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International Journal of Methods in Psychiatric Research logoLink to International Journal of Methods in Psychiatric Research
. 2018 May 22;27(4):e1719. doi: 10.1002/mpr.1719

Relationship between incidence and prevalence in psychotic disorders: An incidence–prevalence–mortality model

Baptiste Pignon 1,2,3,4,✉, Franck Schürhoff 1,2,3,4, Grégoire Baudin 1,2,3,5, Andrea Tortelli 2,3,6, Aziz Ferchiou 1,2,3, Ghassen Saba 1,3, Jean‐Romain Richard 2, Antoine Pelissolo 1,2,3,4, Marion Leboyer 1,2,3,4, Andrei Szöke 1,2,3
PMCID: PMC6877285  PMID: 30232816

Abstract

Objectives

Incidence–prevalence–mortality (IPM) models have been developped to estimate incidence or prevalence when one of these two measures is unavailable. We aimed to test the consistency of an IPM model of psychotic disorders on a recent incidence–prevalence couple dataset and to identify potential causes of inconsistency by applying the model to (a) the whole population, (b) female and male subgroups, (c) migrant subgroups, and (d) psychotic disorders with age at onset (AAO) between 18 and 24 (18–24 AAO).

Methods

We modelled prevalence (MP) using incidence data and the expected mortality and remission values. We then compared the MP to the observed prevalence (OP).

Results

In the whole population, the model significantly underestimated the prevalence (MP = 3.30, 95% CI [2.97, 3.66]; OP = 4.98, 95% CI [4.58, 5.41]). The results were similar for the two genders. In the migrants group, results were in the opposite direction, the model significantly overestimating the prevalence. Finally, in the 18–24 AAO subgroup, the model performed well, with OP and MP not significantly different.

Conclusion

These results suggest that standard IPM models do not perform well for psychotic disorders and more complex models taking into account the heterogeneity of the sample (in terms of remission, mortality, population movements, etc.) need to be developed.

Keywords: psychosis, epidemiology, prevalence, incidence, incidence–prevalence–mortality model

1. INTRODUCTION

Psychotic disorders are among the most common and severe forms of mental illness due to their frequent chronicity, recurrence, as well as their disabling and debilitating symptomatology. In 2004, the World Health Organization estimated that schizophrenia, the most frequent psychotic disorder (van Os & Kapur, 2009), was the fifth leading worldwide cause of global disease burden among males, with 2.8% of total years lived with disability, and sixth among females, with 2.6% of years lived with disability (Millier et al., 2014).

Disease incidence (number of new cases of a disease in a given population during a specific period) and prevalence (proportion of cases in a population during a specific period) provide important information for health service allocations, as well as for cost‐effectiveness analyses and burden of disease calculations (Grimes & Schulz, 2002). However, these types of study are difficult to carry on, and both measures are not always available (Alho, 1992; Manton et al., 1985). To be able to estimate one when the other is available would have practical utility. To address this issue, incidence–prevalence–mortality (IPM) models have been developed (e.g., for breast cancer or diabetes; Barendregt, Baan, & Bonneux, 2000; Kruijshaar, Barendregt, & Van De Poll‐Franse, 2003). All these predictive models are based on the assumption that incidence, prevalence, mortality rates, and duration of a disease in a steady‐state population are interrelated, with prevalence being equal to incidence multiplied by the duration of disease duration, minus the number of deaths (Capocaccia, 1993). The remission rate can be used instead of the disease duration. IPM models differ from each other particularly on the information sources (or on the techniques for estimating them) and the methods of calculation of the different epidemiological indicators. IPM models can be used to predict each one of the four indicators (incidence, prevalence, mortality, and remission rates) from the three others. For instance, an IPM model accurately estimated the incidence of HIV in Africa using two algorithms from cross‐sectional prevalence studies using standard spreadsheet software (Hallett et al., 2008).

With regard to psychotic disorders, the use of IPM models has been relatively rare. After the early Kramer, von Korff, and Kessler (1980) and Manton et al. (1985) studies, Ayuso‐Mateos, Gutierrez‐Recacha, Haro, and Chisholm (2006) estimated a prevalence by modelling from incidence data, remission, and mortality rate estimates. However, this estimated prevalence using the IPM model was not compared with an observed (unavailable) prevalence.

More recently, Saha, Barendregt, Vos, Whiteford, and McGrath (2008) tested the consistency of an IPM model by comparing observed and modelled (from incidence) prevalence rates of psychotic disorders based on published incidence–prevalence pairs of data. This model is easy to use, with its software being free and available. As such, this model may be readily used in large scale studies. Results of the comparisons have revealed discrepancies between the modelled and the observed prevalence (OP) rates. Of the 24 incidence–prevalence identified pairs (from 12 studies), 20 modelled prevalences (MPs) from observed incidence by the IPM model were significantly higher than OP. The authors suggested that this could be partly due to an underestimation of mortality related to the disease and, to a lesser extent, arising from an increase in the remission rate. Among the incidence–prevalence couples included, the most recent was nearly one decade old at the time of publication (Jeffreys et al., 1997; McNaught et al., 1997). Clearly, the IPM model requires testing on more recent data. Moreover, Saha et al. considered the whole population, without any analyses of subgroups. Indeed, regarding psychotic disorders, each IPM model parameter (incidence, prevalence, mortality, and duration of disease) can vary according to regions and population subgroups (Charrel et al., 2015; Saha, Chant, Welham, & McGrath, 2006, 2005), for example, according to ethnicity and migrant characteristics (Amad et al., 2013; Bourque, van der Ven, & Malla, 2011; Cantor‐Graae & Pedersen, 2007), gender (Aleman, Kahn, & Selten, 2003; Millier et al., 2014), or age at onset (AAO; Kao & Liu, 2010; Schürhoff et al., 2004). To analyse discrepancies between OP and MP rates, it would be interesting to investigate the utility of the IPM model in both the whole population as well as in such subgroups.

Between 2010 and 2015, the prevalence and incidence rates of psychotic disorders have been estimated in an urban area in the southeast of Paris, France (Szöke et al., 2014, 2015). The first aim of the present study is to test the consistency of an IPM model, using the same methods as Saha et al. on this incidence–prevalence couple. The second aim is to extend their previous findings by testing the model in subgroups, determined by gender, migrant status, and AAO between 18 and 24 (18–24 AAO).

2. METHODS

2.1. Data

2.1.1. Catchment area and population

The catchment area included two adjacent cities in the southeast of Paris (France): Créteil and Maisons‐Alfort (total adult population 109,397 people). The catchment area is a densely populated area, with 8,568 inhabitants per square kilometre, with a high migrant density (migrants represent 19.8% of the population), and a high unemployment rate (12.6%) (Pignon et al., 2016; Szöke et al., 2016).

Denominator data (i.e., census data per age group) were supplied by the French National Institute for Statistics and Economic Studies (2015; INSEE, data for 2011).

2.1.2. Incidence and prevalence data

Detailed presentations of the methods used to identify the incident and prevalent of study subjects have been provided elsewhere (Szöke et al., 2014, 2015), which are summarised below.

From 2010 to 2014, all subjects living in the catchment area, aged between 18 to 64 years old, and who came into contact with psychiatric services (inpatient and outpatient) for a first episode of psychotic disorder were identified. Diagnoses of these incident cases were made according to DSM‐IV‐TR (American Psychiatric Association, 2000) and included psychotic disorders (codes 295.xx, 297.x, 298.x) and affective disorders with psychotic symptoms (codes 296.x3). All subjects suffering from psychotic disorders due to a medical general conditions or from substance‐induced psychotic disorders were excluded.

Prevalent cases were identified by two 8‐weeks census studies of non‐affective psychotic disorders in 2014 (Créteil) and 2015 (Maisons‐Alfort). All physicians working in the catchment area and likely to treat patients for psychotic disorders, namely, psychiatrists and general practitioners, were contacted. They reported the patients with psychotic disorders according DSM‐IV‐TR that they had seen and for whom they prescribed antipsychotic medication (Szöke et al., 2015). To homogenise incidence and prevalence data, prevalent cases with AAO below 18 or above 65 were excluded. Moreover, as the prevalence study did not gather data on affective psychotic disorders, these patients were excluded from the incidence data for the present analyses.

To minimise the number of missed cases, prospective inclusion of both incident and prevalent cases were completed by retrospective leakage studies. Based on methods described by Kirkbride et al. (2006), this was conducted after the survey to identify patients missed by the screening process. This included reviewing all new mental health registration records of the inclusion period.

2.1.3. Subgroups

To analyse the causes of potential discrepancies between MP and OP, subgroups analyses were conducted in order to test for indications that the values of the different measures used in the IPM model (mortality and rate of remission) are different between the subgroups. To this end, analyses on the whole sample were repeated for each gender, migrant populations, and those with an 18–24 AAO psychotic disorder. These subgroups are known to be associated with variations in incidence, prevalence, remission, and mortality (Aleman et al., 2003; Bourque et al., 2011; Kao & Liu, 2010).

In light of the literature on migrant populations (Cantor‐Graae & Pedersen, 2013; Tortelli et al., 2013; Pignon et al., 2018), migrants were defined as someone born outwith of mainland France (i.e., first‐generation migrants). Subjects born in the French Overseas territories were considered as migrants. INSEE census of migrants (including subjects born in the French Overseas territories) was utilised for migrants subgroup analyses, as denominator data.

2.2. IPM model

For IPM models, when the duration of the disease is not known, the rate of remission can be used instead. Furthermore, the mortality of patients with a disease is equal to the mortality of the population, plus the increased mortality associated with the disease (Capocaccia, 1993).

Saha et al.'s (2008) study was used to model prevalence from incidence, mortality, and remission rates. Indeed, we used the same standardised mortality ratio (SMR) that was calculated in a systematic review of mortality studies in schizophrenia (SMR = 2.58; Saha, Chant, & McGrath, 2007). To calculate the mortality of subjects with psychotic disorders, the increased mortality associated with the disease (calculated with the SMR) was added to the mortality of the general population of the catchment area. Similarly, we used the annualised remission rate (ARR) calculated by Saha et al. (2008), based on data from 12 studies of remission in schizophrenia (ARR = 1.37%/year).

As in Saha et al.'s study, all calculations were done using DisMod II, a computer program developed for the World Health Organization Global Burden of Diseases studies (Barendregt, van Oortmarssen, Vos, & Murray, 2003; Murray & Lopez, 1996). The model uses a set of linear differential equations that describe the transitions between different status states (healthy, diseased, and dead) using the different rates (incidence, SMR, and ARR).

2.3. Statistical analyses

We used the Saha et al.'s IPM model in the catchment area to model the prevalence from the incidence. Then, as in the original article by Saha et al., we compared the OP to the MP in the whole population. Second, to study if the IPM model performed equally well in different subgroups of patients, we modelled prevalence from incidence with the IPM model in several subgroups of the general population, namely, gender, migrants, and the 18–24 AAO.

3. RESULTS

For the total sample, OP rate (expressed as number of cases per 1,000 inhabitants) was significantly higher than MP rate from the incidence data (OP = 4.98, 95% CI [4.58, 5.41] vs. MP = 3.30, 95% CI [2.97, 3.66]). Detailed results per age group and gender are available in Table 1. They show that the difference between OP and MP rates is essentially due to an underestimation of the number of subjects in their fifth decade (between 40 and 49 years old). Results across gender were similar, although the peak of difference between OP and MP rates is earlier in men (40–44 years old) than women (50–54 years‐old).

Table 1.

Observed and MP rates and 95% confidence intervals (95% CI) of psychotic disorders according to age group and gender (in cases/1,000 persons)

Age groups Females Males Total
OP 95% CI− 95% CI+ MP 95% CI− 95% CI+ OP 95% CI− 95% CI+ MP 95% CI− 95% CI+ OP 95% CI− 95% CI+ MP 95% CI− 95% CI+
18–24 1.09 0.16 7.24 1.10 0.55 2.16 2.50 1.58 3.95 3.20 2.14 4.79 1.79 1.22 2.62 2.10 1.48 2.99
25–29 2.27 1.35 3.83 2.60 1.61 4.21 7.03 5.08 9.71 6.50 4.63 9.09 4.43 3.36 5.83 4.50 3.42 5.91
30–34 3.79 2.51 5.74 3.40 2.19 5.27 8.85 6.68 11.71 7.60 5.61 10.19 6.24 4.93 7.87 5.50 4.31 7.07
35–39 4.23 2.79 6.39 3.80 2.46 5.88 6.78 4.86 9.47 8.50 6.31 11.44 5.48 4.22 7.11 6.10 4.76 7.80
40–44 6.29 4.46 8.87 4.10 2.68 6.27 15.09 12.00 18.96 9.10 6.77 12.22 10.55 8.72 12.77 6.40 5.01 8.18
45–49 6.44 4.61 8.98 4.20 2.78 6.34 9.30 6.93 12.46 9.30 6.94 12.47 7.79 6.24 9.71 6.40 5.02 8.16
50–54 7.29 5.27 10.08 4.20 2.75 6.43 6.61 4.58 9.54 9.10 6.65 12.44 6.98 5.47 8.90 6.20 4.79 8.03
55–59 5.18 3.42 7.83 4.20 13.46 21.26 5.17 3.35 7.98 8.40 5.97 11.81 5.18 3.83 6.99 5.90 4.45 7.81
60–64 3.97 2.45 6.45 4.30 2.69 5.84 4.08 2.42 6.83 7.40 5.03 10.87 4.02 2.78 5.66 5.30 3.83 7.12
65+ 1.84 1.29 2.84 1.70 1.08 2.67 1.09 0.56 2.15 2.10 1.29 3.44 1.53 1.06 2.22 2.20 1.61 2.99
Total 3.83 3.79 3.87 2.50 2.47 2.54 6.29 6.25 6.34 5.20 5.16 5.24 4.98 4.58 5.41 3.30 2.97 3.66
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Note. 95% CI− = lower limit of the 95% confidence interval; 95% CI+ = upper limit of the 95% confidence interval; MP = modelled prevalence OP = observed prevalence.

For the migrant group, results were in the opposite direction, with the MP rate being much higher than the OP rate (OP = 1.88, 95% CI [1.49, 2.37] vs. MP = 5.38, 95% CI [4.71, 6.19]). Results across gender were consistent, although the gap between OP and MP is higher in males. Detailed results of migrants OP and MP rates across gender and age groups are shown in Table 2.

Table 2.

Observed and MP rates of psychotic disorders in migrants according to age group and gender (in cases/1,000 persons)

Age groups Females Males Total
OP 95% CI− 95% CI+ MP 95% CI− 95% CI+ OP 95% CI− 95% CI+ MP 95% CI− 95% CI+ OP 95% CI− 95% CI+ MP 95% CI− 95% CI+
18–24 0.00 0.00 2.37 1.00 0.11 3.49 0.84 0.15 4.76 5.00 1.80 9.83 0.36 0.06 2.02 2.85 1.45 5.62
25–29 0.54 0.09 3.07 2.50 1.03 6.03 3.12 1.21 8.01 10.10 5.90 17.23 1.60 0.68 3.74 5.76 3.64 9.01
30–34 1.05 0.28 3.81 3.70 1.79 7.59 2.71 1.16 6.34 11.30 7.39 17.25 1.87 0.90 3.85 6.93 4.74 10.14
35–39 0.51 0.09 2.87 4.50 2.36 8.58 3.95 1.91 8.14 11.60 7.56 17.76 2.14 1.09 4.21 7.49 5.17 10.78
40–44 5.03 2.73 9.23 5.10 2.78 9.31 1.22 0.47 3.14 11.30 8.21 15.54 2.66 1.59 4.46 7.60 5.59 10.34
45–49 2.75 1.26 6.00 5.30 3.00 9.34 2.67 1.14 6.23 10.90 7.10 16.70 2.71 1.52 4.85 7.40 5.19 10.54
50–54 3.13 1.44 6.82 5.50 3.03 9.94 1.12 0.31 4.08 10.40 6.63 16.27 2.16 1.09 4.26 7.03 4.80 10.28
55–59 3.68 1.69 8.02 5.70 3.03 10.70 1.17 0.32 4.24 9.50 5.88 15.31 2.39 1.21 4.72 6.88 4.59 10.31
60–64 2.19 0.74 6.41 5.90 3.00 11.56 2.14 0.73 6.27 8.30 4.72 14.58 2.16 0.99 4.71 6.48 4.11 10.23
65+ 0.66 0.19 2.41 3.10 1.65 5.80 0.73 0.20 2.66 3.00 1.54 5.86 0.69 0.27 1.78 2.78 1.71 4.51
Total 1.90 1.38 2.62 4.20 3.41 4.99 1.85 1.33 2.58 6.60 5.58 7.93 1.88 1.49 2.37 5.38 4.71 6.19
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Note. 95% CI− = lower limit of the 95% confidence interval; 95% CI+ = upper limit of the 95% confidence interval; MP = modelled prevalence OP = observed prevalence.

In the 18–24 AAO subgroup, the MP rate was not significantly different from the OP rate, (OP = 2.41, 95% CI [2.13, 2.71] vs. MP = 2.35, 95% CI [2.05, 2.65]). When analysed separately by gender, the differences were slightly larger, and in opposite direction for each gender (MP underestimating the OP for males and the reverse in females). Detailed results of 18–24 AAO OP and MP rates across gender and age groups are shown in Table 3.

Table 3.

Observed and MP rates of 18–24 age at onset psychotic disorders according to age group and gender (in cases/1,000 persons)

Age groups Females Males Total
OP 95% CI− 95% CI+ MP 95% CI− 95% CI+ OP 95% CI− 95% CI+ MP 95% CI− 95% CI+ OP 95% CI− 95% CI+ MP 95% CI− 95% CI+
18–24 1.09 0.56 2.15 1.10 0.56 2.17 2.50 1.58 3.95 3.20 2.13 4.80 1.79 1.22 2.61 2.10 1.47 2.99
25–29 1.95 0.94 2.86 2.40 1.20 3.31 6.64 4.76 9.27 6.10 4.31 8.64 4.08 3.06 5.43 4.30 3.24 5.68
30–34 1.72 0.94 3.18 2.90 1.80 4.65 5.53 3.88 7.89 6.30 4.51 8.78 3.56 2.61 4.84 4.70 3.59 6.14
35–39 1.54 0.78 3.03 2.80 1.69 4.65 3.19 1.97 5.18 5.90 4.12 8.43 2.35 1.58 3.49 4.40 3.28 5.88
40–44 1.97 1.06 3.61 2.60 1.52 4.42 8.38 6.16 11.39 5.50 3.76 8.03 5.07 3.86 6.69 4.10 3.02 5.57
45–49 3.03 1.87 4.91 2.40 1.39 4.14 4.23 2.74 6.52 5.00 3.36 7.45 3.59 2.60 4.97 3.80 2.81 5.28
50–54 0.81 0.32 2.08 2.20 1.22 3.95 1.89 0.96 3.72 4.60 2.96 7.14 1.31 0.75 2.29 3.50 2.48 4.94
55–59 0.00 0.00 0.90 2.00 1.03 3.87 4.14 2.55 6.71 4.10 2.53 6.68 1.97 1.21 3.20 3.10 2.10 4.57
60–64 1.49 0.68 3.25 1.80 0.88 3.67 1.16 0.46 2.99 3.50 2.00 6.10 1.34 0.73 2.47 2.80 1.83 4.29
65+ 0.37 0.14 0.95 0.70 0.35 1.40 0.27 0.08 0.99 1.10 0.56 2.16 0.33 0.15 0.71 1.20 0.79 1.82
Total 1.32 1.30 1.35 2.60 2.57 2.63 3.67 3.18 4.24 3.32 2.86 3.86 2.41 2.13 2.71 2.35 2.05 2.65
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Note. 95% CI− = lower limit of the 95% confidence interval; 95% CI+ = upper limit of the 95% confidence interval; MP = modelled prevalence OP = observed prevalence.

4. DISCUSSION

Overall, the IPM model of psychotic disorders did not perform well in the whole population. Results were different in the included subgroups, with the IPM model underestimating the prevalence in the whole population, and overestimating the prevalence in the migrant subgroup. However, the model showed a good fit for the 18–24 AAO subgroup. These results are consistent with previous studies showing variation in incidence, duration of disorders, and mortality rates in subgroups of patients with psychotic disorders (Das‐Munshi et al., 2017; Jongsma et al., 2017; Prikryl, Kholova, Kucerova, & Ceskova, 2013; Saha et al., 2005). Such variations may indicate that distinct subgroups of patients with psychotic disorders occur, with differential disease courses.

Although the present the results are in agreement with those of Saha et al. regarding the poor performance of IPM models, there were also important differences. Among the 24 published prevalence–incidence couples included in Saha et al. study, 20 MP were significantly higher than OP, including 19 that were more than 50% higher (Saha et al., 2008). Only three studies reported, as in the present study, OP higher than MP (Bamrah, Freeman, & Goldberg, 1991; Bland, 1984; Nielsen, 1976). These three studies, as with 10 of the 12 included studies, were based on registers, that is, on treated patients (eight registers of one institution, two registers of multiple institutions). The present incident and prevalent cases were not based on such registers but prospectively included treated inpatients and outpatients. Moreover, outcomes and durations of inclusion of the cases of the studies included in the Saha et al.'s study varied widely and make comparisons difficult.

The IPM model showed a good fit for the 18–24 AAO but understimated the prevalence rates of older AAO psychotic disorders. Several underestimations may be due to a number of reasons, which can be divided into (a) explanations concerning the observed data and (b) explanations concerning the IPM model.

Concerning the observed data, the incidence study included only patients who have their first contact with psychiatric services for non‐affective, nonsubstance‐induced and nongeneral medical condition‐induced psychotic disorders. This incidence study could have underestimated the incidence and thus the MP. For instance, patients with substance‐induced psychotic disorders, which were excluded from the incident cases, could be in the same case and evolve toward nonsubstance‐induced psychotic disorders (Fiorentini et al., 2011). Moreover, patients with affective psychotic disorders are in the same case (Salvatore et al., 2009). In an analysis of stability of diagnosis in schizophrenia over 7 years, Chen, Swann, and Burt (1996) showed that nearly one third of patients who initially had a diagnosis other than schizophrenia were later diagnosed with schizophrenia.

Overall, the 18–24 AAO non‐affective psychotic disorders could be the subgroup that best match the concept of schizophrenia on which the Saha et al.'s IPM model is based. A recent systematic review showed that the definition of the outcome in prevalence studies of psychotic disorders had an influence on the results (Simeone, Ward, Rotella, Collins, & Windisch, 2015). In comparison with studies that used the narrow definition of schizophrenia, the use of a broader definition of “schizophrenia spectrum disorders” (including schizophreniform and schizoaffective disorders) increased case identification (by 18–90%).

Another hypothesis concerning observed data is the decreased incidence of psychotic disorders in recent decades. As this is based on actual incidence, it may decrease the MP in the total sample. This phenomenon has been observed in Taiwan (Chiang et al., 2017). In Nottingham, between 1978 and 1999, Kirkbride et al. (2009) observed a decrease of the incidence of schizophrenia and an increased incidence of substance‐induced psychotic disorders (and a steady incidence of whole psychotic disorders), which is consistent with the present study.

Concerning the IPM model, potential explanations of the discrepancies between OP and MP concern mortality and remission rates. Indeed, in the Saha et al. study, the calculation of the ARR (1.37%/year) was based on 12 remission studies (Saha et al., 2008). These studies did not have the same definition of the remission, particularly concerning the duration without hospitalization or the use of antipsychotic medication, with some studies considering the absence of prescription as necessary, other not, for example, in Auslander and Jeste (2004) or Thara (2004) studies. Some patients could have been included in the prevalence data (and thus increase the OP), although they would have been considered as recovered patients in these studies, even with a prescription of antipsychotic medication. As with other epidemiological outcomes, the increased mortality linked to psychotic disorders could have evolved (Healy et al., 2012). For instance, in recent years (Revier et al., 2015), the improvement in the psychiatric care, for example, with the recent use of second‐generation antipsychotic long‐acting depot medication (Tiihonen et al., 2006; Torniainen et al., 2015), could have reduced mortality. Thus, the value of the increased mortality used here could have been overestimated (and thus decrease the MP). Moreover, the IPM model assumes that remission and increased mortality rates of psychotic disorders are constant over time, which may not be the case, both at populational and individual levels (Dutta, Murray, Allardyce, Jones, & Boydell, 2012). Further studies could investigate this more specifically, for example, by age groups, which, to the best of our knowledge, has never previously been investigated. Age‐period‐cohort models may help to address this issue. However, age‐specific mortality and remission rates are not currently available for psychotic disorders. This could partly explain the differences between OP and MP, which are different according to age bands (big differences in 40–44 and 45–49 age bands, lesser in other age bands). As to remission rate, it may be low over the course of the first years of the disease and secondarily improve, for example, due to increased insight after several psychotic episodes (Koren, Viksman, Giuliano, & Seidman, 2013) or because accumulative doses of antipsychotics are necessary to lead to remission (Leucht et al., 2012).

One important problem concerning the IPM model is the stability of the population. Indeed, as this study analysed a chronic disease, the comparison between OP and MP based on incidence data is based on the hypothesis of the steady state of the population in the catchment area (Alho, 1992; Holley, 1998). If the population changes significantly (e.g., by migration in or out) and the populations that migrate (in or out) do not have the same structure (including percentage of psychotic subjects), this could increase (or decrease) the OP. The social drift phenomenon could for instance explain an increased migration of subjects with psychotic disorders to economically deprived areas (Ngamini Ngui et al., 2013). In a precedent study on the same catchment area, we showed that patients with psychotic disorders lived in more deprived neighbourhoods (Pignon et al., 2016).

Comparisons of MP and OP gave opposite results with the migrants subgroup compared with the general population. Several phenomena, both data‐ and IPM model‐related, may contribute to this. Regarding the observed data, misdiagnoses of incident non‐affective psychotic disorders instead of affective psychotic or bipolar disorders could also increase the incidence and thus the MP (Mukherjee, Shukla, Woodle, Rosen, & Olarte, 1983). In the present study, migrants may display better remission rates of psychotic disorders than the general population. Several studies have shown smaller duration of disease among migrant populations, which could reduce the OP (McKenzie et al., 1995, 2001; Morgan et al., 2009). Moreover, the hypothesis of the steady population state may have less validity in the case of migrants. Indeed, as migrants with psychotic disorders may experience chronic social defeat and poor quality of life in their host country, it is possible that some migrants return to their own countries after the onset of the disease and thus reduce the OP. Conversely, migrants with psychotic disorders included in the prevalence data could have an AAO before the migration. The same is obviously true for the native population for subjects that moved in or out of the catchment areas. Finally, the denominator used the present number of migrants. As a consequence of migration waves in recent decades, this denominator was smaller in the past (Thierry, 2004). As young migrants may be proportionaly higher in number, this could increase the incidence and thus the MP.

In conclusion, the present study investigated the MP of psychotic disorders from incidence, using an IPM model developped by Saha et al. and compared the modelled rate to the actual prevalence rate. Contrary to the majority of the incidence–prevalence couples studies on which Saha et al. tested their IPM model, the incidence and prevalence measures used in the present study were recent, almost simultaneous, and strenghtened by leakage studies, hereby improving their accuracy. Moreover, contrary to most of these incidence–prevalence couples, the comparison between the MP and the OP rates in the whole population revealed a significantly higher OP. The most probable explanations of this discrepancy are incident missed cases, an absence of population stability and miscalculated estimations of remission and mortality rates. As the IPM model was fitted for the 18–24 AAO, these rates could concern only this subgroup. These preliminary results may indicate the need for different IPM models according to subgroups, with specific mortality and remission rates, to improve the fit of these models. Moreover, we propose that more sophisticated statistical models need are needed in further studies, for example, age‐period‐cohort models, that could permit to use age‐specific mortality and remission rates (Heo et al., 2017).

DECLARATION OF INTEREST STATEMENT

The authors have declared that there are no conflicts of interest in relation to the subject of this study.

FUNDING SOURCES

No funding was secured for this study.

ACKNOWLEDGEMENT

We want to thank Mr. Jan J. Barendregt for advices.

Pignon B, Schürhoff F, Baudin G, et al. Relationship between incidence and prevalence in psychotic disorders: An incidence–prevalence–mortality model. Int J Methods Psychiatr Res. 2018;27:e1719 10.1002/mpr.1719

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