Statistical Prediction in Pathological Types of Chronic Kidney Disease.

To the Editor: In China, the pathological types such as mild lesion nephrosis (MLN), focal segmental glomerulosclerosis (FSGS), membranous nephropathy (MN), and IgA nephropathy (IgAN) are presented as common types in patients with chronic kidney disease (CKD).[1] For identifying the special CKD pathological types, ultrasound-guided percutaneous renal biopsy is an important diagnostic tool for nephrologists. Clinically, the postbiopsy complications, such as gross hematuria caused by renal hemorrhage, low back pain or abdominal pain caused by perirenal hematoma, or mild fever, will occur in some patients. Further, some CKD patients are unfeasible to perform renal biopsy due to clinical contraindications. Here, a systematic method to evaluate or predict CKD pathological types by the statistical probabilities of clinical indices is proposed. The method is based on frequency differences regarding basic properties, clinical characteristics, and laboratory results of CKD patients. This study aimed to establish an alternative method for identifying CKD pathological types from a nontraumatic statistical perspective.

Data of 520 CKD patients from electronic medical databases of a tertiary referral hospital between July 2014 and July 2016 were collected retrospectively to perform the statistical prediction; those were diagnosed pathologically including MLN (n = 120), FSGS (n = 122), MN (n = 141), and IgAN (n = 137). Further, the indices of CKD cases were classified as basic characteristics, medical history, clinical signs, and laboratory results according to the corresponding standards, which were included in the list of predictive variables; detailed data were shown in Supplementary Materials.

Theory of bi-directional probability for predicting CKD pathological types. CKD: Chronic kidney disease.

Click here for additional data file.

ROC curve of cross comparison in logistic models. (a) ROC area under the curve of distinguishing FSGS versus MLN. (b) ROC area under the curve of distinguishing FSGS versus IgAN. (c) ROC area under the curve of distinguishing IgAN versus MLN. (d) ROC area under the curve of distinguishing IgAN versus MN. (e) ROC area under the curve of distinguishing MN versus MLN. (f) ROC area under the curve of distinguishing MN versus FSGS. ROC: Receiver operating characteristic curve; AR: Accuracy rate (%); ROC-A: ROC area under the curve.

Click here for additional data file.

In accordance with the principle of bi-directional accumulation dichotomy proposed by Yang et al.,[2] The bi-directional probability in each patient can be calculated. Firstly, based on the assumption of random event in CKD, we define 50% as the baseline probability of one CKD pathological type. Further, excess probabilities were calculated by the frequency of clinical indices occurring in each CKD pathological type, which is defined as positive probability (PP) or negative probability (NP). Consequently, the prediction probabilities for one special CKD pathological type were calculated by the following method “∑PP − ∑NP + 50%.” Also, the sampling error of PP or NP was estimated by their mean levels in CKD patients ( or ), respectively. The final calculation formula of bi-directional accumulation probability model of predicting CKD pathological types in the present study is expressed as “{ΣPP ± [ × (1−)/n]1/2} − {ΣNP ± [ × (1−)/n]1/2} + 50%.”

All 520 cases were less than or equal to CKD Stage 4 according to the Kidney Disease: Improving Global Outcomes Guidelines (2012). In addition, MLN group showed a higher proportion of male patients, while IgAN group showed a lower proportion of male patients. The differences of average duration and serum creatinine among four groups were not significant (P > 0.05). Then, NP or PP of four CKD pathological types was calculated according to the above formula, indicating the tendency of occurring one special pathological type, respectively. Further, in case that similar prediction probabilities occur in two or more than two CKD pathological types, the strategy of differential diagnosis needs to be performed by logistic regression analysis to distinguish between two CKD pathological types. Here, six pairs of logistic differential diagnosis models between each two CKD pathological types were established, and the indices for distinguishing special CKD pathological type were evaluated by value of odds ratio (OR) or the repetition times in order. The higher OR values or the more repetition times of the indices suggest an increased predictive probability of the corresponding pathological type occurring; detailed data are shown in Figure 1 and Supplementary Materials.

Figure 1

Prediction indices of different pathological types in logistic models. The indicated indices of four CKD pathological types were proposed, and the value of OR or the mean OR value calculated by the repeatable indices was presented in the corresponding brackets. *The index was repeated twice in models; †The index was repeated thrice in models. CKD: Chronic kidney disease; OR: Odds ratio; Y: Year; Alb: Albumin; P: Phosphorus; Ca: Calcium; UBJP-E: Urine Bence-Jones Protein elevation; TCM/PCM: Traditional Chinese Medicine/Proprietary Chinese Medicine using; FOA: First onset age; BP: Blood pressure; ESR: Erythrocyte sedimentation rate; Glb: Globulin; BL: Blood lipid; Cold/T/UPI: Cold/tonsillitis/upper respiratory infection; U/B/L-infection: Infection of urinary tract/bowel/lung; AKI/AGN: Acute kidney injury/acute glomerulonephritis; hepatitis A/B/TB: Hepatitis A or hepatitis B or tuberculosis; Hyper-KI: Hypertension-related kidney injury; Edema-F/L: Edema of face/lower extremity; Tube-I/PI: Urine tube/pathological tube increase.

In clinical, it is well known that choosing the best treatment strategy for G1–G4 CKD patients depends on the result of CKD pathological diagnosis by renal biopsy and histopathological observation to a large extent. Renal biopsy belongs to a traumatic pathological diagnosis, which can lead to many complications such as renal hemorrhage, perirenal hematoma, mild fever, and gross or microscopic hematuria. In addition, some medical conditions such as coagulation dysfunction or infection make the operation of renal biopsy unfeasible. Some patients are also not willing to accept renal biopsy with surgery. As a result, it is difficult to choose one optimal treatment protocol for CKD patients in case of unknown pathological type. For example, the dosages and treatment cycles of hormones or immunosuppressive agents will be faced a puzzle due to each treatment strategy corresponds to each pathological type. In case of the judgment of the pathological type goes wrong, for example, FSGS is judged incorrectly to be IgAN, the inappropriate treatment in the patients will lead to an increased risk of delayed treatment efficacy or side effects of drugs. So, the statistical prediction of the CKD pathological type becomes valuable for providing a reference of choosing the appropriate treatment strategy in patients. Here, pathological prediction is evaluated by a probability strategy based on the theory of bi-directional probability in CKD patients, and the data are obtained from medical records including the patients’ attributes, symptoms, signs and laboratory results.

In this study, statistical analysis was performed to evaluate the difference of the frequency distribution of clinical indices in different CKD pathological types. Then, a method of bi-directional probability (positive or negative) was applied for statistical prediction of the special CKD pathological types. Furthermore, to distinguish the similar probabilities among CKD pathologic types, the method of logistic regression was used, and the cumulative OR values of tendency indices in six pairs of logistic models were analyzed for discriminating the special CKD pathologic type, providing a reference for the accurate prediction of the pathologic type. In conclusions, this prediction method for the noninvasive pathological diagnosis of CKD pathological types based on a statistical perspective is feasible, providing a reference for choosing the optimal treatment strategy for CKD patients in a clinical setting.

Summarily, the present study indicated that statistical prediction of CKD pathological types can be achieved by the present mode of bi-directional probability and logistic regression, expecting to provide an auxiliary advice by the present method due to the unfeasible conditions in renal biopsy. Of course, there are some shortcomings such as the limited sample size and the limited scope of pathological classification. Furthermore, the more secondary glomerular disease and the coexistence of multiple pathological types should also be explored for the mode of prediction or differential diagnosis in future studies.

Supplementary information is linked to the online version of the paper on the Chinese Medical Journal website.

Financial support and sponsorship

This study was supported by grants from Natural Science Foundation of Hunan Province (No. 2016JJ6106), Platform Construction of Key Laboratory of Hunan Province (No. 2015TP1020-04; No. 2017CT5025), Scientific Research Project of Hunan Education Department (No. 14C0911), and Youth Talents program of Hunan University of Medicine.

Conflicts of interest

There are no conflicts of interest.

Supplementary Table 1

Classification of clinical indices in CKD patients

Basic characteristics

1: Gender (female; male)

2: Marriage (unmarried; married; divorced/widowed)

3: Occupation (farmers/unemployed; worker/employee; freelance worker; student; health-care workers)

Epidemiological history

4: Duration (≤1 Y; >1 Y; ≤3 Y; >3 Y); D, Duration; Y, years

5: Frequency of admission (1; ≥2)

6: First-onset age (<20 Y; 20–40 Y; >40 Y); FOA

7: First drugs use before admission (antibiotics/antiviral drugs; G+/ISD; TCM/PCM; nonspecial drugs)

8: CKD-related inducements (CKD-related inducements 0~10); CKD-RI

Clinical signs

9: Edema signs (none; edema of face/lower extremity); Edema-F/L

10: Hematuria (none; <2 Y; ≥2 Y); hematuria ≥2 Y

11: Proteinuria (none; <2 Y; ≥2 Y); proteinuria ≥2 Y

12: Blood pressure (normal; high blood pressure); BP

Laboratory results

13: Blood lipid (normality; high); BL

14: Blood glucose (normality; elevation); B-Glu

15: Alanine aminotransferase (normality; elevation); ALT

16: Blood urea nitrogen (normality; increase); BUN

17: Serum creatinine (normality; increase); Cr

18: Blood uric acid (normality; elevation); BUA-elevation

19: Blood calcium (normality; lower); Ca

20: Blood phosphorus content (normality; lower; high); P

21: Blood Kalium (normality; lower; increase); K

22: Hemoglobin (normality; reduce); Hb

23: Platelet count (normality; reduce; high)

24: Blood α1-globulin (normality; increase; lower); α1Glb

25: Blood α2-globulin (normality; decrease; elevation); α2Glb

26: Albumin (normality; lower); Alb

27: Serum ferrum (normality; increase; lower); Fe

28: Serum complement 3/4 (normality; lower; increase); C3/C4

29: Thrombin/activated partial thromboplastin time (normality; lengthen; shorten); T/APTT

30: D-dimer (normality; elevation); High-DD

31: Erythrocyte sedimentation rate (normality; quicken); ESR

32: Parathyroid hormone (normality; increase; reduce); PTH

33: Urine bilirubin (negative; positive); U-Bil

34: Urine Bence-Jones protein (normality; lower; elevation); UBJP-E (elevation)

35: Immunoglobulin E (normality; increase); IgE

36: Immunoglobulin G (normality; higher; lower); IgG-lower

37: Immunoglobulin A (normality; increase; decrease); IgA

38: Urine tube/pathological tube (normality; increase); Tube-I/PI

39: Urine leukocyte number (normality; increase); Urine leukocyte I (increase)

40: Urine epithelium number (normality; increase); Urine epithelium I (increase)

Number, indices (classification) and abbreviation are shown in order. G+/ISD: Glucocorticoid +/immunosuppressive drug; TCM/PCM: Traditional Chinese medicine/proprietary Chinese medicine; FOA: First-onset age; Free-worker: The type of occupation is free-worker; CKD-RI 0: CKD of unknown reasons (CKD-UR); CKD-RI 1: Cold/tonsillitis/upper respiratory infection (Cold/T/UPI); CKD-RI 2: Pregnancy/cesarean delivery/anemia (pregnancy/C/A); CKD-RI 3: Hepatitis A or hepatitis B or tuberculosis (hepatitis A/B/TB); CKD-RI 4: Stones/cyst/trauma of kidneys (kidney-stones/C/T); CKD-RI 5: Infection of urinary tract/bowel/lung (U/B/L-infection); CKD-RI 6: Hypertension-related kidney injury (Hyper-KI); CKD-RI 7: Thyroid disease-related kidney injury (thyroid-KI); CKD-RI 8: Rash/ringworm/allergic disease-related kidney injury (Rash/R/A-KI); CKD-RI 9: Acute kidney injury/acute glomerulonephritis (AKI/AGN); CKD-RI 10: Tired/chronic diseases/appendicitis operation later (Tired/C/A).

Supplementary Table 2

Indices for prediction of CKD pathological type

Types	Positive indices (P1, %)		Negative indices (P2, %)
MLN (n = 120)	Male (81.7)	D ≤1Y (65.8)	Proteinuria ≥2Y (1.7)	Hematuria ≥2Y (1.7)
	Proteinuria <2Y (80.8)	High-BL (69.2)	UBJP-E (25.0)	CKD-RI 4 (0.8)
	IgG-lower (42.5)	Edema-F/L (59.2)	High-BP (20.8)	P-lower (5.0)
	FOA.20-40Y (45.0)	Alb-lower (51.7)	High-DD (33.3)	ESR-quicken (22.5)
	Hematuria<2Y (64.2)	Ca-lower (49.2)	Hb-R (6.7) Female (18.3)	FOA.<20Y (25.8)
FSGS (n = 122)	FOA.20-40Y (52.5)	D ≤1Y (62.3)	Proteinuria ≥2Y (9.0)	IgG-lower (27.0)
	Hematuria <2Y (64.8)	Proteinuria <2Y (78.7)	Fe-lower (8.2) High-DD (30.3)	CKD-RI 5/7/8 (1.6)
	Edema-F/L (52.5)	UBJP-E (60.8)	P-lower (6.6) ESR-quicken (32)	K-lower (9.8)
	Ca-lower: (47.5)	High-BL: (63.9)	FOA.<20Y (10.7) α2Glb-elevation (17.2)	α1Glb-lower (18.9)
	CKD-RI 0 (36.1)	Female (53.3)	Tube-I/PI (24.6) HB-R (13.1)	Hematuria ≥2Y (8.2)
MN (n = 141)	FOA.>40Y (60.3)	D ≤1Y (74.5)	α1Glb lower (7.1)	No-proteinuria (2.1)
	Hematuria <2Y (66.7)	Proteinuria <2Y (87.9)	CKD-RI 7/8 (0.7)	Hematuria ≥2Y (0.7)
	Alb-Lower (83.0)	IgG-lower (49.6)	ESR-quicken (47.5)	D >3Y (7.8)
	High-DD (58.2)	Tube-I/PI (54.6)	FOA <20Y (7.1)	P-higher (19.1)
	CKD-RI 0 (38.1)	Edema-F/L (91.5)	Hb-R (18.4)	K-lower (15.6)
	High-BL (85.1)	Ca-lower (66.7)	Proteinuria ≥2Y (9.9)	Fe-Lower (12.8)
	UBJP-E (66.7)
IgAN (n = 137)	Female (59.1)	FOA.20-40Y (70.8)	Hematuria ≥2Y (10.9)	ESR-quicken (9.5)
	Hematuria <2Y (72.3)	Proteinuria <2Y (70.1)	High-BP (31.4)	Edema-F/L (30.7)
			Proteinuria ≥2Y (10.9)	α2Glb elevation (4.4)
	D ≤1Y (67.9)	CKD-RI 1 (38.0)	High-DD (14.6)	K-lower (11.7)
			Hb-R (8.8)	P-lower (6.6)
Prediction of MLN or FSGS or MN or IgAN: ∑ (PP ± SEP1) - ∑ (NP ± SEP2) + 50%

Prediction probability of CKD pathological types was evaluated by calculating the difference of total positive indices frequency minus total negative indices frequency, the formula is expressed as “ΣPP ± [ × (1 − )/n]1/2} − {ΣNP ± [ × (1 − )/n]1/2} + 50%.” Standard error: [ × (1 − )/n]1/2 or [ × (1 − )/n]1/2 was abbreviated as SEP1, SEP2, respectively. SEP1 or SEP2 was calculated by the mean value of PP or NP in one CKD patient, respectively. Edema-F/L: Edema of face/lower extremity; High-DD: D-dimer elevation; Tube-I/PI: Urine tube/pathological tube increase; UBJP-E: Urine Bence-Jones protein elevation; Hb-R: Hemoglobin reduce; ESR-quicken: Erythrocyte sedimentation rate quicken; High-BP: High blood pressure; High-BL: High blood lipid; P-lower: Lower content of blood phosphorus; Alb-lower: Lower albumin content; Ca-lower: Blood calcium lower; K-lower: Blood Kalium lower; Fe-Lower: Serum ferrum lower.

Supplementary Table 3

Calculation of prediction probability in one CKD patient

Predictive indices in CKD patients	Judgments of induces	MLNPP (+)/NP (-)	FSGSPP (+)/NP (-)	MNPP (+)/NP (-)	IgANPP (+)/NP (-)
D ≤1 y	Yes; no	0.328	0.293	0.415	0.349
D >3 y	Yes; no			−0.252
Hematuria <2 y	Yes; no	0.312	0.318	0.334	0.393
Ca-lower	Yes; no	0.159	0.142	0.334
Proteinuria <2 y	Yes; no	0.478	0.457	0.549	0.371
High-DD	Yes; no	−0.167	−0.197	0.082	−0.354
Edema-F/L	Yes; no	0.092		0.415	−0.193
Alb-lower	Yes; no	0.017		0.33
IgG-lower	Yes; no	0.092		0.166
ESR-quicken	Yes; no	−0.275	−0.18		−0.405
UBJP-E	Yes; no	−0.083	0.275	0.334
Tube-I/PI	Yes; no		−0.254	0.046	−0.186
FOA.20-40 y	Yes; no	0.117	0.192		0.378
FOA.>40 y	Yes; no			0.270	−0.202
FOA.<20 y	Yes; no	−0.075	−0.226	−0.262	−0.172
P-lower	Yes; no	−0.28	−0.264	−0.191	−0.264
High-P	Yes; no	−0.033		−0.139
HB-R	Yes; no	−0.433	−0.369	−0.316	−0.412
High-BL	Yes; no	0.192	0.139	0.351
High-BP	Yes; no	−0.292			−0.186
Low-K	Yes; no	−0.166	−0.232	−0.177	−0.213
CKD-RI 0	Yes; no		0.111	0.131
CKD-RI 1	Yes; no	−0.03		−0.128	0.13
Hematuria ≥2 y	Yes; no	−0.316	−0.251	−0.326	−0.224
Fe-lower	Yes; no	−0.233	−0.251	−0.205	−0.224
Proteinuria ≥2 y	Yes; no	−0.316	−0.243	−0.234	−0.213
No-proteinuria	Yes; no			−0.312	−0.151
Female	Yes; no	−0.317	0.033		0.091
Male	Yes; no	0.317
α1Glb lower	Yes; no	−0.158	−0.144	−0.262	−0.187
α2Glb elevation	Yes; no	−0.15	−0.161		−0.289
Definition-PP/NP	PP was defined as “P1-0.5” or “P1-0.33” or “P1-0.25” NP was defined as “0.5-P2” or “0.33-P2” or “0.25-P2”
Range of prediction probability in patients	{∑ (PP + SEP1) − ∑ (NP + SEP2) + 50%} ~ {∑ (PP−SEP1) − ∑ (NP−SEP2) + 50%}

When predictive indices in CKD patients were judged as “yes,” the values of NP or PP in each CKD pathological type was calculated and summed, respectively. If “No,” the corresponding values in CKD pathological types are invalid. Further, SEP1 or SEP2 was calculated by the formula of standard error referred to the mean level of NP or PP in each CKD pathological type. As a result, the probability ranges of each pathological type can be obtained in patients.

Supplementary Table 4

Application of differential diagnosis in one CKD patient

Propensity indices of differential diagnosis	Yes or no of induces	Evaluation of ∑OR1-∑OR2 by logistic models
FSGS	Judgment	OR1 values	∑OR1-∑OR2
Proteinuria≥2Y	Yes; no	11.819	>0
UBJP-E	Yes; no	5.722
TCM/PCM	Yes; no	3.316
FOA>40 Y	Yes; no	2.780
High-BP	Yes; no	2.284
MLN		OR2 values	∑OR1-∑OR2
Male	Yes; no	6.211	<0
IgG-lower	Yes; no	3.425
Tube-I/PI	Yes; no	1.969
FSGS	Judgment	OR1 values	∑OR1-∑OR2
ESR-quicken	Yes; no	3.651	>0
α2Glb lower	Yes; no	2.999
FOA>40 Y	Yes; no	2.505
High-BL	Yes; no	2.217
IgAN		OR2 values	∑OR1-∑OR2
Cold/T/UPI	Yes; no	5.848	<0
U/B/L-infection	Yes; no	4.808
IgAN	Judgment	OR1 values	∑OR1-∑OR2
Proteinuria ≥2 Y	Yes; no	25.986	>0
High-BP	Yes; no	3.555
FOA 20-40 Y	Yes; no	3.089
MLN		OR2 values	∑OR1-∑OR2
Male	Yes; no	13.889	<0
ESR-quicken	Yes; no	3.876
High-BL	Yes; no	3.861
ALB-lower	Yes; no	3.378
IgAN	Judgment	OR1 values	∑OR1-∑OR2
AKI/AGN	Yes; no	19.244	>0
FOA <20 Y	Yes; no	8.79
Hepatitis A/B/TB	Yes; no	7.013
Hyper-RD	Yes; no	5.364
Cold/T/UPI	Yes; no	2.885
MN		OR2 values	∑OR1-∑OR2
Edema-F/L	Yes; no	10.526	<0
High-BL	Yes; no	6.25
ESR-quicken	Yes; no	5.587
MN	Judgment	OR1 values	∑OR1-∑OR2
Proteinuria ≥2 Y	Yes; no	12.284	>0
UBJP-E	Yes; no	4.829
TCM/PCM	Yes; no	4.742
Edema-F/L	Yes; no	3.045
High-BP	Yes; no	2.626
MLN		OR2 values	∑OR1-∑OR2
Student	Yes; no	5.988	<0
Male	Yes; no	3.534
MN	Judgment	OR1 values	∑OR1-∑OR2
Edema-F/L	Yes; no	7.018	>0
P-lower	Yes; no	3.889
Tube-I/PI	Yes; no	3.309
ALB-lower	Yes; no	2.554
High-BL	Yes; no	2.436
FSGS		OR2 values	∑OR1-∑OR2
Free-worker	Yes; no	3.876	<0
Ca-lower	Yes; no	1.957

OR value, value of odds ratio by the analysis of logistic regression model; when the indices of CKD patients were judged as “yes,” the values of OR in each CKD pathological type were calculated and summed, respectively; If “No,” the values of OR in CKD pathological types are invalid; the judgment of CKD pathological types indicates the group with the larger value of ∑OR, ∑ is a symbol of summation in mathematics.

Supplementary Table 5

Assessment of goodness of fit in logistic models

Logistic models	Accuracy rate (%)	ROC area under the curve	Asymptotic 95%CI	H-L test P
FSGS－MLN	78.5	0.858*	0.812–0.904	0.152
FSGS－IgAN	70.3	0.808*	0.757–0.860	0.470
IgAN－MLN	78.2	0.863*	0.820–0.907	0.613
IgAN－MN	83.4	0.929*	0.900–0.959	0.578
MN－MLN	78.9	0.871*	0.828–0.914	0.803
MN－FSGS	75.7	0.829*	0.780–0.878	0.905

*Asymptotic P<0.01. H-L test: Hosmer–Lemeshow fit goodness test; P value of H-L test >0.05 indicates that logistic models are the good and fit for differential diagnosis of CKD pathological types. ROC: Receiver operating characteristic; CI: Confidence interval.