Pain scales in monitoring functional recovery of patients with hip fractures

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Pain Scales in Monitoring Physical

Recovery of Patients with Hip Fractures

L.M. van Noort

Chair and Daily Supervisor: Dr. Y. Wang Secondary Supervisor: Dr. Ir. W. d’Hollosy External Member: Dr. S.M. van den Berg

ABSTRACT

English

This study set out to evaluate if a relationship is present between pain and functional recovery in hip patients. Painscores measured on the Numeric Rating Scale of n = 56 patient was taken from a database of the Ziekenhuisgroep Twente hospital in Almelo. These data were combined with data from movement sensors that had been worn by the same participants during hospitalization. Data were preprocessed and analysed statistically for a possible relationship.

From results is concluded that a large majority of linear models for pain against gait show a decrease in gait with an increase of pain. No relationship could be found between average pain per patient and average gait per patient. Furthermore, linear models showed pain decreases with time of hospitalization while gait increases with time. Causality analysis simultaneously showed a decrease in gait on day m + 1 with an increase of pain on day m, and a decrease in pain on day m + 1 with an increase of gait on day m. No clear causality could be deduced from this. Linear models do in no case suffice to explain the variability in the response variable. Findings were in line with that of found literature. Further research is necessary in order to support or reject conclusions of this study.

Nederlands

Dit onderzoek had als doelstelling te evalueren of er een relatie is tussen pijn en functionele herstelling van heuppati ënten. Pijnscores gemeten op de Numeric Rating Scale van n = 56 pati ënten werd verkregen van de database van de Ziekenhuisgroep Twente. Deze data werden gecombineerd met data van bewegingssensoren die gedragen waren door dezelfde pati ënten tijdens hun ziekenhuisverblijf. Data werden voorbehandeld en statistisch geanalyseerd voor een mogelijke relatie.

Uit resultaten werd geconcludeerd dat een grote meerderheid van de lineaire modellen voor pijn tegen bewegingsintensiteit een afname in bewegingsintensiteit lieten zien met een toename van pijn. Geen relatie kon gevonden worden met betrekking tot gemiddelde dagelijkse pijnscore per pati ¨ent tegenover gemiddelde dagelijkse bewegingsintensiteit per pati ¨ent. Causaliteitsonderzoek liet zowel een afname in beweging op dag m + 1 zien met een toename van pijn op dag m, als een toename van pijn op dag m + 1 met een afname van beweging op dag m. Er kon geen duidelijk oorzaaksverband opgemaakt worden.

Lineaire modellen voldeden in geen geval om de variabiliteit van de data in de respons variabele uit te leggen. Vindingen kwamen overeen met die uit gevonden literatuur. Verder onderzoek is nodig om conclusies uit dit onderzoek te onderbouwen of ondermijnen.

Keywords: Hip fractures, Gait analysis, Pain scales

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CONTENTS

1 Introduction 3

2 Methods and Materials 4

2.1 Study Design . . . . 4 2.2 Setting and Location . . . . 4 2.3 Tools of Measurement . . . . 4

Pain Scores • Movement Sensors

2.4 The Participants . . . 6 2.5 Statistical Analysis . . . 6

3 Results 8

3.1 Correlation Analysis . . . 8 3.2 Time analysis . . . 11 3.3 Causality Analysis . . . 13

4 Discussion 16

4.1 Key findings and interpretation . . . 16 4.2 Strengths and shortcomings of the study . . . 17 4.3 Recommendations . . . 17

5 Conclusions 18

References 19

Appendices 21

Appendix A: All patients and linear models fit to their pain and gait . . . 21 Appendix B: All patients and linear models for causality analysis . . . 24

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1 INTRODUCTION

The number of yearly hip surgeries due to fractures has been rising [1, 2]. In the Netherlands, the incidence is expected to rise by 41% by 2040, due solely to the change in demographics in this period [3]. Hip procedures are associated with excess mortality in Europe and the USA [4, 5], and specifically in the Netherlands, an estimated 20% of total patients and 25% of elderly patients died within a year of their hip fracture [6, 7, 8]. In addition, a reduced quality of life is associated with recovery from hip fractures both in the Netherlands [6] and in general [9, 10, 11, 12].

Recovery from a hip procedure can be measured using various metrics. In this study, gait analysis and pain scale evaluation from patients were investigated for a relationship.

Gait analysis is the study of the gait cycle, which contains one step with the left foot and one step with the right foot [13, 14]. Gait analysis is commonly used in measuring recovery of patients after hip surgery [15, 16]. Within gait analysis, multiple relevant parameters can be measured [17]. One such parameter is movement intensity, calculated from the total signal magnitude area (SMA). Several methods are used to measure gait performance, both wearable and non-wearable systems exist for this purpose [18, 19].

Wearable movement sensors are considered promising in physical rehabilitation because of their ”preci- sion, noninvasiveness and easy deployment” [19]. A comparable conclusion follows from research into various methods of measuring gait [18], which similarly marks wearable sensors as ”promising”. Validity of using an accelerometer for assessment of moderate intensity physical activity has been researched by Hendelman et al. [20]. The latter study suggested that accelerometers might not account for increased energy cost or varying load carriages. This could impair the validity of this method. Yet, a recent (2019) study into the validity of accelerometers for the detection of step speed and gait in an elderly population, supports the validity of this type of movement sensors [21].

Another important measure of recovery is the amount of pain that patients endure throughout the recovery process. Pain scales can be used in order to quantify pain after hip surgery, and are frequently used for that purpose [22, 23, 24, 25, 26, 27]. Popular pain scales include the Numeric Rating Scale (NRS), Visual Analogue Scale (VAS), Verbal Rating Scale (VRS) and Faces Pain Scale-Revised (FPS-R) [28, 29]. Out of these pain scales, Numeric Pain Scales are considered most responsive and valid [29, 30, 31].

Exercise is proven to improve early functional recovery after total hip arthroplasty [32, 33]. There- fore, improved gait performance might lead to improved recovery in hip surgery. On the contrary, chronic pain is shown to be related to poorer functional recovery after hip surgery [24].

Only Erlenwein et al. reported a close relationship between physical functioning and pain [25]. Yet, Erlenwein et al. did not use bodily sensors to analyse gait and no other study has been found that investigated the relationship between physical functioning and pain scales in hip patients.

Therefore the primary aim of this study was to investigate whether there is a relationship between postoperative pain in patients with hip surgery, and the gait performance of these patients.

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2 METHODS AND MATERIALS

2.1 Study Design

The study is a descriptive observational study executed through the retrieval of information from hospital databases. The study was approved by the local ethical committee (ZGT 17-40). This study was part of a larger project of the University of Twente in cooperation with the Ziekenhuisgroep Twente hospital, referred to as the ”Up&Go” project.

The participants of this project had been asked to assess their pain in the morning, afternoon and evening of each day of their hospitalization. Participants had additionally been asked to wear a movement sensor in order to track their movement during this period of hospitalisation. For this research, both the pain scores and movement data were investigated and compared for a possible relationship.

2.2 Setting and Location

Collection of both pain scores and movement data for this research took place in the Ziekenhuisgroep Twente (ZGT) hospital in Almelo. Measurements of the first patient eligible for this research were started in October of 2018, whereas measurements of the last eligible patient were completed in April of 2021.

The study of recorded data took place from April 19^th2021 till June 25^th2021.

2.3 Tools of Measurement 2.3.1 Pain Scores

During hospitalization, patients were asked to assess their pain on a daily basis using the Numeric Rating Scale (NRS), a segmented version of the Visual Analog Scale (VAS). With the NRS a patient is asked to indicate their pain as an integer on a scale from one to ten, wherein a score of zero indicates no pain and a score of ten indicates ”the other pain extreme (e.g. ’pain as bad as you can imagine’)” [34, 35]. NRS is considered valid for use in clinical practice [31].

Protocol for collection said that scores were to be collected three times per day of hospitalization. However, possibly due to administrative error or failing to record scores, not all pain scores were registered in the database. Since data was commonly missing during several parts of the day, the mean daily pain score was calculated and used in analysis. The benefit of this approach is that all measured data points could be taken into account, whilst not causing large gaps of missing data. For days on which no pain score was recorded but only the movement data were recorded, pain scores were interpolated linearly. For these days, missing begin or end values were extrapolated using the nearest value carried forward or backward method.

2.3.2 Movement Sensors

The sensors that were used to collect movement data were MOX1 Accelerometers (Maastricht Instruments BV). [36] These are lightweight (11 grams), sensors that were attached just above the patients’ right knee.

The accelerometers sampled their change of movement in 3D-space with a frequency of 25Hz. Chosen method of using these accelerometers offers an effective way of reliably measuring movement intensity continuously during the day, whilst not causing the patients unnecessary discomfort. The sensors were used to collect information regarding movement intensities during the daily life of these patients. The accumulated data were processed using algorithm 1. All specified algorithms used in this study were written and executed using MATLAB. This algorithm cleaned, filtered and subsequently analysed the data using thresholds. The algorithms output included movement intensity, defined as the signal magnitude area. From the output, movement intensities per patient per day of measuring were obtained. These intensities were generally defined in the period from 7:00 till 22:00 of those days.

Using algorithm 2, the attained movement intensities from algorithm 1 were in turn converted into mean intensities for each day.

The method of using mean values was adopted to ensure that the average accurately reflects the movement of the patients. Since a patients time during hospitalisation is often spent sedentary or lying down, taking the mean is the best way to include every movement the patient makes, even if those are smaller or shorter.

For days on which only a pain score was recorded but no movement data, movement data was interpolated linearly or extrapolated using the nearest value method. Days that had no original recording of pain nor gait were removed from the dataset. Data preparation was done using algorithm 3.

In order to compare movement data of all patients with each other fairly, movement data was normalized for each patient. This encompasses the subtracting of the mean and division by the standard deviation.

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Algorithm 1 Mox Analysis Algorithm [36]

1: procedure SELECTDATA

2: Read Data from SubjectData folder

3:

4: procedure DEFINEPARAMETERS

5: Part of the Day Between Measurements (timestep) ← 1 day of 24 hours of 60 minutes of 60 seconds with 25 measurements per second → 4.62962963e − 7

6: Preprocessing Windowlength (n) ← 3

7: Order of Filter for Butterworth Filter (FilterOrder) ← 4

8: StartTimeAnalysis← Serial number at 7:00

9: StopTimeAnalysis← Serial number at 22:00

10:

11: procedure ANALYSIS FOR EACHSUBJECTFOLDER 12: for All Subject Folders in the SubjectData Folder.

13: do Select all files with .bin extension

14:

15: for All .bin files

16: do Use custom function(ReadMoxBinStruct) to load the data for each .bin file.

17:

18: procedure DATACLEANING

19: for All data from the .bin files divided into packets (data tot)

20: do Calculate the RootMeanSquare (RMS) for each packet

21:

22: if RMS for a packet > 1

23: then Delete that packet

24:

25: for All packets of data tot

26: do Find all unique values

27: Delete duplicated values on x, y and z-axes

28: Replace deleted duplicates with interpolation

29: Delete spikes

30: Find missing hours between 7:00 and 22:00

31:

32: procedure DATAANALYSIS 33: for Cleaned Data

34: do Calculate and apply moving average filter over dataset

35: Apply Butterworth low pass filter

36: Apply high pass filter

37: Sort data into Static and Dynamic components.

38: Sort data into Static and Dynamic components.

39:

40: if Data is below MLY threshold (thMLY).

41: then Classify Data as Sedentary (sedentaryMOX).

42: elseif Data is above SMA threshold (thSMA).

43: then Classify Data as Dynamic (dynamicMOX).

44: elseif Data is Static but not Sedentary

45: then Classify Data as Standing (standingMOX)

46:

47: procedure COLLECTOUTPUT 48: Outputis:

49: Duration (duration)

50: Movement intensity (Signal Magnitude Area, SMATot)

51: Time spent dynamic (dynamicMOX)

52: Time spent standing (standingMOX)

53: Time spent sedentary (sedentaryMOX)

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Algorithm 2 Averages for MOX Data

1: procedure GETINPUT 2: for All Patients

3: do Get their respective file with movement intensities (PatientFile)

4:

5: if PatientFile is empty

6: then Continue to next patient iteration

7:

8: else Load patient number and days of measuring (PatientInformation) from Patientfile

9:

10: procedure CALCULATEAVERAGES 11: for Each day in PatientFile

12: do:

13:

14: if Movement intensities(intensities) for this day are not found

15: then Continue to next day iteration

16:

17: else Calculate the average intensity for this day

18:

19: if This is the first day iteration

20: then Make a table (output) with PatientInformation and avgs

21:

22: else Add a new entry (newentry) containing PatientInformation and avgs to the output table

23:

24: procedure PRODUCEOUTPUT

25: Filename that the output will be written into (filename) ← ”MOXaverages.xlsx”

26: Write output table into file with filename

2.4 The Participants

A group of patients who had undergone hip surgery was investigated. Data of this group were obtained from the database of the Ziekenhuisgroep Twente (ZGT) hospital in Almelo.

Of all patients who had undergone hip surgery, data of movement sensors was available for n = 84 patients.

Out of those 84 patients, n = 56 patients had at least one record of a pain score. This group of 56 patients was therefore selected as the participants.

2.5 Statistical Analysis

Data was analysed using algorithm 3. In order to design linear models to fit data sets, MATLABs function fitlmwas used [37]. From this model, the estimated linear coefficient, t-statistic, p-value and R²were extracted. Here the t-statistic tests the null hypothesis against the alternative, provided the other predictors in the model. Where the null hypothesis is that the corresponding coefficient is zero, while the alternative hypothesis is that it is different from zero. The p-value indicates the probability that the observed results would be at least this extreme, assuming the null hypothesis is true. The R²value suggests the percentage at which the model explains the variability of the response variable.

Linear regression models were computed for pain against gait. Where for respectively all daily data points, daily data points belonging to separate patients, and average data points per patient, a model was constructed and evaluated.

For time against pain, and time against gait, models were calculated. One model was computed where both pain and gait served as predictors, whereas another two models were calculated for respectively pain and gait as a single predictor.

Causality analysis was done using cross-lagged analysis, for which two models were constructed and evaluated. These models were respectively for pain at a certain day (day m), compared to gait at the day after (day m + 1). And for gait at day m compared to pain at day m + 1.

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Algorithm 3 Data Analysis

1: procedure PREPROCESSINGDATA 2: Read all patients results.

3:

4: for All patients

5: do:

6: Read all information from this patient

7: Assign day numbers to data.

8: Find if patient has no recordings of either pain or gait and continue to next iteration if true.

9: Find days on which both pain and gait information is missing and delete these days

10:

11: Interpolate data using linear interpolation

12: Extrapolate data using ”Nearest” method

13: Normalize inter- and extrapolated movement intensities

14: Create new array containing pain at day m matched with gait at day m + 1

15: Create another array containing gait at day m matched with pain at day m + 1

16:

17: procedure ANALYSINGDATA 18: for All patients

19: do:

20: Fit linear model per patient for average daily painscore compared to average daily movement intensity

21: Fit linear model per patient for time against pain

22: Fit linear model per patient for time against gait

23: Retrieve estimated linear coefficient, t-statistic, p-value and R²from this model and write them into table

24:

25: Create model for total pain against gait

26: Create model for time against pain

27: Create model for time against gait

28: Create model for both pain and gait against time

29: Create model for pain at day m matched with gait at day m + 1

30: Create model for gait at day m matched with pain at day m + 1

31:

32: procedure PLOTTINGRESULTS

33: Plot data for pain against gait and plot linear model

34: Plot data for time against pain and plot linear models per patient

35: Plot data for gait against pain and plot linear models per patient

36: Plot data for pain at day m matched with gait at day m + 1 and plot linear model

37: Plot data for gait at day m matched with pain at day m + 1 and plot linear model

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3 RESULTS

3.1 Correlation Analysis

In order to test data for correlation between pain and gait, a linear model was fit for each separate patient.

All patients and variables illustrating these models can be found in appendix A.

A summary of results found in appendix A is provided in table 1. Herein the total number of patients’

models is mentioned that comply with a certain condition. From table 1 can be deduced that the linear regression model for n = 43 patients has a negative slope. A negative slope implies that as pain increases, gait decreases. n = 12 patients have a model with a positive slope. n = 1 patient has a model with no slope, due to only one data point being input into this particular model.

In n = 6 patients, a significance at the 5% significance level was found, which is interpreted from the p-values. Out of those six patients, n = 5 had a negative slope, while one had a positive slope.

To provide a more complete view of the trends in the data, data from all patients was gathered and plotted info figure 1. This figure shows the average daily painscores plotted against the average daily movement intensity. A linear regression model has been applied to the data, represented by a yellow line. Table 2 shows this linear model and several variables which provide information about this model. For this model, the linear coefficient is estimated at −0.13967, which indicates a downwards slope. The combination of the t-statistic and p-value (8.0372E − 05) for this model indicates that the t-statistic is significant at the five percent significance level. This implies the null hypothesis should be rejected, which means the linear coefficient is not zero. The R²for this model indicates that the model explains 3.3% of the variability in the response variable (gait).

Table 1. A summary of results found in appendix A. Number of patients’ models that comply with specified conditions

Total Population n= 56

Estimated Coefficient > 0 n= 12

Estimated Coefficient < 0 n= 43

Estimated Coefficient = 0 n= 1

p-value ≤ 0.05 n= 6

p-value > 0.05 n= 49

0 ≤ R²< 0.25 n= 43

0.25 ≤ R²< 0.50 n= 8

0.50 ≤ R²< 0.75 n= 1

0.75 ≤ R²≤ 1 n= 3

p-value ≤ 0.05, Estimated Coefficient > 0 n= 1 p-value ≤ 0.05, Estimated Coefficient < 0 n= 5

Table 2. Linear Model fit to pain per day versus gait per day and several variables providing information about this model. Here x₁is pain and y is gait.

Linear Regression Model

Estimated Linear Coefficient for x₁

t-statistic p-value R²

y∼ 1 + x₁ −0.13967 −3.9783 8.0372E − 05 0.0326

In figure 2, the mean of the daily pain scores per patient was plotted against the mean of the daily intensities per patient. This plot was fitted with a linear model, which is described in table 3. The estimated linear coefficient of this model suggests a slight upwards trend (0.0055758) in the data. The p-value (0.84251) shows that the t-statistic is not significant at the 5 percent significance level. This means that the null hypothesis (linear coefficient is zero) cannot be rejected.

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Figure 1. Pain per day plotted against gait per day. Line represents linear model for data.

Figure 2. Mean of daily painscores plotted against mean of daily movement intensities. Line represents linear model for data.

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Table 3. Linear Model fit to pain per patient versus gait per patient and several variables providing information about this model

y∼ 1 + x₁ 0.0055758 0.19964 0.84251 0.000738

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3.2 Time analysis

In figures 3 and 4 the days of hospitalization were plotted against respectively the average daily painscores and average daily movement intensities. Table 4 shows a linear regression model fit to both pain and gait as predictors for time in days. Tables 5 and 6 show linear models and their strengths for the time after surgery against respectively painscores and movement intensities.

The estimated linear coefficients following from the model in table 4 are −0.58729 for x₁and 1.7855 for x₂, which indicated a downwards slope regarding pain but an upwards slope regarding gait. Both p-values in this model suggest a significance at the five percent level, encouraging the t-statistics which are −5.2423 and 12.388 respectively for x₁and x₂.

Figure 3. Time of hospitalization plotted against pain. Each color represents a separate patient. A linear model has been fit for each patient. Models are represented by lines.

Table 4. Linear model fit to both pain and gait against time in days. And several metrics providing information about this model. Here x₁is pain, x₂is gait and y is time.

Linear Regres- sion Model

Estimated Lin- ear Coefficient for x₁

t-statistic for x₁ p-value for x₁ R²

y∼ 1 + x₁+ x₂ −0.58729 −5.2423 2.42E − 07 0.314 Estimated Lin-

ear Coefficient for x₂

t-statistic for x₂ p-value for x₂

1.7855 12.388 1.263E − 30

Table 5. Several metrics and their values for evaluating the time of hospitalization against the average daily painscore. Here x₁is time and y is pain.

y∼ 1 + x₁ −0.10419 −6.7586 4.1398E − 11 0.0886

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Figure 4. Time of hospitalization plotted against gait. A linear model has been fit for each patient.

Models are represented by lines.

Table 6. Several metrics and their values for evaluating the time of hospitalization against the average daily gait performance. Here x₁is time and y is gait.

y∼ 1 + x₁ 0.1423 13.19 6.1156E − 34 0.274

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3.3 Causality Analysis

In order to shed light on a possible causality relationship between pain and gait, cross-lagged analysis was applied.

Appendix B shows linear models fit to separate patients, where respectively pain on day m was compared to gait on day m + 1 and gait on day m compared to pain on day m + 1 was looked at. Summaries of the results found in appendix B are given in tables 7 and 8.

In table 7 can be seen that most (n = 32) patients showed a decrease of gait performance on day m+ 1 with an increase of pain on day m. n = 22 patients showed an increase of gait on day m + 1 with an increase of pain on day m. For n = 14 significant relationships at the five percent level, n = 9 were negative whereas n = 5 were positive. In most instances (n = 30), R²was below 0.25, while for n = 14 patients R²was between 0.25 and 0.50, for n = 5 patients R²was between 0.50 and 0.75 and for n = 6 patients R²was higher than 0.75.

Table 8shows that for n = 39 patients, a negative slope was detected. For n = 15 patients this slope was positive. Out of the n = 5 relationships significant at the five percent level, n = 4 were negative. R²was mostly lower than 0.25.

Comparing table 7 to table table 8, it can be seen that a higher percentages of cases show a negative slope when looking at gait on day m compared to pain on day m + 1. This might be due to high movement on one day leading to more pain the next day.

Table 7. A summary of results found in appendix B. Number of patients’ models that comply with specified conditions. Note that population consists of only 55 patients, since lagged analysis was not possible with one original datapoint.

p-value ≤ 0.05 n= 14

p-value > 0.05 n= 40

0 ≤ R²< 0.25 n= 30

0.25 ≤ R²< 0.50 n= 14

0.50 ≤ R²< 0.75 n= 5

0.75 ≤ R²≤ 1 n= 6

Figure 5shows pain against gait, where pain on one day (day m) was plotted against gait on the next day (day m + 1). On the other hand, figure 6 shows gait against pain, where gait on one day (day m) was plotted against pain on the next day (day m + 1). Table 9 shows a model fit to the data of pain at day m, compared to the gait at day m + 1. From the model can be deduced that the estimated linear coefficient equal is to −0.13584. This downwards slope indicates a decrease of gait on day m + 1 with an increase of pain on day m. The t-statistic is −4.1239, which is supported by a p-value of 4.5186e − 05, which indicated a significance at the five percent significance level. The value of R²suggests that the model explains 27% of the variability.

Another model was fit using the gait on day m against the pain at day m + 1. The t-statistic in the model is −3.2566, which is supported by a p-value of 0.0012219. This p-value suggests a significance at the five percent significance level. The R²value (0.0254) argues that 2.5% of variability is explained by this model.

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Table 8. A summary of results found in appendix B. Number of patients’ models that comply with specified conditions. Note that population consists of only 55 patients, since lagged analysis was not possible with one original datapoint.

p-value ≤ 0.05 n= 5

p-value > 0.05 n= 49

0 ≤ R²< 0.25 n= 39

0.25 ≤ R²< 0.50 n= 11

0.50 ≤ R²< 0.75 n= 3

0.75 ≤ R²≤ 1 n= 2

Figure 5. The average daily pain score on a certain day plotted against the average daily movement intensity on the next day. A linear model has been fit and is represented by an orange line in the graph.

Table 9. Several metrics and their values for evaluating the pain on day m against the average gait on day m+ 1. Here x1is pain on day m and y is gait on day m + 1.

y∼ 1 + x₁ −0.13584 −4.1239 4.5186E − 05 0.0401

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Figure 6. The average daily movement intensity on a certain day plotted against the average daily pain score on the next day. A linear model has been fit and is represented by an orange line in the graph.

Table 10. A linear model fit to the gait on day m against the gait on day m+1 and several metrics providing information about this model. Here x₁is gait on day m and y is pain on day m + 1.

y∼ 1 + x₁ −0.19906 −3.2566 0.0012219 0.0254

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4 DISCUSSION

4.1 Key findings and interpretation

Information about pain and gait during hospitalization after hip surgery of the n = 56 participants was analysed and it was found that in a large majority (n = 43) of the patients, a trend was present which implied a decrease of movement with an increase of pain. This could be due to pain causing patients to want to reduce movement. The remaining patients whose model showed a positive slope, could be explained by increased movement causing more pain, and therefore pain increasing with movement.

t-statistics were in 6 of 56 cases significant at the five percent significance level. Out of these 6 cases, n= 5 showed a negative slope. However, in n = 49 cases, the R²value for the model suggested that the model explained for less than 25% of the variability in the response value (gait). This information implies that, though many times the null hypothesis could successfully be rejected, there is a lot of variability left unexplained by the model. The variability could be explained due to several factors, which will be covered in the next section.

As for the model fit to the total data where pain is compared to gait, a negative slope was implied.

This supports the previous results of the separate models, that the movement decreases as pain increases.

Yet, similar to previous models, this model explains little of the variability in the data.

When comparing the mean of the daily painscores per patient to the mean of daily movement intensities per patient, the null hypothesis could not be rejected meaning no linear relationship can be found. This could be explained by several of the factors elaborated upon in next section. It could also be explained by the fact that the used averages of the patients for this model are not dependent on time, since time might be a relevant factor.

When in turn looking at time against pain, it can be concluded that a downwards trend is present.

The t-statistic for the data is significant at the five percent significance level. This implies that as days of hospitalization increase, the pain decreases. Merely 8.9% of variability is explained by this model however. The lack of explanation for variability might be due to the use of a relatively small population.

The found trend could be explained by a recovery being accompanied by a gradual decrease in pain in most instances. This finding is in line with literature, showing a decrease in pain with time after hip surgery [23, 26, 30].

A model for time against gait, shows an upwards trend. This suggests that movement increases as time of hospitalization increases too. The t-statistic for this model is significant at the five percent significance level. An R²value of 0.274 suggests that 27.4% of variability in the response variable, gait, is explained by this model. An upwards trend could be explained due to increased mobility as the muscles around the hip recover after surgery. In literature, gait performance is shown to increase with time after hip surgery as well [38].

The linear regression model for both pain and gait as predictors for time showed a negative estimated coefficient for pain, while that for gait was positive. p-values for both variables showed significance at the five percent level. The model covered 31.4% of the variability. This finding supports previously mentioned relationships between time and respectively pain and gait.

Causality analysis for pain on a certain day compared to gait on the next day again showed a negative trend, implying that higher pain on day m goes together with lower movement on day m + 1. The t-statistic for this model is proven significant at the five percent significance level.

Similarly when comparing gait on day m with pain on day m + 1, the model shows a downward slope.

This implies that gait higher gait on day m goes together with lower pain on day m + 1.

It can be seen that for separate patients, a higher amount of negative slopes are present when looking at gait on day m compared to pain on day m + 1. This could imply a higher likelihood of increased gait causing increased pain than the other way around.

In line with the study of Erlenwein et al. [25], results summarized above support a decrease in gait as pain increases. Yet, linear models cannot successfully explain variability of data.

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4.2 Strengths and shortcomings of the study

The procuring and studying of data from databases took place over a period of ten weeks. Therefore several shortcomings can be named with regards to the study.

Firstly, information of n = 56 total participants was used for this study. Per patient the amount of data points varied strongly, with a minimum of 1 datapoint and a maximum of 12 datapoints before preprocessing the data. A larger participant group would have extended the reliability of the results.

Since results were inter- and extrapolated during preprocessing of data, bias might have been introduced in this data as a result.

Linear regression models have been fit to the retrieved data, however no other type of models have been attempted during this study. Even though linear regression models often suggested a reduction of gait with an increase of pain, those same models frequently did not explain most of the variability in the response variable. This is a large shortcoming to the linear models, which has to be critically taken into consideration when deducing any conclusion from these models.

Existing evidence with regards to the relationship between pain and gait in hip patients is highly limited, since it is a largely unexplored topic. Identified results were, however, in line with the known literature that they were compared to during this study.

In this study, NRS was used to measure pain [31]. NRS is considered a valid metric for pain, although, since patients have to judge their own pain it is inherently subjective. As a metric for functional recovery, movement intensities were calculated from data extracted from a movement sensor. Wearable movement sensors are considered valid, though they might not account for increased energy cost or varying load of carriages [20, 21].

Another shortcoming of this study is that pain medication was not taken into account upon reviewing data.

Since most or all patients received pain medication, this will have influenced their painscores at different times during the day.

4.3 Recommendations

Following the results and shortcoming of this research, recommendations for further research are mentioned below.

The results suggested a decrease of movement with an increase of pain, however further research with a larger group of participants is necessary to verify or reject this trend. Additionally, it is recommended that pain is recorded more frequently to prevent the necessity for data imputation, accompanied by a potential introduction of bias in the results.

In order to include the various factors of functional recovery, it is also recommended to use movement sensors in combination with additional tests and observations to more holistically judge functional recovery.

Pain medication should be factored in in future studies, by recording analgesic consumption during hospitalization.

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5 CONCLUSIONS

From results can be concluded that linear models for pain against gait repetitively show a decrease in gait with an increase of pain. No relationship could be found between average pain per patient and average gait per patient. Furthermore, linear models showed pain decreases with time of hospitalization while gait increases with time. Causality analysis simultaneously showed a decrease in gait on day m + 1 with an increase of pain on day m, as a decrease in pain on day m + 1 with an increase of gait on day m. No clear causality could be deduced from this. Linear models do in no case suffice to explain the variability of the data. Findings were in line with that of literature.

Further research is necessary in order to support or reject conclusions of this study.

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APPENDICES

Appendix A: All patients and linear models fit to their pain and gait.

Individual models have been fit to the pain and gait data of all patients separately, which can be found in table 11. The linear regression model for each patient is y ∼ 1 + x₁, where x₁is pain and y is gait.

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Table 11. All patients and their linear coefficient for pain against gait, t-statistic, R²and p-value Patient# Linear Coefficient t-statistic R² p-value

Up&Go45 0.16109 0.3721 0.044118 0.73455

Up&Go49 -0.0034024 -0.010146 1.7158E-05 0.99223

Up&Go52 0.44245 0.74637 0.15661 0.50961

Up&Go61 -0.22648 -0.20309 0.0051294 0.84413

Up&Go62 -0.045488 -0.12764 0.0014789 0.90074

Up&Go63 -0.22977 -0.33799 0.014078 0.74407

Up&Go69 0.93645 1.3081 0.29962 0.26094

Up&Go70 -1.2098 -1.1159 0.19939 0.3152

Up&Go73 -0.048863 -0.17984 0.0053614 0.8632

Up&Go74 -0.68959 -2.1778 0.30127 0.052064

Up&Go76 -0.06722 -0.16159 0.0051954 0.87795

Up&Go77 -0.36389 -2.5922 0.30938 0.020412

Up&Go80 -0.72715 -2.15 0.36621 0.063775

Up&Go85 0.45132 0.37492 0.033948 0.72675

Up&Go88 -0.25412 -1.595 0.24127 0.14938

Up&Go94 -0.053536 -0.12077 0.0029087 0.90857 Up&Go99 0.016995 0.048648 0.00019718 0.962

Up&Go103 -0.43025 -0.28354 0.013222 0.78629

Up&Go104 -0.52819 -2.2804 0.25744 0.037618

Up&Go107 -0.45677 -2.129 0.24457 0.051492

Up&Go112 -0.98962 -2.2771 0.39325 0.052311

Up&Go114 -3.2613E-16 -1.3045E-15 0 1

Up&Go115 -0.5115 -1.3278 0.18058 0.22089

Up&Go120 -0.15323 -0.70764 0.091034 0.51078

Up&Go121 -0.24539 -0.47698 0.053816 0.65827

Up&Go122 -0.069693 -0.35406 0.024459 0.73773 Up&Go123 -0.0020801 -0.0028234 1.3286e-06 0.99784

Up&Go125 -0.65068 -1.0867 0.16444 0.3189

Up&Go126 -0.3295 -0.60028 0.056654 0.57028

Up&Go129 -0.6807 -2.1726 0.44031 0.072798

Up&Go130 -0.39859 -0.88271 0.079678 0.40035

Up&Go132 -0.42162 -1.4815 0.21529 0.17675

Up&Go133 -1.394E-16 ∞ 1 0

Up&Go138 0.14461 0.36698 0.016556 0.72315

Up&Go140 0.045236 0.061069 0.00062119 0.95329

Up&Go141 -0.12892 -0.36116 0.031579 0.73625

Up&Go142 -1.3248 -9.276 0.95558 0.00075126

Up&Go143 -0.35808 -0.95077 0.11437 0.37338

Up&Go146 -0.068751 -0.24507 0.014793 0.81846

Up&Go153 0.12543 0.22836 0.010322 0.82841

Up&Go158 -1.4072 -2.3577 0.52647 0.064933

Up&Go159 -0.35053 -0.36419 0.025842 0.73061

Up&Go161 0.51503 5.5552 0.83722 0.0014392

Up&Go162 -0.33333 -0.5 0.11111 0.66667

Up&Go168 0 NaN* NaN* NaN*

Up&Go169 -0.045858 -0.17862 0.0079133 0.86692

Up&Go171 -0.30773 -0.62622 0.041753 0.54673

Up&Go173 0.42942 0.7955 0.13659 0.47086

Up&Go174 -0.55584 -2.4699 0.40398 0.035578

Up&Go175 -0.36013 -0.57904 0.077338 0.59361

Up&Go176 -0.22802 -0.89979 0.10367 0.39813

Up&Go177 -0.080405 -0.062322 0.001293 0.95423

Up&Go178 0.2354 0.68068 0.071686 0.52146

Up&Go179 -0.22927 -0.9693 0.19021 0.38729

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*Not a number (NaN). These values could not be calculated for this patient due to only one datapoint being available.

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Appendix B: All patients and linear models for causality analysis.

Individual models have been fit to the pain on day m and gait on day m + 1 data of all patients separately, which can be found in table 12. The linear regression model for each patient is y ∼ 1 + x₁, where x₁is pain on day m and y is gait on day m + 1.

Similarly, individual models for gait on day m versus pain on day m + 1 were fit and displayed in table 13