464 2 3 ; run; proc logistic data=ADE.SIRS; class feeding; model illness/total = feeding; run; proc logistic data=ADE.SIRS; class sex; model illness/total = sex; run; proc logistic data=ADE.SIRS; class sex feeding; model illness/total = sex feeding; run; proc genmod data=ADE.SIRS; class sex feeding; model illness/total = sex feeding/ dist=binomial link=logit; output out=res resraw resdev stdresdev=st_Dev_res; run;

5

10.10 Repeat the analysis of Exercise 6.1, the unmatched case–control study of oral contraceptive use and breast cancer, using logistic regression modelling. Compare results. 6.1 In a case–control study of the use of oral contraceptives (OCs) and breast cancer in New Zealand, Paul et al. (1986) identified cases over a 2-year period from the National Cancer Registry and controls by random selection from electoral rolls. The following data were compiled. Used OCs? Yes No Total

Cases 310 123 433

Controls 708 189 897

(i) Estimate the odds ratio for breast cancer, OC users versus nonusers. Specify a 95 % confidence interval for the true odds ratio. Luego de ajustar el modelo de regresi´on log´ıstica: [model cases/total = UsedOC] en SAS, se obtuvo como resultado el estimador del efecto UsedOCs = −0.3963 para un Odss Ratio = 0.673. El signo negativo en el estimador y el valor del OR < ˆ = e−0.3963 = 0.673, con un IC al 95 % para el OR = Ψ ˆ es (0.517, 0.876) 1 en Ψ sin incluir el 1 (adquiriendo significancia), indica que Yes en UsedOC disminuye la probabilidad del riesgo de c´ancer de seno en 67.3 %. Entonces UsedOC es un factor protector contra el c´ancer de seno. ˆ = 1/0.673 = 1.48 veces mayor Las mujeres con No en UsedOC tienen un riesgo Ψ de sufrir de c´ ancer de seno que las mujeres con Yes en UsedOC. (ii) Test whether OC use appears to be associated with breast cancer. El test de asociaci´ on arroja un resultado de 8.6978 con un valor − p = 0.0032 que al compararlo con un nivel de significancia del 5 %, rechaza la hip´otesis nula y da raz´ on para concluir que si hay asociaci´on estad´ıstica entre UsedOC y la aparici´ on de c´ ancer de seno. Estos resultados son similares a los obtenidos de forma manual para el ejercicio 6.1 pero queda demostrado que bajo la regresi´on log´ıstica se obtienen mayores beneficios como rapidez, exactitud, evidencias y todas las estimaciones y tests bajo un mismo procedimiento. A continuaci´ on el programa y la salida en SAS para lo anteriormente explicado: /* UNMATCHED CASE:CONTROL uso anticonceptivos orales(OC) */ data ADE.OC; input UsaOC casos controles total; cards; 1 310 708 1018 0 123 189 312 ; run; proc logistic data=ADE.OC; model casos/total=UsaOC; run;

6

The LOGISTIC Procedure Model Information Data Set

ADE.OC

Response Variable (Events)

cases

Response Variable (Trials)

total

Model

binary logit

Optimization Technique

Fisher's scoring

Number of Observations Read

2

Number of Observations Used

2

Sum of Frequencies Read

1330

Sum of Frequencies Used

1330

Response Profile Ordered Value

Total Frequency

Binary Outcome

1

Event

433

2

Nonevent

897

Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics Intercept and Covariates Criterion

Intercept Only

Log Likelihood

Full Log Likelihood

AIC

1680.440

1673.872

17.362

SC

1685.633

1684.258

27.748

-2 Log L

1678.440

1669.872

13.362

Testing Global Null Hypothesis: BETA=0 Test

Chi-Square

DF

Pr > ChiSq

Likelihood Ratio

8.5675

1

0.0034

Score

8.7534

1

0.0031

Wald

8.6978

1

0.0032

Analysis of Maximum Likelihood Estimates DF

Estimate

Standard Error

Wald Chi-Square

Pr > ChiSq

Intercept

1

-0.4295

0.1158

13.7476

0.0002

UsedOC

1

-0.3963

0.1344

8.6978

0.0032

Parameter

Odds Ratio Estimates Effect

Point Estimate

UsedOC

95% Wald Confidence Limits

0.673

0.517

0.876

Association of Predicted Probabilities and Observed Responses Percent Concordant

22.4

Somers' D

0.073

Percent Discordant

15.1

Gamma

0.196

62.5

Tau-a

0.032

c

0.537

Percent Tied Pairs

388401

7

10.13 Refer to the venous thromboembolism matched case–control study of Exercise 6.12. In a matched case–control study of venous thromboembolism (VTE) and use of hormone replacement therapy (HRT), Daly et al. (1996) screened women aged 45–64 years admitted to hospitals in the Oxford Regional Health Authority (UK) with a suspected diagnosis of VTE. From these, 103 cases of idiopathic VTE were recruited. Each case was individually matched with up to two hospital controls with diagnoses judged to be unrelated to HRT use, such as diseases of the eyes, ears or skin. Matching criteria were 5-year age group, district of admission and date of admission (between 2 weeks before and 4 months after the admission date of the corresponding case). Altogether there were 178 controls. The data are available from the web site for this book (Appendix A). Confirm the following summary table:

Matching ratio

Case uses HRT?

1:1

yes no yes no

1:2

Number of controls using HRT 0

1

2

7 17 15 27

3 1 15 11

4 3

(i) Use logistic regression to repeat the analysis of Exercise 6.12. Compare results. Using this summary table, a. Test for no association between hormone replacement therapy (HRT) use and venous thromboembolism. b. Estimate the odds ratio, and find the associated 95 % confidence interval, for HRT users versus nonusers.

Al realizar el an´ alisis de forma similar al ejercicio 6.12 pero usando regresi´on log´ıstica y en la cual solo se tiene en cuenta la variable HRT (similar al ejercicio 6.12) se obtienen las siguientes resultados: El estimador del efecto HRT es: β1 = 1.0957 Su signo positivo de β1 y el valor estimado de odds ratio Ψ = 2.991 > 1 indica que usar HRT aumenta el chance de protecci´on para tromboembolismo venoso hasta 3 veces m´ as que cuando no se usa HRT. Entonces el no uso de HRT es un factor de riesgo para VTE. Un IC al 95 %para Ψ de trombosis venosa para las mujeres entre 45 y 64 a˜ nos que no usan HRT comparado con las que usan HRT (1.607,5.568) como el intervalo no incluye el 1, puede concluirse con base en los datos, que el no uso de HRT incrementa el riesgo de sufrir un VTE hasta 5.5 veces m´as que si se usara. El test para verificar si existe asociaci´on entre HRT y VTE (significancia del factor HRT ) arroj´ o una estad´ıstica de 11.9516 con un valor − p = 0.0005, rechazando la hip´ otesis nula y dando raz´on con una significancia del 5 % que si hay asociaci´ on estad´ıstica entre HRT y la aparici´on de VTE.

8

The LOGISTIC Procedure Conditional Analysis Model Information Data Set

ADE.VTE

Response Variable

CC

Number of Response Levels

2

Number of Strata

103

Model

binary logit

Optimization Technique

Newton-Raphson ridge

Number of Observations Read

281

Number of Observations Used

281

Number of Observations Informative

281

Response Profile Ordered Value

CC

Total Frequency

1

0

178

2

1

103

Probability modeled is CC=1. Strata Summary CC

Response Pattern

0

1

Number of Strata

1

1

1

28

56

2

2

1

75

225

Frequency

Newton-Raphson Ridge Optimization Without Parameter Scaling Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics Criterion

Without Covariates

With Covariates

AIC

203.608

192.467

SC

203.608

196.105

-2 Log L

203.608

190.467

Testing Global Null Hypothesis: BETA=0 Test

Chi-Square

DF

Pr > ChiSq

Likelihood Ratio

13.1414

1

0.0003

Score

12.9151

1

0.0003

Wald

11.9516

1

0.0005

Analysis of of Conditional Conditional Maximum Maximum Likelihood Likelihood Estimates Estimates Analysis Parameter Parameter HRT HRT

DF DF

Estimate Estimate

Standard Standard Error Error

Wald Wald Chi-Square Chi-Square

Pr > > ChiSq ChiSq Pr

1 1

1.0957 1.0957

0.3170 0.3170

11.9516 11.9516

0.0005 0.0005

Odds Ratio Estimates Effect

Point Estimate

HRT

2.991

9

95% Wald Confidence Limits 1.607

5.568

Model Information Data Set

ADE.VTE

Response Variable

CC

Number of Response Levels

2

Number of Strata

103

Number of Uninformative Strata

3

Frequency Uninformative

4

Model

binary logit

Esta fue la salida SAS de donde se extrajo laNewton-Raphson informaci´ on para dar los anteriores Optimization Technique ridge resultados, que adem´ as son muy similares a los que se obtuvieron en la realizaci´ on del ejercicio 6.12 (Ψ = 3.00 IC95 %(1.61, 5.59), donde igualmente se concluy´ o que hab´ıa Number of Observations Read 281 asociaci´ on entre HRT y VTE es of decir ambas metodolog´ Number Observations Used 278 ıas conllevan a las mismas Number of ıstica Observations conclusiones, siendo la regresi´ on log´ masInformative acertada274y con mayor detalle. Response Profile

(ii) The associated dataset also includes data on body mass index (BMI), a potential Ordered Total Value between CC Frequency confounding factor in the relationship HRT and venous thromboembolism. 0 176 Test for a significant effect of HRT on1 venous thromboembolism, adjusting for BMI. 2 1 102 Estimate the odds ratio for HRT users versus nonusers, adjusting for BMI. Does BMI Probability modeled is CC=1. appear to have a strong confounding effect? Note: 3 observations were deleted due to missing values for the response, explanatory, or strata variables. Strata Summary CC

Response Pattern

0

1

Number of Strata

1

0

1

2

2

2

1

1

26

52

3

2

0

1

2

4

2

1

74

222

Frequency

Newton-Raphson Ridge Optimization Without Parameter Scaling Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics Criterion

Without Covariates

With Covariates

AIC

198.638

185.741

SC

198.638

192.997

-2 Log L

198.638

181.741

Testing Global Null Hypothesis: BETA=0 Test

Chi-Square

DF

Pr > ChiSq

Likelihood Ratio

16.8968

2

0.0002

Score

16.3724

2

0.0003

Wald

14.8877

2

0.0006

Analysis of Conditional Maximum Likelihood Estimates DF

Estimate

Standard Error

Wald Chi-Square

Pr > ChiSq

HRT

1

1.1115

0.3252

11.6862

0.0006

BMI

1

0.0543

0.0257

4.4637

0.0346

Parameter

Odds Ratio Estimates Effect

Point Estimate

95% Wald Confidence Limits

HRT

3.039

1.607

5.748

BMI

1.056

1.004

1.110

10

Seg´ un los resultados obtenidos para BMI Ψ = 3.039 IC95 %(1.607, 5.748) como covariable de HRT , este no incide como un factor confusor en la relaci´on HRT y VTE. La variaci´ on con respecto a los resultados antes expuestos es m´ınima, casi imperceptible. Adem´ as los resultados de BMI no inciden puesto que su Ψ = 1.056 lo que lleva a concluir que el OR de BMI no afecta el riesgo por HRT para VTE. Programa SAS /* matched case{control study of venous thromboembolism (VTE) data ADE.VTE; input ID CC HRT BMI; cards; 1 1 0 32.74 1 0 0 22.00 1 0 0 29.83 . . . 135 1 0 29.16 135 0 0 24.46 ; run; proc logistic data=ADE.VTE; strata ID; model CC(event=’1’)=HRT ; output; run; proc logistic data=ADE.VTE; strata ID; model CC(event=’1’)=HRT BMI ; run;

11

*/

10.6 Saetta et al. (1991) carried out a prospective, single-blind experiment to determine whether gastric content is forced into the small bowel when gastric-emptying procedures are employed with people who have poisoned themselves. Each of 60 subjects was asked to swallow 20 barium-impregnated polythene pellets. Of the 60, 20 received a gastric lavage, 20 received induced emesis and 20 (controls) received no gastric decontamination. The number of residual pellets, counted by x-ray, in the intestine after ingestion for each subject was, for the induced emesis group: 0, 15, 2, 0, 0, 15, 1, 16, 0, 1, 1, 0, 6, 0, 0, 1, 0, 16, 7, 11 for the gastric lavage group: 9, 3, 4, 15, 3, 5, 0, 0, 2, 11, 0, 0, 0, 0, 7, 5, 9, 0, 0, 0 and for the control group: 0, 9, 0, 0, 4, 5, 0, 0, 13, 0, 0, 12, 0, 0, 1, 0, 4, 4, 6, 7 Considerando estos datos: (i) Implemente ANOVA Como primer paso en esta implementaci´on se decide realizar un an´alisis de normalidad el cual arroja como resultado, la anormalidad de los datos a tratar. Test de ShapiroWilks con estad´ıstica 0.7697 y valor−p < 0.0001 rechazan la hip´otesis nula y confirma que no existe normalidad en los datos; por tal motivo ser´ıa infructuoso realizar un anova ya que no estar´ıa cumpliendo los supuestos nacesarios para sus an´alisis. Sin embargo se decide explorar un anova para observar que est´a sucediendo “por dentro”de la estructura de esos datos “aperezados”. En el anova (con diagnostico de normalidad) se observa una aparente igualdad de medias dentro de las 3 distribuciones de la variable gastric con una estad´ıstica 0.37 y valor − p = 0.6909 se acepta la hip´oteis nula de igualdad de medias y se rescata que pareciera existir homogenidad de varianza dada la estad´ıstica F = 2.37 y valor − p = 0.1024. (ii) Implemente Kruskal-Wallis Como se dijo previamente, la no posible implementaci´on de anova, lleva a tener que tratar los datos como si no tuvieran una estructura definida (non-parametric) y se decide correr un text de Kruskal-Wallis con resultado estad´ıstico de 0.3758 y valor − p = 0.8287 para las tres categor´ıas (control, emesis, lavage) de gastric, poniendo en evidencia la igualdad de sus medias. El valor para cada una de estas medias (grupos ranqueados) es para el grupo control : 28.9, emasis: 32.125 y lavage: 30.475 con una desviaci´on est´andar de 60.75 Salida SAS para el an´ alisis de la implementaci´on Kruskal-Wallis:

12

The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable respel Classified by Variable gastric gastric

N

Sum of Scores

Expected Under H0

Std Dev Under H0

Mean Score

control

20

578.00

610.0

60.751415

28.9000

emesis

20

642.50

610.0

60.751415

32.1250

lavage

20

609.50

610.0

60.751415

30.4750

Average scores were used for ties.

Kruskal-Wallis Test Chi-Square

DF

Pr > ChiSq

0.3758

2

0.8287

Monte Carlo Estimates for the Exact Test Probability Pr >= ChiSq

Estimate 0.8313

99% Confidence Limits 0.8217

0.8409

13

Samples

Seed

10000

364567942

A continuaci´ on se presentan el programa SAS y sus salidas respectivas, que soportan los resultados anteriormente comentados en la implementaci´on anova: Programa SAS %web_drop_table(ADE.GE); FILENAME REFFILE ’/folders/myfolders/ADE/gastric-emptying.csv’; PROC IMPORT DATAFILE=REFFILE DBMS=CSV OUT=ADE.GE; GETNAMES=YES; RUN; PROC CONTENTS DATA=ADE.GE; RUN; %web_open_table(ADE.GE); PROC SORT DATA = ADE.GE; by gastric; run; PROC UNIVARIATE PLOT NORMAL data=ADE.GE ; BY gastric; VAR respel; run; /* ANOVA */ proc glm data=ADE.GE order=data plots=diagnostics; class gastric; model respel=gastric; lsmeans gastric / pdiff cl; mean gastric / hovtest; run; *comparaciones usando t Student; *emesis vs lavage; proc ttest data=ADE.GE; where gastric in (’emesis’,’lavage’); class gastric; var respel; run; *emesis vs control; proc ttest data=ADE.GE; where gastric in (’emesis’,’control’); class gastric; var respel; run; *lavage vs control; proc ttest data=ADE.GE; where gastric in (’lavage’,’control’); class gastric; var respel; run;

14

/* kruskal wallis - Exact Wilcoxon Two-Sample Test */ proc npar1way data=ADE.GE wilcoxon; class gastric; exact wilcoxon / mc; var respel; run; PROC RANK data=ADE.GE OUT=ADE.geranks; VAR respel; run; /* Printing the ranks for the data: */ PROC PRINT DATA=ADE.geranks; run; /* Performing the Bonferroni Multiple Comparisons: */ PROC GLM DATA=ADE.geranks; CLASS gastric; MODEL respel = gastric; LSMEANS gastric / CL PDIFF ADJUST=BON; run;

15

The UNIVARIATE Procedure Variable: respel Moments N

60

Sum Weights

60

Mean

3.83333333

Sum Observations

Std Deviation

5.02929272

Variance

25.2937853

1.2014062

Kurtosis

0.24103148

Corrected SS

1492.33333

Skewness Uncorrected SS

2374

Coeff Variation

131.198941

230

Std Error Mean

0.6492789

Basic Statistical Measures Location

Variability

Mean

3.833333

Std Deviation

Median

1.000000

Variance

25.29379

5.02929

Mode

0.000000

Range

16.00000

Interquartile Range

6.50000

Tests for Location: Mu0=0 Test

Statistic

Student's t

t

Sign

M

Signed Rank

S

p Value

5.903986

Pr > |t|

<.0001

16.5

Pr >= |M|

<.0001

280.5

Pr >= |S|

<.0001

Tests for Normality Test

Statistic

p Value

Shapiro-Wilk

W

0.769273

Pr < W

<0.0001

Kolmogorov-Smirnov

D

0.246741

Pr > D

<0.0100

Cramer-von Mises

W-Sq

0.91413

Pr > W-Sq

<0.0050

Anderson-Darling

A-Sq

5.318862

Pr > A-Sq

<0.0050

Quantiles (Definition 5) Level

Quantile

100% Max

16.0

99%

16.0

95%

15.0

90%

12.5

75% Q3

6.5

50% Median

1.0

25% Q1

0.0

10%

0.0

5%

0.0

1%

0.0

0% Min

0.0

Extreme Observations Lowest Value

Obs

Highest Value

16

Obs

0

49

15

37

0

48

15

38

0

47

15

60

0

46

16

39

0

45

16

40

17

The GLM Procedure Class Level Information Class

Levels

gastric

3

Values control emesis lavage

Number of Observations Read

60

Number of Observations Used

60

The GLM Procedure Dependent Variable: respel Source

DF

Sum of Squares

Mean Square

F Value

Pr > F

Model

2

19.233333

9.616667

0.37

0.6909

Error

57

1473.100000

25.843860

Corrected Total

59

1492.333333

R-Square

Coeff Var

Root MSE

respel Mean

0.012888

132.6179

5.083686

3.833333

Source

DF

Type I SS

Mean Square

F Value

Pr > F

gastric

2

19.23333333

9.61666667

0.37

0.6909

Source

DF

Type III SS

Mean Square

F Value

Pr > F

gastric

2

19.23333333

9.61666667

0.37

0.6909

18

19

The GLM Procedure Least Squares Means gastric

respel LSMEAN

LSMEAN Number

control

3.25000000

1

emesis

4.60000000

2

lavage

3.65000000

3

Least Squares Means for effect gastric Pr > |t| for H0: LSMean(i)=LSMean(j) Dependent Variable: respel i/j

1

1 2

0.4046

3

0.8044

2

3

0.4046

0.8044 0.5569

0.5569

gastric

respel LSMEAN

control

3.250000

95% Confidence Limits 0.973704

5.526296

emesis

4.600000

2.323704

6.876296

lavage

3.650000

1.373704

5.926296

20

Least Squares Means for Effect gastric i

j

Difference Between Means

1

2

-1.350000

95% Confidence Limits for LSMean(i)-LSMean(j) -4.569169

1.869169

1

3

-0.400000

-3.619169

2.819169

2

3

0.950000

-2.269169

4.169169

21

Note: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used.

The GLM Procedure Levene's Test for Homogeneity of respel Variance ANOVA of Squared Deviations from Group Means Source

DF

Sum of Squares

Mean Square

F Value

Pr > F

gastric

2

5173.0

2586.5

2.37

0.1024

57

62138.9

1090.2

Error

The GLM Procedure

22

respel

Level of gastric

N

Mean

Std Dev

control

20

3.25000000

4.24108973

emesis

20

4.60000000

6.29452561

lavage

20

3.65000000

4.46359544

23