EF query for calculating monthly trends
Native T-SQL
I don't know enough about linq to do a proper code review for that, however as far as performance is concerned I think T-SQL would take care of the expensive part of your query more efficiently.
The following query will not get you all the information from your entire query, but it would take care of at least this section:
Year = date.Year,
Month = date.Month,
AllIncidents = incidentsByMonth.Count(),
Flagged = incidentsByMonth.Count(ibm =&gt; ibm.IsSerious),
SentToHospital = incidentsByMonth.Count(x =&gt; x.Treatments.Any(it =&gt; it.TreatmentTypeId == (int)TreatmentTypes.Senttohospital)),
FallsWithInjuries = incidentsByMonth.Count(ibm =&gt; ibm.IncidentTypes.Any(it =&gt; it.IncidentTypeId == (int)IncidentTypes.Fall) &amp;&amp; ibm.InjuryTypes.Any(inj =&gt; inj.InjuryTypeId != (int)InjuryTypes.None)),
FallsWithFracture = incidentsByMonth.Count(ibm =&gt; ibm.IncidentTypes.Any(it =&gt; it.IncidentTypeId == (int)IncidentTypes.Fall) &amp;&amp; ibm.InjuryTypes.Any(inj =&gt; inj.InjuryTypeId == (int)InjuryTypes.Fracture)),

Note that I made assumptions about your schema design and you may need to make some adjustments. Also please note that I used more descriptive table aliases as well to make it easier for Mr. Maintainer.
DECLARE @dateStart DATE = '2014-01-01'; -- or whichever date you want
DECLARE @dateEnd DATE = DATEADD(MONTH, 6, @dateStart); -- 6 months later e.g. July 1 2014
SELECT     
    DATEPART(yyyy, incd.date) AS Year,
    DATEPART(mm, incd.date) AS Month,
    COUNT(incd.IncidentId) AS AllIncidents,
    COUNT(incd.IsSerious) AS Flagged,
    (SELECT COUNT incd.IncidentId
        FROM incd
        WHERE treat.TreatmentType = 'SenttoHospital') AS SentToHospital,
    (SELECT COUNT incd.IncidentId
        FROM incd 
        WHERE incdType = 'Fall' 
        AND injuType.InjuryType &lt;&gt; 'None') AS FallsWithInjuries,
    (SELECT COUNT incd.IncidentId
        FROM incd 
        WHERE incdType = 'Fall' 
        AND injuType.InjuryType = 'Fracture') AS FallsWithFracture,
FROM Incidents AS incd
LEFT JOIN IncidentTypes AS incdType ON inc.IncidenTypeId = incdType.IncidentTypeId
LEFT JOIN InjuryTypes AS injuType ON inc.InjuryTypeId = injuType.InjuryTypeId
LEFT JOIN Treatments AS treat ON inc.TreatmentTypeId = treat.TreatmentTypeId
WHERE incd.date &gt;= @dateStart
AND incd.date &lt; @dateEnd;