Overview

1
Biostatistics Basic Concepts Modul 4
Biostatistik Basale Begreber
8.1 Inter- and intra variation (PHP) 8.2
Referenceregions (PHP)
Biologisk variablitet within-subject og
between-subject variation
Referenceintervaller
Per Hyltoft Petersen Per.Petesen_at_isf.uib.no
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Histogram

• Hyppighed i intervaller

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Histogram og Gauss

• Hyppighed

Gauss-kurve Normalfordeling
4
Histogram og Gauss
Standarddeviation s
Parametre µ og s
s

• Middelværdi µ

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Histogram og Gauss
Parametre µ 100 s 10
95
2½
2½

• µ 1.96s

µ 1.96s
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Histogram og Gauss

• 95 centrale interval referenceinterval

Parametrisk µ 1.96s
95
Non-parametrisk 2½ og 97½ centilerne
2½
2½
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Reference intervals

• Reference individuals
• Reference values
• Reference distribution (of reference values)
• Reference interval
• Reference limits

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East Asian reference values
Serum-CRP
0.02
0.08
Borrowed from Kiyoshi Ichihara, Yamaguchi
University (Japan)
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East Asian reference values
Serum-Alanine Aminotransferase
12
22
Borrowed from Kiyoshi Ichihara, Yamaguchi
University (Japan)
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Criteria for Partitioning
When to partition reference intervals
according to subgroups, e.g., gender,
pregnancy, racial groups etc. ?
Lahti et al. Clin Chem 200248338-52
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Criteria for Partitioning
Lahti et al. Clin Chem 200248338-52
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Criteria for Partitioning
Difference between two upper or lower limits
lt 0.25s No partitioning 0.25 0.75s
Variable gt 0.75s Partitioning or percentage
0.9 and 4.1
Lahti et al. Clin Chem 200248338-52
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The Nordic project on common reference intervals

• The Nordic countries
• Norway-Finland-Iceland-Sweden-Denmark
• More than 100 laboratories
• More than 3000 reference individuals
• Laboratory workers and their family members
• 25 common quantities (Components)
• Common reference preparation
• Common control

Rustad www.furst.no/norip/
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The Nordic project on common reference intervals
Rustad www.furst.no/norip/
Rustad Felding (eds) Scand J Clin Lab Invest
200464263-441
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The Nordic project on common reference intervals
Rustad www.furst.no/norip/
Rustad Felding (eds) Scand J Clin Lab Invest
200464263-441
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Repeated Testing
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Rankit-transformation 1

• Reference population Gauss-distribution

2½
16
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Rankit-transformation 2
Gaussian distribution Frequency distribution

• Accumulation of values from minus infinity

Gaussian distribution Accumulated frequency
16
2½
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Rankit-transformation 3
Gaussian distribution Frequency distribution

• Transformation of the ordinate so that the
  S-shaped curve becomes a straight line

Gaussian distribution Accumulated frequency
When the accumulated frequency shows up as a
straight line, the distribution can be considered
Gaussian
Accumulated frequency
RANKIT
16
2½
Gaussian distribution RANKIT
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Probability paper
Probit Rankit 5 Rankit z
0
50
16
-1
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Probability paper
NORMDISTRIBUTION x-value (5.0) mean value
(8.0) standard deviation (2.0) cumulation (1)
98 80 50 20 . 2
Mean 2s
82
Mean
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Mean 2s
Result 0.07 7
0 5 10
15 20 25
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Probability paper
NORMINV probability (0.99) mean value (8)
standard deviation (2)
98 80 50 20 . 2
99
Mean 2s
Mean
Result 12.7
Mean 2s
12.7
0 5 10
15 20 25
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Probability paper
98 80 50 20 . 2
Cumulated percentage frequency
97½
15,98
13,80
50
11,48
9,10
2½
7,2
4s 8
s 8/4 2
11.5
0 5 10
15 20 25
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Probability paper
98 80 50 20 . 2
6,99
5,98
4,93.5
3,75
ln
2,43
1,3
0 1 2 3 4 5 6 7
8 9 10 11
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Probability paper
98 80 50 20 . 2
6,99
5,98
4,93.5
3,75
ln
2,43
1,3
0 1 2 3 4 5 6
0 0.5 1.0 1.5
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Probability paper
A.G. Frisenette Sønner Aps Postboks
120 Godthåbsvej 4 DK-8400 Ebeltoft Denmark Probabi
lity paper 2110 log-probability paper 2109
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Serum-Prealbumin
Cumulated Percentage Frequency
Parallel straight lines
S-Prealbumin
log-scale
Blaabjerg et al. Upsala J Med Sci 199499315-38
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Serum-Prealbumin
Cumulated Percentage Frequency
S-Prealbumin
Individuals with CRP gt 10 mg/L are decreased
log-scale
Blaabjerg et al. Upsala J Med Sci 199499315-38
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Comparison of Proteins
1.7s (gt 0.75s) Partitioning according to
Lahti
ln-scale
Johnson et al. CCLM 200442792-9
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Confidence interval for percentiles
Formula for the line for the Gaussian
distribution Y z1sPOPULATION
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Confidence interval for percentiles
Formula for the line for the Gaussian
distribution YCI z1sPOPULATION z2(s2/n
z12s2/2n)½
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Comparison of Proteins
Confidence limits
Johnson et al. CCLM 200442792-9
Per Hyltoft Petersen David Curnow Plenary
Lecture. Sydney 2005
Per Hyltoft Petersen Population based reference
intervals
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Serum-TSH
Low risk population
Best estimate of Gaussian distribution
Confidence limits
Jensen et al.Clin Chem Lab Med 2004 42824-32.
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What to do when the distributions of reference
values is not ln-Gaussian ?
1. Perform non-parametric statistics
Practical, but not informative
2. Find criteria for sub-grouping
This may reveal ln-Gaussian sub-groups and may
create new information
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Comparison of Proteins
Johnson et al. CCLM 200442792-9
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Comparison of Proteins

• Distribution of a1-Antitrypsin genotypes

Cumulated Percentage Frequency
Lund et al. Upsala J Med Sci 199499339-46
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S-a1-Antitrypsin, subgroups

• Percentage of subgroups in Denmark 1990
• MM 89
• MS 7
• MZ 4

Lund et al. Upsala J Med Sci 199499339-46
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Comparison of Proteins
Johnson et al. CCLM 200442792-9
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Fordeling af glucose-resultater og low-risk
gruppe i Vejle-projektet

• 2100 personer inviteres (udvalgt efter
  personnummer), ca. 700 deltager, men af disse kan
  ca. 300 karakteriseres som værende i en
  risikogruppe
• første generations diabetikere
• hypertension
• hjertesygdomme
• endocrine sygdomme
• vasculære sygdomme
• etc.
• HbA1c gt 6,3
• Resultat low-risk-grouppe (ca. 400)

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Plasma-Glucose
Oversigt
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Plasma-Glucose
Oversigt
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Plasma-Glucose
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Plasma-Glucose
50
Plasma-Glucose
Oversigt
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Plasma-Glucose
Oversigt
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Plasma-Glucose
Oversigt
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NORIP Fordelinger af glucose efter alder

Oversigt
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OversigtReferenceintervaller