<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>112 - Disclosure - Accrued Expense</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>P01_01_2013To06_30_2013</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001133818</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>us-gaap_AccruedLiabilitiesCurrentAndNoncurrentAbstract</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Accrued Liabilities [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="P01_01_2013To06_30_2013" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>              &lt;table border="0" style="clear:both;width:100%; table-layout:fixed;"&gt;  &lt;tr&gt;  &lt;td&gt;&lt;/td&gt;  &lt;/tr&gt;  &lt;/table&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;MARGIN: 0pt 0px; FONT: 10pt Times New Roman, Times, Serif "&gt;  &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;MARGIN: 0in 0in 0pt; FONT-SIZE: 10pt"&gt;  &lt;table style="clear:both;MARGIN-TOP: 0px; FONT: 10pt Times New Roman, Times, Serif; MARGIN-BOTTOM: 0px"   cellspacing="0" cellpadding="0"&gt;  &lt;tr style="TEXT-ALIGN: justify; VERTICAL-ALIGN: top"&gt;  &lt;td style="WIDTH: 0in"&gt;&lt;/td&gt;  &lt;td style="TEXT-ALIGN: left; WIDTH: 0.25in"&gt;  &lt;div&gt;&lt;b&gt;5.&lt;/b&gt;&lt;/div&gt;  &lt;/td&gt;  &lt;td style="TEXT-ALIGN: justify"&gt;  &lt;div&gt;&lt;b&gt;Accrued Expense&lt;/b&gt;&lt;/div&gt;  &lt;/td&gt;  &lt;/tr&gt;  &lt;/table&gt;  &lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;TEXT-ALIGN: justify; MARGIN: 0pt 0px; FONT: 10pt Times New Roman, Times, Serif"&gt;  &amp;#160;&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;TEXT-ALIGN: justify; MARGIN: 0pt 0px; FONT: 10pt Times New Roman, Times, Serif"&gt;  As of June 30, 2013, Current Liabilities included accrued expense  of $&lt;font style=" FONT-SIZE: 10pt"&gt;4,892&lt;/font&gt; for clinical trial  operations management. Current Liabilities as of June 30, 2013 also  included accrued expense related party of $&lt;font style=" FONT-SIZE: 10pt"&gt;37,050&lt;/font&gt; for MD Anderson clinical trial  hospital expense. (See Note 2.). As of December 31, 2012, Current  Liabilities included accrued expense of $&lt;font style=" FONT-SIZE: 10pt"&gt;137,662&lt;/font&gt; and accrued expense related party  of $&lt;font style=" FONT-SIZE: 10pt"&gt;26,000&lt;/font&gt;.&lt;/div&gt;  &lt;/div&gt;        </NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for accounts payable and accrued liabilities at the end of the reporting period.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 02

 -Paragraph 19

 -Subparagraph a

 -Article 5



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 210

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.5-02.19(a),20,24)

 -URI http://asc.fasb.org/extlink&amp;oid=6877327&amp;loc=d3e13212-122682



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 02

 -Paragraph 20, 24

 -Article 5



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Accrued Expense</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Accrued Expense</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.biopathholdings.com/role/AccruedExpense</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
