Patients suffering from obstructive sleep apnea (OSA) present with a chronic enhancement in sympathetic adrenergic activity that is considered one of the major mechanisms in the development of cardiovascular morbidity in this population. Turan et al. (2015) conducted a study in OSA patients undergoing weight loss (bariatric) surgical procedures to determine if nocturnal intermittent hypoxia consequent to OSA is associated with decreased intraoperative mean arterial pressure (MAP).They examined 281 adult patients who were diagnosed with OSA within two years prior to their bariatric surgery. In addition to MAP, they collected data on demographics, nocturnal oxygen status, comorbidities, type and duration of surgery, vasopressors, and heart rate.

The variables collected include: AGE (years), AHI (apnea-hypopnea index where 1=less than 5; 2=5 to less than 15; 3=15 to less than 30; 4 = at least 30), BMI (body mass index in kg/m²), CAD (coronary artery disease where 1=yes and 0=no), SLEEPTIME (percent of total sleep time spent at oxyhemoglobin saturation SaO₂<90%), SMOKING (current smoker where 1=yes and 0=no), TWA_MAP (time-weighted average of intraoperative MAP in mmHg), TYPE_SURG (type of surgery where 1=gastroenterostomy; 2=gastric restrictive procedure; 3=gastroplasty; 4=removal of gastric restrictive device), VASOPRESSOR (usage of vasopressors, where 1=yes and 0=no). Note that patients missing data were excluded from the analysis.

For questions 1-5, examine the computer output of the five different models provided for you in the separate packet labeled SAS Output #1-SAS Output #5. Match the output with the most appropriate analysis. You may select each letter (method) more than once, once, or not at all.

1. SAS Output #1 a. Two-way ANOVA without an interaction

1. SAS Output #2 b. Two-way ANOVA with an interaction

1. SAS Output #3 c. One-way ANOVA

1. SAS Output #4 d. Multiple linear regression

1. SAS Output #5 e. ANCOVA

SAS Output #1

Sum of

Source DF Squares Mean Square F Value Pr > F

Model A 438.79377 D G 0.2923

Error B C E

Corrected Total 277 32520.35153

R-Square Coeff Var Root MSE TWA_MAP Mean

0.013493 12.16354 10.82063 88.95950

Source DF Type III SS Mean Square F Value Pr > F

AHI 3 438.7937678 146.2645893 G 0.2923

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 89.36138889 B 1.04121536 85.82 <.0001

AHI 1 -3.41086257 B 2.04091630 -1.67 0.0958

AHI 2 0.66405229 B 1.67510657 F 0.6921

AHI 3 -0.42607639 B 1.70692642 -0.25 0.8031

AHI 4 0.00000000 B . . .

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

TWA_MAP LSMEAN

AHI LSMEAN Number

1 85.9505263 1

2 90.0254412 2

3 88.9353125 3

4 89.3613889 4

Least Squares Means for effect AHI

Pr > |t| for H0: LSMean(i)=LSMean(j)

Dependent Variable: TWA_MAP

i/j 1 2 3 4

1 0.2482 0.5339 0.3409

2 0.2482 0.9385 0.9789

3 0.5339 0.9385 0.9945

4 0.3409 0.9789 0.9945

SAS Output #2

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 2 4674.54533 2337.27267 23.26 <.0001

Error 278 27930.82233 100.47058

Corrected Total 280 32605.36766

R-Square Coeff Var Root MSE TWA_MAP Mean

0.143367 11.26125 10.02350 89.00875

Source DF Type III SS Mean Square F Value Pr > F

Smoking 1 642.706075 642.706075 6.40 0.0120

Vasopressor 1 3948.147061 3948.147061 39.30 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 87.08662879 B 1.01420869 85.87 <.0001

Smoking 0 -3.02569493 B 1.19629530 -2.53 0.0120

Smoking 1 0.00000000 B . . .

Vasopressor 0 7.52902032 B 1.20105051 6.27 <.0001

Vasopressor 1 0.00000000 B . . .

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

H0:LSMean1=

TWA_MAP LSMean2

Smoking LSMEAN Pr > |t|

0 87.8254440 0.0120

1 90.8511389

Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

H0:LSMean1=

TWA_MAP LSMean2

Vasopressor LSMEAN Pr > |t|

0 93.1028016 <.0001

1 85.5737813

SAS Output #3

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 3 4991.50174 1663.83391 16.69 <.0001

Error 277 27613.86592 99.68905

Corrected Total 280 32605.36766

R-Square Coeff Var Root MSE TWA_MAP Mean

0.153088 11.21737 9.984440 89.00875

Source DF Type III SS Mean Square F Value Pr > F

Smoking 1 720.364266 720.364266 7.23 0.0076

Vasopressor 1 3929.808058 3929.808058 39.42 <.0001

Smoking*Vasopressor 1 316.956410 316.956410 3.18 0.0757

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 86.09613333 B 1.15290385 74.68 <.0001

Smoking 0 -1.08280000 B 1.61469873 -0.67 0.5030

Smoking 1 0.00000000 B . . .

Vasopressor 0 9.64507879 B 1.68511940 5.72 <.0001

Vasopressor 1 0.00000000 B . . .

Smoking*Vasopressor 0 0 -4.26663793 B 2.39281841 -1.78 0.0757

Smoking*Vasopressor 0 1 0.00000000 B . . .

Smoking*Vasopressor 1 0 0.00000000 B . . .

Smoking*Vasopressor 1 1 0.00000000 B . . .

SAS Output #4

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 3 160.91263 53.63754 0.46 0.7119

Error 277 32444.45503 117.12800

Corrected Total 280 32605.36766

R-Square Coeff Var Root MSE TWA_MAP Mean

0.004935 12.15899 10.82257 89.00875

Source DF Type III SS Mean Square F Value Pr > F

Age 1 117.2682940 117.2682940 1.00 0.3179

BMI 1 7.2161736 7.2161736 0.06 0.8042

Sleeptime 1 17.5523122 17.5523122 0.15 0.6990

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 87.30033909 5.63388003 15.50 <.0001

Age 0.06244618 0.06240881 1.00 0.3179

BMI -0.02211284 0.08908843 -0.25 0.8042

Sleeptime -0.01128420 0.02914968 -0.39 0.6990

SAS Output #5

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 4 5291.18222 1322.79555 13.37 <.0001

Error 276 27314.18545 98.96444

Corrected Total 280 32605.36766

R-Square Coeff Var Root MSE TWA_MAP Mean

0.162279 11.17653 9.948087 89.00875

Source DF Type III SS Mean Square F Value Pr > F

Age 1 587.828536 587.828536 5.94 0.0154

Sleeptime 1 87.973927 87.973927 0.89 0.3466

Smoking 1 340.541473 340.541473 3.44 0.0647

Vasopressor 1 4467.068345 4467.068345 45.14 <.0001

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 80.00509233 B 3.26973846 24.47 <.0001

Age 0.14412242 0.05913516 2.44 0.0154

Sleeptime -0.02453967 0.02602743 -0.94 0.3466

Smoking 0 -2.33894113 B 1.26088034 -1.86 0.0647

Smoking 1 0.00000000 B . . .

Vasopressor 0 8.36870758 B 1.24562318 6.72 <.0001

Vasopressor 1 0.00000000 B . . .