The protocol for this systematic review and meta-analysis was registered in PROSPERO (CRD42020172840) on April 28, 2020 (see Additional file 1) and to an independent Research Committee. This study will adhere to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines  and the checklist with the reported items is provided as an additional file (see Additional file 2).
Study selection criteria
To be included, studies must fulfill the following criteria:
Study design: Prospective or retrospective observational studies.
Population characteristics: Inpatients of a psychiatric department/hospital/facility with an Axis I disorder defined by the International Classification of Diseases 10th Edition (ICD-10), or Axis I or II disorder as defined by the Mini International Neuropsychiatric Interview (MINI), Structured Clinical Interview for DSM-5 (SCID), Diagnostic and Statistical Manual of Mental Disorders 4th Edition (DSM-IV), 4th Edition Text-Revised (IV-TR) or 5th Edition (DSM-5).
Intervention: Modifiable and non-modifiable factors/determinants/predictors of length of stay (sociodemographic characteristics, medical history, diagnosis, disorder, and treatment-related characteristics).
Outcome: Primary outcome is the length of stay in the psychiatric hospital/institution or facility. Only studies which calculated the effect size through reporting of β-coefficients will be included.
There will be no language restrictions for the studies included. Cross-sectional and prospective or retrospective observational studies which do not fulfill all the above criteria for population, intervention, and outcome will be excluded. Duplicate studies assessing the same population which do not report additional data will also be excluded. To reduce the risk of bias by confounders, we will only consider studies reporting the outcomes of interest through adjusted standardized regression coefficients in this meta-analysis.
An independent and experienced librarian (NAAV) will carry out a systematic search in PubMed, Ovid MEDLINE, EMBASE, and PsycINFO to find eligible articles between inception and July 2020. The complete search strategy is provided in an additional file (see Additional file 3). The keywords used were generated through Web of Science and Scopus Controlled vocabulary.
Six reviewers working independently and in duplicate will screen all abstracts and select full-text manuscripts for eligibility. Prior to formal abstract screening, a pilot phase between reviewers will be carried out to clarify misunderstandings and ensure comprehension. Chance-adjusted inter-rater agreement for the title/abstract screening and the full-text eligibility will be calculated using Fleiss’ Kappa, considering a value > 0.7 as indicative of good inter-rater reliability . After title and abstract screening, a second phase of full-text eligibility assessment will ensue. Disagreements at this stage will be resolved by consensus, and reasons for exclusion will be documented by the reviewers. If no consensus is reached, decision will be based on the arbitration of a third reviewer. Abstract screening and full-text selection will be completed using DistillerSR , a web-based software designed for screening and data extraction.
A standardized web-based data extraction form will be designed for the extraction of the information of interest from each study. Data collection will be performed independently and in duplicate by the research team. Discrepancy between reviewers regarding the extracted information will be resolved by consensus or intervention of a third reviewer. From each eligible study the following data will be extracted onto the standardized form:
Study characteristics: Year, country, design, length, type of mental health institution/hospital level, sample size.
Sociodemographic variables: Age, sex, education, ethnicity, marital status, type of insurance, accommodation, occupation, income status.
Medical History: Medical or psychiatric disorders in first- or second-degree family members, psychiatric hospitalization history in first- or second-degree family members, previous and number of psychiatric hospitalizations, previous and number of suicide attempts, time from last psychiatric hospitalization, weight, BMI, medical comorbidities.
Disorder-related: Primary diagnosis, age at diagnosis, time elapsed since diagnosis, severity rated by clinimetry at admission, voluntary or involuntary admission.
Treatment: Pharmacotherapy, dosage, duration, non-pharmacological therapy.
Length of stay: Standardized regression coefficients, total variance, confidence interval, standard errors, mean days of length of stay.
Studies which present compounded terms involving more than one of the aforementioned (i.e., diagnosis plus pharmacotherapy, and age plus diagnosis) will not be considered for the data extraction or the statistical analysis. Furthermore, only standardized regression coefficients that have been adjusted for multiple predictors will be obtained from the included studies. If outcomes or data related to predictions were stated to be assessed in the study but were not reported thereafter either in the results or discussion, we will contact the corresponding author twice through e-mail. If the corresponding author does not respond, we will attempt to contact other authors.
We will provide a qualitative synthesis of the included studies involving their design, country, type of mental health hospital or institution, population characteristics, predictors studied, and a summary of the main findings that includes the average, median or interquartile length for the LOS. For the meta-analysis, we will pool the standardized adjusted regression coefficients (β), sample sizes, and standard error as a measure of the effect size of predictors relative to length of stay [20, 21]. Studies that only report the unadjusted coefficients will be included for the systematic review but not for the quantitative analysis, in order to reduce bias. If 95% confidence intervals, standard deviations, or the interquartile range are provided instead of the standard error, we will estimate it with the data provided . A priori selected predictors for meta-analysis are presented in Additional file 4. Nonetheless, in order to reduce the possibilities of increased false-positive rates, meta-analysis will only be performed for predictors with at least ten studies reporting the standardized regression coefficients . Details concerning further steps to test for this are presented in the following sections. With the pooled results we will generate point estimates with 95% confidence intervals on the relationship between each individual predictor and the LOS. We will consider a two-tailed value of p < 0.05 as statistically significant.
Heterogeneity of the predictors subjected to meta-analysis that have met the described criteria will be assessed through the I2 statistic. A value of I2 > 50% will be taken as indicative of high heterogeneity not explained by chance . Based on the heterogeneity, the results will be presented using a fixed or random-effects model. When low (< 50%), we will perform the statistical analysis using a fixed-effects model. When the heterogeneity is high (> 50%), we will perform the statistical analysis using a random-effects model and conduct thereafter sensitivity analyses to address underlying causes for the significant heterogeneity. This analysis method has been described to reduce the rates of type I error . Specific sensitivity analyses are presented in the next section. All calculations will be performed using the R meta-package [25, 26].
Two reviewers (FCN and ESU) of the research team will address the risk of bias in each individual study. Since studies considered for inclusion have an observational nature, we will use the Newcastle-Ottawa Quality Scale (NOS) for evaluating prospective and retrospective cohort studies. Domains that will be evaluated include selection quality (representativeness, ascertainment of exposure), comparability quality, and outcome quality (assessment of the outcome, follow-up). Studies will be rated and deemed of good, fair, or poor quality according to the conversion thresholds from the NOS to the Agency for Health Research and Quality (AHRQ) . Disagreements on risk of bias between reviewers will be resolved by consensus or by the arbitration of a third reviewer (AFGM).
To assess for publication bias, we will use funnel plots of the effect size compared to the standard error . In the presence of plot asymmetry for a given analysis, we will use the trim-and-fill method to determine the impact of removing smaller studies on the overall estimate and provide adjusted results .
Sensitivity and subgroup analyses
If an appropriate number of studies from diverse countries/continents are found, a subgroup analysis by country, continent, and its income status will be carried out to evaluate if differences observed from the general pooled data are significant in specific countries with lower or higher economic status. We also have pre-planned to perform separate analyses for studies involving only a specific diagnosis (i.e., psychotic disorders and substance abuse) In these cases, meta-analyses of correlation will be performed only for studies of that specific disorder. Other a priori sensitivity analyses will be reported based on the quality of the included studies and meta-bias. For the former, only studies rated as good quality will be included for a subgroup analysis to test for differences with the primary pooled estimate (which includes studies with fair or poor quality). If we obtain point estimates from the quality sensitivity analysis that differ significantly from the overall pooled analysis, we will consider the former with more credibility. Furthermore, if other a priori subgroup or sensitivity analyses report significantly different results in comparison to the overall pooled analysis we will consider the overall quality of the different groups to evaluate the validity of the findings.
The robustness of the pooled standardized regression coefficients will be tested through permutation tests, which has been a recommended method for recalculation of p values and statistical significance [23, 30].