## Introduction

## Data and methods

### Design and sample

### Data collection and instruments

### Predictive models

_{ i }and GE

_{ i }are dummy variables for France and Germany, respectively, AP1 = 1 if AP is “Mixed”, 0 otherwise; AP2 = 1 if AP is “Only Atypical”, 0 otherwise; the complement is when AP is “Only Typical”. i = 1,…,N is the individual dimension, and t = 1,…,5 is the time dimension. The indices i correspond to the patients, and t represents the visit number (1–5). e

_{ it }is an error term specific to individual i at visit t, and u

_{ i }is an error term specific to individual i. Here, it is assumed that corr (u

_{i}, X) = 0, which will be tested with the Hausman’s test.

_{ it }following an autoregressive process of order one, denoted AR [10].

### Statistical analysis

^{®}software was used for all analyses.

## Results

Variable | Proxy for | Mean | SD | Min | Max |
---|---|---|---|---|---|

AGE (in years) | Age | 41.80 | 10.88 | 18.70 | 66.62 |

Multi-attribute EuroQol EQ-5D score | Utility | 0.76 | 0.26 | −0.43 | 1.00 |

SF-6D score | Health-related QoL | 0.71 | 0.13 | 0.30 | 1.00 |

Positive sub-score (PANSS_POS) | Symptoms severity | 11.71 | 5.13 | 7 | 35 |

Negative sub-score (PANSS_NEG) | Symptoms severity | 15.39 | 7.16 | 7 | 43 |

General psychopathology sub-score (PANSS_PSY) | Symptoms severity | 27.87 | 9.65 | 16 | 71 |

Calgary Depression Scale for Schizophrenia (CDSS, range from 1 to 27) | Depressive symptoms | 2.49 | 3.41 | 0 | 21 |

Global Assessment of Functioning (GAF, range 1–100) | Functioning | 52.04 | 15.66 | 0 | 99 |

Barnes Akathisia Scale (BAS, range 1–100) | Extra-pyramidal symptoms | 1.02 | 2.12 | 0 | 36 |

Variable | Proxy for | N | % | ||
---|---|---|---|---|---|

Proportion of males | Gender | 2593 | 63 | ||

Proportion of French patients | Country | 906 | 22 | ||

Proportion of German patients | 2099 | 51 | |||

Proportion of UK patients | 1111 | 27 | |||

Proportion of mixed antipsychotic | Antipsychotic type | 741 | 18 | ||

Proportion of only atypical | 1194 | 29 | |||

Proportion of only typical | 2181 | 53 |

### Predictive model 1: using only the PANSS scores

^{2}of 8.75 %. When PANSS_PSY effect had been removed, none of the variables demonstrated a large contribution to R

^{2}(less or equal to 1 %). In the final model, sex and age variables were retained as well, because they were available in all the studies. PANSS_NEG had a negligible contribution to R

^{2}(0.68 %) and was highly correlated with PANSS_PSY (69 %); it was therefore not used in the analyses.

EQ-5D | Coef. | Std. Err | z |
p > |z| | [95 % Conf. interval] | |
---|---|---|---|---|---|---|

Model 1 (PANSS score only) | ||||||

Constant term | 1.026055 | 0.0277925 | 36.92 | 0.000 | 0.971583 | 1.080527 |

PANSS_PSY | −0.0076876 | 0.0004386 | −17.53 | 0.000 | −0.0085473 | −0.006828 |

Sex | 0.0457537 | 0.0120427 | 3.80 | 0.000 | 0.0221504 | 0.0693569 |

Age | −0.0020646 | 0.0005313 | −3.89 | 0.000 | −0.0031059 | −0.0010233 |

Model 2 (PANSS score and additional covariates) | ||||||

Constant term | 1.011187 | 0.025353 | 39.88 | 0.000 | 0.9614961 | 1.060878 |

CDSS | −0.0192384 | 0.0011701 | −16.44 | 0.000 | −0.0215317 | −0.016945 |

PANSS_PSY | −0.0047262 | 0.0004566 | −10.35 | 0.000 | −0.005621 | −0.0038314 |

Age | −0.0023449 | 0.0004802 | −4.88 | 0.000 | −0.003286 | −0.0014038 |

Sex | 0.0322763 | 0.0108972 | 2.96 | 0.003 | 0.0109182 | 0.0536345 |

_{ i }and X (the p value is 0.1866). Consequently, the GLS estimator of the panel model was consistent. The normality hypothesis was rejected (the p values for skewness = 0, for kurtosis = 3, and for the Jarque–Bera test are 0.0000). However, the skewness and the kurtosis were not large (respectively −1.1125 and 5.8921), and the probability density function was roughly unimodal, as can be seen from the kernel density estimate of the residuals in Fig. 1a (Kernel density estimation is a nonparametric method for estimating the probability density function of a random variable.) Finally, the test of Ramsey reset for linearity of the model was applied, and the null hypothesis of linearity was rejected (the p value is 0.0130).

### Predictive model 2: using additional covariates

^{2}= 16.27 %), PANSS_PSY (contribution to R

^{2}= 3.10 %), and AGE (contribution to R

^{2}= 1.30 %). In the final model, SEX (contribution to R

^{2}= 0.45 %) variable was included as well.

_{ i }and X, and the GLS estimator of the panel model was inconsistent. Fixed individual effect model estimates were then calculated and compared to the random individual effect model estimates (see Table SS4 in Online resource). The problem arose from CDSS variable, which might be correlated with the random individual effect u

_{i}(the fixed effect estimate minus the random effect estimate = 0.00679, with standard error of 0.0007483). The fixed effect model was consistent under this hypothesis and led to a CDSS coefficient estimate of −0.0124, with a confidence interval of [−0.0151; −0.0097].

### Predictive models for the SF-6D

SF-6D | Coef. | Std. Err | z |
p > |z| | [95 % Conf. interval] | |
---|---|---|---|---|---|---|

Model 1 (PANSS score only) | ||||||

Constant term | 0.7958439 | 0.0073481 | 108.31 | 0.000 | 0.781442 | 0.8102459 |

PANSS_PSY | −0.0037952 | 0.0002124 | −17.86 | 0.000 | −0.0042115 | −0.0033788 |

Sex | 0.0243601 | 0.0058699 | 4.15 | 0.000 | 0. 0128554 | 0.0358648 |

Model 2 (PANSS score and additional covariates) | ||||||

Constant term | 0.8198619 | 0.0124882 | 65.65 | 0.000 | 0.7953856 | 0.8443382 |

CDSS | −0.009496 | 0.0005595 | −16.97 | 0.000 | −0.0105926 | −0.0083993 |

PANSS_PSY | −0.0021323 | 0.0002253 | −9.46 | 0.000 | −0.002574 | −0.0016907 |

BAS | −0.0040303 | 0.000773 | −5.21 | 0.000 | −0.0055454 | −0.0025152 |

Age | −0.0008743 | 0.0002373 | −3.68 | 0.000 | −0.0013394 | −0.0004092 |

Sex | 0.0139095 | 0.0053836 | 2.58 | 0.003 | 0.0033579 | 0.0244612 |

### Measuring predictive ability and cross-validation

Dependent variable | Independent variables | Mean | Min | Max | Corr | RMSE | MAE |
---|---|---|---|---|---|---|---|

EQ-5D | Observed | 0.758 | −0.429 | 1 | 1 | 0 | 0 |

EQ-5D | Only PANSS | 0.752 | 0.369 | 0.907 | 0.321 | 0.246 | 0.182 |

EQ-5D | Only PANSS ^{a}
| 0.753 | 0.362 | 0.905 | 0.328 | 0.250 | 0.184 |

EQ-5D | Only PANSS ^{b}
| 0.755 | 0.367 | 0.924 | 0.316 | 0.248 | 0.182 |

EQ-5D | Only PANSS ^{c}
| 0.735 | 0.219 | 0.930 | 0.317 | 0.246 | 0.186 |

EQ-5D | Additional | 0.753 | 0.251 | 0.920 | 0.438 | 0.234 | 0.173 |

EQ-5D | Additional ^{a}
| 0.754 | 0.314 | 0.917 | 0.442 | 0.234 | 0.173 |

EQ-5D | Additional ^{b}
| 0.753 | 0.230 | 0.919 | 0.439 | 0.235 | 0.174 |

EQ-5D | Additional ^{c}
| 0.750 | 0.114 | 0.910 | 0.433 | 0.234 | 0.173 |

SF-6D | Observed | 0.707 | 0.301 | 1 | 1 | 0 | 0 |

SF-6D | Only PANSS | 0.704 | 0.514 | 0.775 | 0.328 | 0.119 | 0.098 |

SF-6D | Only PANSS ^{a}
| 0.706 | 0.552 | 0.774 | 0.342 | 0.119 | 0.098 |

SF-6D | Only PANSS ^{b}
| 0.702 | 0.552 | 0.773 | 0.342 | 0.119 | 0.097 |

SF-6D | Only PANSS ^{c}
| 0.703 | 0.512 | 0.765 | 0.325 | 0.120 | 0.098 |

SF-6D | Additional | 0.704 | 0.466 | 0.782 | 0.465 | 0.112 | 0.091 |

SF-6D | Additional ^{a}
| 0.708 | 0.441 | 0.788 | 0.454 | 0.112 | 0.092 |

SF-6D | Additional ^{b}
| 0.703 | 0.422 | 0.785 | 0.457 | 0.112 | 0.091 |

SF-6D | Additional ^{c}
| 0.706 | 0.399 | 0.786 | 0.466 | 0.112 | 0.092 |