A proposed Multivariate Logistic Regression Model For Osteoporosis Patients

INTRODUCTION

  Osteoporosis is a common silent progressive orthopedic disorder in post-menopausal women and overall aged patients which is characterized by reduced bone mass and strength, and overall mineral density with a deterioration in micro-architectural structures that is commonly associated with increased skeletal fragility and consequently higher risk of fracture which remains asymptomatic till the incidence of the first fracture

According to the Osteoporosis and Related Bone Diseases National Resource Center, osteoporosis is very common, with roughly 53 million people in the United States living with the condition.³ Osteoporosis occurs in both males and females but is particularly common among women following menopause when bone turnover increases and the rate of bone resorption exceeds that of bone formation.⁴ Corresponding with an aging society, the public health impact of osteoporosis is enormous, affecting 200 million individuals worldwide. The reported prevalence of osteoporosis in Caucasian women older than 50 years of age varies from 7.9% to 22.6%.⁵

Although osteoporosis is often preventable and treatable, its inaccurate and delayed diagnosis can result in substantial physical, psychosocial, and economic consequences with main clinical manifestations of chronic pain, pathological fractures, loss of height, loss of bone mineral density (BMD), spinal deformity, and ultimately osteoporotic hip or vertebral fracture.^6-7  

With the ageing population, the incidence rate of osteoporotic vertebral and non-vertebral fracture rises year by year, which has a serious impact on the life of patients, and receives increasing attention.⁸ Effective treatments for osteoporosis are now available, such as bisphosphonates which are first line treatment. Thus, there is interest in identifying people at high risk who should receive targeted therapeutic interventions.^9-10 Dual-energy x-ray absorptiometry (DEXA) is the gold standard for the diagnosis of osteoporosis, but it remains expensive and is not widely available. Furthermore, studies have shown that mass screening for osteoporosis using DEXA is not cost-effective. ^11-12

A research group at the University of Sheffield developed the tool to predict the risk of fractures in a person with osteoporosis within the next 10 years, 10-year Hip Fracture Risk, or major osteoporotic fracture based on the FRAX Score. FRAX stands for Fracture Risk Assessment Tool. It has now become widespread as a clinical tool.¹³ According to the Preventive Services Task Force, if a female is 65 years of age or older or is postmenopausal before the age of 50 years, she should undergo a bone mineral density (BMD) test.¹⁴ 

Clinicians will compare the results with those of a healthy young adult and give the person a T-score. If a person receives a T-score between –1.0 and –2.5, a FRAX score can help doctors determine which treatment is best.¹⁵ A FRAX score can help doctors identify people with a high risk of fractures who may need additional support. The tool consists of questions relating to 12 factors that can increase the risk of fractures. These factors are age, weight, height, sex, smoking, history of fractures, parental history of fractures, presence of rheumatoid arthritis, and use of glucocorticoid medications, having secondary osteoporosis, drinking three or more units of alcohol per day, bone mineral density. ¹⁶

Each day, in consuming a typical western diet, the human body produces approximately 1 mEq/kg of hydrogen ions which are physiologically neutralized via increasing carbon lung dioxide exhalation and acid kidney excretion.¹⁷ Other significant acid-neutralizing mechanisms occur primarily through osteoclast-mediated loss alkaline minerals into the body fluids which will demonstrate a negative calcium balance.¹⁸ Bone is 35 % protein and requires a supply of amino acids to be used for protein turnover.¹⁹ Protein supplementation studies have shown an improvement in bone mineral density (BMD) or other bone indices in some studies but not in others.²⁰ Some associations between dietary protein and bone health will be due to confounding from dietary and lifestyle factors. The quantity of protein consumed and the adequacy of fruits/vegetables and calcium/Vit D intake may also vary between studies. These factors could explain differing results and it must be kept in mind that not all of these observational analyses are multivariate-adjusted.²¹ The primary aim of this study was to construct a new proposed FRAX based multivariate linear regression model for our osteoporosis-related patients who attended the rheumatology clinic that addressed the dietary and lifestyle confounding overall bone effects.

MATERIAL AND METHODS

       This study trial was a single-center, non-funded and non-sponsored retrospective study, conducted for 206 participants who attended the rheumatology clinic between Sep 2021 and Nov 2021 at Prince Rashid Bin Al-Hasan Military Hospital, Royal Medical Services, Irbid, Jordan. Ethical approval was signed by our Institutional Review Board (Ref #35, 12/2021). An informed consent form was waived owing to the study's retrospective design. Aged male and post-menopausal Jordanian’s participants were included in this study. Participants with hip or vertebral anatomy malformity, subjects with a history of renal or non-renal related metabolic osteodystrophy, secondary osteoporosis, cancer affected patients with bone metastasis, participants' history of hip or vertebral osteoporotic fracture, and prior use of any bisphosphonate were excluded from the study.

Dual-emission X-ray absorptiometry (DEXA) scans of the proximal femoral hip and anteroposterior spine participant’s data were retrieved from the DEXA recorded database. Retrievable DEXA recorded database in our study included femoral Hip T-Score (_fHipT-Score), femoral Hip Z-Score (_fHipZ-Score), femoral Hip BMD in g per cm2 (f Hip BMD), Lumbar T-Score, Lumbar Z-Score, Lumbar BMD, the 10-year risk of femoral osteoporotic fracture (10-year _fOHF risk) FRAX score, and 10-year risk of major overall osteoporotic fracture FRAX score. A 10-year _fOHF risk based on a FRAX score of 3% was used in our study to dichotomize the overall cohort into two cohorts; attended rheumatological clinic patients who had assessed 10-year fOHF risk < 3% based on FRAX Score (Group I) and attended rheumatological clinic patients who had assessed 10-year Hip Fracture Risk ≥3% based on FRAX Score (Group II).

The comparative non-dichotomous variables between Group I and Group II were statistically analyzed by Independent T-Test and the results were expressed as Mean±SD and as Mean difference±SEM. While the comparative variables for the total sample were analyzed by One-Sample T-Test and the results were also expressed as Mean±SD. For dichotomous categorical data, a Chi-Square Test was used to express the analysis outcomes as Numbers (Percentages). The correlation strengths of binary categorical variables were also expressed as an odds ratio.

The FRAX score-based variables that were tested in our study include age, weight, height, sex, smoking, history of fractures, parental history of fractures, use of glucocorticoid medications, having secondary osteoporosis, drinking three or more units of alcohol per day, bone mineral density. Co-Morbidities were also tested in our study and including, rheumatoid arthritis (RA), hypertension (HTN), diabetes mellitus (DM), chronic kidney disease (CKD), peptic ulcer disease (PUD), cardiovascular disease (CVD).

In addition to FRAX score-based composite variables, dietary and lifestyle independent variables were included in our study to explore their combined interactive explanation for the prediction of our target of interest (The 10-year fOHF risk). The density of protein consumed in grams per 100 Calories (PD), the consumption pattern of fruits/vegetables (FVCP), the number of daily calcium/Vit D tablet intake (OsCal-D), and the lifestyle of daily activities (ADLs) were the 4 tested variables that were run individually into Univariate Linear Regression and collectively into Multiple Linear Regression analysis. Both the FVCP and ADLS were dichotomized into intermittent versus regular patterns and sedentary versus active lifestyles. The daily OsCal-D tablets were categorized into 1 Tab/day, 2 Tab/day, 3 Tab/day, or 4 Tab/day. Dietary PD in g/100 Cal was roughly estimated based on the attended rheumatology clinic participants’ weekly average consumption quantities of foods that are mentioned in Figure 2. Also, the participants’ PDs were dichotomized into either below 2.5 g/100 Cal or above 2.5 g/100 Cal.

Firstly, we conducted a Univariate Linear Regression Test for the 4 tested variables to individually explore the degree of correlation (R), how much of the total variations in the dependent variable can be explained by the independent variables and a proportion of variation accounted for by the regression model above and beyond the mean model (Coefficient of determination or R²), how much the quality of the prediction of the dependent variable, and how the regression model is a good fit for the data (F-Ratio in the ANOVA table). Also, this test was conducted to abstract the necessary coefficients to individually predict the 10-year _fOHF risk. Thereafter, The Multivariate Linear Regression Test was followed to composite the predictive variables that were significantly correlated and to fit these significant explanatory variables into a proposed multiple linear regression model, after abstracting the significant coefficients, to collectively predict the 10-year _fOHF risk.

After the multivariable linear regression model was constructed, we ran participant composed data into this constructed proposed multivariable linear regression equation into receiver operating characteristic (ROC) and sensitivity analyses to investigate the area under the ROC curve (AUROC) and to explore the optimal cut-off point, sensitivity, specificity, positive and negative predictive values, Youden and accuracy indices, and the negative likelihood ratio for the 10-Year Risk of f Hip OPF percentages based on our proposed multiple regression equation results. Statistical analysis was performed using Statistical Package for Social Science (SPSS) software version 23.0. Statistical significance was set at 5%.

 This study included a total of 206 participants who attended the rheumatology clinic between Sep 2021 and Nov 2021 at Prince Rashid Bin Al-Hasan Military Hospital, Royal Medical Services, Irbid, Jordan. 53.39% of the tested cohort (110 participants) had calculated FRAX score below 3% and so they were allocated to Group I, while the remaining 46.60% of the tested cohort (96 participants) had calculated FRAX score ≥3% and so they were grouped to the other comparative group (Group II). The overall mean age of participants was 59.88±1.673 years.

Group I participants were insignificantly older than Group II participants [59.96±1.98 years versus 59.78±1.23 years, respectively, +0.18±0.23 years, P-value=0.436). Most of the attended rheumatological clinic participants in our study belonged to the female gender. Female to male ratio (F: M) was 5.87: 1 [176 (85.4%) versus 30 (14.6%), respectively, P-value=0.426] in which 15.5% (117 Men) and 84.5% (93 Women) belonged to Group I compared to 13.5% (13 Men) and 86.5% (83 Women) in Group II. The menopausal onset means age for female participants was 48.41±4.41 years which was also insignificantly distributed across Group I-II [48.45±4.60 years vs 48.36±4.21 years, respectively, +0.090±0.67 years, p-value=0.893].

Anthropometrically, all assessed and calculated participants’ anthropometrics were insignificantly distributed between the two comparative groups. Bodyweight (BW), height, body mass index (BMI), ideal body weight (IBW), adjusted body weight (Adj_BW), and body surface area (BSA) were 76.90±7.83 Kg, 160.7±8.62 cm, 30.13±5.214 Kg/m², 56.37±7.29 Kg, 64.59±4.52 Kg, and 1.918±0.049 m² vs 76.80±7.53 Kg, 160.06±7.19 cm, 30.19±4.48 Kg/m², 55.83±6.25 Kg, 64.19±4.41 Kg, and 1.768±0.04 Kg, respectively, p-value>0.05.

All retrievable DEXA recorded database of f HipT-Score, f Hip Z-Score, f Hip BMD, Lumbar T-Score, Lumbar Z-Score, and Lumbar BMD were significantly higher in attended rheumatological clinic participants who had FRAX score below 3% (Group I) comparative to participants who had higher score level (Group II) [-1.25±0.19, -1.15±0.18, 0.78±0.023 g/cm², 0.676±0.578, 0.61±0.53, and 1.05±0.09 g/cm² versus -1.79±0.21, -1.64±0.19, 0.72±0.023 g/cm2, -0.91±0.61, -0.83±0.55, and 0.81±0.09 g/cm² ] with Mean differences±SEM of +0.54±0.03, +0.49±0.03, +0.06±0.003 g/cm² , +1.583±0.083, +1.439±0.075, and +0.237±0.012 g/cm² , respectively, p-value<0.05.

The 10-year hip fracture risk based on the FRAX score was significantly lower in Group I compared to Group II [2.25%±0.59% vs 3.86%±0.62%, -1.61%±0.084%, p-value=0.000]. Similarly, the 10-year major osteoporotic fracture (OPF) was significantly lower in Group I compared to Group II [9.77%±4.12% vs 21.04%±4.35%, -11.27%±0.59%, respectively, p-value=0.000]. Overall weekly consumption quantity of CaC03 was 2619±1138 mg/week which was significantly higher in Group I than in Group II [3297±1153 mg/week vs 1842±356 mg/week, +1455±122, respectively, p-value=0.000]. Also, 25-OH-Cholecalciferol (Vit D) level was significantly higher in Group I than in Group II by +6.199±0.323 ng/ml [18.48±2.26 ng/ml vs 12.28±2.37 ng/ml, respectively, p-value=0.000]. The daily OsCal-D tablet consumption rates were significantly distributed across the two tested groups for which the rates of 3 tab/day and 4 tab/day were allocated in Group I in percentages of 50% and 50%, respectively. While the OsCal-D consumption rate of 1 tab/day and 2 tab/day were allocated in Group II in percentages of 21.9% and 78.1%, respectively.

active ADLS rate of 50%. The odd ratio of ADLS for our tested attended rheumatology clinic participants was 0.36 (95% CI; 0.29-0.45).

The overall protein density intake in the study was 3.19±1.59 g/100 Cal which was significantly higher in Group I participants compared to Group II participants by +2.77±0.11g/100 Cal [4.48±1.06 g/100 Cal vs1.71±0.21 g/100 Cal, respectively, p-value=0.000]. The Group I participants had a consumption rate of 97.3% and 2.7% for diets PD≥ 2.5 g/100 Cal and diets PD<2.5 g/100 Cal, respectively. While all Group II participants had a consumption rate of diet PD below 2.5 g/100 Cal. The odd ratio of diet PD for our tested participants in this study was 33.0 (95% CI; 10.8-100.6).

The participants’ comorbidities distributions across the two tested groups and all the aforementioned comparative variables for cohort people who attended the rheumatology clinic between Sep 2021 and Nov 2021 at Prince Rashid bin Al-Hasan Military Hospital, Royal Medical Services, Irbid, Jordan, among 10-year Hip Fracture Risk≥3% Group (Group II) compared to 10-year Hip Fracture Risk<3% Group (Group I) were summarized in Table I-III.

The degree of correlations (R) and the coefficient of determination (R²) results for the 4 tested variables from the conducted Univariate Linear Regression Test were 0.894 and 0.799, 0.600 and 0.361, 0.732 and 0.536, and 0.930 and 0.865 for PD (g/100 Cal), FVCP (Intermittent/Regular), ADLS (Sedentary/Active), and OsCal-D (1-4 Tab/day), respectively. The abstracted individual coefficients (B± SEM) of each aforementioned tested variable for the 10-year _fOHF risk prediction were -0.563±0.020, -1.983±0.185, -1.653±0.108, and -0.954±0.026, respectively. The necessary coefficients to collectively predict the 10-year Hip Fracture Risk and to present the final form of our proposed multiple linear regression model for the tested osteoporosis patients can be formulated as follows.

10-Year Osteoporosis related Fracture Risk (%) =5.406-0.325×PD-0.885×FVCP-0.447*ADLS-0.169*OsCal-D, Samer Alboun et al proposed a multiple linear regression model for prognosticating the % 10-Year Osteoporosis related Fracture Risk based on 4 tested dietary patterns and lifestyle factors, including PD: Protein density in g per 100 Cal, FVCP: Fruits/Vegetables consumption pattern (Intermittent pattern=0, Regular pattern=1), ADLS: Activities of daily lifestyle (Sedentary life style=0, Active life style=1), and OsCal-D: Supplementary tablet which contains 600 mg CaC03 and 400 IU Vit D3.

After the multiple linear regression model was constructed, we incorporated receiver operating characteristic (ROC) and sensitivity analyses to investigate the area under ROC curve (AUROC) and to explore the optimal cut-off point and the related performances indices for the 10-Year Risk of f Hip OPF percentages based on our proposed multiple regression equation results”. Statistical analysis was performed using Statistical Package for Social Science (SPSS) software version 23.0. Statistical significance was set at 5%.

The AUROC for the constructed ROC based on the run participant's composing data into our proposed multiple linear regression equation against the 10-year risk of fHOP_FRAX score ≥3% (1) or <3% (0), was 0.992±0.05 (95% CI; 0.983-1). Also, we explored the optimal operating dichotomized level of 3.45% for our proposed regression equation to discriminate between lower risk and higher risk cohorts regarding the 10-Year risk of fHOP fracture with the prognosticating performance of 97.27%.