In many clinical trials, patients who are followed up over time may typically measure repeatedly multiple outcomes. Ignoring such repeatedly measured outcome or biomarker and considering cross-sectional analyses can leads to biased estimates. In this context, we presented partial proportional odds model for longitudinal functional status measures among stroke patients at FHRH Bahir Dar, Ethiopia. We considered 400 patients who had stroke under the medical ward outpatient stroke who started treatment from September 2018 to August 2021 by a retrospective cohort study design. Among 400 stroke patients taken from the repository of FHRH, 188(47%) were females. The patients mean age and corresponding 95%CI was (58; 95%CI=55-58) at baseline. Among different candidates of demographic and clinical variables, age, diabetes, blood urea nitrogen, Glasgow coma scale, white blood cell count, and stroke complication were statistically significant predictors. the ordinal longitudinal modeling approach, provides wide-ranging information about the longitudinal pattern of the functional status. Furthermore, the results of the study can be used as a motivation for future scholars. since stroke is one of the most frequent diseases in Ethiopia as well as in the world, it needs more attention and study in a wider study area.
Article
Identifying factors that determine functional status of stroke patients using partial proportional odds model at Felege Hiwot Referral Hospital, Ethiopia
https://doi.org/10.21203/rs.3.rs-4675501/v1
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Stroke
functional status
partial proportional odds model
generalized linear mixed model
Stroke is rapidly growing clinical symptoms of focal or global abnormality of brain functioning that lasts longer than 24 hours or results in death and has no apparent cause other than a vascular origin [1]. Stroke is one of the most frequent noncommunicable diseases, with significant public health consequences globally [2]. A stroke occurs when blood supply to the brain is impeded. As a result, the brain is deprived of getting oxygen and nutrients due to this, the brain cells begin to die within minutes [3].
In 2019, there were 12·2 million incident strokes and 101 million prevalent strokes, 143 million Disability Adjusted Life Years (DALYs) due to stroke, and 6·55 million deaths by stroke around the world. Globally, stroke was the second-leading Level 3 cause of death 11·6% of total deaths following ischemic heart disease, which accounted for 16·2%. Stroke was also the third-leading Level 3 cause of death and disability combined in 2019 5·7% of total DALYs), after neonatal disorders 7·3% and ischemic heart disease 7·2% [4].
A stroke can be classified as an ischemic or a hemorrhagic stroke [1, 5, 6]. By far, the most common type of stroke is the so-called ischemic stroke or cerebral infarction. According to data released by the American Heart Association,87% of strokes are classified as ischemic [7].
According to a report from different countries, stroke is a common cause of death in admitted patients. In these continents, 41.2% in Asia [8], 19% in Europe [9], and 14.9% in Australia [10] of admitted patients in the hospital for stroke have died. Stroke is also commonly occurred in Africa[11, 12], 29 to 84 percent of patients who had stroke have died and 14.3% were disabled[13].
Stroke has a high incidence in Sub – Saharan Africa (SSA) [14, 15]. And, the report also shows at least 6 Africans are suffering per minute, this leads Sub Sahara Africa to be the global capital for stroke. The prevalence of strokes in Ethiopia, to 963 per 100,000 [16]. The burden of stroke is increasing and has become the reason for 7.5–19.3% of hospital admission [6, 10, 17–19]. And, approximately (11–42.8%) of death between (2014–2019) [6, 10, 17].
Stroke leads to different consequences, the most common is sudden death, disability, and depression, and takes 12.4% up to 42.9% of the consequences. In developing countries including Ethiopia, there are several barriers to managing patients who had stroke, including limited stroke units, limited availability of resources, a shortage of adequately trained manpower, stroke prevention and treatment, a shortage of essential drugs, and diagnostic facilities, and a lack of treatment guidelines[13, 16, 20, 21]. The level of severity in functional disability of patients who had stroke is measured by the modified Rankin Scale(mRS)[22].
The modified Rankin Scale is a clinician-reported global impairment measure that is extensively used to assess the effects of stroke on functional status[23]. Therefore, the mRS has six categories, namely no symptom, no significant disability despite symptoms, slight disability, moderate disability, moderately severe disability, and severe disability or death[22].
Age, sex, and race (ethnicity) are non-modifiable risk factors while hypertension, smoking, diet, and physical inactivity are some of the most widely identified modifiable risk factors for both ischemic and hemorrhagic stroke[24]. According to Fekau et, al., 75.9% of those with risk factors had hypertension, which is the most significant risk factor for stroke in the world[25].
According to the Global Burden of Disease (GBD) report in 2019, high blood pressure, obesity, diabetes hyperlipidemia, and renal dysfunction were 90% of stroke risk [26]. The remaining 10% of stroke risk could be a family history of stroke, cigarette smoking, obesity, lack of exercise, alcohol consumption, and unhealthy diets. Hemorrhagic stroke is associated with uncontrolled hypertension, and ischemic stroke is commonly related to diabetes mellitus [27].
The prevalence of stroke has been raised from time to time in developing countries as compared to developed countries, and also there is a lack of knowledge about stroke in developing countries including Ethiopia [2, 28]. In Ethiopia, the burden of stroke is estimated to be 16.2% of hospitals admission. And for those admitted patients, the popular leading factor for stroke is hypertension(49%), alcohol consumption (24.96%), dyslipidemia (20.9%), and the rest (94.86) were caused by other factors [5, 29].
Different studies were conducted to overcome the problem of increasing the prevalence of stroke from time to time by identifying the major risk factors which have a significant effect on the functional status of patients who had stroke using the binary longitudinal mixed model [30–32]. However, those studies were analyzed using a dichotomized result derived by categorizing them into "good" and "bad" categories. This dichotomization discards information and reduces the power of statistical inference, making it less powerful than methods that model probabilities using the mRS.
In this case, longitudinal binary functional status analysis could be less efficient. Therefore, model of longitudinal ordinal would incorporate all information and provide a valid and efficient association between the longitudinal ordinal functional measure.
Study Population, Setting, and Period
Patients who had stroke under the medical ward outpatient at FHRH Bahir Dar, Ethiopia who started treatment from September 2018 to August 2021 was used.
Data source and measurement
Repeatedly measured data was extracted from the patient's chart which contains socio-demographic and clinical information of all adult patients who had stroke under the treatment retrospectively from the repository of FHRH. Patient names were excluded from the data abstraction process to ensure confidentiality.
Inclusion criteria
Patients with age greater than or equal to 18 years, patients with well documented estimated date, and patients with at least three visits were included in this study.
Sample Size Determination
Sampling is a process by which a representative sample is chosen from a population to use the sample. There are many ways from which the sample can be selected. From knowledge of the degree of accuracy required, approximate estimates of the sample size can be made for each plan that is considered. For each program, before making a decision the relative costs and time involved are also compared [33]. This is the crucial issue of the number of patients that are required in longitudinal and survival study. If too few patients are recruited, there may be insufficient information available in the data to enable a treatment difference to be pronounced significant. On the other hand, it is unethical to waste resources on studies that are unnecessarily large [34]. the total sample size will be 381. Hence, by considering 5% contingency the finally total sample size was calculated to be approximately 400. Study participants were selected using a systematic random selection method. This approach was used to select study participants systematically for every two patients (k = 2) based on their card numbers until the required sample size of 400 was reached.
Definition of Variables
Response variable. The response variable in this study was the functional status of stroke patient based on the mRS. The scale was first introduced in 1957 by Dr. John Rankin of Stobhill Hospital, Glasgow, Scotland as a 6-level scale ranging from 1 to 6 [22]. However, Li et al (2010) are categorized into 4 -level scale[35](See Table 1).
Explanatory Variables. The baseline sociodemographic and clinical variables that were related to functional status for patients who had stroke (see Table S1).
Generalized Linear Mixed Model
Generalized linear mixed models (GLMMs) have increasingly become a popular way of modeling longitudinal or clustered ordinal data in the social and health sciences. The basic concepts of GLMMs extend the generalized linear models (GLM), which are a class of fixed effects regression models for the different types of response variables including continuous, dichotomous, and counts, by incorporating random effects into the linear predictors. Mixed-effects models, investigate the effects of covariates on subject-specific mean response trajectories. A distinctive aspect of the mixed-effects models is that the mean response on a particular subject consists of population characteristics that are shared by all subjects (fixed effects) and subject-specific effects which are unique to each subject (random effects) The random effects take into account the heterogeneity between subjects and are routinely assumed to be normally distributed[36, 37].
Ethical considerations
The author requested ethical approval at Bahir Dar University to access data from a repository of FHRH. So, there was no direct relationship between the researcher and the patients during the data abstraction process. Ethical clearance was obtained from research ethics committee of Bahir Dar University, Ethiopia, with reference number: stat-S/169/2014 in accordance with the principles expressed in the Declaration of Bahir Dar University, Ethiopia.
The data consist of 400 stroke patients who were treated under follow-up in FHRH, Bahir Dar, Ethiopia. Among four hundred patients who had stroke taken from the repository of FHRH, 188(47%) were females. The patients mean age and corresponding 95%CI was (58; 95%CI = 55–58). Around 210(53%) of patients were from rural. Regarding the previous history of other diseases(comorbidities), around 166(42%) of the patients were hypertensive, 127(32%) were diabetic, 104 (26%) had heart diseases, and 122 (31%) of the patients had an ischemic stroke respectively (See Table 2).
Table 2: Frequency distribution of predictors variables
|
Characteristic |
Label |
n (%) |
|
Gender |
Gender |
|
|
|
female (0) |
188 (47%) |
|
|
male (1) |
212 (53%) |
|
Residence |
Residence of patients |
|
|
|
rural (0) |
210 (53%) |
|
|
urban (1) |
190 (48%) |
|
Hypertension |
History of hypertension |
|
|
|
no (0) |
234 (59%) |
|
|
yes (1) |
166 (42%) |
|
Diabetes |
History of diabetes |
|
|
|
no (0) |
273 (68%) |
|
|
yes (1) |
127 (32%) |
|
AF |
History of atrial fibrillation |
|
|
|
no (0) |
285 (71%) |
|
|
yes (1) |
115 (29%) |
|
Hdiseases |
History of heart disease |
|
|
|
no (0) |
296 (74%) |
|
|
yes (1) |
104 (26%) |
|
Tstroke |
type of stroke |
|
|
|
hemorrhage (0) |
278 (70%) |
|
|
ischemic (1) |
122 (31%) |
|
|
|
|
|
STcomp |
stroke complications |
|
|
|
no (0) |
290 (73%) |
|
|
yes (1) |
110 (28%) |
|
TIA |
History of transit ischemic attack |
|
|
|
no (0) |
362 (91%) |
|
|
yes (1) |
38 (9.5%) |
|
HIV |
History of HIV/AIDs |
|
|
|
no (0) |
391 (98%) |
|
|
yes (1) |
9 (2.3%) |
|
Glasgow |
Glasgow coma scale score |
|
|
|
13-15 (0) |
254 (64%) |
|
|
3-8 (1) |
100 (25%) |
|
|
9-12 (2) |
46 (12%) |
|
Characteristic |
Label |
Mean(95%CI) |
|
Age |
age of the patients |
56(55-58) |
|
Hemoglobin |
Hemoglobin level |
14.30(14.09-14.51) |
|
SBP |
systolic blood pressure |
133(131-135) |
|
DBP |
diastolic blood pressure |
84(82-85) |
|
BUN |
blood urea nitrogen |
30.56(29.10-32.03) |
|
WBC |
white blood cell count |
9.24(8.79-9.68) |
|
Cholesterol |
Total cholesterol level |
155.48(149.20-161.76) |
Exploring Longitudinal Data using area percentage
Figure 1 shows that at baseline 14% were sample patients who had stroke had no symptoms and/or no disability despite symptoms and the percentage increased at every visit time, whereas the percent of slight and severe disability were 24% and 25% respectively and decrease over time. But the percentage of patients who had stroke having a moderate disability at baseline were 37% and changes through time with some degree of similarity.
Exploring number and percent of observations for functional status
Figure 2 shows the total number of observations for each ordinal outcome in terms of the stroke patient’s functional status. The x axis of the bar graph displays a cumulative number of treatment observations within each functional status status group. The bar graph showed that patients with a moderate disability had the highest cumulative number of treatment observations 1335(37.04%) and slight disability had lowest cumulative number of treatment observation 758(21.05%). And also, the study observed that patient with no symptom and sever/dead had 670(18.6%) and 841(23.35%) number of treatments.
Frequency Profile Plot for Functional status
Figure 3 shows that the total number of patients with a moderate disability was higher at the baseline, and then it strictly decreased after 3 months. Because they have more probability of experiencing dropout and death overtime and the same is true for slight disability However, the number of patients with no symptoms or slight disability despite symptoms increased until 12 months, and then it decreased monotonically.
Partial Proportional Odds Model (PPOM)
Univariate analysis for PPOM
In this sub-section a univariate analysis was done and then Age, diabetes, Stroke complication, blood urea nitrogen, white blood cell count, and Glasgow coma scale were selected.
Proportional Odds Assumption
Based on POM assumption checking Age, Stroke complication, blood urea nitrogen, and Glasgow coma scale. Had significant interaction with threshold value This indicates that the proportional odds assumption is violated for those variables.
Multivariable Analysis for PPOM
Multivariable analysis was done by using all the significant predictors together by assuming a partial proportional odds model (See Table 3).
Table 3 showed that age, blood urea nitrogen, Glasgow coma scale, and stroke complication had statistically significant interaction effects with thresholds. indicated that the effects of the predictors can’t be assumed identical across the three cumulative logits. By holding this assumption, the result can be interpreted as follows.
age has a significant effect on the odds of patients who had stroke being in the “no symptoms or no disability despite symptoms” functional status (aOR = 0.97; 95%CI: 0.96–0.97), meaning for a 1-year increase in patient's age the chance of being in the “no symptoms or no disability despite symptoms” functional status reduced by 3%. Similarly, for a 1-year increase in patient's age the chance of being in the “no symptoms or no disability despite symptoms or slight disability” functional status increased by 2%(aOR = 1.02;95%CI = 1.01–1.03), controlling the effect of all other variables in the model. Furthermore, age has different effects and directions across thresholds, indicating that as age increases the level of disability also increases or decreases the level of functional status.
The odds of being in “no symptoms or no disability despite symptoms” of functional status for 1 unit increase in blood urea nitrogen is 0.98(aOR = 0.98;95%CI = 0.97–0.99) and 1.03(aOR = 1.03;95%CI = 1.02–1.04) for being in the “no symptoms or no disability despite symptoms or slight disability”, keeping all other variables in the model as constant.
For the Glasgow coma scale, the odds of being no symptoms or no disability despite symptoms versus slight disability, moderate, or severe/dead with GCS 3–8 is 1.62(aOR = 1.62;95%CI = 1.25–2.1) times higher than that of patients whose Glasgow coma scale 13–15. The odds of being no symptoms or no disability despite symptoms or slight disability versus moderate or severe/dead with GCS 3–8 is 1.36(aOR = 1.36;95%CI = 1.01–1.83) times higher than that of patients whose
Table 3: Estimate and 95% CI for the PPOM.
|
Effect |
Proportional odds |
Non-proportional odds |
||
|
|
Exp (β) (95%CI)
|
Exp (β) (95%CI) No vs slight, moderate, severe/death
|
Exp (β) (95%CI) No, slight vs moderate, severe/death
|
Exp (β) (95%CI) No, slight, moderate vs severe/death
|
|
Thresholds |
|
|
|
|
|
No Symptom |
0.09(0.01,0.99)* |
0.09(0.01,0.99)* |
- |
- |
|
Slight disability |
8.04(5.08, 12.73)*** |
- |
8.04(5.08,12.73)*** |
- |
|
Moderate disability |
194269.2(74500.42,506581.25)*** |
- |
- |
194269.2(74500.42,506581.25)*** |
|
Predictors |
|
|
|
|
|
Age |
- |
1.11(1.06, 1.13)*** |
1(0.99, 1.01) |
1.06(1.04, 1.07)*** |
|
Bun |
- |
1.04(1.01, 1.07)* |
0.97(0.96, 0.98)*** |
1(0.99, 1.01) |
|
glasgow:3-8 vs 13-15 |
- |
4.15(1.08, 15.99)* |
0.64(0.45, 0.9)* |
3.86(2.44, 6.17)*** |
|
glasgow:9-12 vs 13-15 |
- |
10.86(1.84, 63.94)** |
0.61(0.44, 0.85)** |
0.8(0.45, 1.4) |
|
time slopes |
|
|
|
|
|
diabetes: yes vs no |
1.78(1.69,1.88)*** |
- |
- |
- |
|
WBC |
0.99(0.98,0.995)*** |
- |
- |
- |
|
stroke complications: yes vs no |
- |
0.88(0.84,0.92)*** |
1.17(1.08,1.15)*** |
1.24(1.16,1.30)*** |
*p < 0.05, **p < 0.01, ***p < 0.001.
BUN, Blood Urea Nitrogen; PPOM, Partial Proportional Odds Model; WCC, White Cell Count
Glasgow coma scale 13–15. The odds of being no symptoms or no disability despite symptoms, slight disability, moderate versus severe/dead with GCS 3–8 is 0.28(aOR = 0.28;95%CI = 0.19–0.39) times lower than that of patients whose Glasgow coma scale 13–15. Similarly, 0.49(aOR = 0.49;95%CI = 0.34–0.72) times lower to be being no symptoms or no disability despite symptoms versus slight disability, moderate, or severe/dead, 2.44(aOR = 2.44;95%CI = 1.84–3.22) times higher to be being no symptoms or no disability despite symptoms or slight disability versus moderate or severe/dead, and 3.78(aOR = 3.78;95%CI = 2.36–6.11) times higher to be being no symptoms or no disability despite symptoms, slight disability, or moderate versus severe/dead comparing with patients whose Glasgow coma scale 13–15.
Considering the interaction effects of the covariates with time, since we didn’t reject the proportional odds assumption for WBC and diabetes, therefore, we assumed an identical effect across three cumulative logit models for those covariates. for every white blood cell increase with follow-up time the odds of being in the first, second, and third category are the same and it is1.01(1.01;95%CI = 1.007–1.02). the odds of diabetic patients who had stroke with follow-up time being in “no symptoms or no disability despite symptoms versus slight disability, moderate, or severe/dead”, in “no symptoms or no disability despite symptoms, slight disability versus moderate, severe/dead”, and in “no symptoms or no disability despite symptoms, slight disability, moderate versus severe/dead” are the same(aOR = 1.96;95%CI = 1.89–2.1).
Finally, by considering the time slope with nonproportionality, the odds of patients with stroke complications being in the “no symptoms or no disability despite symptoms versus slight disability, moderate, or severe/dead” is 1.1(aOR = 1.1;95%CI = 1.06–1.13), being in the “no symptoms or no disability despite symptoms slight disability versus moderate, or severe/dead” is 0.93(aOR = 0.93;95%CI = 0.9–0.96), and being in the “no symptoms or no disability despite symptoms, slight disability, or moderate versus severe/dead” is 0.89(aOR = 0.89;95%CI = 0.85–0.93) with follow-up time.
model Diagnosis
In fact, a crucial step in the modeling process is the application of diagnostic procedures for model checking. The adequacy of the fitted model was checked for the possible presence of outliers and influential values were presented in Fig. 4 for the appropriateness of the PPOM using Q-Q plot and Empirical Bayes (EB) estimates of the random effects in multilevel models to represent how individuals deviate from the population averages and are often extracted to detect outliers or used as predictors in the follow-up analysis. To sum up, figures given below declared the PPOM was adequately fitted the data (Fig. 4).
The global assumption of mixed proportionality of odds can be checked by LRT, where the deviance of the model assuming proportional odds \(\:({D}_{ev}PO\)) is compared to the deviance of the partial proportional odds model \(\:({D}_{ev}PPO\))
Under the null hypothesis, the asymptotic distribution of statistics in the above equation is chi-square with degrees of freedom given by l = (d.f PPO − d.f PO) [38].
Table 4 shows that: The LRT = 116.8091 (p < 0.001), indicating that the proportional odds assumption for the full model was not satisfied. This suggested that the effect of one or more of the explanatory variables was likely to differ across separate binary models fit for the cumulative thresholds.
Table 4: Checking the fit of the model for longitudinal model
|
Model |
AIC |
BIC |
Deviance |
chisq |
P(>chisq) |
|
Proportional odds |
4892.416 |
4936.323 |
4870.416 |
|
|
|
Partial-proportional odds |
4795.607 |
4879.428 |
4753.607 |
116.8091 |
<0.001 |
This study models the functional status of patients who had stroke in the study period, September 2018 to August 2021 at FHRH. Functional status of stroke patient is frequently measured on an ordinal scale[39]. This analysis demonstrated the association between functional status, baseline and trend analysis of functional status, and factors affecting functional status using partial proportional odds model. The partial proportional odds model has statistical and clinical significance. Statistically, it takes into account longitudinal ordinal outcomes for the longitudinal data types so that one can infer the dependence and association between the longitudinal biomarker and assess the effect of covariates[40]. As a result, it reduces bias and provides an improvement in efficiency[41]. Clinically also, the partial proportional odds model provide more efficient estimates of the longitudinal measure of functional status, measure the influence of clinical variables on functional status measure, and it is good to assess the prognostic factors[36].
The assumption of proportional odds is relaxed by a partial proportional odds or non-proportional odds model. The partial proportional-odds model will frequently be a preferable substitute when the proportionality assumption is not met[42, 43]. When using a partial proportional odds model, it is possible to model some predictors with the proportional odds assumption while the other variables could be modeled with the none proportional odds assumption.
Age had a statistically significant association with functional status. This finding is in line with studies conducted by [44]. Diabetes mellitus was significantly associated with poor functional status i.e., the odds of patients who had stroke with the presence of diabetes being in a lower functional status is higher than patients without diabetes. This finding was in line with [45]. This study shows that the increment of blood urea nitrogen in patients who had stroke was significantly associated with functional status. The result is directly consistent with [46, 47]. While in the study conducted by you et al., the increased BUN at admission is not a significant prognostic factor associated with poor functional status [48]. This may be due to measurement scale, data type, study period, and/or sample size difference.
The previous studies on white blood cell count on outcomes after acute ischemic stroke have been in agreement with our findings [48–51]. support the notion that a higher WBC count is associated with poor.
This study showed that stroke complication was a statistically significant factor in the functional status of patients who had stroke. The result showed that stroke complication was associated with poor functional status. This finding was in lined with a study conducted by Rohweder et al., finding patients who had stroke with complications had a significant association with the functional status[52].
This study aimed to model functional status measures on patients who had stroke at FHRH Bahir Dar, Ethiopia. Now a day PPOM model is frequently used in longitudinal data, where it is of interest to examine the association and dependency between those ordinal data natures.
Hence, the model revealed age, diabetes, blood urea nitrogen, Glasgow coma scale, white blood cell count, and stroke complication were statistically significant predictors in the longitudinal model for functional status. Functional status varied among patients, with the majority showing moderate functional status initially.
Acknowledgments We would also like to thank all FHRH staff in the stroke patient ward of Amhara region, Ethiopia for their cooperation during data collection.
Author contributions H.B. was responsible for the study concept and methods design, data analysis, initial manuscript draft writing, and figure and table creation. Y.B. was responsible for data analysis and interpretation, initial manuscript draft writing and manuscript editing. M.Z, H.W, G.G and S.M. designed the study, entered the data, and edited the manuscript. All authors have read and agreed to the published version of the manuscript.
Funding No funding.
Competing Interests declared no competing interests.
Data availability the dataset used and analyzed for the study is available from the corresponding author for reasonable request.
Ethics declaration the author requested ethical approval at Bahir Dar university to access data from repository of FHRH. So, there were no direct relationship between the researcher and the patients during data collection. Due to the retrospective nature of the study, research ethics committee of Bahir Dar University, Ethiopia waived the need of obtaining informed consent.
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No competing interests reported.