Trade-off between costs and quality of care
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A. Regarding section 2.4 – checking model assumptions/outliers/missing values/interpretation of changes in MCS 8
We tested regression assumptions with regard to normality of residuals and multicollinearity. Kolmogorov-Smirnov Test indicated normality of residuals. Variance inflation factor (VIF) statistics with a cut-off value>10 indicated that multicollinearity was not present [1]. For more information on VIF statistics, please see below (section B). We analysed studentized residuals and cook’s d to identify outliers and excluded two cases with extreme values. For missing data we assumed missing completely at random. We imputed missing values by the group mean for the only variable with missing values, the variable BMI at admission (less than 3%).
We computed effect sizes according to Cohen’s d to evaluate magnitude of change in MCS 8 scores [2]. We assessed whether the change in overall functioning of mental health was clinically meaningful and perceptible by the patient using the minimal clinical important difference (MCID) [3]. For Short Form Surveys the MCID for changes in the mental component summary (MCS) is typically around 3 points [4, 5].
B. Regarding Section 2.4 -Variance Inflation Factor (VIF) statistics
VIF is a statistic which expresses to what extent multicollinearity among independent variables negatively impacts the precision of the estimation in a regression model. Multicollinearity results from strong linear relationships among independent variables. VIF for Xj is computed as
where p is the number of predictor variables and Rj2 the square of the multiple correlation coefficient that results from regressing Xj on all the other independent variables. Each model in which an independent variable is regressed on all the remaining predictor variables will generate a R2 value and VIF value. If Xj is strongly correlated with the other independent variables, then R2 would be close to 1 and VIF be large. VIF values that exceed 10 may be taken as sign that multicollinearity is present in the data potentially causing problems in estimation. If Xj is linearly independent from the other predictors, then R2 would be 0 and the VIF value 1 [1, 6]. In this study we used a cut-off value of VIF>10 to avoid multicollinearity issues.
C. Regarding section 2.5 – Inclusion of covariates in the model
In the regression analysis, we controlled for the patient characteristics “age”, “gender”, “body mass index at admission” [7-9]. “Body mass index at admission” was included since there is evidence that patients with chronic pain undergoing psychosomatic treatment have a more positive mental health outcome if the BMI is lower [10, 11].It is known that socio-demographic variables play a major role for treatment success in patients with chronic pain [9, 12]. We included the variable “civil status” to control for different levels of social support. Marriage may reinforce the patient’s “sick role” exacerbating symptoms, or may have a positive effect on the patient’s symptoms [13]. Furthermore it is well known that divorced, widowed or separated individuals display worse mental health in comparison to married or cohabiting individuals [14, 15]. We controlled for “work status”, since unemployment and receiving compensation are negative predictors of outcome in pain patients. If disability pension is dependent on the continuation of symptoms, the patient may become stuck in a sick role [13, 16, 17].We included a variable for “formal school education in years”, since there is evidence that low levels of education are related to chronic pain [7] and that the level of education is an indicator for treatment outcomes after psychosomatic pain therapy [18].“Country of origin” was included in the model, since there is evidence that treatment outcomes in mental health can be influenced by the patient’s cultural or ethnic reference group e.g. by patient’s language abilities or cultural factors that relate to the psychosocial environment [19].
Furthermore we included “number of co-morbidity groups per patient” and “presence of psychiatric co-morbidity” [9, 20]. High levels of co-morbidity including mental co-morbidity have repeatedly been found to be associated with high symptom levels and worse treatment outcome [21].
As pain-related variables we included “duration of pain in years since onset” and “number of pain sites at admission” [22, 23],since literature suggests a strong relationship between pain and reduction in overall health and psychological health. To collect “number of pain sites at admission” we summed persistent and bothersome pain problems as indicated by the patient at admission in the body areas “head”, “back and neck”, “abdominal pain”, “joints - arthritis or rheumatism” or “other problem” (range 0-5) [22, 23]. Furthermore, literature suggests that patients with psychosomatic disorders that attribute the origin of illness mainly to somatic factors while excluding or neglecting psychosocial factors (somatic attribution) may be less open to psychosomatic treatment [24-27], feel more incapacitated by bodily symptoms, have a higher subjective need for medical diagnostic examinations, show worse treatment response and long-term mental health outcomes [24, 26-28].
To take effects of subjective illness theories into account, we formed the variable “somatic attribution” [24, 28], which distinguishes between patients with somatoform pain disorder that at admission attributed the origin of their pain mainly to a somatic cause (somatic attribution=1) and all other patients that also considered psychosocial explanations or did not know the cause for the pain (somatic attribution=0).
To control for the hypothesized differing effects of resource input (“total costs per case”) on the outcome variable conditional on patients’ causal attribution style, we included the interaction term between “total costs per case” and “somatic attribution”.
D. Regarding section 2.5 – Inclusion of multiplicative terms between covariates
We allowed for further interactions to control for non-additive effects of covariates on the outcome [29]. We mean-centred continuous predictor variables before calculating interactions [29]. We did not allow for interactions containing categorical variables (>2 levels) and the variables “total costs per case” or “somatic attribution” to keep interpretation of variables straightforward. We used the traditional stepwise approach in Proc Glmselect in SAS 9.2. to obtain a basic set of interaction terms (see table I in this section). We used significance level to entry (SLE) of p<0.2, and a significance level to stay (SLS) of p<0.05. Thus, in a first step interaction terms were selected based on significance level (p<0.05).We only retained the interaction terms in the model if these were in line with medical judgement/evidence, if there were no problems with small cell sizes in interaction terms and with multicollinearity in the model (using VIF statistics[1]). We only retained the effect if the p-value was<0.05. Eta-Square and Omega Square were used to measure the magnitude of the effect. Eta-Square is the proportion of total variation accounted for by the independent variable, while Omega-Square estimates the proportion of variation accounted for by the independent variable in the underlying population [2]. The process of effect selection is displayed in detail in table I in thissection. To verify the final set of interaction terms retained in the model, we conducted backward selection (default SLS of p<0.1). We retained the same interaction effect in the model (please see table II in this section).
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Trade-off between costs and quality of care
Table I. Selection process of interaction effects using stepwise methodSTEPWISE METHOD –AS USED IN ANALYSIS (Significance level to enter, SLE <0.2, significance level to stay, SLS <0.05) a
Effects suggested by procedure / In accordance with expert knowledge / Cell sizes small (n<30) / VIF Value (cut off value>10) / Eta-/Omega Square (95% confidence intervals)b / p-Value / Decision to retain or exclude effects: order of removal of interaction term/reason for removal
1) Number of co-morbidity groups per Patient* Presence of Psychiatric Co-morbidity / yes / Patients without Psychiatric Co-morbidity n=27 / Interaction: VIF=10.8 (“Number of comorbidity groups per Patient”: VIF=14.4) / 0.0734/0.0680 (0.0062-0.1852) / 0.0003 / 3. removal/ high VIF of interaction and variable “Number of comorbidity groups per Patient”
2) Number of co-morbidity groups per Patient* Number of Pain Sites at Admission / yes / no / Interaction: VIF=1.4 / 0.0280/0.0229 (0.0000-0.1170) / 0.0209 / 5./exclusion, p=0.0696 after having excluded other interaction effects
3) Presence of Psychiatric Co-morbidity* Duration of Pain in Years since Onset / yes / no / Interaction: VIF=3.3 (“Presence of Psychiatric Co-morbidity”: VIF=10.8) / 0.0240/0.0189 (0.0000-0.1097) / 0.0321 / 4.removal/ high p-value=0.5656; eta-squared=0.0001,after having excluded other interaction effects
4) Number of Pain Sites at Admission* Duration of Pain in Years since Onset / yes / no / Interaction: VIF=1.5 / 0.1133/0.1078 (0.0226-0.2350) / <0.0001 / Retained, (Eta-/Omega-Squared/95% Cl: 0.0739/0.0665/0.0063-0.1860)
5) Presence of Psychiatric Co-morbidity*Gender / Lack of evidence / Patients without Psychiatric Co-morbidity n=27; Male Patients: n=19 / Interaction: VIF=11.4 (“Presence of Psychiatric Co-morbidity”: VIF=10.8) / 0.0799/0.0745 (0.0083-0.1938) / 0.0002 / 1.removal/ lack of evidence
6) Number of Pain Sites at Admission*Gender / Lack of evidence / Male Patients: n=19 / Interaction: VIF=8.8 / 0.0376/0.0324 (0.0000-0.1333) / 0.0078 / 2.removal/lack of evidence
a excluded interaction term in the stepwise process: gender*BMI at admission (p=0.1784, thus is above the SLS of p<0.05). Even if included besides the only retained interaction effect in the model, the VIF value of this interaction would have been extremely high with VIF>60.
b Multiplied by 100, both measures yield an index of percent of variation explained in the dependant variable by the interaction effect.
Table II. Selection process of interaction effects using backward method as alternative approach
Backward Method (default, SLS<0.1)Interaction Terms suggested by procedure / Cell sizes small (n<30) / In accordance with expert knowledge / VIF Value (cut-off value>10) / Eta-/Omega Square (95% confidence intervals) / p-value / Decision to retain or exclude suggested effects: order of removal of interaction term/reason for removal d
1) Number of co-morbidity groups per Patient*Presence of Psychiatric Co-morbidity / Patients without Psychiatric Co-morbidity n=27 / yes / Interaction: VIF=10.8 (“Number of co-morbidity groups per Patient”: VIF=14.3/”Presence of Psychiatric Co-morbidity”: VIF=10.8) / 0.0521/0.0465 (0.0005-0.1555) / 0.0003 / 2.removal/high VIF values: interaction VIF= 10.5; VIF “Number of Co-morbidity Groups per Patient”=13.7
2) Presence of Psychiatric Co-morbidity*Duration of Pain in Years since Onset / Patients without Psychiatric Co-morbidity n=27 / yes / Interaction: VIF= 3.2 (“Presence of Psychiatric Co-morbidity”: VIF=10.8/” Duration of Pain in Years since Onset”: VIF=9.8) / 0.0038/0.0000 (0.0000-0.0609) / 0.0555 / 3.removal/effect size is almost 0 after excluding the other interaction terms (0.0012/p-value=0.6778)
3) Number of Pain Sites at Admission*Duration of Pain in Years since Onset / no / yes / VIF: Interaction= 1.5 (”Number of Pain Sites at Admission”: VIF=9.3/ Duration of Pain in Years since Onset”: VIF=9.8) / 0.0769/0.0711 (0.0073-0.1898) / <0.0001 / Retained, (Eta-/Omega-Squared/95% Cl: Cl:0.0739/0.0665/CL:0.0063-0.1860)
4) Presence of Psychiatric Co-morbidity*Gender / Patients without Psychiatric Co-morbidity n=27/
Male Patients: n=19 / Lack of evidence / Interaction: VIF= 11.2 (“Presence of Psychiatric Co-morbidity”: VIF=10.8/”Gender”: VIF=7.2) / 0.0542/0.0486 (0.0010-0.1586) / p=0.0004 / 1.removal/lack of evidence, high VIF value
5) Number of Pain Sites at Admission*Gender / Male Patients: n=19 / Lack of evidence / Interaction VIF: 8.8 (”Number of Pain Sites at Admission”: VIF=9.3/”Gender”: VIF=7.2) / 0.0341/0.0286 (0.0000-0.1275 / p=0.0136 / 1.removal /lack of evidence
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Trade-off between costs and quality of care
E. Regarding section 2.6 – Hausman Test for Endogeneity
In case of violation of independence of errors, OLS-coefficients would be biased and inconsistent and a more advanced estimation technique “two-stage least squares regression” should then be employed, resulting in consistent regression estimators. However, under exogeneity of costs, the OLS-estimator would still be the more efficient estimator. The Hausman Test required the use of instrumental variables, that is, variables that were highly correlated with the potentially endogenous variables total costs per case and the interaction between total costs per case and somatic attribution, but have zero correlation with the error term. We selected overhead costs per case (including costs for non-medical infrastructures) and the interaction between overhead costs per case and somatic attribution as instrumental variables [30]. Both instruments showed a high explanatory power with F-values >10 and p-values <0.0001. The Hausman Test failed to reject the null hypothesis (p=0.6389). Thus, we assume that there is no endogeneity problem.
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