Descriptive statistics

Descriptive stats at baseline

## Number of subjects: 120
## Number of subjects in control group: 60
## Number of subjects in treatment group: 60
## 
##  Age treatment
## Mean: 67.9598448551221
## Standard Deviation: 8.68625493698399
## Range:
## 48.5639972621492 - 87.3593429158111
## 
##  Age control
## Mean: 66.6892083048141
## Standard Deviation: 11.2674775428205
## Range:
## 40.7008898015058 - 86.3846680355921
## 
##  Height treatment
## Mean: 169.947368421053
## Standard Deviation: 8.07425594234889
## Range:
## 156  -  189
## 
##  Height control
## Mean: 171.077586206897
## Standard Deviation: 7.82248318593223
## Range:
## 156  -  190
## 
##  Weight treatment
## Mean: 82.359649122807
## Standard Deviation: 15.3796463321904
## Range:
## 59  -  129
## 
##  Weight control
## Mean: 82.801724137931
## Standard Deviation: 13.0686244243079
## Range:
## 57  -  112
## 
##  BMI treatment
## Mean: 28.4109769648317
## Standard Deviation: 4.16643954511763
## Range:
## 21.585557299843  -  37.448347107438
## 
##  BMI control
## Mean: 28.2710240901857
## Standard Deviation: 3.98320553533097
## Range:
## 21.4535737137265  -  38.5674931129477
## 
##  Hypertension
## Percentage in treatment: 55
## Percentage in control: 41.6666666666667
## 
##  Ischemic heart disease
## Percentage in treatment: 8.33333333333333
## Percentage in control: 0
## 
##  Coronary artery disease
## Percentage in treatment: 5
## Percentage in control: 6.66666666666667
## 
##  Stroke
## Percentage in treatment: 3.33333333333333
## Percentage in control: 0
## 
##  High cholesterol
## Percentage in treatment: 35
## Percentage in control: 33.3333333333333
## 
##  Diabetes
## Percentage in treatment: 11.6666666666667
## Percentage in control: 15
## 
##  Hypothyroidism
## Percentage in treatment: 15
## Percentage in control: 11.6666666666667
## 
##  Asthma
## Percentage in treatment: 5
## Percentage in control: 18.3333333333333
## 
##  Dementia
## Percentage in treatment: 0
## Percentage in control: 0
## 
##  Cancer
## Percentage in treatment: 6.66666666666667
## Percentage in control: 11.6666666666667
## 
##  Sciatica
## Percentage in treatment: 26.6666666666667
## Percentage in control: 30
## 
##  Osteoporosis
## Percentage in treatment: 0
## Percentage in control: 0
## 
##  Osteoarthritis
## Percentage in treatment: 45
## Percentage in control: 51.6666666666667
## 
##  Baseline WOMAC score in treatment
## Mean: 39.7692307692308
## Standard Deviation: 14.843781803173
## Range:
## 10  -  74
## 
##  baseline WOMAC score in control
## Mean: 40.6938775510204
## Standard Deviation: 13.3607074438953
## Range:
## 16  -  73
## 
##  Baseline HHS treatment
## Mean: 55.3428571428571
## Standard Deviation: 19.2163434904473
## Range:
## 14.6  -  95.95
## 
##  Baseline HHS control
## Mean: 68.2060344827586
## Standard Deviation: 12.0385786215342
## Range:
## 39  -  92

Descriptive stats at Follow-up

## 
##  Follow up WOMAC score treatment
## Mean: 9.22222222222222
## Standard Deviation: 10.0065635025873
## Range:
## 0  -  44
## 
##  Follow up WOMAC score control
## Mean: 34.8484848484849
## Standard Deviation: 18.6750522290455
## Range:
## 4  -  62
## 
##  Follow up HHS treatment
## Mean: 91.5166666666667
## Standard Deviation: 7.17868530632683
## Range:
## 62.95  -  96
## 
##  Follow up HHS control
## Mean: 76.6907894736842
## Standard Deviation: 14.2466205346104
## Range:
## 53.25  -  96

WP4 (per protocol)

Investigating the effects of intervention on treatment group and comparing it with control group

# here is where the data was converted to long format, including it to confirm if it was done correctly

long_data_wmc <- wp1_data %>%
  pivot_longer(cols = c(bl_wmc_sum, fup6_wmc_sum, fup12_wmc_sum), names_to = "time_point", values_to = "outcome")

long_data_hhs <- wp1_data %>%
  pivot_longer(cols = c(bl_hhs_total, fup_hhs_total), names_to = "time_point", values_to = "outcome")

Analysis

Normality testing

Shapiro-Wilk normality testing

This is a summary of all the shapiro wilk tests for normality carried out below

baseline WOMAC in group 1 : normally distributed
baseline WOMAC in group 2 : normally distributed
baseline HHS in group 1 : normally distributed
baseline HHS in group 2 : not normally distributed
follow-up WOMAC in group 1 : not normally distributed
follow-up WOMAC in group 2 : not normally distributed
follow-up HHS in group 1 : not normally distributed
follow-up HHS in group 2 : not normally distributed

I used parametric methods for testing (based on large sample size), we need to confirm from a statistician whether this is okay considering the distribution of data.

## [1] "Shapiro-Wilk test for testing normality of distribution of baseline WOMAC in both groups "
## $`1`
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.98199, p-value = 0.8217
## 
## 
## $`2`
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.98509, p-value = 0.6138
## [1] "Histogram of distribution of baseline WOMAC in both groups "

## [1] "Shapiro-Wilk test for testing normality of distribution of baseline HHS in both groups "
## $`1`
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.95129, p-value = 0.0777
## 
## 
## $`2`
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.95782, p-value = 0.01561
## [1] "Histogram of distribution of baseline HHS in both groups "

## [1] "Shapiro-Wilk test for testing normality of distribution of follow-up WOMAC in both groups "
## $`1`
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.93496, p-value = 0.05993
## 
## 
## $`2`
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.84257, p-value = 1.657e-05
## [1] "Histogram of distribution of follow-up WOMAC in both groups "

## [1] "Shapiro-Wilk test for testing normality of distribution of follow- up HHS in both groups "
## $`1`
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.89771, p-value = 0.003434
## 
## 
## $`2`
## 
##  Shapiro-Wilk normality test
## 
## data:  X[[i]]
## W = 0.68018, p-value = 6.029e-09
## [1] "Histogram of distribution of follow-up HHS in both groups "

Results

T-tests

Comparing mean WOMAC in both groups at baseline and follow-up

Baseline: The t-test was conducted to compare the baseline WOMAC scores of Group 1 and Group 2. The calculated t-value was -2.18 with 99 degrees of freedom. The associated p-value was 0.03, which is less than the chosen significance level of 0.05. Since the p-value is more than the chosen significance level (α = 0.05), we reject the null hypothesis. This indicates that there was a significant difference in baseline WOMAC scores between Group 1 and Group 2, with mean score being higher in group 2. Effect size of this difference was small to medium (Cohen’s D = 0.46)

Follow-up: The t-test was conducted to compare the follow-up womac scores of Group 1 and Group 2. The calculated t-value was 8.48 with 76 degrees of freedom. The associated p-value was <0.001 , which is less than the chosen significance level of 0.05. Since the p-value is less than the chosen significance level (α = 0.05), we reject the null hypothesis. This indicates that there Was a significant difference in follow-up WOMAC scores between Group 1 and Group 2, with mean score being lower in group 2. The effect size for the difference was large (Cohen’s D > 0.8).

## WOMAC scores in treatment and control gorup at baseline
## 
##  Two Sample t-test
## 
## data:  bl_wmc_sum by tvcco
## t = -2.1879, df = 99, p-value = 0.03103
## alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0
## 95 percent confidence interval:
##  -12.0579748  -0.5887784
## sample estimates:
## mean in group 1 mean in group 2 
##        36.08571        42.40909
## 
##  Effect size (cohen's D)
## [1] 0.4574987
## WOMAC scores in treatment and control gorup at follow-up
## 
##  Two Sample t-test
## 
## data:  fup12_wmc_sum by tvcco
## t = 8.4843, df = 76, p-value = 1.299e-12
## alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0
## 95 percent confidence interval:
##  20.68910 33.38228
## sample estimates:
## mean in group 1 mean in group 2 
##       36.354839        9.319149
## 
##  Effect size (cohen's D)
## [1] 1.963054

HHS: Comparing mean HHS in both groups at baseline and follow-up

Baseline: The t-test was conducted to compare the baseline Harris hip scores of Group 1 and Group 2. The calculated t-value was 3.56 with 112 degrees of freedom. The associated p-value was <0.001, which is less than the chosen significance level of 0.05. Since the p-value is less than the chosen significance level (α = 0.05), we reject the null hypothesis. This indicates that there was significant difference in means of baseline Harris hip score between Group 1 and Group 2, with mean score being lower in group 2.The effect size for the difference was medium to large (Cohen’s d = 0.69).

Follow-up: The t-test was conducted to compare the follow-up Harris hip scores of Group 1 and Group 2. The calculated t-value was -6.44 with 81 degrees of freedom. The associated p-value was <0.001, which is less than the chosen significance level of 0.05. Since the p-value is less than the chosen significance level (α = 0.05), we reject the null hypothesis. This indicates that there was significant difference in means of follow-up Harris hip score between Group 1 and Group 2, with mean score being higher in group 2. The effect size for the difference was large (Cohen’s d > 0.8).

## HHS in treatment and control gorup at baseline
## 
##  Two Sample t-test
## 
## data:  bl_hhs_total by tvcco
## t = 3.5683, df = 112, p-value = 0.0005302
## alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0
## 95 percent confidence interval:
##   5.059251 17.692871
## sample estimates:
## mean in group 1 mean in group 2 
##        69.17195        57.79589
## 
##  Effect size (cohen's D)
## [1] 0.6964006
## HHS in treatment and control group at follow-up
## 
##  Two Sample t-test
## 
## data:  fup_hhs_total by tvcco
## t = -6.4407, df = 81, p-value = 7.912e-09
## alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0
## 95 percent confidence interval:
##  -20.25124 -10.69215
## sample estimates:
## mean in group 1 mean in group 2 
##        75.78143        91.25313
## 
##  Effect size (cohen's D)
## [1] 1.431596

ANCOVA

ANCOVA: Testing the difference in mean follow-up WOMAC scores

ANCOVA was carried out for testing the difference in mean follow-up WOMAC scores between treatment and control groups, while controlling/adjusting for baseline differences in mean WOMAC scores

The independent variable tvcco (Treatment) demonstrated a highly significant effect on the dependent variable (follow-up WOMAC score)(estimate = -27.4139, SE = 3.2386, t value = -8.465, p < 0.001***) i.e there was a difference of approximately -27.4 points in WOMAC scores of both groups after controlling for the baseline values.

The co-variate “baseline womac score” was marginally significant, suggesting a potential influence on the dependent variable.

# ANCOVA



model_ancova_wmc = lm (fup12_wmc_sum ~ bl_wmc_sum + tvcco ,
              data = wp1_data) # Is the model selection okay?

summary(model_ancova_wmc)
## 
## Call:
## lm(formula = fup12_wmc_sum ~ bl_wmc_sum + tvcco, data = wp1_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -29.123  -7.363  -1.331   8.435  35.070 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  25.8778     4.8430   5.343 1.18e-06 ***
## bl_wmc_sum    0.2684     0.1153   2.327    0.023 *  
## tvcco2      -27.4139     3.2386  -8.465 3.50e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.03 on 67 degrees of freedom
##   (50 observations deleted due to missingness)
## Multiple R-squared:  0.5204, Adjusted R-squared:  0.5061 
## F-statistic: 36.35 on 2 and 67 DF,  p-value: 2.044e-11
# Checking assumptions of the model
 
hist(residuals(model_ancova_wmc),
     col="darkgray")

## A histogram of residuals from a linear model.

plot(fitted(model_ancova_wmc),
     residuals(model_ancova_wmc))

ANCOVA:Testing the difference in mean follow-up Harris hip scores

ANCOVA was carried out for testing the difference in mean follow-up Harris hip scores between treatment and control groups, while controlling/*adjusting for baseline differences in mean Harris hip scores

The independent variable tvcco (Treatment) demonstrated a highly significant effect on the dependent variable (follow-up Harris hip score)(estimate = 17.34785, SE = 2.72063, t value = 6.376, p < 0.001***) i.e there was a difference of approximately 17 points in HHS scores of both groups after controlling for the baseline values.

The co-variate “baseline Harris hip sccore” was not significant, suggesting no influence on the dependent variable.

model_ancova_hhs = lm (fup_hhs_total ~ bl_hhs_total + tvcco ,
              data = wp1_data)

summary(model_ancova_hhs)
## 
## Call:
## lm(formula = fup_hhs_total ~ bl_hhs_total + tvcco, data = wp1_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -27.634  -8.172   1.945   5.329  21.645 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  69.33487    6.13483  11.302  < 2e-16 ***
## bl_hhs_total  0.08284    0.08114   1.021    0.311    
## tvcco2       17.34785    2.72063   6.376 1.34e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.75 on 75 degrees of freedom
##   (42 observations deleted due to missingness)
## Multiple R-squared:  0.3715, Adjusted R-squared:  0.3548 
## F-statistic: 22.17 on 2 and 75 DF,  p-value: 2.725e-08
# Checking assumptions of the model
 
hist(residuals(model_ancova_hhs),
     col="darkgray")

## A histogram of residuals from a linear model.

plot(fitted(model_ancova_hhs),
     residuals(model_ancova_hhs))

MIXED MODELS

Linear mixed model for testing differences in follow-up WOMAC scores

The mixed-effects model was fitted to investigate the impact of the treatment variable (tvcco) on the outcome variable (WOMAC scores), accounting for potential interactions with time_point and individual-specific variations (id).

The results revealed that there was no significant difference in WOMAC scores between both groups at baseline (tvcco2, Est. 5.78, p-value = 0.06). The WOMAC score was significantly lower in group 2 at both 6 month (tvcco2:time_pointfup6_wmc_sum, Est. -19.79, p-value < 0.001) and 12 month (tvcco2:time_pointfup12_wmc_sum, Est. -30.71, p-value <0.001) follow up.

Pairwise comparisons revealed no significant differences in baseline WOMAC scores and scores at 6-month and 12-month follow-ups within Group 1. In Group 2, WOMAC scores were significantly lower at both the 6-month and 12-month follow-up assessments compared to the baseline scores within the same group. No significant differences were observed in baseline WOMAC scores between the two groups. However, at both the 6-month and 12-month follow-up time points, WOMAC scores were significantly lower in Group 2 compared to Group 1

#mixed model

l2 <- lmer(outcome ~ tvcco * time_point + (1|id), data = long_data_wmc, REML= FALSE)
summ(l2)
Observations 262
Dependent variable outcome
Type Mixed effects linear regression
AIC 2115.52
BIC 2144.07
Pseudo-R² (fixed effects) 0.39
Pseudo-R² (total) 0.71
Fixed Effects
Est. S.E. t val. d.f. p
(Intercept) 36.42 2.46 14.78 194.92 0.00
tvcco2 5.78 3.05 1.89 193.24 0.06
time_pointfup12_wmc_sum -0.31 2.63 -0.12 166.10 0.91
time_pointfup6_wmc_sum -4.20 2.55 -1.64 161.71 0.10
tvcco2:time_pointfup12_wmc_sum -30.71 3.34 -9.21 167.86 0.00
tvcco2:time_pointfup6_wmc_sum -19.79 3.25 -6.09 164.62 0.00
p values calculated using Satterthwaite d.f.
Random Effects
Group Parameter Std. Dev.
id (Intercept) 10.75
Residual 10.23
Grouping Variables
Group # groups ICC
id 110 0.52 
lsmeans(l2, pairwise~tvcco * time_point)
## Registered S3 methods overwritten by 'broom':
##   method            from  
##   tidy.glht         jtools
##   tidy.summary.glht jtools
## $lsmeans
##  tvcco time_point    lsmean   SE  df lower.CL upper.CL
##  1     bl_wmc_sum      36.4 2.49 202     31.5     41.3
##  2     bl_wmc_sum      42.2 1.82 197     38.6     45.8
##  1     fup12_wmc_sum   36.1 2.61 216     31.0     41.3
##  2     fup12_wmc_sum   11.2 2.07 236      7.1     15.3
##  1     fup6_wmc_sum    32.2 2.56 208     27.2     37.3
##  2     fup6_wmc_sum    18.2 2.03 229     14.2     22.2
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast                                    estimate   SE  df t.ratio p.value
##  tvcco1 bl_wmc_sum - tvcco2 bl_wmc_sum         -5.782 3.09 200  -1.872  0.4222
##  tvcco1 bl_wmc_sum - tvcco1 fup12_wmc_sum       0.305 2.66 173   0.115  1.0000
##  tvcco1 bl_wmc_sum - tvcco2 fup12_wmc_sum      25.238 3.24 216   7.788  <.0001
##  tvcco1 bl_wmc_sum - tvcco1 fup6_wmc_sum        4.196 2.59 169   1.622  0.5849
##  tvcco1 bl_wmc_sum - tvcco2 fup6_wmc_sum       18.208 3.21 213   5.669  <.0001
##  tvcco2 bl_wmc_sum - tvcco1 fup12_wmc_sum       6.088 3.18 210   1.912  0.3977
##  tvcco2 bl_wmc_sum - tvcco2 fup12_wmc_sum      31.020 2.09 178  14.867  <.0001
##  tvcco2 bl_wmc_sum - tvcco1 fup6_wmc_sum        9.978 3.14 204   3.178  0.0210
##  tvcco2 bl_wmc_sum - tvcco2 fup6_wmc_sum       23.991 2.04 177  11.766  <.0001
##  tvcco1 fup12_wmc_sum - tvcco2 fup12_wmc_sum   24.933 3.33 224   7.483  <.0001
##  tvcco1 fup12_wmc_sum - tvcco1 fup6_wmc_sum     3.890 2.62 162   1.483  0.6757
##  tvcco1 fup12_wmc_sum - tvcco2 fup6_wmc_sum    17.903 3.30 221   5.419  <.0001
##  tvcco2 fup12_wmc_sum - tvcco1 fup6_wmc_sum   -21.043 3.29 219  -6.395  <.0001
##  tvcco2 fup12_wmc_sum - tvcco2 fup6_wmc_sum    -7.030 2.17 167  -3.243  0.0176
##  tvcco1 fup6_wmc_sum - tvcco2 fup6_wmc_sum     14.013 3.26 216   4.296  0.0004
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 6 estimates

Linear mixed model for testing differences in follow-up Harris hip scores

The mixed-effects model was fitted to investigate the impact of the treatment variable (tvcco) on the outcome variable (Harris hip scores), accounting for potential interactions with time_point and individual-specific variations (id). The results revealed that the baseline Harris hip scores were significantly lower in group2 when compared to group 1 (tvcco2, Estimate = -11.44, SE = 2.76, t value = -4.15, p = <0.001). At follow-up, the Harris Hip score was significantly higher in group 2 when compared to group 1 (tvcco2:time_pointfup_hhs_total , Estimate = 27.31 , SE = 3.95, t value = 6.92, p = <0.001)

Pairwise comparisons revealed no significant difference in baseline and follow-up HHS in group 1. On the other hand, the follow-up HHS was significantly higher in group 2 when compared to the baseline score in the same group.

l3 <- lmer(outcome ~ tvcco * time_point + (1|id), data = long_data_hhs, REML= FALSE)
summ(l3)
Observations 197
Dependent variable outcome
Type Mixed effects linear regression
AIC 1613.64
BIC 1633.34
Pseudo-R² (fixed effects) 0.46
Pseudo-R² (total) 0.53
Fixed Effects
Est. S.E. t val. d.f. p
(Intercept) 69.22 2.21 31.34 193.71 0.00
tvcco2 -11.44 2.76 -4.15 193.87 0.00
time_pointfup_hhs_total 6.18 3.06 2.02 77.50 0.05
tvcco2:time_pointfup_hhs_total 27.31 3.95 6.92 84.52 0.00
p values calculated using Satterthwaite d.f.
Random Effects
Group Parameter Std. Dev.
id (Intercept) 5.10
Residual 13.19
Grouping Variables
Group # groups ICC
id 119 0.13 
lsmeans(l3, pairwise~tvcco * time_point)
## $lsmeans
##  tvcco time_point    lsmean   SE  df lower.CL upper.CL
##  1     bl_hhs_total    69.2 2.23 199     64.8     73.6
##  2     bl_hhs_total    57.8 1.67 199     54.5     61.1
##  1     fup_hhs_total   75.4 2.42 200     70.6     80.2
##  2     fup_hhs_total   91.3 2.07 201     87.2     95.3
## 
## Degrees-of-freedom method: kenward-roger 
## Confidence level used: 0.95 
## 
## $contrasts
##  contrast                                    estimate   SE    df t.ratio
##  tvcco1 bl_hhs_total - tvcco2 bl_hhs_total      11.44 2.79 198.8   4.102
##  tvcco1 bl_hhs_total - tvcco1 fup_hhs_total     -6.18 3.09  96.8  -1.998
##  tvcco1 bl_hhs_total - tvcco2 fup_hhs_total    -22.05 3.04 200.2  -7.248
##  tvcco2 bl_hhs_total - tvcco1 fup_hhs_total    -17.63 2.94 199.8  -5.996
##  tvcco2 bl_hhs_total - tvcco2 fup_hhs_total    -33.49 2.53 116.4 -13.232
##  tvcco1 fup_hhs_total - tvcco2 fup_hhs_total   -15.86 3.18 200.7  -4.988
##  p.value
##   0.0003
##   0.1958
##   <.0001
##   <.0001
##   <.0001
##   <.0001
## 
## Degrees-of-freedom method: kenward-roger 
## P value adjustment: tukey method for comparing a family of 4 estimates