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Prevalence Estimation 
Unlike the incidence rate comparison, all SEARCH Cohort Study participants can be 
used for the prevalence rate analyses since the incident rate calculations need to remove 
participants who have the outcome present at visit 1 from the analyses.  With this in mind 
we estimate that there will be 3166 participants available to contribute to prevalence rate 
estimates.  Based on this, Table 6-3 shows a variety of scenarios for detectable 
differences comparing groups (i.e., type 1 vs type 2, non-Hispanic white vs others, etc) 
using a chi-square test to compare groups with alpha=0.05 (2-sided). 
 
Table 6-3:  Scenarios for Detecting Statistical Differences in Prevalence of Retinopathy and 
Neuropathy 
Outcome 316/2849 
473/2692 
2112/1049 
(Anticipated 
NHW 
vs. Other Race Split) 
 
Percentage with trait in smaller group 
 10% 
20% 
10% 
20% 
10% 
20% 
 
Detectable Difference (Power) 
Retinopathy 
.16 (81) 
.28 (86) 
.15 (82) 
.27 (89) 
.14 (89) 
.25 (88) 
 5% 
15% 
5% 
15% 
5% 
15% 
Neuropathy 
.10 (85) 
.22 (83) 
.09 (84) 
.21 (85) 
.08 (88) 
.20 (93) 
 

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Section 6B - Statistical Considerations (Phase 3 - 12/2010) 
Section 6B - Page 6 
 Cohort 
Study
 
 
2
2
2
2
1
/ 2
1
1
(1
)(
) (
)
r
Z
Z
k
n
α
β
σ
σ
−
−
−
+
+
Δ =
Based on this table, we see that there is 81% power to detect a difference between Type 1 
and Type 2 participants on their prevalence of retinopathy: 10% in the Type 1 group and 
16% or higher in the Type 2 group, a realistic potential comparison given early pilot 
findings of 18% of youth with evidence of DR among the first 38 evaluated. 
6.2.3.
 
Longitudinal Models Component 
For the purposes of estimating the sample size needed to detect a significant difference 
with sufficient power, calculations were based on comparing measurements after 
adjusting for visit 1 data.  These calculations need to account for the proportion of the 
variance in the outcome that is explained by the visit 1 values.  
 
Although our full 
longitudinal models 
will incorporate all 
intermediate time points 
into the final analysis, our power 
calculation is based on examining the difference in the outcome of interest adjusting only 
for the visit 1 assessment of the outcome.  Therefore, these power calculations will be 
conservative, since the additional information provided by the intermediate assessments 
of outcome measures are not included. 
The following formula was used to describe the minimum detectable difference in terms 
of standard deviations between the participants in groups (i.e., Type 1 versus Type 2).  In 
the formula, r2 is the percent of the variance of the follow-up outcome explained by the 
visit 1 measurements, Z
1-α/2
 is the value from the standard normal distribution 
corresponding to the alpha level chosen (1.96, which corresponds to alpha=0.05 [two 
sided]), Z
1-β 
corresponds to the power chosen for the study (80%), σ
2
 
is the variance of the 
outcome of interest (i.e. systolic blood pressure), n
1
 is the number of participants in the 
Type 1, k is the ratio of n
1
/n
2 
(sample size in type 1 and type 2 groups, respectively) and 
Δ corresponds to the detectable difference in the mean values of the two groups being 
compared.  Using this formula, we examined the detectable differences for several 
possible r
2
 values assuming 80% power and alpha=0.05. From SEARCH 1 and 2, 
standard deviations for systolic blood pressure, BMI - Z-scores and LDL cholesterol were 
estimated as 12.7, .85 and 29, respectively.  Using these numbers, Table 6-4 describes the 
detectable differences if there were 450 participants in the Type 2 group and 2711 in the 
Type 1 group.   
 
 

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Section 6B - Statistical Considerations (Phase 3 - 12/2010) 
Section 6B - Page 7 
 Cohort 
Study
 
 
Table 6-4:  Detectable Differences in Systolic Blood Pressure, BMI Z-Score and 
LDL-Cholesterol Given 450 Type 2 Participants 2711 Type 1 Participants 
Detectable Differences 
with 80% Power 
Correlation Between Baseline and Follow-Up Measures 
Sample Size (n
1
/n
2
) 
(2711/450) 
.50 .65  .75 
.86 
Systolic Blood Pressure 
1.57 mmHg 
1.38 mmHg 
1.20 mmHg 
0.95 mmHg 
BMI (Z-Score) 
.11 (SD) 
.09 (SD) 
.08 (SD) 
.06 (SD) 
LDL-Cholesterol 
3.58 mg/dl 
3.14 mg/dl 
2.73 mg/dl 
2.18 mg/dl 
As can be seen, if the correlation between the baseline and follow-up measurements is 
moderate (.50) then we have 80% power to detect a difference of 1.51 mmHg for the 
Type 1 versus Type 2 comparison of blood pressure change.  As stated above, these 
estimates should be conservative because when the additional yearly measurements are 
incorporated into the longitudinal analyses, there will be additional precision which 
should reduce variability and allow for smaller between group differences to be detected. 

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Section 6B - Statistical Considerations (Phase 3 - 12/2010) 
Section 6B - Page 8 
 Cohort 
Study
 
 
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SEARCH Phase 3 Protocol - Section 7 
Data Management 
Table of Contents