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Biomed Pap Med Fac Univ Palacky Olomouc Czech Repub. 2009, 153(2):137–144.

© K. Langova, H. Pribylova, M. Kajabova, J. Luza

ASSESSMENT OF HAEMOGLOBIN A1C EVOLUTION USING TWO STATISTICAL

APPROACHES (SURVIVAL ANALYSIS AND LINEAR REGRESSION) IN PERSONS

WITH DIABETES MELLITUS

Katerina Langovaa*, Helena Pribylovab, c, Marketa Kajabovad, Jiri Luzab

a Department of Biophysics, Faculty of Medicine and Dentistry, Palacky University Olomouc, Czech Republic

b Department of Physiology, Faculty of Medicine and Dentistry, Palacky University Olomouc

c Department of Nursing, Faculty of Health Sciences, Palacky University Olomouc

d Department of Clinical Biochemistry, University Hospital Olomouc

e-mail: langova@tunw.upol.cz

Received: September 7, 2008; Accepted (with revision): December 12, 2008

Key words: Survival analysis/Linear regression/Haemoglobin A1c/Continuous glucose monitoring/Diabetes mellitus

Background: Intensive selfmonitoring is an important and cost-demanding part of diabetes treatment. Continuous

glucose monitoring (CGM) using transcutaneous sensors offers “real time” information on glycemia. In the present

study, we assessed the therapeutic efficacy of CGM on metabolic control using two different statistical methods: linear

regression and “survival analysis”.

Objectives: (1) to assess the therapeutic efficacy of CGM on metabolic control using two different statistical meth-

ods: linear regression and survival analysis; (2) to demonstrate the particular advantages of each statistical method.

Methods: A total of 42 persons with diabetes mellitus treated by means of an insulin pump participated in this

study. According to the means of selfmonitoring persons with diabetes were divided into two groups: 1. intervention

group of 17 persons using CGM, 2. control group of 25 persons using a glucometer. Each person was followed for a

period of three months. At the beginning of the study and at the end of each month HbA1c was determined.

Results: Both the regression analysis and survival analysis brought evidence of significant changes of the HbA1c

in either of the groups. The method of linear regression enables to analyse the evolution of HbA1c in each individual

person followed by comparison of the groups. The survival analysis demonstrated that the probability of HbA1c de-

crease to the predefined level as well as its further maintaining at this level was higher in the CGM group. The mean

time interval necessary to HbA1c decrease was shorter in the CGM group.

Conclusions: The efficacy of CGM was demonstrated. In addition to linear regression, survival analysis appears

to be an useful complementary method in the statistical evaluation of the treatment efficacy.

INTRODUCTION

Intensive selfmonitoring is an important and costly

part of diabetes treatment5, 17, 19, 29, particularly in persons

using insulin pumps27. In recent years, continuous glu-

cose monitoring (CGM) with transcutaneous sensors,

transmitters and monitors has become a sophisticated

approach offering “real time” information on glycemia.

Several studies have shown the effectiveness of CGM2, 6.

However, the benefits, hazards, accuracy, reliability and

clinical applicability of CGM6, 12, 13 need to be re-estab-

lished using both case reports and appropriate statistical

methods even though recent trials demonstrate that in-

terstinal fluid glucose and blood glucose concentrations

could be made identical by resorting to algorithmus based

on concurrent blood glucose levels alone20.

Since 2002 we have done statistical analyses for a

number of clinical studies on diabetes (7-13, 21, 23-26). The

glycaemic profiles and haemoglobin A1c were evaluated

as parameters of diabetes control indicating the success

of treatment. Concentration of haemoglobin A1c highly

correlates with the mean plasma glucose concentration.

Various statistical methods but survival analysis were ap-

plied according to the analyzed data and objectives of the

respective study.

Linear regression is a form of regression analysis in

which the relationship between one or more independent

variables and another variable (dependent variable), is

modelled by a special function, namely, linear regression

equation1.

Survival analysis is a set of statistical methods which

evaluate the time interval from the beginning of the obser-

vation until the occurrence of a certain event. Generally,

this time interval is called the survival interval (although

it does not need to identify the survival of a patient). The

survival interval identifies the number of years, months,

weeks or days from the beginning of the observation until

the occurrence of a defined event.

Most studies are complete before the observed event

occurs for all subjects. This situation is in survival analysis

described as “censoring”.

An example of such event would be the achieve-

ment of a certain level of diabetes compensation.

Survival analysis was first described by Kaplan and Meier

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K. Langova, H. Pribylova, M. Kajabova, J. Luza

in 195814, 15 and was used to evaluate the survival time

of oncological patients. This statistical method has been

mostly used in epidemiological studies3, 4, 16, 22, 28.

In the present study, in order to describe the therapeu-

tic effects of continuous glucose monitoring on metabolic

control (i.e. mean plasma glucose concentrations over

the last 2–3 months represented by HbA1c concentra-

tions) two different statistical methods were applied: 1)

the widely used linear regression analysis and 2) the sur-

vival analysis of data which has not been routinely used

for this purpose26.

The objective of this study was (1) to assess the thera-

peutic efficacy of CGM on metabolic control using two

different statistical methods: linear regression and survival

analysis, and (2) to demonstrate the particular advantages

of each statistical method applied.

METHODS

The data in this statistical analysis were gathered at

The Faculty of Medicine and Dentistry, Palacky University

Olomouc and the University Hospital Olomouc since the

year 2006 until the year 2008. Each subject was followed

in the outpatient clinic for a period of three months.

HbA1c was assesed at the beginning HbA1c1and at the

end of each month (HbA1c2, HbA1c3, HbA1c4).

Study subjects

Two independent groups of persons with diabetes mel-

litus were followed (Table 1):

1. An intervention group of 17 persons with diabetes

using transcutaneous sensors, 11 men and 6 women,

aged 19–69 years, (mean 44.9 years, SE 4.0).

2. A control group of 25 persons with diabetes using a

glucometer, 13 men and 12 women, aged 24-66 years

(mean 44.9 years, SE 2.9).

Determination of Haemoglobin A1c

The HbA1c concentration in blood was determined us-

ing the sophisticated HPLC procedure in the Department

of Clinical Biochemistry, University Hospital Olomouc

(Table 2).

Principles of the HbA1c estimation. The analyzer

PDQ Plus employs the principles of boronate affinity

and high-performance liquid chromatography (HPLC).

Glycated proteins (haemoglobins and plasma proteins)

differ from non-glycated proteins by the attachment of

sugar moiety to the former at various binding sites by

means of a ketoamine bond. GHb and GPP thus contain

1,2-cis-diol groups not found in non-glycated proteins.

These diol groups provide the basis for separation of gly-

cated and non-glycated components by boronate afinity

chromatography. In this analytical technique, a boronate

is bonded to the surface of the column support. When a

solution of proteins is passed through the column, the

glycated component is retained by the complexing of its

diol groups with the boronate. After the unretained non-

glycated component elutes from the column, the glycated

component is eluted from the column with a reagent that

displaces it from the boronate. Both components are de-

tected spectrofotometrically at 413 ± 2 nm.

Parameters of reliability. Limit of quantitation: 3.0 %,

Linearity: up to 19.5 %

Repeatability (within-run imprecision): 1.4 %.

Reproducibility (between-run imprecision): 1.4 %.

Reference range for normal population: 2.8 to 4.0 %.

Table 1. Characteristics of the intervention (CGM) and of the control group.

Group CGMControlSignificance (P)

N 1725

Male/Female11/613/120.414

Age (mean ± SE) [years]44.9 ± 4.044.9 ± 2.60.996

Age range [years]19–6924–66

Duration of diabetes (mean ± SE) [years] 17.8 ± 2.915.4 ± 2.00.482

Duration of diabetes range [years]1–452–43

Table 2. Evaluation of metabolic control in persons with diabetes according to HbA1c concentration in blood.

Metabolic control in diabetes Calibration according to DCCT

(valid before 1. 1. 2004)

Calibration according to IFCC

(valid since 1. 1. 2004)

Excellent< 6.5 % < 4.5 %

Satisfactory6.5 – 7.5 % 4.5 – 6.0 %

Unsatisfactory> 7.5 % > 6.0 %

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Assessment of haemoglobin A1c evolution using two statistical approaches (survival analysis and linear regression)

in persons with diabetes mellitus

Statistical Analysis

The Program SPSS v.15,0, SPSS, Inc., Chicago, IL,

USA was used in the statistical analysis.

First, the method of regression analysis was used to

evaluate the development of the HbA1c values in the

course of three months. In each subject, regression coef-

ficient was calculated in order to describe the evolution

of HbA1c (see Table 3a and Table 3b). Two samples t-

test was applied to compare the regression coefficients

of subjects in the intervention and in the control group.

Second, the method of survival analysis was applied to

evaluate the same data. The survival analysis was aimed at

the occurrence of the followed events in time in subjects

in both of the groups.

A total of 8 various events was empirically defined,

and analyzed:

1. first decrease of HbA1c below the 5 % value deter-

mined in the laboratory,

2. maintained decrease of HbA1c below the 5 % labora-

tory value in two consecutive controls,

3. first decrease of HbA1c by at least 3 % from the base-

line (this event was defined considering the reliability,

repeatibility and reproducibility of HbA1c determina-

tion),

4. maintained decrease of HbA1c by at least 3 % from

the baseline in two consecutive controls,

5. first decrease of HbA1c by at least 5 % from the base-

line (this event was defined empirically),

6. maintained decrease of HbA1c by at least 5 % from

the baseline in two consecutive controls,

7. first decrease of HbA1c by at least 10 % from the base-

line (this event was defined empirically),

8. maintained decrease of HbA1c by at least 10 % from

the baseline in two consecutive controls.

The aim of the survival analysis was to determine the

probability of HbA1c decrease below an empirically de-

fined value over time. For the graphic representation of

the probability of the HbA1c decrease below the defined

value the Kaplan-Meier curve presenting one minus “sur-

vival function“ was used. The final curve is of ascend-

ing character which is the optic equivalent for increasing

probability in the course of time.

The statistical significance of differences between sur-

vival curves in the control and intervention group was

evaluated by means of log-rank test. P < 0.05 was consid-

ered significant.

RESULTS

Linear regression analysis (Fig. 1)

In the intervention group, the mean regression co-

efficient was – 0.246 (the negative value demonstrates

a decrease of HbA1c in the course of the observa-

tional period), SD 0.395, range from – 1.24 to 0.47.

In the control group the mean regression coefficient

was 0.138 (positive value demonstrates an increase

of HbA1c in the course of the observational period),

SD 0.248, range from -0.46 to 0.72. Two samples t-test

Fig. 1. Regression analysis: Distribution of regression

coefficients in the intervention (n = 17) and con-

trol group (n = 25). P-significance of difference

(two samples t-test between both groups).

Fig. 2. Survival analysis: Kaplan-Meier curve showing

the probability of the first decrease of HbA1c

below the 5 % value determined in the laboratory

in the intervention (CGM) and control group.

P – significance of difference (log-rank test).

revealed a significant difference between the mean regres-

sion coefficients (p = 0.001). See box graph in Fig. 1.

Survival analysis (Fig. 2, Fig. 3 and Table 4).

The probability of HbA1c decrease below the de-

fined value (5 %) and the probability of maintaining the

decrease in at least two consecutive controls is shown

in Kaplan – Meier curves in Fig. 2–3. The estimates of

mean time interval until the decrease below the defined

value for both intervention and control group and the

significance of the log-rank test are shown in Table 4. A

significant difference between the intervention and the

control group was shown in all defined events. The mean

time interval until the HbA1c decrease was proved to be

significantly shorter in the intervention group.

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K. Langova, H. Pribylova, M. Kajabova, J. Luza

Fig. 3. Survival analysis: Kaplan-Meier curve showing

the probability of maintained decrease of HbA1c

below the 5 % laboratory value in two consecutive

controls in the intervention (CGM) and control

group. P – significance of difference (log-rank

test).

Table 3a. Intervention group: Evoluation of HbA1c from the introduction of CGM (HbA1c 1)

to the end 3rd month (HbA1c 4).

DISCUSSION

Linear regression analysis and survival analysis are

two methods evaluating the development of change in

an independent manner. While linear regression enables

the assesment of change in a complete time interval, sur-

vival analysis expresses the probability of occurrence of

an expected event. Currently, survival analysis is mainly

used in epidemiological studies which follow mortality.

Recently the role of HbA1c as a risk factor for heart fail-

ure in persons with diabetes was assessed using the sur-

vival function22. Our aim was to point out the possibility

of survival analysis application in clinical studies which

follow therapeutic efficiency.

In our study, in the intervention group the negative

value of regression coefficient appeared in 13 of 17 per-

sons with diabetes (76 %) showing a decrease of HbA1c.

On the other hand, in the control group the negative value

of regression coefficient appeared only in 8 of 25 persons

(32 %). So, using two samples t-test a significant diference

between the distribution of regression coefficients in both

groups was demonstrated.

Survival analysis shows the decrease of HbA1c below

the defined values in the intervention group using CGM

in the course of three months. Fig. 2 and 3 shows that

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Assessment of haemoglobin A1c evolution using two statistical approaches (survival analysis and linear regression)

in persons with diabetes mellitus

Table 3b. Control group: Evoluation of HbA1c without CGM from beginning of the study (HbA1c 1)

to the end 3rd month (HbA1c 4).

the probability of this change is significantly higher in the

intervention group than in the control group. The same

applies on all other criteria of HbA1c decrease which we

have defined pragmatically. It is evident that the prob-

ability of maintaining a longer lasting HbA1c decrease is

below the defined value for at least until the next control

(one month) is smaller than the probability of achieving

at least one HbA1c value below the defined value (Fig. 2

vs. Fig. 3). Table 4 shows that the HbA1c decrease is

achieved significantly sooner in the intervention group

in comparison to the control group. The results of sur-

vival analysis show (similarly as the slopes-analysis in

individual subjects using regression analysis) the positive

effect of CGM on HbA1c values which is in accordance

with conclusions of various studies using other statistical

methods such as paired t-test etc.

CONCLUSIONS

We can conclude that CGM is an effective tool to

improve diabetes control. In addition to linear regression

survival analysis has proven to be an useful method com-

plementing other statistical methods used for evaluation

of the treatment efficacy for diabetes. It may be applied

in situations with fluctuating therapeutic outcomes with

alternative remissions and relapses.